Numpyro_MC_Sampling.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true,
      "authorship_tag": "ABX9TyPF1yc3M2BXn5d8IhKFv6O0",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/jecampagne/JaxTutos/blob/main/Numpyro_MC_Sampling.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "24X51kUtew4g",
        "outputId": "6545cb3d-8718-4f02-d616-c857b03fe2b8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[?25l     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/291.7 KB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m291.7/291.7 KB\u001b[0m \u001b[31m12.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h"
          ]
        }
      ],
      "source": [
        "! pip install -q numpyro==0.10."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpyro\n",
        "from numpyro.diagnostics import hpdi\n",
        "import numpyro.distributions as dist\n",
        "from numpyro import handlers\n",
        "from numpyro.infer import HMC, NUTS,  BarkerMH,  MCMC, init_to_sample\n"
      ],
      "metadata": {
        "id": "kfS-bBBMfZTP"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import jax\n",
        "import jax.numpy as jnp\n",
        "import jax.scipy as jsc\n",
        "from jax import grad, jit, vmap\n",
        "from jax import jacfwd, jacrev, hessian\n",
        "#import jaxopt\n",
        "\n",
        "from functools import partial\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib as mpl\n",
        "import matplotlib.pyplot as plt\n",
        "mpl.rc('image', cmap='jet')\n",
        "mpl.rcParams['font.size'] = 18\n",
        "\n",
        "from jax.config import config\n",
        "config.update(\"jax_enable_x64\", True)\n",
        "\n",
        "import scipy as sc\n",
        "from scipy.optimize import minimize as sc_minimize\n",
        "import scipy.stats as scs\n",
        "import scipy.integrate as sc_integrate\n"
      ],
      "metadata": {
        "id": "6Jhbc3J6f9_F"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "! pip install corner"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TpkmOjy7iBrT",
        "outputId": "97514bb1-de27-4e12-b290-e0c58cb7857b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting corner\n",
            "  Downloading corner-2.2.1-py3-none-any.whl (15 kB)\n",
            "Requirement already satisfied: matplotlib>=2.1 in /usr/local/lib/python3.8/dist-packages (from corner) (3.2.2)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.8/dist-packages (from matplotlib>=2.1->corner) (1.4.4)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.8/dist-packages (from matplotlib>=2.1->corner) (0.11.0)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.8/dist-packages (from matplotlib>=2.1->corner) (3.0.9)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.8/dist-packages (from matplotlib>=2.1->corner) (2.8.2)\n",
            "Requirement already satisfied: numpy>=1.11 in /usr/local/lib/python3.8/dist-packages (from matplotlib>=2.1->corner) (1.21.6)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.8/dist-packages (from python-dateutil>=2.1->matplotlib>=2.1->corner) (1.15.0)\n",
            "Installing collected packages: corner\n",
            "Successfully installed corner-2.2.1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "! pip install arviz"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "evvQ-UCViHkX",
        "outputId": "1741c5e2-19bd-4244-8ffc-5ba5a629235c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: arviz in /usr/local/lib/python3.8/dist-packages (0.12.1)\n",
            "Requirement already satisfied: packaging in /usr/local/lib/python3.8/dist-packages (from arviz) (23.0)\n",
            "Requirement already satisfied: numpy>=1.12 in /usr/local/lib/python3.8/dist-packages (from arviz) (1.21.6)\n",
            "Requirement already satisfied: scipy>=0.19 in /usr/local/lib/python3.8/dist-packages (from arviz) (1.7.3)\n",
            "Requirement already satisfied: typing-extensions>=3.7.4.3 in /usr/local/lib/python3.8/dist-packages (from arviz) (4.5.0)\n",
            "Requirement already satisfied: matplotlib>=3.0 in /usr/local/lib/python3.8/dist-packages (from arviz) (3.2.2)\n",
            "Requirement already satisfied: xarray-einstats>=0.2 in /usr/local/lib/python3.8/dist-packages (from arviz) (0.5.1)\n",
            "Requirement already satisfied: xarray>=0.16.1 in /usr/local/lib/python3.8/dist-packages (from arviz) (2022.12.0)\n",
            "Requirement already satisfied: netcdf4 in /usr/local/lib/python3.8/dist-packages (from arviz) (1.6.2)\n",
            "Requirement already satisfied: setuptools>=38.4 in /usr/local/lib/python3.8/dist-packages (from arviz) (57.4.0)\n",
            "Requirement already satisfied: pandas>=0.23 in /usr/local/lib/python3.8/dist-packages (from arviz) (1.3.5)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.8/dist-packages (from matplotlib>=3.0->arviz) (2.8.2)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.8/dist-packages (from matplotlib>=3.0->arviz) (3.0.9)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.8/dist-packages (from matplotlib>=3.0->arviz) (0.11.0)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.8/dist-packages (from matplotlib>=3.0->arviz) (1.4.4)\n",
            "Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.8/dist-packages (from pandas>=0.23->arviz) (2022.7.1)\n",
            "Requirement already satisfied: cftime in /usr/local/lib/python3.8/dist-packages (from netcdf4->arviz) (1.6.2)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.8/dist-packages (from python-dateutil>=2.1->matplotlib>=3.0->arviz) (1.15.0)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import corner\n",
        "import arviz as az"
      ],
      "metadata": {
        "id": "sisjwogPh483"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "numpyro.__version__"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "id": "_HIWBHpjfB0T",
        "outputId": "2f88675a-07a7-4499-8433-7cd90bbdcb8c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'0.10.0'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Simple gaussian dist."
