examples/diagnostics_and_criticism/model_averaging.ipynb

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    "(model_averaging)=\n",
    "# Model Averaging\n",
    "\n",
    ":::{post} Aug 2024\n",
    ":tags: model comparison, model averaging\n",
    ":category: intermediate\n",
    ":author: Osvaldo Martin\n",
    ":::"
   ]
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     "text": [
      "Running on PyMC v5.16.2+24.g799c98f41\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "\n",
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc as pm\n",
    "\n",
    "print(f\"Running on PyMC v{pm.__version__}\")"
   ]
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   "source": [
    "rng = np.random.seed(2741)\n",
    "az.style.use(\"arviz-darkgrid\")"
   ]
  },
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   "source": [
    "When confronted with more than one model we have several options. One of them is to perform model selection as exemplified by the PyMC examples {ref}`pymc:model_comparison` and the {ref}`GLM-model-selection`, usually is a good idea to also include posterior predictive checks in order to decide which model to keep. Discarding all models except one is equivalent to affirm that, among the evaluated models, one is correct (under some criteria) with probability 1 and the rest are incorrect. In most cases this will be an overstatment that ignores the uncertainty we have in our models. This is somewhat similar to computing the full posterior and then just keeping a point-estimate like the posterior mean; we may become overconfident of what we really know. You can also browse the {doc}`blog/tag/model-comparison` tag to find related posts. \n",
    "\n",
    "An alternative to this dilemma is to perform model selection but to acknowledge the models we discarded. If the number of models are not that large this can be part of a technical discussion on a paper, presentation, thesis, and so on. If the audience is not technical enough, this may not be a good idea.\n",
    "\n",
    "Yet another alternative, the topic of this example, is to perform model averaging. The idea is to weight each model by its merit and generate predictions from each model, proportional to those weights. There are several ways to do this, including the three methods that will be briefly discussed in this notebook. You will find a more thorough explanation in the work by {cite:t}`Yao_2018` and {cite:t}`Yao_2022`. \n",
    "\n",
    "\n",
    "## Pseudo Bayesian model averaging\n",
    "\n",
    "Bayesian models can be weighted by their marginal likelihood, which is known as Bayesian Model Averaging. While this is theoretically appealing, it is problematic in practice: on the one hand the marginal likelihood is highly sensitive to the specification of the prior, in a way that parameter estimation is not, and on the other, computing the marginal likelihood is usually a challenging task. Additionally, Bayesian model averaging is ﬂawed in the $\\mathcal{M}$-open setting in which the true data-generating process is not one of the candidate models being ﬁt {cite:t}`Yao_2018`. A more robust approach is to compute the  expected log pointwise predictive density (ELPD).\n",
    "\n",
    "$$\n",
    "\\sum_i^N \\log \\int \\ p(y_i \\mid \\theta) \\; p(\\theta \\mid y) d\\theta\n",
    "$$\n",
    "\n",
    "where $N$ is the number of data points, $y_i$ is the i-th data point, $\\theta$ are the parameters of the model, $p(y_i \\mid \\theta)$ is the likelihood of the i-th data point given the parameters, and $p(\\theta \\mid y)$ is the posterior distribution.\n",
    "\n",
    "Once we have computed the ELPD for each model we can compute weights by doing\n",
    "\n",
    "$$w_i = \\frac {e^{dELPD_i}} {\\sum_j^M e^{dELPD_i}}$$\n",
    "\n",
    "Where $dELPD_i$ is the difference between the model with the best ELPD and the i-th model.\n",
    "\n",
    "This approach is called pseudo Bayesian model averaging, or Akaike-like weighting and is an heuristic to compute the relative probability of each model (given a fixed set of models). Note that we exponetiate to \"revert\" the effect of the logarithm in the ELPD formula and the denominator is a normalization term to ensure that the weights sum up to one. With a pinch of salt, we can interpret these weights as the probability of each model explaining the data.\n",
    "\n",
    "So far so good, but the ELPD is a theoretical quantity, and in practice we need to approximate it. To do so ArviZ offers two methods\n",
    "\n",
    "* WAIC, Widely Applicable Information Criterion\n",
    "* LOO, Pareto-Smooth-Leave-One-Out-Cross-Validation.\n",
    "\n",
    "Both require and InferenceData with the log-likelihood group and are equally fast to compute. We recommend using LOO because it has better practical properties, and better diagnostics (so we known when we are having issues with the ELPD estimation).\n",
