examples/diagnostics_and_criticism/model_averaging.ipynb

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    "(model_averaging)=\n",
    "# Model Averaging\n",
    "\n",
    ":::{post} Aug 2022\n",
    ":tags: diagnostics, model selection, model comparison\n",
    ":category: intermediate\n",
    ":author: Osvaldo Martin\n",
    ":::"
   ]
  },
  {
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on PyMC3 v3.11.5\n"
     ]
    }
   ],
   "source": [
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc3 as pm\n",
    "\n",
    "print(f\"Running on PyMC3 v{pm.__version__}\")"
   ]
  },
  {
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   "execution_count": 2,
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   "source": [
    "RANDOM_SEED = 8927\n",
    "np.random.seed(RANDOM_SEED)\n",
    "az.style.use(\"arviz-darkgrid\")"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "# Model averaging\n",
    "\n",
    "When confronted with more than one model we have several options. One of them is to perform model selection, using for example a given Information Criterion as exemplified the [model comparison notebook](../generalized_linear_models/model_comparison.ipynb) and the [GLM model selection notebook](../generalized_linear_models/GLM-model-selection.ipynb). Model selection is appealing for its simplicity, but we are discarding information about the uncertainty in our models. This is somehow similar to computing the full posterior and then just keep a point-estimate like the posterior mean; we may become overconfident of what we really know.\n",
    "\n",
    "One alternative is to perform model selection but discuss all the different models together with the computed values of a given Information Criterion. It is important to put all these numbers and tests in the context of our problem so that we and our audience can have a better feeling of the possible limitations and shortcomings of our methods. If you are in the academic world you can use this approach to add elements to the discussion section of a paper, presentation, thesis, and so on.\n",
    "\n",
    "Yet another approach is to perform model averaging. The idea now is to generate a meta-model (and meta-predictions) using a weighted average of the models. There are several ways to do this and PyMC includes 3 of them that we are going to briefly discuss, you will find a more thorough explanation in the work by [Yuling Yao et. al.](https://arxiv.org/abs/1704.02030)\n",
    "\n",
    "## Pseudo Bayesian model averaging\n",
    "\n",
    "Bayesian models can be weighted by their marginal likelihood, this 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 sensible 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. An alternative route is to use the values of WAIC (Widely Applicable Information Criterion) or LOO (pareto-smoothed importance sampling Leave-One-Out cross-validation), which we will call generically IC, to estimate weights. We can do this by using the following formula:\n",
    "\n",
    "$$w_i = \\frac {e^{ - \\frac{1}{2} dIC_i }} {\\sum_j^M e^{ - \\frac{1}{2} dIC_j }}$$\n",
    "\n",
    "Where $dIC_i$ is the difference between the i-esim information criterion value and the lowest one. Remember that the lowest the value of the IC, the better. We can use any information criterion we want to compute a set of weights, but, of course, we cannot mix them. \n",
    "\n",
    "This approach is called pseudo Bayesian model averaging, or Akaike-like weighting and is an heuristic way to compute the relative probability of each model (given a fixed set of models) from the information criteria values. Look how the denominator is just a normalization term to ensure that the weights sum up to one.\n",
    "\n",
    "## Pseudo Bayesian model averaging with Bayesian Bootstrapping\n",
    "\n",
    "The above formula for computing weights is a very nice and simple approach, but with one major caveat it does not take into account the uncertainty in the computation of the IC. We could compute the standard error of the IC (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 implemented in PyMC is known as [_stacking of predictive distributions_](https://arxiv.org/abs/1704.02030). 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",
    "$$\\max_{w} \\frac{1}{n} \\sum_{i=1}^{n}log\\sum_{k=1}^{K} w_k p(y_i|y_{-i}, M_k)$$\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 $p(y_i|y_{-i}, M_k)$ 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 we can approximate the exact leave-one-out predictive distribution using LOO (or even WAIC), and that is what we do in practice.\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 a weighted posterior predictive samples. PyMC offers functions to perform these steps in a simple way, so let see them in action using an example.\n",
    "\n",
    "The following example is taken from the superb book [Statistical Rethinking](http://xcelab.net/rm/statistical-rethinking/) by Richard McElreath. You will find more PyMC examples from this book in this [repository](https://github.com/aloctavodia/Statistical-Rethinking-with-Python-and-PyMC3). We are going to explore a simplified version of it. Check the book for the whole example and a more thorough discussion of both, the biological motivation for this problem and a theoretical/practical discussion of using Information Criteria to compare, select and average models.\n",
    "\n",
    "Briefly, our problem is as follows: We want to explore the composition of milk across several primate species, it is hypothesized that females from species of primates with larger brains produce more _nutritious_ milk (loosely speaking this is done _in order to_ support the development of such big brains). This is an important question for evolutionary biologists and try to give an answer we will use 3 variables, two predictor variables: the proportion of neocortex compare to the total mass of the brain and the logarithm of the body mass of the mothers. And for predicted variable, the kilocalories per gram of milk. With these variables we are going to build 3 different linear models:\n",
    " \n",
    "1. A model using only the neocortex variable\n",
    "2. A model using only the logarithm of the mass variable\n",
    "3. A model using both variables\n",
    "\n",
    "Let start by uploading the data and centering the `neocortex` and `log mass` variables, for better sampling."