      ],
      "metadata": {
        "id": "g5R4n-bCff16"
      }
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "dFpx6r2NfzVT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# One possibility to use jit on function in the class is to use a off-class function \n",
        "# this is due to the self arg\n",
        "# There are alternatives w/o any class\n",
        "@jit\n",
        "def _logpdf(x, loc, scale, weights):\n",
        "  log_probs = jax.scipy.stats.norm.logpdf(x,loc=loc, scale=scale)\n",
        "  return jax.scipy.special.logsumexp(jnp.log(weights) + log_probs, axis=0)\n",
        "\n",
        "class MixtureModel_jax():\n",
        "    def __init__(self, locs, scales, weights, *args, **kwargs):\n",
        "        super().__init__(*args, **kwargs)\n",
        "        self.loc = jnp.array([locs]).T\n",
        "        self.scale = jnp.array([scales]).T\n",
        "        self.weights = jnp.array([weights]).T\n",
        "        norm = jnp.sum(self.weights)\n",
        "        self.weights = self.weights/norm\n",
        "\n",
        "        self.num_distr = len(locs)\n",
        "\n",
        "    def pdf(self, x):\n",
        "        probs = jax.scipy.stats.norm.pdf(x,loc=self.loc, scale=self.scale)\n",
        "        return jnp.dot(self.weights.T,probs).squeeze()\n",
        "    \n",
        "    def logpdf(self, x):\n",
        "        return _logpdf(x, self.loc, self.scale, self.weights)[0]\n"
      ],
      "metadata": {
        "id": "dQ5agYU2f2Cu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# \\phi(x)\n",
        "def phi(x):\n",
        "    return x**2\n"
      ],
      "metadata": {
        "id": "02tIXpR2f43z"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "single_gaussian_model = MixtureModel_jax([0],[1],[1])"
      ],
      "metadata": {
        "id": "BRA59xGTgMSI"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "Integ_true,_=sc_integrate.quad(lambda x: phi(x)*single_gaussian_model.pdf(x),-7,7)"
      ],
      "metadata": {
        "id": "lSZ1l3p8gNPL"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "single_gaussian_model.logpdf(0.)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "u_Kq3iCngrdm",
        "outputId": "b7de39e7-998a-4b42-f353-bf19caf2f096"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DeviceArray(-0.91893853, dtype=float64)"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Integ. true: \",Integ_true)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FJzCahohgP0V",
        "outputId": "15e3d239-fc9c-46cb-ae32-052fc626482c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Integ. true:  0.9999999998695543\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "rng_key = jax.random.PRNGKey(42)\n",
        "_, rng_key = jax.random.split(rng_key)\n",
        "\n",
        "# Use a HMC \n",
        "kernel = HMC(potential_fn=lambda x: -single_gaussian_model.logpdf(x))  # negative log\n",
        "num_samples = 1_000_000\n",
        "n_chains    = 1\n",
        "mcmc = MCMC(kernel, num_warmup=2_000, num_samples=num_samples, num_chains=n_chains, \n",
        "            progress_bar=False) # progress_bar=True ralentit bcq... donc ok pour num_samples=1000.\n",
        "mcmc.run(rng_key, init_params=jnp.zeros(n_chains))\n",
        "mcmc.print_summary()\n",
        "samples_1 = mcmc.get_samples()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-rdiCPhVgSLf",
        "outputId": "57215506-dbf2-49e9-fb45-ee2e97be779c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
            "Param:0[0]     -0.00      1.00     -0.00     -1.65      1.64 219315.47      1.00\n",
            "\n",
            "Number of divergences: 0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "fig = plt.figure()\n",
        "x_axis = np.arange(-5, 5, 0.01)\n",
        "#mixture_pdf = jax.vmap(mixture_gaussian_model.pdf)(x_axis)\n",
        "plt.hist(np.array(samples_1.squeeze()), bins=100, density=True, label=\"HMC samples\");\n",
        "plt.plot(x_axis, single_gaussian_model.pdf(x_axis),'r-', lw=5, alpha=0.6, label='true pdf')\n",
        "plt.xlim([-5,5])\n",
        "plt.yscale('log')\n",
        "plt.grid()\n",
        "plt.legend();\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 273
        },
        "id": "r0puMANXgdaA",
        "outputId": "3113f4d8-99b3-473f-bafb-69b05ec9a90c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "You can use the samples to compute $\\int \\phi(x) p(x) dx$"
      ],
      "metadata": {
        "id": "fkwDBSt0hgVz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "phi_spl1 = phi(samples_1)\n",
        "Integ_HMC1 = np.mean(phi_spl1)\n",
        "print(f\"Integ_HMC:{Integ_HMC1:.6e}, err. relat: {np.abs(Integ_HMC1-Integ_true)/Integ_true:.6e}, sample size : {len(samples_1.flatten())}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nUC6jMZ3hGAf",
        "outputId": "a3efa65e-d1d9-4048-9a85-d5d7f05d9e57"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Integ_HMC:9.977529e-01, err. relat: 2.247060e-03, sample size : 1000000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# realtive effective sample size\n",
        "az.ess(np.array(samples_1.squeeze()), relative=True)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "McSwvdc6hvxB",
        "outputId": "7a2c952e-2dfa-4868-8549-732d243b9855"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.21931631741854699"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "So the Relative ESS is of about 22% which is quite ok but this is for a simple case."
      ],
      "metadata": {
        "id": "yjvhkEe2iiRz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Mixture of gaussian dist."