    "\n",
    "## Pseudo Bayesian model averaging with Bayesian Bootstrapping\n",
    "\n",
    "The above formula for computing weights is a nice and simple approach, but with one major caveat: it does not take into account the uncertainty in the computation of the ELPD. We could compute the standard error of the ELPD value (assuming a Gaussian approximation) and modify the above formula accordingly. Or we can do something more robust, like using a [Bayesian Bootstrapping](http://www.sumsar.net/blog/2015/04/the-non-parametric-bootstrap-as-a-bayesian-model/) to estimate, and incorporate this uncertainty.\n",
    "\n",
    "## Stacking\n",
    "\n",
    "The third approach we will discuss is known as _stacking of predictive distributions_ by {cite:t}`Yao_2018`. We want to combine several models in a metamodel in order to minimize the divergence between the meta-model and the _true_ generating model. When using a logarithmic scoring rule this is equivalent to:\n",
    "\n",
    "$$\\max_{w} \\frac{1}{n} \\sum_{i=1}^{n}log\\sum_{k=1}^{K} w_k p(y_i \\mid y_{-i}, M_k)$$\n",
    "\n",
    "Where $n$ is the number of data points and $K$ the number of models. To enforce a solution we constrain $w$ to be $w_k \\ge 0$ and  $\\sum_{k=1}^{K} w_k = 1$. \n",
    "\n",
    "The quantity $p(y_i \\mid y_{-i}, M_k)$ is the leave-one-out predictive distribution for the $M_k$ model. Computing it requires fitting each model $n$ times, each time leaving out one data point. Fortunately, this is exactly what LOO approximates in a very efficient way. So we can use LOO and stacking together. To be fair, we can also use WAIC, even when WAIC approximates the ELPD in a different way.\n",
    "\n",
    "## Weighted posterior predictive samples\n",
    "\n",
    "Once we have computed the weights, using any of the above 3 methods, we can use them to get weighted posterior predictive samples. We will illustrate how to do it using the body fat dataset {cite}`penrose1985`. This dataset has measurements from 251 individuals, including their weight, height, the circumference of the abdomen, the circumference of the wrist etc. Our purpose is to predict the percentage of body fat, as estimated by the siri variable, also available from the dataset.\n",
    "\n",
    "Let's start by loading the data"
   ]
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>siri</th>\n",
       "      <th>age</th>\n",
       "      <th>weight</th>\n",
       "      <th>height</th>\n",
       "      <th>neck</th>\n",
       "      <th>chest</th>\n",
       "      <th>abdomen</th>\n",
       "      <th>hip</th>\n",
       "      <th>thigh</th>\n",
       "      <th>knee</th>\n",
       "      <th>ankle</th>\n",
       "      <th>biceps</th>\n",
       "      <th>forearm</th>\n",
       "      <th>wrist</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12.3</td>\n",
       "      <td>23</td>\n",
       "      <td>70.1</td>\n",
       "      <td>172</td>\n",
       "      <td>36.2</td>\n",
       "      <td>93.1</td>\n",
       "      <td>85.2</td>\n",
       "      <td>94.5</td>\n",
       "      <td>59.0</td>\n",
       "      <td>37.3</td>\n",
       "      <td>21.9</td>\n",
       "      <td>32.0</td>\n",
       "      <td>27.4</td>\n",
       "      <td>17.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6.1</td>\n",
       "      <td>22</td>\n",
       "      <td>78.8</td>\n",
       "      <td>184</td>\n",
       "      <td>38.5</td>\n",
       "      <td>93.6</td>\n",
       "      <td>83.0</td>\n",
       "      <td>98.7</td>\n",
       "      <td>58.7</td>\n",
       "      <td>37.3</td>\n",
       "      <td>23.4</td>\n",
       "      <td>30.5</td>\n",
       "      <td>28.9</td>\n",
       "      <td>18.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>25.3</td>\n",
       "      <td>22</td>\n",
       "      <td>70.0</td>\n",
       "      <td>168</td>\n",
       "      <td>34.0</td>\n",
       "      <td>95.8</td>\n",
       "      <td>87.9</td>\n",
       "      <td>99.2</td>\n",
       "      <td>59.6</td>\n",
       "      <td>38.9</td>\n",
       "      <td>24.0</td>\n",
       "      <td>28.8</td>\n",
       "      <td>25.2</td>\n",
       "      <td>16.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10.4</td>\n",
       "      <td>26</td>\n",
       "      <td>84.0</td>\n",
       "      <td>184</td>\n",
       "      <td>37.4</td>\n",
       "      <td>101.8</td>\n",
       "      <td>86.4</td>\n",
       "      <td>101.2</td>\n",
       "      <td>60.1</td>\n",
       "      <td>37.3</td>\n",
       "      <td>22.8</td>\n",
       "      <td>32.4</td>\n",
       "      <td>29.4</td>\n",
       "      <td>18.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>28.7</td>\n",
