MCMC_A2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "MCMC A2.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "-9vpWfp5Q31t",
        "colab_type": "code",
        "outputId": "920e7c7c-0f14-4c37-fae0-ebfbd11ba68a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "import numpy as np\n",
        "import scipy.stats as sts\n",
        "import matplotlib.pyplot as plt\n",
        "import pystan\n",
        "import elfi\n",
        "import time"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "INFO:root:Generating grammar tables from /usr/lib/python3.6/lib2to3/Grammar.txt\n",
            "INFO:root:Generating grammar tables from /usr/lib/python3.6/lib2to3/PatternGrammar.txt\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p7X1N7bLrL0X",
        "colab_type": "text"
      },
      "source": [
        "# 1. Data\n",
        "\n",
        "The underlying data generation is a simple autoregressive model with one step dependency: $$y_{t} = \\alpha + \\beta y_{t-1} + err$$\n",
        "where the error term is a simple Gaussian noise: $$err \\sim \\mathcal{N}(0, \\sigma)$$\n",
        "\n",
        "Thus, we have three parameters in the model: $\\alpha, \\beta, \\sigma$ to infer. With the model above, we can generate some data. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6XFawnDuQ4VH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Number of data point\n",
        "N = 100\n",
        "\n",
        "#Sample the true values of the parameters\n",
        "alpha_true = sts.norm(0, 2).rvs(size=1)\n",
        "beta_true = sts.norm(0, 1).rvs(size=1)\n",
        "sigma_true = sts.expon(0.01).rvs(size=1)\n",
        "\n",
        "#Data generation\n",
        "y = np.ones(N)*0.1\n",
        "y[0] = sts.norm(y[0], sigma_true).rvs()\n",
        "for _ in range(1, N):\n",
        "    y[_] = sts.norm(alpha_true + beta_true*y[_-1], sigma_true).rvs()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BZN_55iVwf_g",
        "colab_type": "text"
      },
      "source": [
        "Then we can print out the true values of the parameters, as well as plot the data points."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2zVDSD2jQ9EQ",
        "colab_type": "code",
        "outputId": "4058e3e8-4335-4564-bafc-febd147bdc86",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 534
        }
      },
      "source": [
        "print(alpha_true)\n",
        "print(beta_true)\n",
        "print(sigma_true)\n",
        "\n",
        "plt.figure(figsize=(12,8))\n",
        "plt.plot(range(N), y)\n",
        "plt.show()"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.23345612]\n",
            "[-0.56225923]\n",
            "[0.49002828]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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4+Hu/8hL+v8/e3/RT2UrkjWxXnsttScPIeJZ7Vgkv3PS92UaF0s3YMCgNo4PouFDe0NS/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\n2CeRVsrVLF8xNwztuOtET4NMz0lyxEhBw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DXLUjER4/GnD4OrWd5G/c1I8gPtx/fvCNWF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\nHzxg4MMGnv8SAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "red9_tuEt-rE",
        "colab_type": "text"
      },
      "source": [
        "# MCMC"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rFmYb1LhwpmB",
        "colab_type": "text"
      },
      "source": [
        "Assume we don't know the true parameters value, we can use MCMC to infer these values from the data we have. Autoregressive models are pretty tricky due to their temporal dependency, so we restrict ourself to a small region of exploration by setting the priors as: \n",
        "\n",
        "$$\\alpha \\sim \\mathcal{N}(0, 2)$$\n",
        "$$\\beta \\sim \\mathcal{N}(0, 1)$$\n",
        "$$\\alpha \\sim Uniform(0, 2)$$\n",
        "\n",
        "Using these priors, we can set up an MCMC sampling procedure using the NUTS algorithm by Stan. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pcOvuzoTQ-mC",
        "colab_type": "code",
        "outputId": "0baf63df-fcba-41e0-ef0d-93c5f6d34dcb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "model = \"\"\"\n",
        "data {\n",
        "  int<lower=0> N;\n",
        "  vector[N] y;\n",
        "}\n",
        "\n",
        "parameters {\n",
        "  real alpha;\n",
        "  real beta;\n",
        "  real<lower=0> sigma;\n",
        "}\n",
        "\n",
        "model {\n",
        "  alpha ~ normal(0, 2);\n",
        "  beta ~ normal(0, 1);\n",
        "  sigma ~ uniform(0, 2);\n",
        "  for (n in 2:N)\n",
        "    y[n] ~ normal(alpha + beta * y[n-1], sigma);\n",
        "}\n",
        "\"\"\"\n",
        "stan_model = pystan.StanModel(model_code=model)"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_b5a086ae6bad5cee247db4366ccfead1 NOW.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QqBgMpM6n6s8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "outputId": "5ee28f68-5e9f-4cb5-9a70-8a9837f7c4b8"
      },
      "source": [
        "data = {\n",
        "    'N': N,\n",
        "    'y': y\n",
        "}\n",
        "\n",
        "start = time.time()\n",
        "stan_results = stan_model.sampling(data=data)\n",
        "print(\"Elapsed time:\", time.time()-start)\n",
        "print(stan_results)"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Elapsed time: 0.5627293586730957\n",
            "Inference for Stan model: anon_model_b5a086ae6bad5cee247db4366ccfead1.\n",
            "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
            "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
            "\n",
            "        mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
            "alpha    0.3  7.7e-4   0.05   0.21   0.27    0.3   0.33   0.38   3536    1.0\n",
            "beta   -0.59  1.4e-3   0.08  -0.75  -0.65  -0.59  -0.54  -0.42   3319    1.0\n",
            "sigma   0.42  5.1e-4   0.03   0.36   0.39   0.41   0.44   0.48   3470    1.0\n",
            "lp__   36.96    0.03   1.23  33.91   36.4  37.29  37.87  38.39   1931    1.0\n",
            "\n",
            "Samples were drawn using NUTS at Mon Mar 23 14:04:46 2020.\n",
            "For each parameter, n_eff is a crude measure of effective sample size,\n",
            "and Rhat is the potential scale reduction factor on split chains (at \n",
            "convergence, Rhat=1).\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eYRSovPBpcGI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "outputId": "88378f0d-0ad3-4687-9226-a58e29d03f21"
      },
      "source": [
        "plt.figure(figsize=(21,7))\n",
        "plt.subplot(1,3,1)  \n",
        "plt.hist(stan_results.extract()['alpha'], color='g', bins=30, alpha=0.2, label='NUTS')\n",
        "plt.axvline(alpha_true, color='black', label='True')\n",
        "plt.legend()\n",
        "plt.title('Alpha')\n",
        "\n",
        "plt.subplot(1,3,2)\n",
        "plt.hist(stan_results.extract()['beta'], color='g', bins=30, alpha=0.2, label='NUTS')\n",
        "plt.axvline(beta_true, color='black', label='True')\n",
        "plt.legend()\n",
        "plt.title('Beta')\n",