      ],
      "metadata": {
        "id": "AqcihXPDiwMn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mixture_gaussian_model = MixtureModel_jax([0,1.5],[0.5,0.1],[8,2])"
      ],
      "metadata": {
        "id": "gC3b9CUYhzT7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "Integ_true,_=sc_integrate.quad(lambda x: phi(x)*mixture_gaussian_model.pdf(x),-7,7)"
      ],
      "metadata": {
        "id": "Z6t3aiFXiy9z"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Integ. true: \",Integ_true)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0q707y-Di0_i",
        "outputId": "eedad983-4bbb-441e-fa47-46f281efa069"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Integ. true:  0.652\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "rng_key = jax.random.PRNGKey(42)\n",
        "_, rng_key = jax.random.split(rng_key)\n",
        "\n",
        "kernel = HMC(potential_fn=lambda x: -mixture_gaussian_model.logpdf(x),\n",
        "            trajectory_length=1.0)  # negative log\n",
        "num_samples = 1_000_000\n",
        "n_chains    = 1\n",
        "mcmc = MCMC(kernel, num_warmup=2_000, num_samples=num_samples, num_chains=n_chains, \n",
        "            progress_bar=False)\n",
        "mcmc.run(rng_key, init_params=jnp.zeros(n_chains))\n",
        "mcmc.print_summary()\n",
        "samples_1 = mcmc.get_samples()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aC8i-nCGi2tC",
        "outputId": "83d2c1b1-7eca-4e9b-c26f-16396624be84"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
            "Param:0[0]      0.30      0.75      0.16     -0.63      1.64  28707.19      1.00\n",
            "\n",
            "Number of divergences: 0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "fig = plt.figure()\n",
        "x_axis = np.arange(-3, 3, 0.01)\n",
        "#mixture_pdf = jax.vmap(mixture_gaussian_model.pdf)(x_axis)\n",
        "plt.hist(np.array(samples_1.squeeze()), bins=100, density=True, label=\"samples\");\n",
        "plt.plot(x_axis, mixture_gaussian_model.pdf(x_axis),'r-', lw=5, alpha=0.6, label='true pdf')\n",
        "plt.xlim([-3,3])\n",
        "plt.title(f\"HMC sampling ({len(samples_1.flatten())} spls)\")\n",
        "plt.legend();"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "val4NXIQi6cr",
        "outputId": "e4bc8b4b-d122-47e8-a438-532d2aa71bb9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "phi_spl1 = phi(samples_1)\n",
        "Integ_HMC1 = np.mean(phi_spl1)\n",
        "print(f\"Integ_HMC:{Integ_HMC1:.6e}, err. relat: {np.abs(Integ_HMC1-Integ_true)/Integ_true:.6e}, sample size : {len(samples_1.flatten())}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qskURTuqjJ1c",
        "outputId": "4249c00f-2bc1-4514-a2a3-5a6a4b991844"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Integ_HMC:6.555026e-01, err. relat: 5.372124e-03, sample size : 1000000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "az.ess(np.array(samples_1.squeeze()), relative=True)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WKLV9TJdjPe9",
        "outputId": "04c080b3-d089-423d-c72e-f2da69ddbc8d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.03852060519618474"
            ]
          },
          "metadata": {},
          "execution_count": 79
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "So we get a less good sampling efficiency (3.8%) on this case with secondary peak. Even if HMC is an improvement compared to M-H (reminder: eff. of 0.1%) we can find a better method. Moreover, one can play with the `trajectory_lengt` parameter of the HMC and see the result sensitivity."
      ],
      "metadata": {
        "id": "qSvMxC8ejZIG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "rng_key = jax.random.PRNGKey(42)\n",
        "_, rng_key = jax.random.split(rng_key)\n",
        "\n",
        "kernel =  BarkerMH(potential_fn=lambda x: -mixture_gaussian_model.logpdf(x),\n",
        "                   target_accept_prob=0.4)  # negative log\n",
        "num_samples = 1_000_000\n",
        "n_chains    = 2\n",
        "mcmc = MCMC(kernel, num_warmup=2_000, num_samples=num_samples, num_chains=n_chains, \n",
        "            progress_bar=False)\n",
        "mcmc.run(rng_key, init_params=jnp.zeros(n_chains))\n",
        "mcmc.print_summary()\n",
        "samples_2 = mcmc.get_samples()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UaGoTSGQjUMM",
        "outputId": "faa25cb6-4613-4403-eb52-f5b409ed9603"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-83-bb7778eca129>:8: UserWarning: There are not enough devices to run parallel chains: expected 2 but got 1. Chains will be drawn sequentially. If you are running MCMC in CPU, consider using `numpyro.set_host_device_count(2)` at the beginning of your program. You can double-check how many devices are available in your system using `jax.local_device_count()`.\n",
            "  mcmc = MCMC(kernel, num_warmup=2_000, num_samples=num_samples, num_chains=n_chains,\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
            "   Param:0      0.30      0.75      0.16     -0.63      1.64  93946.83      1.00\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "phi_spl1 = phi(samples_2)\n",
        "Integ_NUTS = np.mean(phi_spl1)\n",
        "print(f\"Integ_NUTS:{Integ_NUTS:.6e}, err. relat: {np.abs(Integ_NUTS-Integ_true)/Integ_true:.6e}, sample size : {len(samples_1.flatten())}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gFWlzpaFkk_P",
        "outputId": "41622a43-6056-4f7e-862d-e9ba2cdcf12d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Integ_NUTS:6.518708e-01, err. relat: 1.981045e-04, sample size : 1000000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "az.ess(np.array(samples_2.squeeze()), relative=True)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sXubm4sXk-ET",
        "outputId": "2e161e67-5987-45f4-e6ab-4154d5831d1a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.07508978475976032"
            ]
          },
          "metadata": {},
          "execution_count": 85
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "rng_key = jax.random.PRNGKey(42)\n",
        "_, rng_key = jax.random.split(rng_key)\n",
        "\n",
        "kernel =  NUTS(potential_fn=lambda x: -mixture_gaussian_model.logpdf(x))  # negative log\n",
        "num_samples = 1_000_000\n",
        "n_chains    = 1\n",
        "mcmc = MCMC(kernel, num_warmup=2_000, num_samples=num_samples, num_chains=n_chains, \n",
        "            progress_bar=False)\n",
        "mcmc.run(rng_key, init_params=jnp.zeros(n_chains))\n",
        "mcmc.print_summary()\n",
        "samples_3 = mcmc.get_samples()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XCHIcmmGlKg7",
        "outputId": "5f669027-83f2-4e53-92c9-f37ac6d63793"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
            "Param:0[0]      0.30      0.75      0.16     -0.63      1.64  16740.41      1.00\n",
            "\n",
            "Number of divergences: 0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "az.ess(np.array(samples_3.squeeze()), relative=True)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9ljX9wBom6ig",
        "outputId": "abf65ee0-c85a-4831-dff9-571b0680ccf3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.021933060207131323"
            ]
          },
          "metadata": {},
          "execution_count": 93
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In low dimension BarkerMH may be better than HMC/NUTS. BarkerMH use a proposal distribution that uses the gradient of the potential. In particular the proposal distribution is skewed in the direction of the gradient at the current sample."