       "      <td>24</td>\n",
       "      <td>83.8</td>\n",
       "      <td>181</td>\n",
       "      <td>34.4</td>\n",
       "      <td>97.3</td>\n",
       "      <td>100.0</td>\n",
       "      <td>101.9</td>\n",
       "      <td>63.2</td>\n",
       "      <td>42.2</td>\n",
       "      <td>24.0</td>\n",
       "      <td>32.2</td>\n",
       "      <td>27.7</td>\n",
       "      <td>17.7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   siri  age  weight  height  neck  chest  abdomen    hip  thigh  knee  ankle  \\\n",
       "0  12.3   23    70.1     172  36.2   93.1     85.2   94.5   59.0  37.3   21.9   \n",
       "1   6.1   22    78.8     184  38.5   93.6     83.0   98.7   58.7  37.3   23.4   \n",
       "2  25.3   22    70.0     168  34.0   95.8     87.9   99.2   59.6  38.9   24.0   \n",
       "3  10.4   26    84.0     184  37.4  101.8     86.4  101.2   60.1  37.3   22.8   \n",
       "4  28.7   24    83.8     181  34.4   97.3    100.0  101.9   63.2  42.2   24.0   \n",
       "\n",
       "   biceps  forearm  wrist  \n",
       "0    32.0     27.4   17.1  \n",
       "1    30.5     28.9   18.2  \n",
       "2    28.8     25.2   16.6  \n",
       "3    32.4     29.4   18.2  \n",
       "4    32.2     27.7   17.7  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "try:\n",
    "    d = pd.read_csv(os.path.join(\"..\", \"data\", \"body_fat.csv\"))\n",
    "except FileNotFoundError:\n",
    "    d = pd.read_csv(pm.get_data(\"body_fat.csv\"))\n",
    "\n",
    "d.head()"
   ]
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    "Now that we have the data we are going to build two models, both are simple linear regressions the difference is that for the first one we are going to use the variables `abdomen`, and for the second one we are going to use the variables `wrist`, `height` and `weight`."
   ]
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     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [alpha, beta, sigma]\n"
     ]
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     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 7 seconds.\n",
      "Sampling: [siri]\n"
     ]
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       "\n"
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   "source": [
    "with pm.Model() as model_0:\n",
    "    alpha = pm.Normal(\"alpha\", mu=0, sigma=1)\n",
    "    beta = pm.Normal(\"beta\", mu=0, sigma=1)\n",
    "    sigma = pm.HalfNormal(\"sigma\", 5)\n",
    "\n",
    "    mu = alpha + beta * d[\"abdomen\"]\n",
    "\n",
    "    siri = pm.Normal(\"siri\", mu=mu, sigma=sigma, observed=d[\"siri\"])\n",
    "\n",
    "    idata_0 = pm.sample(idata_kwargs={\"log_likelihood\": True}, random_seed=rng)\n",
    "    pm.sample_posterior_predictive(idata_0, extend_inferencedata=True, random_seed=rng)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
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     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [alpha, beta, sigma]\n"
     ]
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       "\n"
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     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 36 seconds.\n",
      "Sampling: [siri]\n"
     ]
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       "\n"
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   "source": [
    "with pm.Model() as model_1:\n",
    "    alpha = pm.Normal(\"alpha\", mu=0, sigma=1)\n",
    "    beta = pm.Normal(\"beta\", mu=0, sigma=1, shape=3)\n",
    "    sigma = pm.HalfNormal(\"sigma\", 5)\n",
    "\n",
    "    mu = alpha + pm.math.dot(beta, d[[\"wrist\", \"height\", \"weight\"]].T)\n",
    "\n",
    "    siri = pm.Normal(\"siri\", mu=mu, sigma=sigma, observed=d[\"siri\"])\n",
    "\n",
    "    idata_1 = pm.sample(idata_kwargs={\"log_likelihood\": True}, random_seed=rng)\n",
    "    pm.sample_posterior_predictive(idata_1, extend_inferencedata=True, random_seed=rng)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before LOO (or WAIC) to compare and or average models we should check that we do not have sampling issues and posterior predictive checks are reasonable. For the sake of brevity we are going to skip these steps and instead jump to the model averaging.\n",
    "\n",
    "First we need to call `az.compare` to compute the LOO values for each model and the weights using `stacking`. These are the default options, if you want to perform pseudo Bayesian model averaging you can use the `method='BB-pseudo-BMA'` that includes the Bayesian Bootstrap estimation of the uncertainty in the ELPD.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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       "      <th>rank</th>\n",
       "      <th>elpd_loo</th>\n",