   ]
  },
  {
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   "execution_count": 3,
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     "status": "completed"
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    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>kcal.per.g</th>\n",
       "      <th>neocortex</th>\n",
       "      <th>log_mass</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.49</td>\n",
       "      <td>-12.415882</td>\n",
       "      <td>-0.831486</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.47</td>\n",
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       "      <th>6</th>\n",
       "      <td>0.56</td>\n",
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       "      <td>0.89</td>\n",
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       "      <td>-0.579032</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.92</td>\n",
       "      <td>1.274118</td>\n",
       "      <td>-1.884978</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "   kcal.per.g  neocortex  log_mass\n",
       "0        0.49 -12.415882 -0.831486\n",
       "5        0.47  -3.035882  0.158913\n",
       "6        0.56  -3.035882  0.181513\n",
       "7        0.89   0.064118 -0.579032\n",
       "9        0.92   1.274118 -1.884978"
      ]
     },
     "execution_count": 3,
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     "output_type": "execute_result"
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   ],
   "source": [
    "d = pd.read_csv(\n",
    "    \"https://raw.githubusercontent.com/pymc-devs/resources/master/Rethinking_2/Data/milk.csv\",\n",
    "    sep=\";\",\n",
    ")\n",
    "d = d[[\"kcal.per.g\", \"neocortex.perc\", \"mass\"]].rename({\"neocortex.perc\": \"neocortex\"}, axis=1)\n",
    "d[\"log_mass\"] = np.log(d[\"mass\"])\n",
    "d = d[~d.isna().any(axis=1)].drop(\"mass\", axis=1)\n",
    "d.iloc[:, 1:] = d.iloc[:, 1:] - d.iloc[:, 1:].mean()\n",
    "d.head()"
   ]
  },
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   "source": [
    "Now that we have the data we are going to build our first model using only the `neocortex`."
   ]
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, beta, alpha]\n"
     ]
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       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:08<00:00 Sampling 2 chains, 0 divergences]\n",
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       "    "
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     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 2_000 draw iterations (2_000 + 4_000 draws total) took 20 seconds.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_0:\n",
    "    alpha = pm.Normal(\"alpha\", mu=0, sigma=10)\n",
    "    beta = pm.Normal(\"beta\", mu=0, sigma=10)\n",
    "    sigma = pm.HalfNormal(\"sigma\", 10)\n",
    "\n",
    "    mu = alpha + beta * d[\"neocortex\"]\n",
    "\n",
    "    kcal = pm.Normal(\"kcal\", mu=mu, sigma=sigma, observed=d[\"kcal.per.g\"])\n",
    "    trace_0 = pm.sample(2000, return_inferencedata=True)"
   ]
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   "source": [
    "The second model is exactly the same as the first one, except we now use the logarithm of the mass"
   ]
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   "outputs": [
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     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, beta, alpha]\n"
     ]
    },
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       "\n",
       "    <div>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:05<00:00 Sampling 2 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
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     },
     "metadata": {},
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 2_000 draw iterations (2_000 + 4_000 draws total) took 14 seconds.\n",
      "The acceptance probability does not match the target. It is 0.8826043398520717, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_1:\n",
    "    alpha = pm.Normal(\"alpha\", mu=0, sigma=10)\n",
    "    beta = pm.Normal(\"beta\", mu=0, sigma=1)\n",
    "    sigma = pm.HalfNormal(\"sigma\", 10)\n",
    "\n",
    "    mu = alpha + beta * d[\"log_mass\"]\n",
    "\n",
    "    kcal = pm.Normal(\"kcal\", mu=mu, sigma=sigma, observed=d[\"kcal.per.g\"])\n",
    "\n",
    "    trace_1 = pm.sample(2000, return_inferencedata=True)"
   ]
  },
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    "tags": []
   },
   "source": [
    "And finally the third model using the `neocortex` and `log_mass` variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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     "status": "completed"
    },
    "tags": []
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   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, beta, alpha]\n"
     ]
    },
    {
     "data": {
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       "\n",
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       "    /* Turns off some styling */\n",
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       "        /* gets rid of default border in Firefox and Opera. */\n",
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       "\n",
       "    <div>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:07<00:00 Sampling 2 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