      ],
      "metadata": {
        "id": "ogxONDutnqQk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Bayesian forward modeling of a simple 4-parameters use-case"
      ],
      "metadata": {
        "id": "DiA4FXSQo5Vq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Dataset generation method1 "
      ],
      "metadata": {
        "id": "yJPg51zFwd8o"
      }
    },
    {
      "cell_type": "code",
      "source": [
        " def mean_fn(x, params):\n",
        "    \"\"\" a mean/determinist fnt with a split at t=0 \"\"\"\n",
        "    R0 = params[\"R0\"]\n",
        "    v  = params[\"v\"]\n",
        "    k  = params[\"k\"]\n",
        "    tau =  params[\"tau\"]\n",
        "    return jnp.where(x < 0, R0 + v*x, R0 + v*x - k*(1.-jnp.exp(-x/tau)))\n"
      ],
      "metadata": {
        "id": "wFxTbxP-nCrj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#dataset (method 1)\n",
        "rng_key = jax.random.PRNGKey(42)\n",
        "rng_key, rng_key0, rng_key1, rng_key2 = jax.random.split(rng_key, 4)\n",
        "tMes = jax.random.uniform(rng_key0,minval=-5.,maxval=5.0,shape=(20,))\n",
        "tMes=jnp.append(tMes,0.0)\n",
        "tMes=jnp.sort(tMes)\n",
        "par_true={\"R0\":35.0, \"v\":2.20, \"k\":15.5, \"tau\": 1.0}\n",
        "sigma_obs=1.0\n",
        "\n",
        "RMes = mean_fn(tMes,par_true) + sigma_obs * jax.random.normal(rng_key1,shape=tMes.shape)"
      ],
      "metadata": {
        "id": "4DWO8bbEpFHr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.errorbar(tMes,RMes,yerr=sigma_obs,fmt='o', linewidth=2, capsize=0, c='k', label=\"data\")\n",
        "plt.xlabel(\"t\")\n",
        "plt.ylabel(\"R\")\n",
        "plt.legend()\n",
        "plt.grid();\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "Law0Zunwpk-X",
        "outputId": "32403387-0608-4467-c303-94b2a47d9f11"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## The (Numpyro) fowrward model"
      ],
      "metadata": {
        "id": "S-KGYPxKpzs6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def model(t,Robs=None,\n",
        "          R0_min=10.,v_min = 0.5,k_min = 1., tau_min=0.1,\n",
        "          R0_max=50.,v_max = 3.5,k_max = 10., tau_max=5.0,\n",
        "          sigma= 1.0):\n",
        "    \n",
        "    # priors on the parameters (stochastic but can be used as regular variables)\n",
        "    # the variable naming is necessary in the dictionnary produced\n",
        "    R0 = numpyro.sample(\"R0\", dist.Uniform(R0_min,R0_max))\n",
        "    v  = numpyro.sample(\"v\", dist.Uniform(v_min,v_max))\n",
        "    k  = numpyro.sample(\"k\", dist.Uniform(k_min,k_max))\n",
        "    tau= numpyro.sample(\"tau\", dist.Uniform(tau_min,tau_max))\n",
        "\n",
        "    params = {\"R0\":R0, \"v\":v, \"k\":k, \"tau\":tau}\n",
        "    mu = mean_fn(t,params) # the mean\n",
        "    \n",
        "    with numpyro.plate(\"obs\", t.shape[0]):  # each mesure is a random variable iid\n",
        "        numpyro.sample('R', dist.Normal(mu, sigma), obs=Robs) # the likelihood\n"
      ],
      "metadata": {
        "id": "Q2OJJejtpqxv"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Diagramatic representation"
      ],
      "metadata": {
        "id": "7ZZZ7eZlqa7m"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "! pip install -q graphviz"
      ],
      "metadata": {
        "id": "B_N-ae9_W82_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "numpyro.render_model(model, model_args=(jnp.array([0.]),jnp.array([1.])),\n",
        "                    render_distributions=True)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 291
        },
        "id": "eKZFS4XxqYga",
        "outputId": "e53bb0fc-7b6d-495c-dd90-aaec6ee70dc8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f4a2f05c8b0>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.43.0 (0)\n -->\n<!-- Title: %3 Pages: 1 -->\n<svg width=\"392pt\" height=\"202pt\"\n viewBox=\"0.00 0.00 391.50 202.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 198)\">\n<title>%3</title>\n<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-198 387.5,-198 387.5,4 -4,4\"/>\n<g id=\"clust1\" class=\"cluster\">\n<title>cluster_obs</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"100,-8 100,-83 170,-83 170,-8 100,-8\"/>\n<text text-anchor=\"middle\" x=\"152.5\" y=\"-15.8\" font-family=\"Times,serif\" font-size=\"14.00\">obs</text>\n</g>\n<!-- R0 -->\n<g id=\"node1\" class=\"node\">\n<title>R0</title>\n<ellipse fill=\"white\" stroke=\"black\" cx=\"27\" cy=\"-152.5\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-148.8\" font-family=\"Times,serif\" font-size=\"14.00\">R0</text>\n</g>\n<!-- R -->\n<g id=\"node5\" class=\"node\">\n<title>R</title>\n<ellipse fill=\"grey\" stroke=\"black\" cx=\"135\" cy=\"-57\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"135\" y=\"-53.3\" font-family=\"Times,serif\" font-size=\"14.00\">R</text>\n</g>\n<!-- R0&#45;&gt;R -->\n<g id=\"edge1\" class=\"edge\">\n<title>R0&#45;&gt;R</title>\n<path fill=\"none\" stroke=\"black\" d=\"M39.29,-136.18C45.95,-128.29 54.52,-118.73 63,-111 77.06,-98.18 94.16,-85.49 108.16,-75.74\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"110.16,-78.61 116.43,-70.08 106.2,-72.84 110.16,-78.61\"/>\n</g>\n<!-- v -->\n<g id=\"node2\" class=\"node\">\n<title>v</title>\n<ellipse fill=\"white\" stroke=\"black\" cx=\"99\" cy=\"-152.5\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"99\" y=\"-148.8\" font-family=\"Times,serif\" font-size=\"14.00\">v</text>\n</g>\n<!-- v&#45;&gt;R -->\n<g id=\"edge2\" class=\"edge\">\n<title>v&#45;&gt;R</title>\n<path fill=\"none\" stroke=\"black\" d=\"M105.44,-134.78C110.86,-120.69 118.72,-100.28 124.97,-84.05\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"128.29,-85.16 128.62,-74.57 121.76,-82.65 128.29,-85.16\"/>\n</g>\n<!