       "      <th>p_loo</th>\n",
       "      <th>elpd_diff</th>\n",
       "      <th>weight</th>\n",
       "      <th>se</th>\n",
       "      <th>dse</th>\n",
       "      <th>warning</th>\n",
       "      <th>scale</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>model_1</th>\n",
       "      <td>0</td>\n",
       "      <td>-817.216895</td>\n",
       "      <td>3.626704</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.639236</td>\n",
       "      <td>10.496342</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>False</td>\n",
       "      <td>log</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_0</th>\n",
       "      <td>1</td>\n",
       "      <td>-825.344978</td>\n",
       "      <td>1.832909</td>\n",
       "      <td>8.128083</td>\n",
       "      <td>0.360764</td>\n",
       "      <td>9.970768</td>\n",
       "      <td>8.698358</td>\n",
       "      <td>False</td>\n",
       "      <td>log</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         rank    elpd_loo     p_loo  elpd_diff    weight         se       dse  \\\n",
       "model_1     0 -817.216895  3.626704   0.000000  0.639236  10.496342  0.000000   \n",
       "model_0     1 -825.344978  1.832909   8.128083  0.360764   9.970768  8.698358   \n",
       "\n",
       "         warning scale  \n",
       "model_1    False   log  \n",
       "model_0    False   log  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_dict = dict(zip([\"model_0\", \"model_1\"], [idata_0, idata_1]))\n",
    "comp = az.compare(model_dict)\n",
    "comp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the column `weight`, that `model_1` has a weight of $\\approx 0.6$ and `model_2` has a weight $\\approx 0.4$. To use this weights to generate posterior predictive samples we can use the `az.weighted_posterior` function. This function takes the InferenceData objects and the weights and returns a new InferenceData object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:     (siri_dim_2: 251, sample: 3999)\n",
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       "  * siri_dim_2  (siri_dim_2) int64 0 1 2 3 4 5 6 ... 244 245 246 247 248 249 250\n",
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       "  * draw        (sample) int64 682 691 550 397 831 520 ... 638 997 295 483 606 9\n",
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       "    siri        (siri_dim_2, sample) float64 17.75 16.43 14.7 ... 30.98 27.67\n",
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       "    created_at:                 2024-08-23T16:10:41.836182+00:00\n",
       "    arviz_version:              0.20.0.dev0\n",
       "    inference_library:          pymc\n",
       "    inference_library_version:  5.16.2+24.g799c98f41</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-30be2444-7de5-41b0-9df6-9f2cdc6e33b2' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-30be2444-7de5-41b0-9df6-9f2cdc6e33b2' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>siri_dim_2</span>: 251</li><li><span class='xr-has-index'>sample</span>: 3999</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-fba04221-594d-4639-8667-0ee8cfeaeb8d' class='xr-section-summary-in' type='checkbox'  checked><label for='section-fba04221-594d-4639-8667-0ee8cfeaeb8d' class='xr-section-summary' >Coordinates: <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 class='xr-has-index'>siri_dim_2</span></div><div class='xr-var-dims'>(siri_dim_2)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 246 247 248 249 250</div><input id='attrs-88c62c32-deaf-4b37-8280-f71c51f7ee8c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-88c62c32-deaf-4b37-8280-f71c51f7ee8c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0aebba92-9cbd-4c58-a86e-e48104577afa' class='xr-var-data-in' type='checkbox'><label for='data-0aebba92-9cbd-4c58-a86e-e48104577afa' 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,   1,   2, ..., 248, 249, 250])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>sample</span></div><div class='xr-var-dims'>(sample)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>MultiIndex</div><input id='attrs-c1278449-a440-4619-aaa5-ee20d111a21a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-c1278449-a440-4619-aaa5-ee20d111a21a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b2c8ecd4-935a-4a81-93e1-51bfee3bae1f' class='xr-var-data-in' type='checkbox'><label for='data-b2c8ecd4-935a-4a81-93e1-51bfee3bae1f' 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([(2, 682), (3, 691), (1, 550), ..., (2, 483), (1, 606), (2, 9)],\n",