        "\n",
        "plt.subplot(1,3,3)\n",
        "plt.hist(stan_results.extract()['sigma'], color='g', bins=30, alpha=0.2, label='NUTS')\n",
        "plt.axvline(sigma_true, color='black', label='True')\n",
        "plt.legend()\n",
        "plt.title('Sigma')\n",
        "plt.show()"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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S/7O7/8uiFw7APgm8AACAleqhTJ78e31VPS3JTFVdO1y7sLvfM7tzVT0nyauT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\nNlH+B7RacS5XN4XzAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1512x504 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TTLfn4rGxU4i",
        "colab_type": "text"
      },
      "source": [
        "We can see that te posterior inferred by the MCMC algorithm reasonably cover the true values of the parameters. The estimation of $\\beta$ seems to be the most accurate whereas for $\\alpha$ and $\\sigma$ the posteriors are not very accurate, although they still cover the true parameter values. Looking at the diagnosis of convergence for Stan, we can see that the posteriors converged. Maybe $\\alpha$ and $\\sigma$ are both linearly combined to $y_{t-1}\\beta$, and the true values are quite close to each other, thus the posterior of $\\alpha$ in the first graphh overrestimates the true value, while the posterior of $\\sigma$ underrestimates in the third graph. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8wqR-VWMpc7e",
        "colab_type": "text"
      },
      "source": [
        "# ABC"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FteLPIPo1SSz",
        "colab_type": "text"
      },
      "source": [
        "Now if we assumes that the likelihood in the above model is intractable, and can only be simulated, we can turn to ABC. Using the package ELFI, we can define a simulation procedure such that it can generate data resembles the real data we have, and compare the synthetic data with the real data by calculating the distance between the two in some measurment. These measurements are called summary statistics in ELFI. \n",
        "\n",
        "One important choice in specifying an ABC model is the summary statistic. It has to be representative of the data so that we can get an accurate sense of whether the synthetic data is similar to our real data in important ways. For an autoregressive model, simple statistics, such as the mean or variance, are unsuitable because they do not represent the regressive curve very well (for example, a mean is very misleading for a regression curve because many curves (with different underlying data generation schemes) can have the same mean). As summary statistics, we experiment with both the autocovariance and autocorrelation. The autocovariance is defined as the covariance between the datapoints shifted by a lag, and the autocorrelation is similarly defined as the correlation between shifted datapoints. We use the lag values of 1 and 2. \n",
        "\n",
        "Another choice in specifying the model is the sampling algorithm. In this experiment, we use both rejection ABC and Sequential Monte Carlo ABC (SMC ABC). Rejection ABC is simpler: rejecting the synthetic data completely within a fixed tolerance, thus usually takes a lot of time for convergence especially when the sampler enters the regions where the mode is concentrated (we tend to reject more). SMC ABC uses a schedule of the tolerance to waste less time exploring the regions where the mode is not concentrated, and to focus on regions where it is. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QhP_aH0XRbmc",
        "colab_type": "code",
        "outputId": "7c14aa7a-7026-4892-9549-743b6937e07b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 464
        }
      },
      "source": [
        "#Autocovariance\n",
        "m2 = elfi.new_model()\n",
        "\n",
        "alpha = elfi.Prior(\"norm\", 0, 2, model=m2)\n",
        "beta = elfi.Prior(\"norm\", 0, 1, model=m2)\n",
        "sigma = elfi.Prior(\"uniform\", 0, 2, model=m2)\n",
        "\n",
        "def simulator(alpha, beta, sigma, batch_size=1, random_state=None):\n",
        "    result = np.ones(shape=(batch_size, N))*0.1\n",
        "    for _ in range(1, N): \n",
        "        result[:, _] = sts.norm.rvs(alpha + beta*result[:, _-1], sigma, size=batch_size, random_state=random_state)\n",
        "    return result\n",
        "\n",
        "def autocov(y, lag=1):\n",
        "    C = np.mean(y[:,lag:] * y[:,:-lag], axis=1)\n",
        "    return C\n",
        "\n",
        "def autocorr(y, t=1):\n",
        "    r = []\n",
        "    for _ in range(y.shape[0]):\n",
        "        r.append(np.corrcoef(np.array([y[_, :-t], y[_, t:]]))[0, 1])\n",
        "    return np.array(r)\n",
        "\n",
        "sim2 = elfi.Simulator(simulator, alpha, beta, sigma, observed=y.reshape(1, -1))\n",
        "\n",
        "S12 = elfi.Summary(autocov, sim2)\n",
        "S22 = elfi.Summary(autocov, sim2, 2)\n",
        "\n",
        "d2 = elfi.Distance('euclidean', S12, S22)\n",
        "elfi.draw(d2)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f88e30fd828>"
            ],
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fill=\"#000000\">alpha</text>\n</g>\n<!-- sim2 -->\n<g id=\"node4\" class=\"node\">\n<title>sim2</title>\n<ellipse fill=\"#cccccc\" stroke=\"#000000\" cx=\"105.5473\" cy=\"-194.1892\" rx=\"28.6953\" ry=\"28.6953\"/>\n<text text-anchor=\"middle\" x=\"105.5473\" y=\"-190.4892\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">sim2</text>\n</g>\n<!-- alpha&#45;&gt;sim2 -->\n<g id=\"edge1\" class=\"edge\">\n<title>alpha&#45;&gt;sim2</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M49.473,-266.7827C59.2476,-254.1284 71.2748,-238.5581 81.6807,-225.0867\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"84.5725,-227.0684 87.9157,-217.0149 79.0327,-222.7892 84.5725,-227.0684\"/>\n</g>\n<!-- beta -->\n<g id=\"node2\" class=\"node\">\n<title>beta</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"105.5473\" cy=\"-291.2837\" rx=\"25.9954\" ry=\"25.9954\"/>\n<text text-anchor=\"middle\" x=\"105.5473\" y=\"-287.5837\" font-family=\"Times,serif\" font-size=\"14.00\" 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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "agxru8FEiQJ5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 464
        },
        "outputId": "49328e59-69fd-4243-a490-e0b137ba71f0"
      },
      "source": [
        "#Autocorrelation\n",
        "m = elfi.new_model()\n",
        "\n",
        "alpha = elfi.Prior(\"norm\", 0, 2, model=m)\n",
        "beta = elfi.Prior(\"norm\", 0, 1, model=m)\n",
        "sigma = elfi.Prior(\"uniform\", 0, 2, model=m)\n",
        "\n",
        "def simulator(alpha, beta, sigma, batch_size=1, random_state=None):\n",
        "    result = np.ones(shape=(batch_size, N))*0.1\n",
        "    for _ in range(1, N): \n",
        "        result[:, _] = sts.norm.rvs(alpha + beta*result[:, _-1], sigma, size=batch_size, random_state=random_state)\n",
        "    return result\n",
        "\n",
        "def autocov(y, lag=1):\n",