-- k -->\n<g id=\"node3\" class=\"node\">\n<title>k</title>\n<ellipse fill=\"white\" stroke=\"black\" cx=\"171\" cy=\"-152.5\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"171\" y=\"-148.8\" font-family=\"Times,serif\" font-size=\"14.00\">k</text>\n</g>\n<!-- k&#45;&gt;R -->\n<g id=\"edge3\" class=\"edge\">\n<title>k&#45;&gt;R</title>\n<path fill=\"none\" stroke=\"black\" d=\"M164.56,-134.78C159.14,-120.69 151.28,-100.28 145.03,-84.05\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"148.24,-82.65 141.38,-74.57 141.71,-85.16 148.24,-82.65\"/>\n</g>\n<!-- tau -->\n<g id=\"node4\" class=\"node\">\n<title>tau</title>\n<ellipse fill=\"white\" stroke=\"black\" cx=\"243\" cy=\"-152.5\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"243\" y=\"-148.8\" font-family=\"Times,serif\" font-size=\"14.00\">tau</text>\n</g>\n<!-- tau&#45;&gt;R -->\n<g id=\"edge4\" class=\"edge\">\n<title>tau&#45;&gt;R</title>\n<path fill=\"none\" stroke=\"black\" d=\"M230.71,-136.18C224.05,-128.29 215.48,-118.73 207,-111 192.94,-98.18 175.84,-85.49 161.84,-75.74\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"163.8,-72.84 153.57,-70.08 159.84,-78.61 163.8,-72.84\"/>\n</g>\n<!-- distribution_description_node -->\n<g id=\"node6\" class=\"node\">\n<title>distribution_description_node</title>\n<text text-anchor=\"start\" x=\"296.5\" y=\"-178.8\" font-family=\"Times,serif\" font-size=\"14.00\">R0 ~ Uniform</text>\n<text text-anchor=\"start\" x=\"296.5\" y=\"-163.8\" font-family=\"Times,serif\" font-size=\"14.00\">v ~ Uniform</text>\n<text text-anchor=\"start\" x=\"296.5\" y=\"-148.8\" font-family=\"Times,serif\" font-size=\"14.00\">k ~ Uniform</text>\n<text text-anchor=\"start\" x=\"296.5\" y=\"-133.8\" font-family=\"Times,serif\" font-size=\"14.00\">tau ~ Uniform</text>\n<text text-anchor=\"start\" x=\"296.5\" y=\"-118.8\" font-family=\"Times,serif\" font-size=\"14.00\">R ~ Normal</text>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {},
          "execution_count": 104
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## The forward model can be used also to generate dataset"
      ],
      "metadata": {
        "id": "I9VKs96HqlDi"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#dataset method 2\n",
        "\n",
        "from numpyro.handlers import seed, trace, condition\n",
        "# So, let's generate the data at the fiducial parameters\n",
        "fiducial_model = condition(model, par_true)\n",
        "# Run the conditionned model (if not conditionned the priors are executed)\n",
        "trace_data = trace(seed(fiducial_model, jax.random.PRNGKey(42))).get_trace(tMes, sigma=sigma_obs)\n"
      ],
      "metadata": {
        "id": "fkheh6bMqdR-"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "RMes_bis = trace_data['R'][\"value\"]"
      ],
      "metadata": {
        "id": "MQvW9chbq5Ch"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.errorbar(tMes,RMes,yerr=sigma_obs,fmt='o', linewidth=2, capsize=0, c='k', label=\"dataset 1\")\n",
        "plt.errorbar(tMes,RMes_bis,yerr=sigma_obs, fmt='o', linewidth=2, capsize=0, c='r', \n",
        "             label=\"dataset 2\")\n",
        "plt.xlabel(\"t\")\n",
        "plt.ylabel(\"R\")\n",
        "plt.legend()\n",
        "plt.title(\"dataset gen. from the same true params\")\n",
        "plt.grid();\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "id": "ppfs9jXlq80y",
        "outputId": "c4fcc0df-6afb-4d63-8fd8-695aa0f76b50"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Use sampler"
      ],
      "metadata": {
        "id": "OmuDPROfra1T"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Run NUTS.\n",
        "kernel = NUTS(model, dense_mass=True, target_accept_prob=0.9,\n",
        "              init_strategy=numpyro.infer.init_to_median())\n",
        "num_samples = 5_000\n",
        "n_chains = 4\n",
        "mcmc = MCMC(kernel, num_warmup=1_000, num_samples=num_samples,  \n",
        "            num_chains=n_chains,\n",
        "            chain_method='vectorized', # chain in paralell on the same device\n",
        "            progress_bar=False)\n",
        "mcmc.run(rng_key, t=tMes, Robs=RMes,sigma=sigma_obs, k_max = 20.)\n",
        "mcmc.print_summary()\n",
        "samples_nuts = mcmc.get_samples()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Z-A2UJaMq-e6",
        "outputId": "bb9f416a-200f-476a-bfae-802e3079d257"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
            "        R0     35.30      0.54     35.31     34.40     36.17   6548.26      1.00\n",
            "         k     16.56      1.32     16.58     14.46     18.84   4771.67      1.00\n",
            "       tau      0.95      0.11      0.95      0.77      1.14  13207.26      1.00\n",
            "         v      2.36      0.21      2.36      2.01      2.71   5912.98      1.00\n",
            "\n",
            "Number of divergences: 0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "If you want to observe the progress bar with chain_method='vectorized' it will give only one string maybe but it is 4 that will be generated. This progress bar in some cases slows down the generation a lot. You can choose chain_method='sequential', while `parallel` requires like pmap a number of devices identical to the number of strings.\n",
        "\n",
        "\n",
        "You can play on `num_warmup`, `num_samples`and `n_chains` to see how the sampling quality evolves...\n",
        "\n",
        "We have to look at: `r_hat` which must be 1. The number of divergences which if not null indicates that the generation has been cut because of a problem (ex. frontier, squeezed proba...). Finally, `n_eff` which if divided by 4x5000 gives the generation efficiency. There is another (standard) way to calculate this efficiency via arviz.ess. This efficiency is related to the auto-correlation length of the Markov chain, or in other words to the independence of the samples.\n",
        "\n"
      ],
      "metadata": {