       "      dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(sample)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>2 3 1 2 1 2 3 3 ... 1 0 0 2 0 2 1 2</div><input id='attrs-a5743eb0-b5ee-4872-8df1-86e337d84d17' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a5743eb0-b5ee-4872-8df1-86e337d84d17' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d36d8a35-d890-450a-8b00-1c45f030deda' class='xr-var-data-in' type='checkbox'><label for='data-d36d8a35-d890-450a-8b00-1c45f030deda' 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([2, 3, 1, ..., 2, 1, 2])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(sample)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>682 691 550 397 ... 295 483 606 9</div><input id='attrs-64f0df5a-5c12-4fc3-83d2-5bedcf4c03d6' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-64f0df5a-5c12-4fc3-83d2-5bedcf4c03d6' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-3fa1c5d5-bf8f-41cb-836d-0dbc2c99fe18' class='xr-var-data-in' type='checkbox'><label for='data-3fa1c5d5-bf8f-41cb-836d-0dbc2c99fe18' 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([682, 691, 550, ..., 483, 606,   9])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f00d1779-9c88-4d5b-b9eb-46da96959bb2' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f00d1779-9c88-4d5b-b9eb-46da96959bb2' class='xr-section-summary' >Data variables: <span>(1)</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>siri</span></div><div class='xr-var-dims'>(siri_dim_2, sample)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>17.75 16.43 14.7 ... 30.98 27.67</div><input id='attrs-796d0b2d-5998-4771-9352-2992733a73bb' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-796d0b2d-5998-4771-9352-2992733a73bb' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2d92ba45-b59b-49c4-af7c-81f96cea970f' class='xr-var-data-in' type='checkbox'><label for='data-2d92ba45-b59b-49c4-af7c-81f96cea970f' 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([[17.7507863 , 16.43165785, 14.70207536, ..., 20.07166666,\n",
       "         6.30707594, 23.71432073],\n",
       "       [21.24130963, 13.56310432, 21.81044629, ..., 23.6387914 ,\n",
       "         8.40753315, 29.83233935],\n",
       "       [12.49832099,  9.77179084, 14.61533337, ..., 13.92368941,\n",
       "         8.26722381, 27.29269372],\n",
       "       ...,\n",
       "       [27.34331012, 26.61542596, 17.51539238, ..., 28.37461601,\n",
       "        26.33929509, 20.2096418 ],\n",
       "       [23.22195584, 16.43333399, 32.8961469 , ..., 23.99824582,\n",
       "        11.98555006, 19.34159072],\n",
       "       [29.07441247, 26.16213246, 35.62032494, ..., 25.61299541,\n",
       "        30.98457422, 27.66946849]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-9ddd7265-ef01-460f-9c16-3e4f50dbc25b' class='xr-section-summary-in' type='checkbox'  ><label for='section-9ddd7265-ef01-460f-9c16-3e4f50dbc25b' class='xr-section-summary' >Indexes: <span>(2)</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-index-name'><div>siri_dim_2</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-31003cab-0856-4130-b60d-1e18968445bd' class='xr-index-data-in' type='checkbox'/><label for='index-31003cab-0856-4130-b60d-1e18968445bd' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
       "       ...\n",
       "       241, 242, 243, 244, 245, 246, 247, 248, 249, 250],\n",
       "      dtype=&#x27;int64&#x27;, name=&#x27;siri_dim_2&#x27;, length=251))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>sample<br>chain<br>draw</div></div><div class='xr-index-preview'>PandasMultiIndex</div><div></div><input id='index-e5296ff4-2d4d-46aa-9e6c-68d7f22be09f' class='xr-index-data-in' type='checkbox'/><label for='index-e5296ff4-2d4d-46aa-9e6c-68d7f22be09f' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(MultiIndex([(2, 682),\n",
       "            (3, 691),\n",
       "            (1, 550),\n",
       "            (2, 397),\n",
       "            (1, 831),\n",
       "            (2, 520),\n",
       "            (3,  31),\n",
       "            (3, 491),\n",
       "            (3, 114),\n",
       "            (3, 744),\n",
       "            ...\n",
       "            (3, 593),\n",
       "            (3, 153),\n",
       "            (1, 286),\n",
       "            (0, 859),\n",
       "            (0, 638),\n",
       "            (2, 997),\n",
       "            (0, 295),\n",
       "            (2, 483),\n",
       "            (1, 606),\n",
       "            (2,   9)],\n",
       "           name=&#x27;sample&#x27;, length=3999))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-14de8ce8-a0fb-41cd-90be-f70dc66851c1' class='xr-section-summary-in' type='checkbox'  checked><label for='section-14de8ce8-a0fb-41cd-90be-f70dc66851c1' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2024-08-23T16:10:41.836182+00:00</dd><dt><span>arviz_version :</span></dt><dd>0.20.0.dev0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.16.2+24.g799c98f41</dd></dl></div></li></ul></div></div><br></div>\n",
       "                      </ul>\n",