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       "<IPython.core.display.HTML object>"
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     },
     "metadata": {},
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 2_000 draw iterations (2_000 + 4_000 draws total) took 14 seconds.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_2:\n",
    "    alpha = pm.Normal(\"alpha\", mu=0, sigma=10)\n",
    "    beta = pm.Normal(\"beta\", mu=0, sigma=1, shape=2)\n",
    "    sigma = pm.HalfNormal(\"sigma\", 10)\n",
    "\n",
    "    mu = alpha + pm.math.dot(beta, d[[\"neocortex\", \"log_mass\"]].T)\n",
    "\n",
    "    kcal = pm.Normal(\"kcal\", mu=mu, sigma=sigma, observed=d[\"kcal.per.g\"])\n",
    "\n",
    "    trace_2 = pm.sample(2000, return_inferencedata=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "end_time": "2020-11-29T12:14:54.072799",
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     "start_time": "2020-11-29T12:14:54.022563",
     "status": "completed"
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    "tags": []
   },
   "source": [
    "Now that we have sampled the posterior for the 3 models, we are going to compare them visually. One option is to use the `forestplot` function that supports plotting more than one trace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "traces = [trace_0, trace_1, trace_2]\n",
    "az.plot_forest(traces, figsize=(10, 5));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.052958,
     "end_time": "2020-11-29T12:14:55.196722",
     "exception": false,
     "start_time": "2020-11-29T12:14:55.143764",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Another option is to plot several traces in a same plot is to use `densityplot`. This plot is somehow similar to a forestplot, but we get truncated KDE (kernel density estimation) plots (by default 95% credible intervals) grouped by variable names together with a point estimate (by default the mean)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "papermill": {
     "duration": 2.61715,
     "end_time": "2020-11-29T12:14:57.866426",
     "exception": false,
     "start_time": "2020-11-29T12:14:55.249276",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '95% Credible Intervals: sigma')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 993.6x331.2 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = az.plot_density(\n",
    "    traces,\n",
    "    var_names=[\"alpha\", \"sigma\"],\n",
    "    shade=0.1,\n",
    "    data_labels=[\"Model 0 (neocortex)\", \"Model 1 (log_mass)\", \"Model 2 (neocortex+log_mass)\"],\n",
    ")\n",
    "\n",
    "ax[0, 0].set_xlabel(\"Density\")\n",
    "ax[0, 0].set_ylabel(\"\")\n",
    "ax[0, 0].set_title(\"95% Credible Intervals: alpha\")\n",
    "\n",
    "ax[0, 1].set_xlabel(\"Density\")\n",
    "ax[0, 1].set_ylabel(\"\")\n",
    "ax[0, 1].set_title(\"95% Credible Intervals: sigma\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.055089,
     "end_time": "2020-11-29T12:14:57.977616",
     "exception": false,
     "start_time": "2020-11-29T12:14:57.922527",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Now that we have sampled the posterior for the 3 models, we are going to use WAIC (Widely applicable information criterion) to compare the 3 models. We can do this using the `compare` function included with PyMC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "papermill": {
     "duration": 0.239084,
     "end_time": "2020-11-29T12:14:58.272998",
     "exception": false,
     "start_time": "2020-11-29T12:14:58.033914",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rank</th>\n",
       "      <th>loo</th>\n",
       "      <th>p_loo</th>\n",
       "      <th>d_loo</th>\n",
       "      <th>weight</th>\n",
       "      <th>se</th>\n",
       "      <th>dse</th>\n",
       "      <th>warning</th>\n",
       "      <th>loo_scale</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>model_2</th>\n",
       "      <td>0</td>\n",
       "      <td>8.365702</td>\n",
       "      <td>3.159733</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>2.523747</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>False</td>\n",
       "      <td>log</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_1</th>\n",
       "      <td>1</td>\n",
       "      <td>4.485976</td>\n",
       "      <td>2.017674</td>\n",
       "      <td>3.879726</td>\n",
       "      <td>5.162537e-15</td>\n",
       "      <td>2.054953</td>\n",
       "      <td>1.705681</td>\n",
       "      <td>False</td>\n",
       "      <td>log</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_0</th>\n",
       "      <td>2</td>\n",
       "      <td>3.419154</td>\n",
       "      <td>2.078996</td>\n",
       "      <td>4.946548</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>1.577262</td>\n",
       "      <td>2.453546</td>\n",
       "      <td>False</td>\n",
       "      <td>log</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         rank       loo     p_loo     d_loo        weight        se       dse  \\\n",
       "model_2     0  8.365702  3.159733  0.000000  1.000000e+00  2.523747  0.000000   \n",
       "model_1     1  4.485976  2.017674  3.879726  5.162537e-15  2.054953  1.705681   \n",