        "id": "23NxHbPfrw9t"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "az.ess(samples_nuts, relative=True)  # relative efficiency "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 270
        },
        "id": "lkbOvsUhreVo",
        "outputId": "37597470-4ae3-49b7-d8df-3e061e4dcf13"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<xarray.Dataset>\n",
              "Dimensions:  ()\n",
              "Data variables:\n",
              "    R0       float64 0.3233\n",
              "    k        float64 0.2213\n",
              "    tau      float64 0.6673\n",
              "    v        float64 0.2876"
            ],
            "text/html": [
              "<div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
              "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "</symbol>\n",
              "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n",
              "<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "</symbol>\n",
              "</defs>\n",
              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body[data-theme=dark],\n",
              "body.vscode-dark {\n",
              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
              "}\n",
              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
              "}\n",
              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
              "}\n",
              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
              "}\n",
              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
              "}\n",
              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
              "}\n",
              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-index-preview {\n",
              "  grid-column: 2 / 5;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data,\n",
              ".xr-index-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data,\n",
              ".xr-index-data-in:checked ~ .xr-index-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-index-name div,\n",
              ".xr-index-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data,\n",
              ".xr-index-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2,\n",
              ".xr-no-icon {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  ()\n",
              "Data variables:\n",
              "    R0       float64 0.3233\n",
              "    k        float64 0.2213\n",
              "    tau      float64 0.6673\n",
              "    v        float64 0.2876</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-b444ff71-5d6b-4927-b970-cf1cf29c8cc0' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-b444ff71-5d6b-4927-b970-cf1cf29c8cc0' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-361aa793-2cd6-4f61-876c-7f748cf543bf' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-361aa793-2cd6-4f61-876c-7f748cf543bf' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-edcf870c-ae3b-491d-9c7c-2b6991f7d8d9' class='xr-section-summary-in' type='checkbox'  checked><label for='section-edcf870c-ae3b-491d-9c7c-2b6991f7d8d9' class='xr-section-summary' >Data variables: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>R0</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.3233</div><input id='attrs-cee384cd-94ca-418a-a1f1-aa13f109953a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-cee384cd-94ca-418a-a1f1-aa13f109953a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f02eeeeb-08a9-4bcb-bf2c-fe8e6b7443ea' class='xr-var-data-in' type='checkbox'><label for='data-f02eeeeb-08a9-4bcb-bf2c-fe8e6b7443ea' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.32334327)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>k</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.2213</div><input id='attrs-6150a651-f3cc-46c8-a10e-1d1c5a9a2804' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-6150a651-f3cc-46c8-a10e-1d1c5a9a2804' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2d6e5188-59da-4816-a47b-17c4f3e374df' class='xr-var-data-in' type='checkbox'><label for='data-2d6e5188-59da-4816-a47b-17c4f3e374df' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.22130161)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>tau</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.6673</div><input id='attrs-e0aa2b6a-1044-4b6a-9e81-0915a36655cc' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e0aa2b6a-1044-4b6a-9e81-0915a36655cc' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-48fd7860-2a88-4a60-9cc7-342d2ffcedf3' class='xr-var-data-in' type='checkbox'><label for='data-48fd7860-2a88-4a60-9cc7-342d2ffcedf3' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.6673444)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>v</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.2876</div><input id='attrs-b503fa5a-b527-4bb7-ac75-9338e1cb1305' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b503fa5a-b527-4bb7-ac75-9338e1cb1305' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-17daddeb-ce0b-4db3-b9a9-529a445c0fe8' class='xr-var-data-in' type='checkbox'><label for='data-17daddeb-ce0b-4db3-b9a9-529a445c0fe8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.28764502)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-96ae6cde-6ac6-4b39-a3ac-c7ebbef40b74' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-96ae6cde-6ac6-4b39-a3ac-c7ebbef40b74' class='xr-section-summary'  title='Expand/collapse section'>Indexes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-bcfc6d6b-eaf6-4d3b-9aeb-63c2999ec303' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-bcfc6d6b-eaf6-4d3b-9aeb-63c2999ec303' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 112
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note that the efficiency is >= 25% which is very good. A simple MCMC usually reaches 0.1% or less and we then have to generate a lot of samples, and then we proceed to a thinning which is very problematic from a statistical point of view because we have no guarantee to produce an iid batch."