       "                  </div>\n",
       "            </li>\n",
       "            \n",
       "            <li class = \"xr-section-item\">\n",
       "                  <input id=\"idata_observed_dataa4d8b668-ecf9-4908-bae5-087361da27b3\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
       "                  <label for=\"idata_observed_dataa4d8b668-ecf9-4908-bae5-087361da27b3\" class = \"xr-section-summary\">observed_data</label>\n",
       "                  <div class=\"xr-section-inline-details\"></div>\n",
       "                  <div class=\"xr-section-details\">\n",
       "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
       "                          <div style=\"padding-left:2rem;\"><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",
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       "  --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:     (siri_dim_0: 251)\n",
       "Coordinates:\n",
       "  * siri_dim_0  (siri_dim_0) int64 0 1 2 3 4 5 6 ... 244 245 246 247 248 249 250\n",
       "Data variables:\n",
       "    siri        (siri_dim_0) float64 12.3 6.1 25.3 10.4 ... 33.6 29.3 26.0 31.9\n",
       "Attributes:\n",
       "    created_at:                 2024-08-23T16:10:41.440917+00:00\n",
       "    arviz_version:              0.20.0.dev0\n",
       "    inference_library:          pymc\n",
       "    inference_library_version:  5.16.2+24.g799c98f41</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-d6d43455-0774-4df2-b641-cf370813d760' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-d6d43455-0774-4df2-b641-cf370813d760' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>siri_dim_0</span>: 251</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-a972198b-3706-4b34-a5cc-2ca2d918d5f1' class='xr-section-summary-in' type='checkbox'  checked><label for='section-a972198b-3706-4b34-a5cc-2ca2d918d5f1' class='xr-section-summary' >Coordinates: <span>(1)</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 class='xr-has-index'>siri_dim_0</span></div><div class='xr-var-dims'>(siri_dim_0)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 246 247 248 249 250</div><input id='attrs-7cb61985-3315-41a2-892b-ee63b6dc2850' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7cb61985-3315-41a2-892b-ee63b6dc2850' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-36528e3f-02e3-4526-a8ce-8e5ef0e27b1a' class='xr-var-data-in' type='checkbox'><label for='data-36528e3f-02e3-4526-a8ce-8e5ef0e27b1a' 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,   1,   2, ..., 248, 249, 250])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-ea2d9f77-76f4-47f2-857e-4a0d519aa2ed' class='xr-section-summary-in' type='checkbox'  checked><label for='section-ea2d9f77-76f4-47f2-857e-4a0d519aa2ed' class='xr-section-summary' >Data variables: <span>(1)</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>siri</span></div><div class='xr-var-dims'>(siri_dim_0)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>12.3 6.1 25.3 ... 29.3 26.0 31.9</div><input id='attrs-cc104193-2ee8-4eed-a630-2d576825a054' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-cc104193-2ee8-4eed-a630-2d576825a054' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8e1443da-b50a-42d0-a4e5-2f09334d6ac9' class='xr-var-data-in' type='checkbox'><label for='data-8e1443da-b50a-42d0-a4e5-2f09334d6ac9' 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([12.3,  6.1, 25.3, 10.4, 28.7, 20.9, 19.2, 12.4,  4.1, 11.7,  7.1,\n",
       "        7.8, 20.8, 21.2, 22.1, 20.9, 29. , 22.9, 16. , 16.5, 19.1, 15.2,\n",
       "       15.6, 17.7, 14. ,  3.7,  7.9, 22.9,  3.7,  8.8, 11.9,  5.7, 11.8,\n",
       "       21.3, 32.3, 40.1, 24.2, 28.4, 32.6, 34.5, 32.9, 31.6, 32. ,  7.7,\n",
       "       13.9, 10.8,  5.6, 13.6,  4. , 10.2,  6.6,  8. ,  6.3,  3.9, 22.6,\n",
       "       20.4, 28. , 31.5, 24.6, 26.1, 29.8, 30.7, 25.8, 32.3, 30. , 21.5,\n",
       "       13.8,  6.3, 12.9, 24.3,  8.8,  8.5, 13.5, 11.8, 18.5,  8.8, 22.2,\n",
       "       21.5, 18.8, 31.4, 26.8, 18.4, 27. , 27. , 26.6, 14.9, 23.1,  8.3,\n",
       "       14.1, 20.5, 18.2,  8.5, 24.9,  9. , 17.4,  9.6, 11.3, 17.8, 22.2,\n",
       "       21.2, 20.4, 20.1, 22.3, 25.4, 18. , 19.3, 18.3, 17.3, 21.4, 19.7,\n",
       "       28. , 22.1, 21.3, 26.7, 16.7, 20.1, 13.9, 25.8, 18.1, 27.9, 25.3,\n",
       "       14.7, 16. , 13.8, 17.5, 27.2, 17.4, 20.8, 14.9, 18.1, 22.7, 23.6,\n",
       "       26.1, 24.4, 27.1, 21.8, 29.4, 22.4, 20.4, 24.9, 18.3, 23.3,  9.4,\n",
       "       10.3, 14.2, 19.2, 29.6,  5.3, 25.2,  9.4, 19.6, 10.1, 16.5, 21. ,\n",
       "       17.3, 31.2, 10. , 12.5, 22.5,  9.4, 14.6, 13. , 15.1, 27.3, 19.2,\n",
       "       21.8, 20.3, 34.3, 16.5,  3. ,  0.7, 20.5, 16.9, 25.3,  9.9, 13.1,\n",
       "       29.9, 22.5, 16.9, 26.6,  0. , 11.5, 12.1, 17.5,  8.6, 23.6, 20.4,\n",