        "    C = np.mean(y[:,lag:] * y[:,:-lag], axis=1)\n",
        "    return C\n",
        "\n",
        "def autocorr(y, t=1):\n",
        "    r = []\n",
        "    for _ in range(y.shape[0]):\n",
        "        r.append(np.corrcoef(np.array([y[_, :-t], y[_, t:]]))[0, 1])\n",
        "    return np.array(r)\n",
        "\n",
        "sim3 = elfi.Simulator(simulator, alpha, beta, sigma, observed=y.reshape(1, -1))\n",
        "\n",
        "S13 = elfi.Summary(autocorr, sim3)\n",
        "S23 = elfi.Summary(autocorr, sim3, 2)\n",
        "\n",
        "d3 = elfi.Distance('euclidean', S13, S23)\n",
        "elfi.draw(d3)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f88e30ff240>"
            ],
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-diojmMcRPQa",
        "colab_type": "code",
        "outputId": "1d300218-b73e-4afa-f3f9-75418a151037",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "start = time.time()\n",
        "rej2 = elfi.Rejection(d2, batch_size=10000)\n",
        "res2 = rej2.sample(10000, threshold=.1)\n",
        "print(\"Elapsed time:\", time.time()-start)\n",
        "\n",
        "start = time.time()\n",
        "rej3 = elfi.Rejection(d3, batch_size=10000)\n",
        "res3 = rej3.sample(10000, threshold=.1)\n",
        "print(\"Elapsed time:\", time.time()-start)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Progress: |██████████████████████████████████████████████████| 100.0% Complete\n",
            "Elapsed time: 12.353216171264648\n",
            "Progress: |██████████████████████████████████████████████████| 100.0% Complete\n",
            "Elapsed time: 46.24461102485657\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P893bV59RebY",
        "colab_type": "code",
        "outputId": "da8152ce-d9cc-44e2-b0c2-e73f54df9b49",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        }
      },
      "source": [
        "schedule = [0.7, 0.4, 0.1]\n",
        "\n",
        "rej_smc2 = elfi.SMC(d2, batch_size=10000, seed=251)\n",
        "start = time.time()\n",
        "result_smc2 = rej_smc2.sample(10000, schedule)\n",
        "print(\"Elapsed time:\", time.time()-start)\n",
        "\n",
        "rej_smc3 = elfi.SMC(d3, batch_size=10000, seed=251)\n",
        "start = time.time()\n",
        "result_smc3 = rej_smc3.sample(10000, schedule)\n",
        "print(\"Elapsed time:\", time.time()-start)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "INFO:elfi.methods.parameter_inference:---------------- Starting round 0 ----------------\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            ""
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "INFO:elfi.methods.parameter_inference:---------------- Starting round 1 ----------------\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            ""
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "INFO:elfi.methods.parameter_inference:---------------- Starting round 2 ----------------\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Progress: |██████████████████████████████████████████████████| 100.0% Complete\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "INFO:elfi.methods.parameter_inference:---------------- Starting round 0 ----------------\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Elapsed time: 19.033515214920044\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "INFO:elfi.methods.parameter_inference:---------------- Starting round 1 ----------------\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            ""
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "INFO:elfi.methods.parameter_inference:---------------- Starting round 2 ----------------\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Progress: |██████████████████████████████████████████████████| 100.0% Complete\n",
            "Elapsed time: 37.95256447792053\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5e3zY9prTwks",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plot_elfi(result1, result2, name1, name2):\n",
        "    plt.figure(figsize=(21,7))\n",
        "    plt.subplot(1,3,1)  \n",
        "    plt.hist(result1.samples['alpha'], color='b', bins=30, alpha=0.2, label=name1)\n",
        "    plt.hist(result2.samples['alpha'], color='r', bins=30, alpha=0.2, label=name2)\n",
        "    plt.axvline(alpha_true, color='black', label='True')\n",
        "    plt.legend()\n",
        "    plt.title('Alpha')\n",
        "\n",
        "    plt.subplot(1,3,2)\n",
        "    plt.hist(result1.samples['beta'], color='b', bins=30, alpha=0.2, label=name1)\n",
        "    plt.hist(result2.samples['beta'], color='r', bins=30, alpha=0.2, label=name2)\n",
        "    plt.axvline(beta_true, color='black', label='True')\n",
        "    plt.legend()\n",
        "    plt.title('Beta')\n",
        "    \n",
        "    plt.subplot(1,3,3)\n",
        "    plt.hist(result1.samples['sigma'], color='b', bins=30, alpha=0.2, label=name1)\n",
        "    plt.hist(result2.samples['sigma'], color='r', bins=30, alpha=0.2, label=name2)\n",
        "    plt.axvline(sigma_true, color='black', label='True')\n",
        "    plt.legend()\n",
        "    plt.title('Sigma')\n",
        "    plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yaLQEAoHigF8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "outputId": "0ff6a42d-4b12-4dfa-f494-ba9a9c3061f3"
      },
      "source": [
        "plot_elfi(res2, res3, \"Rejection + Autocov\", \"Rejection + Autocorr\")"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Y2sM14iV1Ftsd7ciutDk7TIRFxDxKa3x9ICJWUHr64xXAjyLiXOBF4Iyi+n3A\nycBzQDMwrQhsVURcBjxR1PuXzQvn76y+ffvyxhtvMGDAAP8g1KbM5I033qBv377lDkWSpF7BPpja\nwz6YKlV7v892LbHuY7ujHdnVNqc9T408q41DE1qpm8AFrdQlM38A/GCnomvF4MGDWbFiBU1NTR29\nlHq5vn37Mnjw4HKHIUlSr2AfTO1lH0xSZ7DdUXvsSpuzq1Mjy2a33XZj2LBh5Q5DkiSpqtgHkyR1\nJ9sddZUOPzVSkiRJkiRJqgQVNyJMkiRJktS7+MwpSd3FEWGSJEmSJEmqCo4IkyRJak3L4Qlvvvlu\nmY8MkyRJqliOCJMkSZIkSVJVcESYJEnq/Vx8RpIkSTgiTJIkSZIkSVXCRJgkSZIkSZKqgokwSZIk\nSZIkVQUTYZIkSZIkSaoKJsIkSZIkSZJUFUyESZIkSZIkqSqYCJMkSZIkSVJVMBEmSZIkSZKkqmAi\nTJIkSZIkSVWhttwBSOokDQ3tqzd2bNfGIUmSJElSD+WIMEmSJEmSJFUFE2GSpB4lIn4QEa9FxNMt\nyvaNiAci4r+Kf/cpyiMiro+I5yLitxFxRItzphb1/ysippbjXiRJkiT1LCbCJEk9za3AxG3KZgIP\nZuZw4MFiH+AkYHjxMx2YBaXEGfAN4GjgKOAbm5NnkiRJkqqXiTBJUo+Smb8AVm1TPAmYU2zPAU5r\nUT43Sx4D+kfE/sAngQcyc1VmrgYe4L3JNUmSJElVxkSYJKkS7JeZLxfbrwD7FduDgOUt6q0oytoq\nf4+ImB4RiyJiUVNTU+dGLUmSJKlHMREmSaoomZlAduL1ZmdmfWbWDxw4sLMuK0mSJKkHqi13AFKP\n19BQ7ggkwasRsX9mvlxMfXytKF8JDGlRb3BRthIYv035gm6IU5IkSVIP5ogwSVIluBfY/OTHqcA9\nLcrPLp4eeQywtphCeT9wYkTsUyySf2JRJkmSJKmKOSJMktSjRMQ8SqO5PhARKyg9/fEK4EcRcS7w\nInBGUf0+4GTgOaAZmAaQmasi4jLgiaLev2TmtgvwS5IkSaoyJsIkST1KZp7VxqEJrdRN4II2rvMD\n4AedGJokSZKkCufUSEmSJEmSJFUFR4RJkiRJktQOO/McrbFjuy4OSbvOEWGSJEmSJEmqCibCJEmS\nJEmSVBWcGilJkiRJ6hI7M5VQkrqDiTBJkqSd0danOheDkSRJ6vGcGimVSWNj6UeSJEmSJHUPE2GS\nJEmSJEmqCibCJEmSJEmSVBVMhEmSJEmSJKkqmAiTJEmSJElSVTARJkmSJEmSpKpgIkySJEmSJElV\nwUSYJEmSJEmSqoKJMEmSJPk3WHMAACAASURBVEmSJFUFE2GSJEmSJEmqCibCJEmSJEmSVBVqyx2A\nVG0aG8sdgSRJkiRJ1ckRYZIkSZIkSaoKJsIkSZIkSZJUFUyESZIkSZIkqSqYCJMkSZIkSVJVMBEm\nSZIkSZKkqmAiTOqhGhuhubncUUiSJEmS1HuYCJMkSZIkSVJVMBEmSZIkSZKkqmAiTJIkSZIkSVXB\nRJgkSZIkSZKqgokwqYdzwXxJkiRJkjpHbbkDkMqmoaHcEUiSJEmSpG7kiDBJkiRJkiRVhQ4lwiLi\nnyLi9xHxdETMi4i+ETEsIhZGxHMRMT8idi/q9in2nyuOD+2MG5AkSZIkSZLaY5cTYRExCLgIqM/M\nkUANcCZwJXBNZn4UWA2cW5xyLrC6KL+mqCdJkiRJkiR1i45OjawF9oiIWqAOeBn4BHBXcXwOcFqx\nPanYpzg+ISKig68vSZIkSZIktcsuJ8IycyVwNfASpQTYWqABWJOZG4pqK4BBxfYgYHlx7oai/oBt\nrxsR0yNiUUQsampq2tXwJEmSJEmSpK10ZGrkPpRGeQ0DDgD2BCZ2NKDMnJ2Z9ZlZP3DgwI5eTpIk\nSZIkSQI6NjXyb4ClmdmUme8A/wEcB/QvpkoCDAZWFtsrgSEAxfF+wBsdeH1JkiRJkiSp3TqSCHsJ\nOCYi6oq1viYAfwAeBj5b1JkK3FNs31vsUxx/KDOzA68vSZIkSZIktVvtjqu0LjMXRsRdwGJgA/Ak\nMBv4T+COiLi8KLu5OOVm4LaIeA5YRekJk5IkSZ2noaHcEUiSJKkH2+VEGEBmfgP4xjbFLwBHtVJ3\nHTC5I68nSZIkSZIk7aqOTI2UJEmSJEmSKoaJMEmSJEmSJFUFE2GSJEmSJEmqCh1aI0xSBdqZhaTH\nju26OCRJkiRJ6mYmwiRJkiRpGxHRH7gJGAkk8D+BPwLzgaHAMuCMzFwdEQFcB5wMNAPnZObiMoSt\nHqS93z/73bPUvZwaKZVZY2O5I5AkSVIrrgN+lpkHA6OBRmAm8GBmDgceLPYBTgKGFz/TgVndH64k\nqT1MhEmSJElSCxHRD/g4cDNAZq7PzDXAJGBOUW0OcFqxPQmYmyWPAf0jYv9uDluS1A4mwiRJkiRp\na8OAJuCWiHgyIm6KiD2B/TLz5aLOK8B+xfYgYHmL81cUZVuJiOkRsSgiFjU1NXVh+JKktpgIk3qY\nxsb3TpdsrUySJEldphY4ApiVmYcDf+bdaZAAZGZSWjus3TJzdmbWZ2b9wIEDOy1YSVL7mQiTJEmS\npK2tAFZk5sJi/y5KibFXN095LP59rTi+EhjS4vzBRZkkqYcxESZJkiRJLWTmK8DyiDioKJoA/AG4\nF5halE0F7im27wXOjpJjgLUtplBKknqQ2nIHIOndaY8jRpQ3DkmSJG1xIXB7ROwOvABMozSQ4EcR\ncS7wInBGUfc+4GTgOaC5qCtJ6oFMhEmSKkZE/BPw95TWZPkdpQ8a+wN3AAOABuDvMnN9RPQB5gJj\ngTeAKZm5rBxxS5IqT2YuAepbOTShlboJXNDlQUmSOsypkZKkihARg4CLgPrMHAnUAGcCVwLXZOZH\ngdXAucUp5wKri/JrinqSJEmSqpiJMElSJakF9oiIWqAOeBn4BKVFjAHmAKcV25OKfYrjEyIiujFW\nSZIkST2MUyMlSRUhM1dGxNXAS8DbwM8pTYVck5kbimorgEHF9iBgeXHuhohYS2n65OvdGriqR0ND\n6+Vjx3ZvHJIkSWqTI8IkSRUhIvahNMprGHAAsCcwsROuOz0iFkXEoqampo5eTpIkSVIPZiJM6kE2\nPz1SUqv+BliamU2Z+Q7wH8BxQP9iqiTAYGBlsb0SGAJQHO9HadH8rWTm7Mysz8z6gQMHdvU9SJIk\nSSojE2GSpErxEnBMRNQVa31NAP4APAx8tqgzFbin2L632Kc4/lDxVC9JkiRJVcpEmCSpImTmQkqL\n3i8GfkepDZsNfAn4fEQ8R2kNsJuLU24GBhTlnwdmdnvQkiRJknoUF8uXJFWMzPwG8I1til8Ajmql\n7jpgcnfEJUmSJKkyOCJMkiRJkiRJVcERYZIkSZKkdmtoKHcEkrTrHBEmSZIkSZKkqmAiTJIkSZIk\nSVXBRJgkSZIkSZKqgokwSZIkSZIkVQUTYZIkSZIkSaoKJsKkbtTYWO4IJEmSJEmqXibCJEmSJEmS\nVBVMhEmSJEmSJKkqmAiTJEmSJElSVTARJkmSJEmSpKpgIkySJEmSJElVwUSYJEmSJEmSqoKJMEmS\nJEmSJFWF2nIHIEmSJElStWpoaF+9sWO7Ng6pWjgiTJIkSZIkSVXBRJgkSZIkSZKqgokwSZIkSZIk\nVQUTYZIkSZIkSaoKJsIkSZIkSZJUFUyESZIkSZIkqSqYCJMkSZIkSVJVMBEmSZIkSZKkqmAiTJIk\nSZIkSVXBRJgkSZIkSZKqQm25A5AkSdppDQ3ljkCSJEkVyBFhkiRJkiRJqgomwiRJkiRJklQVTIRJ\nkiRJkiSpKpgIkyRJkiRJUlUwESZJkiRJkqSqYCJMkiRJkiRJVcFEmCRJkiRJkqqCiTBJkiRJkiRV\nBRNhkiRJkiRJqgodSoRFRP+IuCsinomIxog4NiL2jYgHIuK/in/3KepGRFwfEc9FxG8j4ojOuQVJ\nkiRJkiRpxzo6Iuw64GeZeTAwGmgEZgIPZuZw4MFiH+AkYHjxMx2Y1cHXliRJkiRJktptlxNhEdEP\n+DhwM0Bmrs/MNcAkYE5RbQ5wWrE9CZibJY8B/SNi/12OXJIkSZIkSdoJHRkRNgxoAm6JiCcj4qaI\n2BPYLzNfLuq8AuxXbA8Clrc4f0VRtpWImB4RiyJiUVNTUwfCkyRJkiRJkt7VkURYLXAEMCszDwf+\nzLvTIAHIzARyZy6ambMzsz4z6wcOHNiB8CRJkiRJkqR3dSQRtgJYkZkLi/27KCXGXt085bH497Xi\n+EpgSIvzBxdlkiRJkiRJUper3dUTM/OViFgeEQdl5h+BCcAfip+pwBXFv/cUp9wL/ENE3AEcDaxt\nMYVSUjs0NsKIEd34gg0N7as3dmzXxiFJkiRJUifY5URY4ULg9ojYHXgBmEZplNmPIuJc4EXgjKLu\nfcDJwHNAc1FXkiRJFcjvSiRJUiXqUCIsM5cA9a0cmtBK3QQu6MjrSZIkaeeZtJIkSSrp6IgwSZIk\ndSKTVpIkSV3HRJgkSZKA9ifhJEmSKpWJMEmSpK60veySw7okSZK61fvKHYAkSZIkSZLUHRwRJkmS\nVIGcxihJ1WVn3vcdcCy1zRFhkiRJkiRJqgqOCJMkSVKX8SmYkiSpJ3FEmCRJkiRJkqqCiTBJUsWI\niP4RcVdEPBMRjRFxbETsGxEPRMR/Ff/uU9SNiLg+Ip6LiN9GxBHljl+SJElSeZkIkyRVkuuAn2Xm\nwcBooBGYCTyYmcOBB4t9gJOA4cXPdGBW94crSZIkqSdxjTD1Lj5CS+q1IqIf8HHgHIDMXA+sj4hJ\nwPii2hxgAfAlYBIwNzMTeKwYTbZ/Zr7czaFLkiRJ6iEcESZJqhTDgCbgloh4MiJuiog9gf1aJLde\nAfYrtgcBy1ucv6Io20pETI+IRRGxqKmpqQvDlyRJklRuJsIkSZWiFjgCmJWZhwN/5t1pkAAUo79y\nZy6ambMzsz4z6wcOHNhpwUqSJEnqeZwaKUmqFCuAFZm5sNi/i1Ii7NXNUx4jYn/gteL4SmBIi/MH\nF2WSeqCdWd1g7Niui0OSJPVujgiTJFWEzHwFWB4RBxVFE4A/APcCU4uyqcA9xfa9wNnF0yOPAda6\nPpgkSZJU3RwRJkmqJBcCt0fE7sALwDRKX+r8KCLOBV4Ezijq3gecDDwHNBd1JUmSJFUxE2GSpIqR\nmUuA+lYOTWilbgIXdHlQkiRJkiqGUyMlSZIkSZJUFUyESZIkSZIkqSqYCJMkSZIkSVJVcI0wqRs0\nNpY7AkmSJEmS5IgwSZIkSZIkVQUTYZIkSZLUioioiYgnI+Knxf6wiFgYEc9FxPyI2L0o71PsP1cc\nH1rOuCVJbTMRJkmSJEmt+0eg5SIXVwLXZOZHgdXAuUX5ucDqovyaop4kqQcyESZJkiRJ24iIwcCn\ngJuK/QA+AdxVVJkDnFZsTyr2KY5PKOpLknoYE2GSJEmS9F7XAl8ENhX7A4A1mbmh2F8BDCq2BwHL\nAYrja4v6W4mI6RGxKCIWNTU1dWXskqQ2mAiTJEmSpBYi4hTgtcxs6MzrZubszKzPzPqBAwd25qUl\nSe1UW+4AJEmSJKmHOQ44NSJOBvoCewPXAf0jorYY9TUYWFnUXwkMAVZERC3QD3ij+8OWJO2II8Ik\nSZIkqYXM/HJmDs7MocCZwEOZ+TngYeCzRbWpwD3F9r3FPsXxhzIzuzFkSVI7mQiTJEmSpPb5EvD5\niHiO0hpgNxflNwMDivLPAzPLFJ8kaQecGilJkiRJbcjMBcCCYvsF4KhW6qwDJndrYJKkXWIiTJIk\nSZKkXqShnY95GDu2a+OQeiITYZIkqedqb09ekiRJagcTYZIkSZKkLlHX2L4vNJpHODRJUvcwESZJ\nkiRJkqSt7czI/AqaZ+tTIyVJkiRJklQVHBEmSZK0ixob21dvxIiujUOSpJbaOyW1kkbxSJ3FEWGS\nJEmSJEmqCibCJEmSJEmSVBWcGilJktTF2ppC2dy9YUhSp2n31DtJ6mEcESZJkiRJkqSqYCJMkiRJ\nkiRJVcGpkZIkSZIklcnOTDNtHuFTHqWOckSYJEmSJEmSqoIjwiRJUlVoa8H6bY0Y0bVxSJLey1FR\n2q6GnXg4w1h/P7R9JsJUGXbmjU+SpA5oLWHW3Nz2sY5o64OfH/IkSerFTOyVlVMjJUmSJEmSVBUc\nESZJkiRJavcolbpOHh3bVVqOuq1pfvM9ZbvCEbtS5TMRJkmSJEmqGB1NZqkFp+ipCjk1UpIkSZIk\nSVXBEWGSJEmSJKl3aO8ot/aOcHPUXK9jIkySJEmSpCq0M09Ddnm0XmRnknvlumYXJhWdGilJkiRJ\nkqSq4IgwSR3ncGFJkqSeqytGf0jqHp091VMmwiRJkiRJOzdNTlIPY8K73UyESZIkqaL45bgk9WDO\nFlEP5xphkiRJkiRJqgqOCJMkSZIkSdXFqYRVq8OJsIioARYBKzPzlIgYBtwBDAAagL/LzPUR0QeY\nC4wF3gCmZOayjr6+JEmSJEndoa7R5IlU6TpjRNg/Ao3A3sX+lcA1mXlHRNwInAvMKv5dnZkfjYgz\ni3pTOuH1JUmSJElSV3IElXqJDq0RFhGDgU8BNxX7AXwCuKuoMgc4rdieVOxTHJ9Q1JckSZIkSZK6\nXEcXy78W+CKwqdgfAKzJzA3F/gpgULE9CFgOUBxfW9TfSkRMj4hFEbGoqampg+FJkiRJkiRJJbs8\nNTIiTgFey8yGiBjfWQFl5mxgNkB9fX121nUlSZIkSZK6jNNHK0JH1gg7Djg1Ik4G+lJaI+w6oH9E\n1BajvgYDK4v6K4EhwIqIqAX6UVo0X5IkSZIkSepyu5wIy8wvA18GKEaEfSEzPxcRdwKfpfTkyKnA\nPcUp9xb7vymOP5SZjviSJEmSJKkdfGql1HEdXSOsNV8CPh8Rz1FaA+zmovxmYEBR/nlgZhe8tiRJ\nkiRJktSqjkyN3CIzFwALiu0XgKNaqbMOmNwZrydJkiRJkiTtrK4YESZJkiRJkiT1OJ0yIkySJEmS\nJGmn+JRFlYGJMElSRYmIGmARsDIzT4mIYZQe0DIAaAD+LjPXR0QfYC4wltJTiqdk5rIyha0u1NhY\n7ggkSZJUKZwaKUmqNP8ItEx9XAlck5kfBVYD5xbl5wKri/JrinqSJEmSqpiJMElSxYiIwcCngJuK\n/QA+AdxVVJkDnFZsTyr2KY5PKOpLkiRJqlJOjZQkVZJrgS8CexX7A4A1mbmh2F8BDCq2BwHLATJz\nQ0SsLeq/3vKCETEdmA7woQ99qEuDlyRJqlTtXYpgxIiujUPqKEeESZIqQkScAryWmZ26qmpmzs7M\n+sysHzhwYGdeWpIkSVIP44gwSVKlOA44NSJOBvoCewPXAf0jorYYFTYYWFnUXwkMAVZERC3Qj9Ki\n+ZIkSZKqlCPCJEkVITO/nJmDM3MocCbwUGZ+DngY+GxRbSpwT7F9b7FPcfyhzMxuDFmSJElSD2Mi\nTJJU6b4EfD4inqO0BtjNRfnNwICi/PPAzDLFJ0mSJKmHcGqkJKniZOYCYEGx/QJwVCt11gGTuzUw\nSZIkST2aI8IkSZIkSZJUFRwRJkmSepyG4tmgde18VLskSZLUHo4IkyRJkiRJUlUwESZJkiRJkqSq\nYCJMkiRJkiRJVcFEmCRJkiRJkqqCiTBJkiRJkiRVBRNhkiRJkiRJqgomwiRJkiRJklQVTIRJkiRJ\nkiSpKtSWOwBJklTlGhreU1TXWIY4JEmS1OuZCJMkSVKv1EqOtU1jx3ZdHJIkqedwaqQkSZIkSZKq\ngiPCJHWv9n4971fzkiRJkqROZiJMkiRJkiR1isadWOdzxIiui0Nqi1MjJUmSJEmSVBUcESZJktTD\n1DW2Po28eYTTxiVJkjrCEWGSJEmSJEmqCibCJEmSJEmSVBVMhEmSJEmSJKkqmAiTJEmSJElSVXCx\nfEmS1CENra/r3qqxrvUuSZKkMjIRJkmSuk1rSbO6xu6PQ5IklV9jO/sAI0Z0bRyqLibCVD47M4RA\nkiRJkiSpg1wjTKowjY3t/+ZEkiRJkiS9y0SYJEmSJEmSqoKJMEmSJEmSJFUFE2FSF3MaoyRJkiRJ\nPYOJMEmSJElqISKGRMTDEfGHiPh9RPxjUb5vRDwQEf9V/LtPUR4RcX1EPBcRv42II8p7B5KktpgI\nkyRJkqStbQD+OTMPAY4BLoiIQ4CZwIOZORx4sNgHOAkYXvxMB2Z1f8iSpPYwESZJkiRJLWTmy5m5\nuNh+E2gEBgGTgDlFtTnAacX2JGBuljwG9I+I/bs5bElSO5gIkyRJkqQ2RMRQ4HBgIbBfZr5cHHoF\n2K/YHgQsb3HaiqJs22tNj4hFEbGoqampy2KWJLWtttwBSJIkSeXW0NC+emPHdm0c6lki4v3Aj4GL\nM/O/I2LLsczMiMiduV5mzgZmA/9/e/cfJElZ33H8/eXgsFARCIjIoUAFdUklUe5E8EdAEIWLeqaS\nEFJKQLGIAlaMmohaSaXyT1ATDClNDAETiERQRLwYLH4JSVQO4cjBKStwEpXDEzAqSl0Vin7zRz8r\nfcv+mN2d6e7Zfr+qpnamp2f3sz3PdM985+nnYc2aNQt6rCRpOOwRJkmSJEnTRMQuVEWwSzLzirL4\ngalTHsvPB8vy+4EDag9fVZZJkjrGHmGSJEmSVBNV168LgcnMPLd213rgFOCc8vOzteVnRcSlwIuA\nh2unUEpaosnJwdedmBhdDi0PFsIkSZIkaUcvAU4GNkfEprLsvVQFsE9GxGnAt4ATy31XAWuBLcB2\n4I3NxpUkDcpCmCRJkiTVZOYXgZjl7mNnWD+BM0caSpI0FI4RJkmSJEmSpF6wECZJkiRJkqRe8NRI\nSZIkSVrGFjLQuCQtd/YIkyRJkiRJUi9YCJMkSZIkSVIvWAiTJEmSJElSL1gIkyRJkiRJUi9YCJMk\nSZIkSVIvOGukJEma0caNbSeQJEmShmvRhbCIOAC4GNgXSOD8zDwvIvYCLgMOBL4JnJiZP4iIAM4D\n1gLbgVMz87alxZckSeqP3SZnrk5un1jdcBJJkqTxtJQeYY8B78zM2yLiqcDGiLgWOBW4PjPPiYiz\ngbOBdwMnAIeUy4uAfyg/JUmSJEmSlmxycrD1JiZGm0PdtegxwjJz21SPrsz8MTAJ7A+sAy4qq10E\nvK5cXwdcnJUNwB4Rsd+ik0uSJEmSJEkLMJTB8iPiQOAFwM3Avpm5rdz1XapTJ6Eqkt1Xe9jWsmz6\n7zo9Im6NiFsfeuihYcSTJEmSJEmSll4Ii4inAJ8G3p6ZP6rfl5lJNX7YwDLz/Mxck5lr9tlnn6XG\nkyRJkiRJkoAlzhoZEbtQFcEuycwryuIHImK/zNxWTn18sCy/Hzig9vBVZZkkSeqB2QZ6lyRJkpqy\nlFkjA7gQmMzMc2t3rQdOAc4pPz9bW35WRFxKNUj+w7VTKCVpRxsX8IF5tbOl9YGzFUuSJElaqqWc\nGvkS4GTgmIjYVC5rqQpgx0XEPcArym2Aq4B7gS3APwFnLOFvS5L6Z2q24kOBI4AzI+JQqtmJr8/M\nQ4Dry23Ycbbi06lmK5YkSZLUY4vuEZaZXwRilruPnWH9BM5c7N+TJPVb6UW8rVz/cUTUZys+uqx2\nEXAj8G5qsxUDGyJij6lT95vO3iUL6WwpSZIkLTdDmTVSkqQmOVuxJEmSpMWwECZJGivOVixJkiRp\nsZY0a6Q0I8+7kTQizlYsSZIkaSkshEmSxoKzFUuSJGlYJicHW29iYrQ51DwLYZKkcTE1W/HmiNhU\nlr2XqgD2yYg4DfgWcGK57ypgLdVsxduBNzYbV5IkSVLXWAiTJI0FZyuW1AULGQFi9erR5ZAkSYvj\nYPmSJEmSJEnqBXuESZK0DDhPiSRJkjQ/e4RJkiRJkiSpFyyESZIkSZIkqRcshEmSJEmSJKkXLIRJ\nkiRJkiSpFyyESZIkSZIkqRecNVKSJEmSxo3TBUuNmJwcfN2JidHl0PDYI0waU5OTC9spS5IkSZLU\ndxbCJEmSJEmS1AsWwiRJkiRJktQLjhEmSZI05nabnHmsoO0TqxtOIklSfw06dM1CxhIbxe/sO3uE\nSZIkSZIkqRfsESZJkoZqtt5JkiRJUtvsESZJkiRJkqResEeYJEkdtdGOVZIkSdJQWQiTNP4GrRas\ndtBoSZIkSe0adAB8jYaFMA3OrgmSJEmSJGmMOUaYJEmSJEmSesFCmCRJkiRJknrBUyMlSZIkSZLG\n2ELGHZuYGF2OcWCPMEmSJEmSJPWChTBJkiRJkiT1goUwSZIkSZIk9YKFMEmSJEmSJPWCg+VLI7KQ\nwQolSZIkSdLo2SNMkiRJkiRJvWCPMEmSJGkENm4cbL3Vq0ebQ5IkPc5CmCRJ0jK12+TslZjtE1Zf\nJEnqo0GH8ZmYGG2OtlgIkyRJkiRJ0g6Wa8HMMcIkSZIkSZLUCxbCJEmSJEmS1AsWwqQxN2h3VUmS\nJEmS+s4xwiT1x6DTd4FTeEmSJEnSMmQhTJIkLcpcMxJKkiRJ0w08AP8I+yVYCJMkSeqh2QqZ20f5\nzlOSJKllFsIkSZIkSZK0KOM2brWFsL5byJhJGsi47QQkSZIkSeoLC2GSJDXM7yAkSZKkduzUdgBJ\nkiRJkiSpCRbCJEmSJEmS1AsWwqRlYHLSsckkSZIkSZqPhTBJkiRJkiT1goPlS5IkSS1ayAQaq1eP\nLofGi2cDSNLi2CNMkiRJkiRJvWCPMEmSNKvdJhfQVUXLwmzP+fYJuyJJkqTxZyFMGiK7qC8jg56n\n4jkqkiRJkjQ2LIQtVwsZbELS4lkwkyQ1yMOOJElL4xhhkiRJkiRJ6gV7hElD0JVTIicnYWKi7RSS\npOXIscMkSdJyYI8waZmZnOxOYU6SJEmSpC6xR9g4cdwvSdKIODukJEmS+qDxQlhEHA+cB6wALsjM\nc5rO0DkWuMZaV3tf1XN5umQHLOR17gjHQ+MxRxq9uYqonjapvvG4I0nd12ghLCJWAB8BjgO2ArdE\nxPrMvLPJHNJSdbX4pWXCKcGGwmPOzOz5pSYttL1ZONM487gjSeOh6R5hhwNbMvNegIi4FFgHjObg\nYE8rDYmFL2ksNXvMwcOOtFTDLNT2vag2iv2R37/Mq/HjjiRp4ZouhO0P3Fe7vRV4UX2FiDgdOL3c\nfCQi7moo20z2Br7X4t+fS5ezQbfzjV22Q09e00KUJ+jydoNu5+tqtme3HWDE5j3mQOeOO9Dd9jKI\nZZ+9I/vj6Zb9du8osy9c7487Qz7mdLkNdjbboSev6Wy2osv5zLY4ZluMk5ecbdZjTucGy8/M84Hz\n284BEBG3ZmYn3/F2ORt0O5/ZFqfL2aDb+bqcTd067sB4txezt8Ps7TC7FmOYx5wuP49mW7wu5zPb\n4phtcUaZbadR/NI53A8cULu9qiyTJGnYPOZIkprkcUeSxkDThbBbgEMi4qCIWAmcBKxvOIMkqR88\n5kiSmuRxR5LGQKOnRmbmYxFxFnA11ZTCH8vMrzWZYYE6c6rMDLqcDbqdz2yL0+Vs0O18Xc62bI3h\nMWfKOLcXs7fD7O0wu3bQwnGny8+j2Ravy/nMtjhmW5yRZYvMHNXvliRJkiRJkjqj6VMjJUmSJEmS\npFZYCJMkSZIkSVIvWAibR0Q8PyI2RMSmiLg1Ig5vO1NdRLwtIr4eEV+LiA+0nWe6iHhnRGRE7N12\nlrqI+GDZbndExGciYo8OZDo+Iu6KiC0RcXbbeaZExAERcUNE3Fna2R+1nWm6iFgREf8TEZ9rO0td\nROwREZeXtjYZEUe2nUndExG/W15bP4+IWaeI7uI+IiL2iohrI+Ke8nPPWdb7QPkfJyPi7yIims46\nQ6ZBsz8rIq4p2e+MiAObTTpjpoGyl3V3j4itEfHhJjPOZpDs5b3XTaXN3BERv9dG1lqeOV97EbFr\nRFxW7r+5C21kygDZ31Ha9R0RcX1EPLuNnHqipbS7iHhPWX5XRLyqhWyztquI+Fn5XLUpIoY+kcAA\n2U6NiIdqGd5cu++Usm+6JyJOaSHbh2q57o6IH9buG/V2+1hEPBgRX53l/ijH7y3leT2sdt+ot9t8\n2V5fMm2OiC9HxK/X7vtmWb4pIm5tIdvREfFw7bn789p9I31fN0C2P6nl+mppY3uV+0a93eb9fDny\nNpeZXua4ANcAJ5Tra4Eb285Uy/Zy4Dpg13L76W1nmpbvAKrBQr8F7N12nmnZXgnsXK6/H3h/y3lW\nAN8ADgZWArcDh7a9nUq2/YDDyvWnAnd3JVst4zuAfwM+13aWabkuAt5crq8E9mg7k5fuXYAJ4LnA\njcCaWdbp5D4C+ABwclwIBgAACTNJREFUdrl+9kz7UuDFwJfK/7ACuAk4ehyyl/tuBI4r158C7DYu\n2cv955X944fbzr2ANvMc4JBy/ZnAtrb2n4O89oAzgI+W6ycBl7W9nReQ/eVTbRp4a1ey9/2ylHYH\nHFrW3xU4qPyeFV1pV8AjLW+3U2faHwJ7AfeWn3uW63s2mW3a+m+jmmxh5Nut/P7fAA4DvjrL/WuB\nzwMBHAHc3MR2GzDbi6f+JnDCVLZy+5uM8HPoANmOZobPJwttD6PINm3d1wBfaHC7zfv5ctRtzh5h\n80tg93L9acB3Wswy3VuBczLzUYDMfLDlPNN9CPhTqm3YKZl5TWY+Vm5uAFa1mQc4HNiSmfdm5k+A\nS4F1LWcCIDO3ZeZt5fqPgUlg/3ZTPS4iVgG/CVzQdpa6iHga1QHoQoDM/Elm/nDuR6mPMnMyM++a\nZ7Wu7iPWURV8KT9fN8M6CTyJ6o3ersAuwAONpJvbvNkj4lCqL02uBcjMRzJze3MRZzXIdiciVgP7\nUn2p1xXzZs/MuzPznnL9O8CDwD6NJdzRIK+9+v90OXBsRPu9Hhkge2beUGvTXXg/pMpS2t064NLM\nfDQz/xfYUn5fY9labFdLOVa+Crg2M7+fmT8ArgWObzHb7wOfGOLfn1Nm/hfw/TlWWQdcnJUNwB4R\nsR+j327zZsvML5e/DQ3vxwbYbrMZ+fu6BWZrur0N8vlypG3OQtj83g58MCLuA/4aeE/LeeqeA7ys\ndIf+z4h4YduBpkTEOuD+zLy97SwDeBNVtblN+wP31W5vpUPFpilRdbt/AXBzu0l28LdUBdeftx1k\nmoOAh4B/juq0zQsi4slth9LY6uo+Yt/M3Fauf5eq6LKDzLwJuIGqV8824OrMnGwu4qzmzU51nP1h\nRFxRXscfjIgVzUWc1bzZI2In4G+AdzUZbACDbPdfiGpIipVU35y3YZDX3i/WKV+yPQz8UiPp5rbQ\n/cZptP9+SJWltLtRHy+W2q6eFNVwMxsiYsYifgPZfrucanV5RBywwMeOOhtRnUp6EPCF2uJRbrdB\nzJa/a+9Ppre3BK6JiI0RcXpLmY6MiNsj4vMR8StlWWe2W0TsRlVI+nRtcWPbbY7PlyNtczsv9AHL\nUURcBzxjhrveBxwL/HFmfjoiTqTq3fGKjmTbmapL4BHAC4FPRsTBWfoMtpztvVSnH7ZmrnyZ+dmy\nzvuAx4BLmsw2jiLiKVQ7yLdn5o/azgMQEa8GHszMjRFxdNt5ptmZqjvy2zLz5og4j+o0oD9rN5ba\nMMj+qKvm2df/QmZmRDzh+BMRv0x1+ufUN7TXRsTLMvO/hx72iX97SdmpXscvo3qD9m3gMqrTai4c\nbtInGkL2M4CrMnNr052ThpB96vfsB/wrcEpmdu3LjmUlIt4ArAGOajuLlo9Z2tWzM/P+iDgY+EJE\nbM7MJgvd/w58IjMfjYg/pOpVd0yDf38QJwGXZ+bPasva3m6dFxEvpyqEvbS2+KVluz2d6v3H10tP\nqabcRvXcPRIRa4ErgUMa/PuDeA3wpcys9x5rZLu1+fnSQhiQmbMWtiLiYmBq8LZP0fDpV/Nkeytw\nRSl8fSUifg7sTdULpbVsEfGrVN9i3F7efK8CbouIwzPzu01kmyvflIg4FXg1cGxTxcM53E81ptqU\nVWVZJ0TELlQ7qUsy84q289S8BHhtObA8Cdg9Ij6emW9oORdU305szcypbzcupyqEqYfm2x8NoLV9\nxDzHoQciYr/M3FaKFjOdov9bwIbMfKQ85vPAkcDIC2FDyL4V2JSZ95bHXEn15dPIC2FDyH4kVa/x\nM6jGNlsZEY9k5sj3Q0PITkTsDvwHVbF4w4iiDmKQ197UOlsjYmeqoTT+r5l4cxpovxERr6AqUh6V\nZbgNtW4p7W7Ux4sltavMvL/8vDcibqT6omFYBZ15s2Vm/bV5AdW4hVOPPXraY28cUq6BstWcBJxZ\nXzDi7TaI2fKPersNJCJ+jer5PKH+HNe224MR8RmqUxIbK4TVizuZeVVE/H1Uk8h16bPfSUw7LbKJ\n7TbA58uRtjlPjZzfd3j8W4xjgHtazDLdlVSDURIRz6E6deB7rSYCMnNzZj49Mw/MzAOpPkgc1mQR\nbD4RcTzV6XSvzW6M93ILcEhEHBQRK6l2SEOfEWYxyngTFwKTmXlu23nqMvM9mbmqtLOTqAZ57EIR\njNLe74uI55ZFxwJ3thhJ462r+4j1wNRsPacAM/Vu+zZwVETsXN70HEU1FkTbBsl+C9WYFFPjUx1D\nN17H82bPzNdn5rPK/vFdVONsdKEYP2/20sY/Q5X58gazzWSQ1179f/odqmNR21+wwQDZI+IFwD9S\nvR/q2lizfbaUdrceOCmqWSUPoup98pUms83WriJiz4jYtVzfm+oLzWHuUwfJtl/t5mt5/Hh0NfDK\nknFPqjNbrm4yW8n3PKoBwG+qLRv1dhvEeuAPonIE8HA5zX3U221eEfEs4Arg5My8u7b8yRHx1Knr\nJduMMyiOMNszymepqVP9d6IqWHfifV1UYxofRe1Y3MR2G/Dz5WjbXI5oJoDlcqHqWrmRaiaHm4HV\nbWeqZVsJfJyqYd4GHNN2pllyfpPuzRq5herc4k3l8tEOZFpLNWPGN6i+AW99O5VcL6U6T/yO2vZa\n23auGXIeTfdmjXw+cGvZdlcy5Fl0vCyPC1WPqa3Ao1SDyF9dlj+T6tS2qfU6t4+gGo/meqovia4D\n9irL1wAXlOsrqD4QTVK9cT+37dyDZi+3jyuv4c3AvwArxyV7bf1T6c6skYO0mTcAP60dczYBz28x\n8xNee8BfUn3Ih6pH8qfKe4uvAAe3vZ0XkP26st+Z2s7r287sZeDnbtZ2R9UT6xvAXVQ9ZDrRrqhm\n99tM9blqM3BaC9n+CvhayXAD8LzaY99UtucW4I1NZyu3/4JqMrT645rYbp+gGsfzp1TvSU4D3gK8\npdwfwEdK9s3UZrluYLvNl+0C4Ae19nZrWX5w2Wa3l+d86O+dBsh2Vq29bQBePFd7aDJbWedUqsk1\n6o9rYrvN+PmyyTYX5RdJkiRJkiRJy5qnRkqSJEmSJKkXLIRJkiRJkiSpFyyESZIkSZIkqRcshEmS\nJEmSJKkXLIRJkiRJkiSpFyyESZIkSZIkqRcshEmSJEmSJKkX/h/hURRpWB9HjAAAAABJRU5ErkJg\ngg==\n",