      ],
      "metadata": {
        "id": "u1I5Xv_hs53E"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Run NUTS.\n",
        "kernel = HMC(model)\n",
        "num_samples = 5_000\n",
        "n_chains = 4\n",
        "mcmc = MCMC(kernel, num_warmup=1_000, num_samples=num_samples,  \n",
        "            num_chains=n_chains,\n",
        "            chain_method='vectorized', # chain in paralell on the same device\n",
        "            progress_bar=False)\n",
        "mcmc.run(rng_key, t=tMes, Robs=RMes,sigma=sigma_obs, k_max = 20.)\n",
        "mcmc.print_summary()\n",
        "samples_hmc = mcmc.get_samples()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Xrx1mfvjsr0n",
        "outputId": "fbab2c77-cd6f-47ad-d3d2-1d7b9cbab0ab"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
            "        R0     35.32      0.54     35.31     34.43     36.20   7522.59      1.00\n",
            "         k     16.55      1.31     16.54     14.33     18.66  14340.34      1.00\n",
            "       tau      0.95      0.11      0.94      0.77      1.12    546.41      1.01\n",
            "         v      2.36      0.21      2.36      2.02      2.71  31397.59      1.00\n",
            "\n",
            "Number of divergences: 0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "az.ess(samples_hmc, relative=True)  # relative efficiency "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 270
        },
        "id": "DLB2_opotJQ0",
        "outputId": "274cb4be-7eec-4ddc-dc0e-f9227ee0a93d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<xarray.Dataset>\n",
              "Dimensions:  ()\n",
              "Data variables:\n",
              "    R0       float64 0.3797\n",
              "    k        float64 0.7071\n",
              "    tau      float64 0.02874\n",
              "    v        float64 1.544"
            ],
            "text/html": [
              "<div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
              "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "</symbol>\n",
              "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n",
              "<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "</symbol>\n",
              "</defs>\n",
              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body[data-theme=dark],\n",
              "body.vscode-dark {\n",
              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
              "}\n",
              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
              "}\n",
              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
              "}\n",
              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
              "}\n",
              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
              "}\n",
              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
              "}\n",
              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-index-preview {\n",
              "  grid-column: 2 / 5;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data,\n",
              ".xr-index-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data,\n",
              ".xr-index-data-in:checked ~ .xr-index-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-index-name div,\n",
              ".xr-index-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data,\n",
              ".xr-index-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2,\n",
              ".xr-no-icon {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  ()\n",
              "Data variables:\n",
              "    R0       float64 0.3797\n",
              "    k        float64 0.7071\n",
              "    tau      float64 0.02874\n",
              "    v        float64 1.544</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-48cec024-8f16-48d7-8bdf-98cd68cb2c18' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-48cec024-8f16-48d7-8bdf-98cd68cb2c18' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-2ed2b96c-8028-4f20-b0a0-733a7049ef91' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-2ed2b96c-8028-4f20-b0a0-733a7049ef91' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-6ac3bea2-f9f6-4bd6-9066-be5fd3543635' class='xr-section-summary-in' type='checkbox'  checked><label for='section-6ac3bea2-f9f6-4bd6-9066-be5fd3543635' class='xr-section-summary' >Data variables: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>R0</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.3797</div><input id='attrs-dc27888a-48c4-4e5b-ab6b-5f20e9bac774' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-dc27888a-48c4-4e5b-ab6b-5f20e9bac774' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-43d2db68-b1d2-415a-8139-77db9f654961' class='xr-var-data-in' type='checkbox'><label for='data-43d2db68-b1d2-415a-8139-77db9f654961' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.37968056)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>k</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.7071</div><input id='attrs-2e2a9d62-1f1b-486b-aec3-19b7a56e444a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2e2a9d62-1f1b-486b-aec3-19b7a56e444a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-3ba5abf6-b085-460a-a0f4-d93a4dab036a' class='xr-var-data-in' type='checkbox'><label for='data-3ba5abf6-b085-460a-a0f4-d93a4dab036a' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.70714533)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>tau</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.02874</div><input id='attrs-cd00213e-66b4-4a80-965c-cd75a43c3f59' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-cd00213e-66b4-4a80-965c-cd75a43c3f59' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-66ab03ef-4cc8-4986-9188-14e0a39b65dc' class='xr-var-data-in' type='checkbox'><label for='data-66ab03ef-4cc8-4986-9188-14e0a39b65dc' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.02874355)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>v</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.544</div><input id='attrs-5f8f20b2-e016-4cd0-bc5c-cb8e262138a0' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-5f8f20b2-e016-4cd0-bc5c-cb8e262138a0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-7756cf19-c781-4923-9679-2daffb21ea40' class='xr-var-data-in' type='checkbox'><label for='data-7756cf19-c781-4923-9679-2daffb21ea40' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.54371077)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-79cbc668-53f7-4411-b540-73772e4d1dc8' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-79cbc668-53f7-4411-b540-73772e4d1dc8' class='xr-section-summary'  title='Expand/collapse section'>Indexes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-cd00e86b-585c-4ac0-a4a5-c38e0aa412d4' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-cd00e86b-585c-4ac0-a4a5-c38e0aa412d4' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 114
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Notice the poor efficiency for the $\\tau$ sampling."