       "       20.5, 24.4, 11.4, 38.1, 15.9, 24.7, 22.8, 25.5, 22. , 17.7,  6.6,\n",
       "       23.6, 12.2, 22.1, 28.7,  6. , 34.8, 16.6, 32.9, 32.8,  9.6, 10.8,\n",
       "        7.1, 27.2, 19.5, 18.7, 19.5, 47.5, 13.6,  7.5, 24.5, 15. , 12.4,\n",
       "       26. , 11.5,  5.2, 10.9, 12.5, 14.8, 25.2, 14.9, 17. , 10.6, 16.1,\n",
       "       15.4, 26.7, 25.8, 18.6, 24.8, 27.3, 12.4, 29.9, 17. , 35. , 30.4,\n",
       "       32.6, 29. , 15.2, 30.2, 11. , 33.6, 29.3, 26. , 31.9])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-77366353-7dc0-45e1-ae7c-9321e90cdd33' class='xr-section-summary-in' type='checkbox'  ><label for='section-77366353-7dc0-45e1-ae7c-9321e90cdd33' class='xr-section-summary' >Indexes: <span>(1)</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-index-name'><div>siri_dim_0</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-cbb6260e-b513-419d-bb08-0c08b43405a3' class='xr-index-data-in' type='checkbox'/><label for='index-cbb6260e-b513-419d-bb08-0c08b43405a3' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
       "       ...\n",
       "       241, 242, 243, 244, 245, 246, 247, 248, 249, 250],\n",
       "      dtype=&#x27;int64&#x27;, name=&#x27;siri_dim_0&#x27;, length=251))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f5279a72-1a64-4bf7-af6b-7b6343a37d2f' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f5279a72-1a64-4bf7-af6b-7b6343a37d2f' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2024-08-23T16:10:41.440917+00:00</dd><dt><span>arviz_version :</span></dt><dd>0.20.0.dev0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.16.2+24.g799c98f41</dd></dl></div></li></ul></div></div><br></div>\n",
       "                      </ul>\n",
       "                  </div>\n",
       "            </li>\n",
       "            \n",
       "              </ul>\n",
       "            </div>\n",
       "            <style> /* CSS stylesheet for displaying InferenceData 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.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;\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",
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       "  display: grid;\n",
       "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
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       "\n",
       ".xr-sections.group-sections {\n",
       "  grid-template-columns: auto;\n",
       "}\n",
       "\n",
       ".xr-section-item {\n",
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       "\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",
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       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
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       "\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",
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       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
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       "  grid-template-columns: 20px auto;\n",
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       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
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       "\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",
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       "\n",
       ".xr-dim-list {\n",
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       "  list-style: none;\n",
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       "  margin: 0;\n",
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       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
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       "\n",
       ".xr-dim-list:before {\n",
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       "\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",
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       "\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",
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       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
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       "\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-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",
       "  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",
       "  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-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-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",
       "  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",
       ".xr-wrap{width:700px!important;} </style>"
      ],
      "text/plain": [
       "Inference data with groups:\n",
       "\t> posterior_predictive\n",
       "\t> observed_data"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ppc_w = az.weight_predictions(\n",