            "text/plain": [
              "<Figure size 1512x504 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pVgSkXeei98S",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "outputId": "4fddd6c3-9eec-42e9-d81a-02b2d8e9a694"
      },
      "source": [
        "plot_elfi(result_smc2, result_smc3, \"SMC + Autocov\", \"SMC + Autocorr\")"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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cAAAA8JQUwgAAttSmbj640QAAMO2ZGgkAAABALyiEAQAAANALCmEAAAAA9IJC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\ngg==\n",
            "text/plain": [
              "<Figure size 1512x504 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KmgcmI8O70TE",
        "colab_type": "text"
      },
      "source": [
        "For both samplers, we can see that for $\\alpha$ both the autocorrelation and autocovariance converged to the true value, but the autocovariance is better in zeroing down the true value, as we can see by the smaller variance. For $\\beta$ the autocorrelation performs better, but we can see that both also roughly converged. For $\\sigma$, the autcovariance performs quite well while the autocorrelation seems like it did not converge."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_-GBUoHFjCNj",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "outputId": "0a68e519-6fdd-432f-9767-2851168265a1"
      },
      "source": [
        "plot_elfi(res2, result_smc2, \"Rejection + Autocov\", \"SMC + Autocov\")"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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WzZTGvaiM2hoMrARuAo7blgDbysxpwDSo3Llk4+M77rgjgwcP3t63kSSpKrY7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\nRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1512x504 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XF0hRbnwjFNF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "outputId": "fe95d4b5-3c92-4241-97ef-a253a3b5c924"
      },
      "source": [
        "plot_elfi(res3, result_smc3, \"Rejection + Autocorr\", \"SMC + Autocorr\")"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3O/vBD9h37705/n//b/Y64AAAPnP88ewxciSNzzzT7uNQNyuSo63SzW2s0vTW\nP2W05vGzRSLslmZDIxdn5sDidQAvZ+bAiLgFuCAz7yvW3UkpQTYW6JeZ5xXlXwdez8zvtfBeEyn1\nJmOHHXYY/cxaHzgNDQ3suuuu7TpYVZ9u/39p4ZOioeGd1SacPxGAK7429R3r2h1uJX3yqEeIiPrM\nrCt3HD1JXV1dzp49u9xhqAdo7YXfuj56V30hmzlzZqfE0xN4Daa2aOn/xfPOmlo65/TGdtbaDlRd\nPZr3iSeeAGCXXXZZd6Wu6O3V2gNrx3s3zJvHrsuXt3m7itXa7zttyd6U870r4PtbJR/O+s45HZ4s\nv+j9teFsWuv3NzUz6zKzbvDgwZ21W0mSJEmSJFW5DQ6NXIcXImLbzHyuGPr4YlG+EBjarN6Qomwh\nbw+lXFU+s53vLUmSJEmS1qGlUSkt6WUdEKVWaW8i7GZgAnBB8fumZuWfi4gZlCbGX1Iky24Dvt1s\ngvyDgbPaG3RmUhqRKa1ba4b9dqb6eujfyhOOJEmVyGswtUZ3X4P1NrYztUZmgm2t+3TFcEuVzQYT\nYRExnVJvrq0jYgGlpz9eAFwbEScCzwCfKKrfChwKzAOWAicAZOZLEfEt4I9FvW+umji/rfr168ei\nRYsYNGiQJwitU2ayaNEi+vXrV+5QJEnqFbwGU2t4DdYxtjO1RmayaMkS+lVbIsxklDpJa54aeew6\nVo1roW4Cp6xjPz8Dftam6FowZMgQFixYQFNTU0d3pV6uX79+DBkypNxhSJLUK3gNptbyGqz9emM7\ne/PN1tXbZJOujeP5558HYOXKleuu1Npg26K1B9aW986kXyZD1ncsktapvUMjy2bjjTdm2LBh5Q5D\nkiSpqngNJnW93tjOWtuJZ+TIro3j5JNPBjbwNN+u6HHU2gOzt5PUbTr81EhJkiRJkiSpElRcjzCp\n27Xy7owT5UuSJKka2HlJUiWzR5gkSZIkSZKqgj3CJEmS2mldvSJeeeWd60eP7vp4JEmStH72CJMk\nSZIkSVJVsEeYJEmqGs5rI0mSVN3sESZJkiRJkqSqYCJMkiRJkiRJVcGhkZIkSZIklUl9PfRv2HC9\nXXft+likamCPMEmSJEmSJFUFE2GSJEmSJEmqCibCJEmSJEmSVBVMhEmSJEmSJKkqOFm+JEmSJDUT\nEf2Ae4C+lL4zXZ+Z50TE5cABwJKi6vGZOTciApgMHAosLcrndH/klau+vvV1R4/uujjUMzW04mEC\nq/hQAW2IiTBJkiRJWtMbwIGZ+WpEbAzcFxH/r1j35cy8fq36HwJ2Kn72BqYUvyXpHRoaShnz1jDx\n2/lMhEk9zPrudnh3Q5Ikqc/hxeAAACAASURBVOtlZgKvFosbFz+5nk2OAK4stnswIgZGxLaZ+VwX\nhypJaiPnCJMkSZKktURETUTMBV4Ebs/Mh4pV50fEIxFxYUT0Lcq2B+Y323xBUbb2PidGxOyImN3U\n1NSl8UuSWmaPMElSjxIRPwMOA17MzOFF2buAa4BaoBH4RGa+vL45WSJiAvB/i92el5lXdOdxSJIq\nW2auAEZFxEDgxogYDpwFPA9sAkwFvgJ8sw37nFpsR11d3fp6mGlDWjupmOPKJK3FRJgkqae5HPgR\ncGWzsjOBOzPzgog4s1j+CuuYk6VInJ0D1FEaylIfETdn5svddhSSpF4hMxdHxO+BQzLze0XxGxFx\nGfClYnkhMLTZZkOKMlWI+nro34oJ2Z2qRKp8JsIkST1KZt4TEbVrFR8BjC1eXwHMpJQIa3FOlqLu\n7Zn5EkBE3A4cAkzv4vAlSb1ARAwG3iqSYJsCBwHfWTXvV9Ej+Ujg0WKTm4HPRcQMSjdmllTi/GBt\neXJjJWg+Ifkrr5R+97ZjlNR2JsIkSZVgm2ZfKJ4Htiler2tOllbN1QKl+VqAiQA77LBDJ4YsSapg\n2wJXREQNpXmVr83MWyLiriJJFsBc4KSi/q2UhunPo5R7OaEMMUtttr4Hda3N3nDqLUyESZIqSmZm\nRHTavCrO1yJJWltmPgLs0UL5geuon8ApXR2XSlo7jFGSWmIiTGqjttw1kdRpXmg2HGVbSk/wgnXP\nybKQt4dSriqf2Q1xSpIkva0VYzFN6knda6NyByBJUivcDEwoXk8AbmpWflyU7MPbc7LcBhwcEVtF\nxFbAwUWZJEmSpCpmjzBJUo8SEdMp9ebaOiIWUHr64wXAtRFxIvAM8ImieotzsmTmSxHxLeCPRb1v\nrpo4X+qo/g0bvrtfs/QVVvTfohuikSRJzbV2BI9znlUvE2GSpB4lM49dx6pxLdRd55wsmfkz4Ged\nGJokSepirbnZIHUnHyjQ+5gIkyRJkiRJqhKtmLqu7PscPbpz99eciTCpt2jtJ09XfqJIUoWzJ4Ik\nSepR2pJh8rteqzhZviRJkiRJkqqCPcIkSZK6QM3SVzbcw8w7t5IkVaVW90J33rFOZ48wSZIkSZIk\nVQV7hEmSJHWDlp46tbSFenYSk9TZumJibEndo7VPrfSJla1njzBJkiRJkiRVBXuESZIkSZIkVbCG\nhpZ7muudTIRJkiRJkqRO0dqhfOBwPpWHQyMlSZIkSZJUFUyESZIkSZIkqSo4NFKSJPV+xSPT+rdh\nuIYkqXP0b/CxlZJ6DnuESZIkSZIkqSrYI0ySJEmS1Cut6o1Ws/SVNZaltkzqr97FHmGSJEmSJEmq\nCvYIkyRJkiSpFdrSi2jXXbsuDkntZyJMkiRJkqRO5tA7qWcyESZJkiRJktbLxJ56CxNhql71TpQp\nSZIkSVI1MREmSZIkSZJU4Vr7VNSlu47u4kh6Np8aKUmSJEmSpKpgIkySJEmSJElVwUSYJEmSJEmS\nqoJzhEmSJEmSJHWQT9asDPYIkyRJkiRJUlUwESZJkiRJkqSqYCJMkiRJkiRJVcFEmCRJkiRJkqqC\nk+VLkiRJktTDORG71DlMhEnr4IlGkiRJkqTexaGRkiRJkiRJqgodSoRFxBci4rGIeDQipkdEv4gY\nFhEPRcS8iLgmIjYp6vYtlucV62s74wAkSZIkSZKk1mh3IiwitgdOA+oyczhQAxwDfAe4MDN3BF4G\nTiw2ORF4uSi/sKgnSZIkST1KcYP/DxHxp+LG/zeKcm/6S1KF6+jQyD7AphHRB+gPPAccCFxfrL8C\nOLJ4fUSxTLF+XEREB99fkiRJkjrbG8CBmTkSGAUcEhH74E1/Sap47U6EZeZC4HvAs5QSYEuAemBx\nZi4vqi0Ati9ebw/ML7ZdXtQftPZ+I2JiRMyOiNlNTU3tDU+SJEmS2iVLXi0WNy5+Em/6S1LF68jQ\nyK0ofeAPA7YDNgMO6WhAmTk1M+sys27w4MEd3Z0kSZIktVlE1ETEXOBF4Hbgb3jTX5IqXp8ObPu/\ngKczswkgIn4J7AcMjIg+xQlgCLCwqL8QGAosKIZSDgAWdeD9JUmSJKlLZOYKYFREDARuBN7TCfuc\nCkwFqKury47uT6p0DQ3ljkDVqCOJsGeBfSKiP/A6MA6YDfwe+DgwA5gA3FTUv7lYnlWsvysz/fCX\nJEmS1GNl5uKI+D2wL970l1RF+jfUt7ru0l1Hd2EknavdibDMfCgirgfmAMuBhynd3fgNMCMizivK\nphWbTAN+HhHzgJcoPWFSkiSpQ+pbcY3W3zvOktogIgYDbxVJsE2BgyhNgO9Nf0mqcB3pEUZmngOc\ns1bxU8BeLdRdBhzdkfeTJEmSpG6wLXBFRNRQmlf52sy8JSL+gjf9JamidSgRJkmSJEm9TWY+AuzR\nQrk3/SWpwrX7qZGSJEmSJElSJbFHmCRJUpm0ahLa0ZUz+awkSVJPZyJMqiDrerzwrrt2bxySJEmS\nJFUih0ZKkiRJkiSpKpgIkyRJkiRJUlUwESZJkiRJkqSqYCJMkiRJkiRJVcFEmCRJkiRJkqqCiTBJ\nkiRJkiRVBRNhkiRJkiRJqgp9yh2AJElSR/RvqC93CJIkSWqFVl+3jR7dZTGYCJMkVYyI+ALwGSCB\nPwMnANsCM4BBQD3w6cx8MyL6AlcCo4FFwPjMbCxH3JIkSVJvVkk3Jh0aKUmqCBGxPXAaUJeZw4Ea\n4BjgO8CFmbkj8DJwYrHJicDLRfmFRT1JkiRJVcxEmCSpkvQBNo2IPkB/4DngQOD6Yv0VwJHF6yOK\nZYr14yIiujFWSZIkST2MQyMlSRUhMxdGxPeAZ4HXgd9RGgq5ODOXF9UWANsXr7cH5hfbLo+IJZSG\nT/6jWwOX2qihYc3lpeup24XTZ0iSJPVK9giTJFWEiNiKUi+vYcB2wGbAIZ2w34kRMTsiZjc1NXV0\nd5IkSZJ6MBNhkqRK8b+ApzOzKTPfAn4J7AcMLIZKAgwBFhavFwJDAYr1AyhNmr+GzJyamXWZWTd4\n8OCuPgZJkiRJZWQiTJJUKZ4F9omI/sVcX+OAvwC/Bz5e1JkA3FS8vrlYplh/V2ZmN8YrSZIkqYcx\nESZJqgiZ+RClSe/nAH+mdA6bCnwF+GJEzKM0B9i0YpNpwKCi/IvAmd0etCRJkqQexcnyJUkVIzPP\nAc5Zq/gpYK8W6i4Dju6OuCRJkiRVBhNhkiRJkqQ2699QX+4QJKnNHBopSZIkSZKkqmAiTJIkSZIk\nSVXBRJgkSZIkSZKqgokwSZIkSZIkVQUTYZIkSZIkSaoKJsIkSZIkSZJUFUyESZIkSZIkqSqYCJMk\nSZIkSVJVMBEmSZIkSZKkqmAiTJIkSZIkSVXBRJgkSZIkSZKqgokwSZIkSZIkVYU+5Q5A6lT19eWO\nQJIkSZIk9VD2CJMkSZIkSVJVsEeYJEmSJDUTEUOBK4FtgASmZubkiDgX+CzQVFT9ambeWmxzFnAi\nsAI4LTNv6/bAO0H/BkdYSOrdTIRJkiRJ0pqWA/+ZmXMiYgugPiJuL9ZdmJnfa145It4LHAPsBmwH\n3BERO2fmim6NWpJaodoT3ibCpGrTlnnURo/uujgkSa3S6otVP7OlTpOZzwHPFa9fiYgGYPv1bHIE\nMCMz3wCejoh5wF7ArC4PVpLUJs4RJkmSJEnrEBG1wB7AQ0XR5yLikYj4WURsVZRtD8xvttkCWkic\nRcTEiJgdEbObmprWXi1J6gYmwiRJkiSpBRGxOXADcHpm/hOYAvw7MIpSj7Hvt2V/mTk1M+sys27w\n4MGdHq8kacNMhEmSJEnSWiJiY0pJsKsy85cAmflCZq7IzJXATygNfwRYCAxttvmQokyS1MOYCJMk\nSZKkZiIigGlAQ2b+oFn5ts2qHQU8Wry+GTgmIvpGxDBgJ+AP3RWvJKn1nCxfkiRJkta0H/Bp4M8R\nMbco+ypwbESMAhJoBP4PQGY+FhHXAn+h9MTJU3xipCT1TCbCJEmSJKmZzLwPiBZW3bqebc4Hzu+y\noCRJncKhkZIkSZIkSaoKJsIkSZIkSZJUFRwaKUmSeqT6+tbV69+1YUiSJKkXsUeYJEmSJEmSqoKJ\nMEmSJEmSJFUFE2GSJEmSJEmqCibCJEmSJEmSVBVMhEmSJEmSJKkqmAiTJEmSJElSVTARJkmSJEmS\npKpgIkySJEmSJElVwUSYJEmSJEmSqkKHEmERMTAiro+IxyOiISL2jYh3RcTtEfFk8Xurom5ExA8j\nYl5EPBIR7+ucQ5AkSZIkSZI2rKM9wiYDv83M9wAjgQbgTODOzNwJuLNYBvgQsFPxMxGY0sH3liRJ\nkiRJklqt3YmwiBgAfACYBpCZb2bmYuAI4Iqi2hXAkcXrI4Ars+RBYGBEbNvuyCVJkiRJkqQ26EiP\nsGFAE3BZRDwcET+NiM2AbTLzuaLO88A2xevtgfnNtl9QlK0hIiZGxOyImN3U1NSB8CRJkiRJkqS3\ndSQR1gd4HzAlM/cAXuPtYZAAZGYC2ZadZubUzKzLzLrBgwd3IDxJkiRJkiTpbR1JhC0AFmTmQ8Xy\n9ZQSYy+sGvJY/H6xWL8QGNps+yFFmSRJkiRJktTl+rR3w8x8PiLmR8QumfkEMA74S/EzAbig+H1T\nscnNwOciYgawN7Ck2RBKSR3Q0NBy+a67dm8ckiRJkiT1ZO1OhBVOBa6KiE2Ap4ATKPUyuzYiTgSe\nAT5R1L0VOBSYBywt6kqSJEmSJEndokOJsMycC9S1sGpcC3UTOKUj7ydJkiRJkiS1V0fmCJMkSZIk\nSZIqhokwSZIkSZIkVYWOzhEmSZKkMmn+sJSl66k3enSXhyJJklQRTIRJkqQeqX9DfblDkCRJUi/j\n0EhJkiRJkiRVBRNhkiRJkiRJqgomwiRJkiRJklQVTIRJkiRJkiSpKpgIkyRVjIgYGBHXR8TjEdEQ\nEftGxLsi4vaIeLL4vVVRNyLihxExLyIeiYj3lTt+SZIkSeVlIkySVEkmA7/NzPcAI4EG4Ezgzszc\nCbizWAb4ELBT8TMRmNL94UqSJEnqSfqUOwCp3Boayh2BpNaIiAHAB4DjATLzTeDNiDgCGFtUuwKY\nCXwFOAK4MjMTeLDoTbZtZj7XzaFLkiRJ6iHsESZJqhTDgCbgsoh4OCJ+GhGbAds0S249D2xTvN4e\nmN9s+wVF2RoiYmJEzI6I2U1NTV0YviRJkqRyMxEmSaoUfYD3AVMycw/gNd4eBglA0fsr27LTzJya\nmXWZWTd48OBOC1aSJElSz+PQSFWG+vpyRyCp/BYACzLzoWL5ekqJsBdWDXmMiG2BF4v1C4GhzbYf\nUpRJkiRJqlL2CJMkVYTMfB6YHxG7FEXjgL8ANwMTirIJwE3F65uB44qnR+4DLHF+MElSa0TE0Ij4\nfUT8JSIei4jPF+U+qViSKpw9wiRJleRU4KqI2AR4CjiB0k2dayPiROAZ4BNF3VuBQ4F5wNKiriRJ\nrbEc+M/MnBMRWwD1EXE7pQe23JmZF0TEmZR6Jn+FNZ9UvDelJxXvXZbIJUnrZSJMklQxMnMuUNfC\nqnEt1E3glC4PSpLU6xQ9iJ8rXr8SEQ2UHrjik4olqcI5NFKSJEmS1iEiaoE9gIfwScWSVPFMhEmS\nJElSCyJic+AG4PTM/GfzdT6pWJIqk4kwSZIkSVpLRGxMKQl2VWb+sih+oXhCMT6pWJIqk4kwSZIk\nSWomIgKYBjRk5g+arfJJxZJU4ZwsX5IkSZLWtB/waeDPETG3KPsqcAE+qViSKpqJMEmSJElqJjPv\nA2Idq31SsSRVMIdGSpIkSZIkqSqYCJMkSZIkSVJVMBEmSZIkSZKkqmAiTJIkSZIkSVXBRJgkSZIk\nSZKqgokwSZIkSZIkVQUTYZIkSZIkSaoKfcodgCRJkjquf0P9hiuNHt31gUiSJPVgJsIkrVt9K75U\ngV+sJEmSJEkVwUSYJEnqNq3NrwP077owJEmSVKWcI0ySJEmSJElVwUSYJEmSJEmSqoKJMEmSJEmS\nJFUFE2GSJEmSJEmqCibCJEmSJEmSVBVMhEmSJEmSJKkqmAiTJEmSJElSVTARJkmSJEmSpKpgIkyS\nJEmSJElVwUSYJEmSJEmSqoKJMEmSJEmSJFUFE2GSJEmSJEmqCn3KHYDUHRoayh2BJEnls+o8uHQD\n9UaP7vJQJEmSysoeYZIkSZIkSaoKJsIkSZIkSZJUFUyESZIkSZIkqSqYCJMkSZIkSVJVMBEmSZIk\nSZKkquBTIyVJUrfr31Bf7hAkSZJUhewRJkmSJEmSpKpgjzCpF2toaLl81127Nw5JkiRJknoCe4RJ\nkiRJkiSpKpgIkyRJkiRJUlUwESZJkiRJkqSqYCJMkiRJkiRJVaHDk+VHRA0wG1iYmYdFxDBgBjAI\nqAc+nZlvRkRf4EpgNLAIGJ+ZjR19f0mSJEnqbBHxM+Aw4MXMHF6UnQt8Fmgqqn01M28t1p0FnAis\nAE7LzNu6Pej16N9QX+4QJKlH6IweYZ8Hmj+b7jvAhZm5I/AypZMBxe+Xi/ILi3qSJEmS1BNdDhzS\nQvmFmTmq+FmVBHsvcAywW7HNj4sOA5KkHqZDibCIGAJ8GPhpsRzAgcD1RZUrgCOL10cUyxTrxxX1\nJUmSJKlHycx7gJdaWf0IYEZmvpGZTwPzgL26LDhJUrt1tEfYRcAZwMpieRCwODOXF8sLgO2L19sD\n8wGK9UuK+muIiIkRMTsiZjc1Na29WpIkSZLK6XMR8UhE/CwitirKVn/XKTT/HrSa33UkqfzanQiL\niFXj5Tt1sHlmTs3MusysGzx4cGfuWpIkSZI6Ygrw78Ao4Dng+23Z2O86klR+HZksfz/gIxFxKNAP\n2BKYDAyMiD5Fr68hwMKi/kJgKLAgIvoAAyhNmi9JkiRJPV5mvrDqdUT8BLilWFz1XWeV5t+DJEk9\nSLt7hGXmWZk5JDNrKU0MeVdmfgr4PfDxotoE4Kbi9c3FMsX6uzIz2/v+kiRJktSdImLbZotHAY8W\nr28GjomIvhExDNgJ+EN3xydJ2rCO9Ahbl68AMyLiPOBhYFpRPg34eUTMozTp5DFd8N6SJElah/4N\nrZzRYvTorg1EqgARMR0YC2wdEQuAc4CxETEKSKAR+D8AmflYRFwL/AVYDpySmSvKEbckaf06JRGW\nmTOBmcXrp2jhCSmZuQw4ujPeT5IkSZK6UmYe20LxtBbKVtU/Hzi/6yKSJHWGjj41UpIkSZIkSaoI\nJsIkSZIkSZJUFUyESZIqSkTURMTDEXFLsTwsIh6KiHkRcU1EbFKU9y2W5xXra8sZtyRJkqTy64rJ\n8qXWqW/lhL2StKbPAw3AlsXyd4ALM3NGRFwKnAhMKX6/nJk7RsQxRb3x5QhYkiRJUs9gjzBJUsWI\niCHAh4GfFssBHAhcX1S5AjiyeH1EsUyxflxRX5IkSVKVMhEmSaokFwFnACuL5UHA4sxcXiwvALYv\nXm8PzAco1i8p6q8hIiZGxOyImN3U1NSVsUuSJEkqMxNhkqSKEBGHAS9mZqeOq87MqZlZl5l1gwcP\n7sxdS5IkSephnCNMklQp9gM+EhGHAv0ozRE2GRgYEX2KXl9DgIVF/YXAUGBBRPQBBgCLuj9sSZIk\nST2FiTBJHdeWBx+MHt11cahXy8yzgLMAImIs8KXM/FREXAd8HJgBTABuKja5uVieVay/KzOzu+OW\nJEmS1HM4NFKSVOm+AnwxIuZRmgNsWlE+DRhUlH8ROLNM8UmSJEnqIewRJkmqOJk5E5hZvH4K2KuF\nOsuAo7s1MEmSJEk9mj3CJEmSJEmSVBVMhEmSJEmS/v/27j1Gl7u8D/j3wcamh0uwY8cx2MZGdZrj\nqATwKQUCxdzBFXGipK6jYGziyqVAlahNFbeRWtQoKqQqFSgpiQMoJgq3Ei5uCgFjoKQBE/tQX9mA\nD64JxznYLrfgOiWB/PrHzMLLevfsu7vvZXbn85Fe7bwz8+5+57Jzed6Z3wCMgkIYAAAAAKOgEAYA\nAADAKCiEAQAAADAKCmEAAAAAjIJCGAAAAACjoBAGAAAAwCgohAEAAAAwCgphAAAAAIzCscsOAADs\nfgcPLjsBAABszhVhAAAAAIyCQhgAAAAAo+DWSBihlZX1++/fv9gcAAAAsEiuCAMAAABgFFwRBgAA\nsMt4SAnA9iiEAQCQZOLW+ZXNz7D3v/jc+YYBAJgDt0YCAAAAMAoKYQAAAACMgkIYAAAAAKOgEAYA\nAADAKCiEAQAAADAKCmEAAAAAjMKxyw4As/Sdx74DsDT7Vg4uOwIAAKzLFWEAAABrVNWbq+qeqrp1\not+JVXVNVd3e/zyh719V9fqqOlRVN1fVE5eXHICjUQgDAAB4oN9J8oI1/a5Icm1r7ewk1/bvk+SF\nSc7uX5cnecOCMgKwRQphAAAAa7TWPp7kK2t6X5Dkqr77qiQ/MdH/La1zXZJHVtWpi0kKwFYohAEA\nAEznlNbakb77S0lO6bsfneSLE+Md7vt9j6q6vKpuqKob7r333vkmBWBdCmEAAABb1FprSdoWP3Nl\na+1Aa+3AySefPKdkAByNQhgAAMB07l695bH/eU/f/64kp0+Md1rfD4CBUQgDAACYztVJLum7L0ny\nvon+L+mfHvnkJF+fuIUSgAE5dtkBAAAAhqaq3pbkvCQnVdXhJP8uyauTvLOqLkvyhSQX9qO/P8n5\nSQ4luT/JSxceGICpKIQBAACs0Vr7mQ0GPXudcVuSV8w3EQCz4NZIAAAAAEZBIQwAAACAUVAIAwAA\nAGAUFMIAAAAAGAWFMAAAAABGQSEMAAAAgFE4dtkBgJE5eHC68c49d745AAAAGB1XhAEAAAAwCgph\nAAAAAIyCWyOZvWlvfQMAAABYIFeEAQAAADAKCmEAAAAAjIJbIwEA2DpPAQYAdqFtF8Kq6vQkb0ly\nSpKW5MrW2uuq6sQk70hyZpI7k1zYWvtqVVWS1yU5P8n9SS5trX16Z/EBAFiGlZXpxtuvDgYADMhO\nbo38VpJ/2Vo7J8mTk7yiqs5JckWSa1trZye5tn+fJC9Mcnb/ujzJG3bwtwEAAABgS7Z9RVhr7UiS\nI333N6pqJcmjk1yQ5Lx+tKuSfCzJL/X939Jaa0muq6pHVtWp/e8BAIbuKLfC7Zvy6iAAAFimmTSW\nX1VnJnlCkk8lOWWiuPWldLdOJl2R7IsTHzvc91v7uy6vqhuq6oZ77713FvEAAAAAYOeFsKp6WJLf\nT/ILrbW/mBzWX/3VtvL7WmtXttYOtNYOnHzyyTuNBwAAAABJdvjUyKp6cLoi2O+11t7d97579ZbH\nqjo1yT19/7uSnD7x8dP6fgDAAK29E9LtjwDDs29lyie4ApBkB1eE9U+BfFOSldbaaycGXZ3kkr77\nkiTvm+j/kuo8OcnXtQ8Gw7Kysv4LhqCqTq+qj1bVZ6rqtqr6+b7/iVV1TVXd3v88oe9fVfX6qjpU\nVTdX1ROXOwUAAMCy7eTWyB9LcnGSZ1XVjf3r/CSvTvLcqro9yXP690ny/iR3JDmU5LeTvHwHfxuA\n8fG0YgAAYEd28tTI/5mkNhj87HXGb0lesd2/B8C4eVoxAACwUzN5aiQALJKnFQMAANuhEAbAruJp\nxQAAwHbt6KmRsCwacIdx8rRiAABgJ1wRBsCu4GnFAADATrkiDIDdYvVpxbdU1Y19v3+T7unE76yq\ny5J8IcmF/bD3Jzk/3dOK70/y0sXGBQAAhkYhDIBdwdOKAQCAnXJrJAAAAACjoBAGAAAAwCgohAEA\nAAAwCtoIY3oHDy47AQAAAMC2uSIMAAAAgFFQCAMAAABgFBTCAAAAABgFhTAAAAAARkFj+QAAAFtQ\nVXcm+UaSbyf5VmvtQFWdmOQdSc5McmeSC1trX11WRgDW54owAACArXtma+3xrbUD/fsrklzbWjs7\nybX9ewAGxhVhwDAdPDj9uOeeO78cAADTuSDJeX33VUk+luSXlhUGgPUphAEAMDe+12CPakk+VFUt\nyW+11q5Mckpr7Ug//EtJTln7oaq6PMnlSXLGGWcsKisAExTCAAAAtuZprbW7quoHklxTVX86ObC1\n1voiWdb0vzLJlUly4MCBBwwHYP4UwgBgZLZyhQ4AD9Rau6v/eU9VvSfJk5LcXVWnttaOVNWpSe5Z\nakgA1qWxfAAAgClV1UOr6uGr3Umel+TWJFcnuaQf7ZIk71tOQgCOxhVhAAAA0zslyXuqKunOp97a\nWvvDqro+yTur6rIkX0hy4RIzArABhTBgUysrGw/bv39xOQAAlq21dkeSH12n/5eTPHvxiQDYCoUw\nBu1oBRgAYPj2rWzeKN39+z0uEgBYDG2EAQAAADAKCmEAAAAAjIJCGAAAAACjoI0wAGCqdpwAAGC3\nc0UYAAAAAKOgEAYAAADAKCiEAQAAADAKCmEAAAAAjILG8sfuoMaRAQAAgHFwRRgAAAAAo+CKMAAA\nBmHaC9XPPXe+OQCAvUshDACApdq3snkF7P79ql8AwM65NRIAAACAUVAIAwAAAGAUFMIAAAAAGAVt\nhAE7srKyfv/9+xcYQuvKsLF1/j/2bfB/CwAAe51CGADsEevVhBW9AADguxTCAADYVaa9EDhxMTAA\n8L0UwoDxcOYEsGvtW5luG37/fttvAGBjCmEMwkbtTAEAAADMiqdGAgAAADAKrgjbq7ZyCxgAAADA\nCLgiDAAAAIBRUAgDAAAAYBQUwgAAAAAYBYUwAAAAAEZBY/kAAOwZ+1ameGDQuefOPwgAMEgKYbuJ\nJ0ECjM7RNv1rT/j3zTkL7EYrKw/sd/8646mNAcA4KIQBc7HeiUeS7N+/2BwAAACwSiGMhdqoOMJ4\nKJABAACwLAphAOuZ9lZk99IAAADsGgphAACMynoN6q/bltj+B37Z4fsPANjdHrTsAAAAAACwCK4I\nG4I9+DRIbYEBHN0e3PQDAMDgLbwQVlUvSPK6JMckeWNr7dWLzsBsKHYxS7u2EX1tiQ3aIPc5/Tqz\nzzYUBm/aWyg3suV9fWt1mwAADYpJREFUmH3FrjfI/Q4A32OhhbCqOibJbyR5bpLDSa6vqqtba59Z\nZI6F8FU/zMSuLZCttZVtghOhmVjGPmeaxawABuOx1S8N759iHLuI4RrVuQ7ALrboK8KelORQa+2O\nJKmqtye5IMl8dg4jL0a5Ygt2KVeZzcpi9zlZ/+oRgGlNsw05mOVt++12NrXw/Q4AW7foQtijk3xx\n4v3hJH9/coSqujzJ5f3b+6rqs0f5fScl+T8zTThMpnNv+c50nnPxgSVHmZvRLctd6jHLDjBnm+5z\nki3vd45m6OvDkPPt2WwL2M7v2Xk3Z0POlgw7306yjX6/M8N9TrJ315O5OufiA4PN1htyPtm2R7bt\nuHjH2Tbc5wyusfzW2pVJrpxm3Kq6obW2ZysJq0zn3jKG6RzDNCbjmc69biv7naMZ+vow5Hyybd+Q\n88m2fUPON+Rsu8Gs9jnJsJeFbNs35HyybY9s2zPPbA+axy89iruSnD7x/rS+HwDMmn0OAItkvwOw\nCyy6EHZ9krOr6qyqOi7JRUmuXnAGAMbBPgeARbLfAdgFFnprZGvtW1X1yiQfTPdI4Te31m7bwa+c\nyWXFu4Dp3FvGMJ1jmMZkPNO5K81hn7OZoa8PQ84n2/YNOZ9s2zfkfEPOtlT2O99Dtu0bcj7Ztke2\n7Zlbtmqtzet3AwAAAMBgLPrWSAAAAABYCoUwAAAAAEZhVxbCquofVdVtVfU3VXVgov+ZVfWXVXVj\n//rNZebcqY2msx/2r6vqUFV9tqqev6yMs1ZVr6qquyaW4fnLzjQrVfWCfnkdqqorlp1nXqrqzqq6\npV9+Nyw7z6xU1Zur6p6qunWi34lVdU1V3d7/PGGZGVmsaZd/Vb2mqm7tX/94gPl+rd/XrFTV66uq\nhpCtqp45sS+4sar+X1X9xBCy9eOdUVUf6ufbZ6rqzHln22K+b0/Mu4U01r2VbWJVPaKqDlfVry8i\n27T5quoxVfXpfr7dVlUvG1C2x1fVJ/tcNy9qe7KFde4Pq+prVfUHi8i112123FhVx1fVO/rhn5rc\nBs37PGGKbP+i3y7eXFXXVtVjJobNdds0RbZLq+reiQz/ZGLYJf16fntVXbKEbP95ItfnquprE8Pm\nPd8ecJy7ZnhVd4xwqF+uT5wYNu/5tlm2n+0z3VJVn6iqH50YNtfzkimynVdVX59Ydv92Ythczw2n\nyPavJnLd2q9jJ/bD5j3fTq+qj/bbiduq6ufXGWe+61xrbde9kuxP8neSfCzJgYn+Zya5ddn5FjCd\n5yS5KcnxSc5K8vkkxyw774ym+VVJfnHZOeYwXcf0y+mxSY7rl985y841p2m9M8lJy84xh+n6B0me\nOLmNSfJrSa7ou69I8ppl5/Ra6Dqx6fJP8g+TXJPu4TQPTfdEsUcMKN9Tk/xxv406Jsknk5w3hGxr\nxj8xyVeS7BtKtn7f/Ny++2GLyLbFfPctIs92l2uS1yV5a5JfH1K+fh99/MRyvTPJowaS7YeSnN13\nPyrJkSSPHEK2ftizk7woyR8set3ba69pjhuTvDzJb/bdFyV5R9891/OEKbM9c3WbmOSfrWbr389t\n2zRltkvX2+70+5k7+p8n9N0nLDLbmvH/ebqHLcx9vvW//wHHuWuGn5/kA0kqyZOTfGoR823KbE9d\n/ZtJXriarX9/Z+Z4XjJFtvPW2yZudX2YR7Y1474oyUcWON9OTfLEvvvhST63zv/qXNe5XXlFWGtt\npbX22WXnmLejTOcFSd7eWvtma+1/JzmU5EmLTccWPSnJodbaHa21v0ry9nTLkV2itfbxdCfiky5I\nclXffVWSuV+twqBMs/zPSfLx1tq3Wmv/N8nNSV4woHwtyUPSn/wneXCSuweSbdJPJ/lAa+3+uabq\nbJqtqs5Jcmxr7Zokaa3dt6BsU+VboqmyVdW5SU5J8qEF5Vq1ab7W2l+11r7Zvz0+i7t7Yppsn2ut\n3d53/3mSe5KcPIRsfaZrk3xjAXnGYJrjxsnl8q4kz66qyvzPEzbN1lr76MQ28bokp83w7+8o21E8\nP8k1rbWvtNa+mu5LrFnur7ea7WeSvG2Gf/+oNjjOnXRBkre0znVJHllVp2b+823TbK21T/R/O1ns\n+jbNfNvI3M8Nt5ht0evbkdbap/vubyRZSfLoNaPNdZ3blYWwTZxVVf+rqv5HVT192WHm5NFJvjjx\n/nAeuOLsZq/sL398c+2dW832+jKb1JJ8qKoOVtXlyw4zZ6e01o703V9Kd2LHeEyz/G9K8oKq2ldV\nJ6X7lvz0oeRrrX0yyUfTXVlyJMkHW2srQ8i2xkVZ3AHaNNl+KMnXqurd/THHf6yqYwaUL0keUlU3\nVNV1tYBbSqfNVlUPSvKfkvzigjJNmmre9bds3Jxuv/2avug0iGyrqupJ6QrYn593sNjXLcM0x43f\nGae19q0kX0/y/VN+dt7ZJl2W7qqOVfPcNk2b7af6c413VdXqPnkw8626W0nPSvKRid7L2KZP2ij/\n0M5x1q5vQzgveUpV3VRVH6iqH+n7DWa+VdW+dIWk35/ovbD5Vt1t3U9I8qk1g+a6zh271Q8sSlV9\nOMkPrjPol1tr79vgY0eSnNFa+3L/beN7q+pHWmt/MbegO7TN6dzVjjbNSd6Q5FfS/fP9SrqD5Z9b\nXDpm4Gmttbuq6geSXFNVf9p/I7GntdZaVbVl52C2NtlefcdGy7+19qGq+ntJPpHk3nS3Hn57KPmq\n6m+nuw1/9dvTa6rq6a21P1p2tonfc2qSv5vkgzvNNMNsxyZ5eroDtz9L8o50t9u8aSD5kuQx/bb4\nsUk+UlW3tNZ2XDSZQbaXJ3l/a+1wzaE5ulnMu9baF5M8rqoele5Y8l2ttR1fKTnj/4nfTXJJa+1v\ndpprltlgUlW9OMmBJM+Y6D2XbdMW/Lckb2utfbOq/mm6q+qetcC/P42LkryrtTZ5vLDs+TZ4VfXM\ndIWwp030XvZ5yafTLbv7qmv7+r1Jzl7g35/Gi5L8cWtt8uqxhcy3qnpYugLcLyy6ZjPYQlhr7Tnb\n+Mw3k3yz7z5YVZ9P963tYBvs3s50Jrkr33tFwWl9v11h2mmuqt9OslcaXN3Vy2wrWmt39T/vqar3\npLv0d68Wwu6uqlNba0f6E5N7lh2I2Tra9qqqplr+rbVfTfKr/Wfemq4dhKHk+8kk17XW7us/84Ek\nT0my40LYLOZd78Ik72mt/fVOM80w2+EkN7bW7ug/89507VfMpBA2o/VudVt8R1V9LF3RbscnTTPI\n9pQkT6+ql6drg+u4qrqvtTaThoJnuN6ltfbn1TUy/PR0t54tPVtVPSLJf0/3hel1O800y2zM1DTH\njavjHK6qY5N8X5IvT/nZeWdLVT0nXSH1Ge27txvPbds0bbbW2pcn3r4xXRt4q589b81nPzajXFNl\nm3BRkldM9pjzfJvGRvnnPd+mUlWPS7c8Xzi5jJd9XjJZ3Gmtvb+q/kt/h8CQzg0fcNX9IuZbVT04\nXRHs91pr715nlLmuc3vq1siqOnn11oS+Wn52usbT9pqrk1xU3dNizko3nX+y5Ewz0R9grfrJJOs+\n5WIXuj7J2VV1VlUdl26Ds5CneC1SVT20qh6+2p3kedk7y3A9VydZfVLJJUn25FWcbGjT5V9Vx1TV\n9/fdj0vyuCyuXaRp1s8/S/KMqjq2PyB5Rrp2GoaQbdVC263IdNmuT9dWxWr7TM9K8pkFZEumW+9O\nqKrj++6TkvzYgvJtmq219rOttTNaa2emuz3yLbMqgs0iX1WdVlV/q+8+Id2VBYtol3aabMcleU+6\nebbjwtwsszFz0xw3Ti6Xn07X0HXL/M8TNs1WVU9I8ltJfry1ds9E/3lvm6bJNnmu8eP57j7vg0me\n12c8Id0x7MyuRJ4mW5/vh9M1AP7JiX7L2qZPujrJS6rz5CRf72+Znvd821RVnZHk3Ukubq19bqL/\n0s9LquoHq7rLn6u7pf1B6QrWgzg3rKrvS3fs976JfnOfb/08eVOSldbaazcYbb7rXJvTkwDm+UpX\nIDmc7uqvu9O1aZIkP5XktiQ3prsM8UXLzjqP6eyH/XK6bwE+m67yvfS8M5rm301yS7oGpa9Ocuqy\nM81w2s5PdyXI59N9k7v0THOYxsemaxPppv5/cc9MZ7oT8SNJ/rr/v7wsXVsc1ya5PcmHk5y47Jxe\nC10n1l3+6W4DeWPf/ZB0B6ufSdeA6+MHlu+YdCcrK33G1w4lW//+zHTf/D1oSPOtf//cfl91S5Lf\nSXLcUPKle4LWLf22+JYklw0l25rxL81inxo5zbxbXa439T8vH1C2F/f7oBsnXnPfpmzhf+KP0t0C\n/pfp9pPPX9Sy3YuvrHPcmOTfpysuJd3+5b+mawz/T5I8duKzcz1PmCLbh9Odu6yup1f3/ee+bZoi\n239Id4x6U7o2Mn944rM/18/PQ0leuuhs/ftXJXn1ms8tYr6td5z7siQv64dXkt/os9+S5MAC59tm\n2d6Y5KsT69sNff+5n5dMke2VE+vbdUmeerT1YZHZ+nEuTfdwjcnPLWK+PS1dU0g3Tyy38xe5zlX/\niwAAAABgT9tTt0YCAAAAwEYUwgAAAAAYBYUwAAAAAEZBIQwAAACAUVAIAwAAAGAUFMIAAAAAGAWF\nMAAAAABG4f8DhwZfsgfENqcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 1512x504 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m7GwR_Ye-NJ7",
        "colab_type": "text"
      },
      "source": [
        "Generally both samplers give similar result when comparing only the summary statistics."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kexAm27G-dF0",
        "colab_type": "text"
      },
      "source": [
        "# Conclusion\n",
        "\n",
        "We can see that for autoregressive model it is a bit difficult for both MCMC and ABC to infer the true parameter values, although both generally converged to reasonable posteriors given only a 100 datapoints. ABC takes significantly more time due to the simulation procedures even with vectorization to aid paralellization, so for models that can be specified it is more suitable to use MCMC, whereas ABC is more suitable for models that are complex and require simulators. \n",
        "\n",
        "This simple example also demonstrates the importance of choosing the right summary statistics. Not only there will be difference in simulation time but also in the quality of the posterior received. Summary statistics, thus, should be chosen to represent aspects of the data we care most about, and sufficiently so. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wr9SlgQp_bor",
        "colab_type": "text"
      },
      "source": [
        "# References\n",
        "\n",
        "ELFI Developers. (2017). $\\textit{ElFI Tutorial}$. Retrieved from: https://elfi.readthedocs.io/en/latest/usage/tutorial.html\n",
        "\n",
        "Stan Developers. (n.d.). $\\textit{Autoregressive Models}$. Retrieved from: https://mc-stan.org/docs/2_22/stan-users-guide/autoregressive-section.html"
      ]
    }
  ]
}