      ],
      "metadata": {
        "id": "0UuZN82gtVMQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Posterior contours"
      ],
      "metadata": {
        "id": "xfX6srokwz0F"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data = az.from_dict(\n",
        "    posterior=samples_nuts  # dictionary od samplings\n",
        ")\n",
        "     \n"
      ],
      "metadata": {
        "id": "dleAaf5vtSdM"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# mean value of the parameter posterior\n",
        "param_mean = np.mean(np.array(list(samples_nuts.values())),axis=1)\n",
        "param_mean\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "48pDAlsIwAc_",
        "outputId": "79fb52b5-914c-4618-d429-1a0aff245200"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([35.30460682, 16.56110037,  0.95456448,  2.35695582])"
            ]
          },
          "metadata": {},
          "execution_count": 136
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "figure = corner.corner(data, \n",
        "                       levels=(0.393, 0.865, 0.989),  #Plot 1sigma, 2sigma, 3sigma 2D contours\n",
        "                        quantiles=[0.16, 0.84], #68% CL 1D plmlots = 1sigma\n",
        "                       show_titles=True,\n",
        "                       )\n",
        "#true parameter positions\n",
        "tmp = np.array([par_true[\"R0\"],par_true[\"k\"], par_true[\"tau\"], par_true[\"v\"]])\n",
        "corner.overplot_lines(figure, tmp, color=\"blue\")\n",
        "corner.overplot_points(figure, tmp[None], marker=\"s\", color=\"blue\")\n",
        "#mean MCMC parameter positions\n",
        "corner.overplot_lines(figure, param_mean, color=\"red\")\n",
        "corner.overplot_points(figure, param_mean[None], marker=\"s\", color=\"red\")\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 721
        },
        "id": "WlFMXEQUt6AE",
        "outputId": "bfcbbbee-c21f-4090-973e-d9298902c9bc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 698.4x698.4 with 16 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Prediction: mean, error bands..."
      ],
      "metadata": {
        "id": "Zbc04mHzwYB4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "t_val = np.linspace(-5,5,100) # some new values of the t (time)"
      ],
      "metadata": {
        "id": "PjEr_TJSvZVN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "Rtrue_val = mean_fn(t_val,par_true) # prediction with True parameter values (like method1 dataset)"
      ],
      "metadata": {
        "id": "oLPcMJKuxDEY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "func = jax.vmap(lambda x: mean_fn(t_val,x))"
      ],
      "metadata": {
        "id": "3-KmhDVExFjl"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "Rall_val= func(samples_nuts)  # use of MCMC chain samples"
      ],
      "metadata": {
        "id": "JK0UHswgxQGc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "Rmean_val = jnp.mean(Rall_val,axis=0) # mean expectation (predict)"
      ],
      "metadata": {
        "id": "yM-JhK9ZxVlj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "std_R_val = jnp.std(Rall_val,axis=0) # standard error"
      ],
      "metadata": {
        "id": "C91l2WygxaS_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig=plt.figure(figsize=(10,8))\n",
        "plt.errorbar(tMes,RMes,yerr=sigma_obs,fmt='o', linewidth=2, capsize=0, c='k', label=\"data\")\n",
        "plt.plot(t_val,Rtrue_val,c='k',label=\"true\")\n",
        "\n",
        "plt.fill_between(t_val, Rmean_val-2*std_R_val, Rmean_val+2*std_R_val, \n",
        "                    color=\"lightblue\",label=r\"$2-\\sigma$\")\n",
        "plt.fill_between(t_val, Rmean_val-std_R_val, Rmean_val+std_R_val, \n",
        "                    color=\"lightgray\",label=r\"$1-\\sigma$\")\n",
        "# plot mean prediction\n",
        "plt.plot(t_val, Rmean_val, \"blue\", ls=\"--\", lw=2.0, label=\"mean\")\n",
        "\n",
        "plt.xlabel(\"t\")\n",
        "plt.ylabel(\"R\")\n",
        "plt.legend()\n",
        "plt.grid();\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        },
        "id": "qZCbmE6Vxi62",
        "outputId": "58b15d79-8f77-4841-d6ca-ab16c714680e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Possible exos:\n",
        "- Resume the dataset generation exercise without conditioning by fixed parameters but leave the generation by priors free:  `trace_data = trace(seed(model, jax.random.RNGKey(42))).get_trace(tMes, sigma=sigma_obs)` \n",
        "extract the parameters (R0,v,k,tau) generated and continue until the last comparison figure (truth/prediction).\n",
        "\n",
        "- In the forward model, we have used Uniform priors, but we can wonder if this is a choice that does not condition the result too much. If you take a look at the documentation, I suggest that you change the distribution to LogNormal, HalfCauchy, InverseGamma... "
      ],
      "metadata": {
        "id": "oxuA0CiLxzNq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Takeaway \n",
        "\n",
        "- You have learned how to code a Bayesian model with Numpyro that involves priors and likelihood.\n",
        "\n",
        "- A new method is available (forward modeling) to generate datasets from this model.\n",
        "\n",
        "- Markov chain generation via NUTS/HMC... is simple to code and you can add arviz to help diagnostics\n",
        "\n",
        "- Note that besides Pyro has its JAX version (ie. Numpyro), PyMC3 is faster with JAX [(read this)](https://docs.pymc.io/en/v3/pymc-examples/examples/samplers/GLM-hierarchical-jax.html)"
      ],
      "metadata": {
        "id": "ENLzNrtOyeIt"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "dactEtCPye9N"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}