    "    [model_dict[name] for name in comp.index],\n",
    "    weights=comp.weight,\n",
    ")\n",
    "ppc_w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the following plot we can see that the avearged model is a combination of the two models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_kde(\n",
    "    idata_0.posterior_predictive[\"siri\"].values,\n",
    "    plot_kwargs={\"color\": \"C0\", \"linestyle\": \"--\"},\n",
    "    label=\"model_0\",\n",
    ")\n",
    "az.plot_kde(\n",
    "    idata_1.posterior_predictive[\"siri\"].values,\n",
    "    plot_kwargs={\"color\": \"C0\", \"linestyle\": \"--\"},\n",
    "    label=\"model_1\",\n",
    ")\n",
    "az.plot_kde(\n",
    "    ppc_w.posterior_predictive[\"siri\"].values,\n",
    "    plot_kwargs={\"color\": \"C1\", \"linewidth\": 2},\n",
    "    label=\"average_model\",\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## To do or not to do?\n",
    "\n",
    "Model averaging is a good idea when you want to improve the robustness of your predictions. Usually a combinations of models will have better predictive performance than any single model. This is specially true when the models are complementary. Something we have not explored in this example is to assign weights to models in a way that they vary for different parts of the data. This can be done as discussed in {cite:t}`Yao_2022`.\n",
    "\n",
    "When not do to model averaging? Many times we can create new models that effectively work as averages of other models. For instance in this example we could have created a new model that includes all the variables. That's actually a very sensible thing to do. Notice that if a model excludes a variable thats equivalent to setting the coefficient of that variable to zero. If we average a model with the variable and without it, it's like setting the coefficient to a value between zero and the value of the coefficient in the model that includes the variable. This is a very simple example, but the same reasoning applies to more complex models.\n",
    "\n",
    "Hierarchical models are another example were we build a continuous version of a model instead of dealing with discrete versions. A toy example is to imagine that we have a coin and we want to estimated its degree of bias, a number between 0 and 1 having a 0.5 equal chance of head and tails (fair coin). We could think of two separate models: one with a prior biased towards heads and one with a prior biased towards towards tails. We could fit both separate models and then average them. An alternative is to build a hierarchical model to estimate the prior distribution. Instead of contemplating two discrete models, we would be computing a continuous model that considers the discrete ones as particular cases. Which approach is better? That depends on our concrete problem. Do we have good reasons to think about two discrete models, or is our problem better represented with a continuous bigger model?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Authors\n",
    "\n",
    "* Authored by Osvaldo Martin in June 2017 ([pymc#2273](https://github.com/pymc-devs/pymc/pull/2273))\n",
    "* Updated by Osvaldo Martin in December 2017 ([pymc#2741](https://github.com/pymc-devs/pymc/pull/2741))\n",
    "* Updated by Marco Gorelli in November 2020 ([pymc#4271](https://github.com/pymc-devs/pymc/pull/4271))\n",
    "* Moved from pymc to pymc-examples repo in December 2020 ([pymc-examples#8](https://github.com/pymc-devs/pymc-examples/pull/8))\n",
    "* Updated by Raul Maldonado in February 2021 ([pymc#25](https://github.com/pymc-devs/pymc-examples/pull/25))\n",
    "* Updated Markdown and styling by @reshamas in August 2022, ([pymc-examples#414](https://github.com/pymc-devs/pymc-examples/pull/414))\n",
    "* Updated notebook to use pymc 5 by Adrien Porter in November 2023 \n",
    "* Updated by Osvaldo Martin in August 2024 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    ":::{bibliography}\n",
    ":filter: docname in docnames\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "papermill": {
     "duration": 0.127595,
     "end_time": "2020-11-29T12:16:06.392237",
     "exception": false,
     "start_time": "2020-11-29T12:16:06.264642",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Fri Aug 23 2024\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.11.5\n",
      "IPython version      : 8.16.1\n",
      "\n",
      "arviz     : 0.20.0.dev0\n",
      "pandas    : 2.1.2\n",
      "pymc      : 5.16.2+24.g799c98f41\n",
      "numpy     : 1.24.4\n",
      "matplotlib: 3.8.4\n",
      "\n",
      "Watermark: 2.4.3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{include} ../page_footer.md\n",
    ":::"
   ]
  }
 ],
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