       "model_0     2  3.419154  2.078996  4.946548  0.000000e+00  1.577262  2.453546   \n",
       "\n",
       "         warning loo_scale  \n",
       "model_2    False       log  \n",
       "model_1    False       log  \n",
       "model_0    False       log  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_dict = dict(zip([\"model_0\", \"model_1\", \"model_2\"], traces))\n",
    "comp = az.compare(model_dict)\n",
    "comp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.056609,
     "end_time": "2020-11-29T12:14:58.387481",
     "exception": false,
     "start_time": "2020-11-29T12:14:58.330872",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "We can see that the best model is `model_2`, the one with both predictor variables. Notice the DataFrame is ordered from lowest to highest WAIC (_i.e_ from _better_ to _worst_ model). Check [model_comparison notebook](model_comparison.ipynb) for a more detailed discussion on model comparison.\n",
    "\n",
    "We can also see that we get a column with the relative `weight` for each model (according to the first equation at the beginning of this notebook). This weights can be _vaguely_ interpreted as the probability that each model will make the correct predictions on future data. Of course this interpretation is conditional on the models used to compute the weights, if we add or remove models the weights will change. And also is dependent on the assumptions behind WAIC (or any other Information Criterion used). So try to not overinterpret these `weights`. \n",
    "\n",
    "Now we are going to use computed `weights` to generate predictions based not on a single model, but on the weighted set of models. This is one way to perform model averaging. Using PyMC we can call the `sample_posterior_predictive_w` function as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "papermill": {
     "duration": 31.463179,
     "end_time": "2020-11-29T12:15:29.907492",
     "exception": false,
     "start_time": "2020-11-29T12:14:58.444313",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
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       "<IPython.core.display.HTML object>"
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
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       "      <progress value='4000' class='' max='4000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
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   ],
   "source": [
    "ppc_w = pm.sample_posterior_predictive_w(\n",
    "    traces=traces,\n",
    "    models=[model_0, model_1, model_2],\n",
    "    weights=comp.weight.sort_index(ascending=True),\n",
    "    progressbar=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.058454,
     "end_time": "2020-11-29T12:15:30.024455",
     "exception": false,
     "start_time": "2020-11-29T12:15:29.966001",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Notice that we are passing the weights ordered by their index. We are doing this because we pass `traces` and `models` ordered from model 0 to 2, but the computed weights are ordered from lowest to highest WAIC (or equivalently from larger to lowest weight). In summary, we must be sure that we are correctly pairing the weights and models.\n",
    "\n",
    "We are also going to compute PPCs for the lowest-WAIC model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "papermill": {
     "duration": 25.204481,
     "end_time": "2020-11-29T12:15:55.287049",
     "exception": false,
     "start_time": "2020-11-29T12:15:30.082568",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "ppc_2 = pm.sample_posterior_predictive(trace=trace_2, model=model_2, progressbar=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.058214,
     "end_time": "2020-11-29T12:15:55.404271",
     "exception": false,
     "start_time": "2020-11-29T12:15:55.346057",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "A simple way to compare both kind of predictions is to plot their mean and hpd interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "papermill": {
     "duration": 0.301319,
     "end_time": "2020-11-29T12:15:55.764128",
     "exception": false,
     "start_time": "2020-11-29T12:15:55.462809",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
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      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_w = ppc_w[\"kcal\"].mean()\n",
    "hpd_w = az.hdi(ppc_w[\"kcal\"].flatten())\n",
    "\n",
    "mean = ppc_2[\"kcal\"].mean()\n",
    "hpd = az.hdi(ppc_2[\"kcal\"].flatten())\n",
    "\n",
    "plt.plot(mean_w, 1, \"C0o\", label=\"weighted models\")\n",
    "plt.hlines(1, *hpd_w, \"C0\")\n",
    "plt.plot(mean, 0, \"C1o\", label=\"model 2\")\n",
    "plt.hlines(0, *hpd, \"C1\")\n",
    "\n",
    "plt.yticks([])\n",
    "plt.ylim(-1, 2)\n",
    "plt.xlabel(\"kcal per g\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.05969,
     "end_time": "2020-11-29T12:15:55.884685",
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     "status": "completed"
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    "tags": []
   },
   "source": [
    "As we can see the mean value is almost the same for both predictions but the uncertainty in the weighted model is larger. We have effectively propagated the uncertainty about which model we should select to the posterior predictive samples. You can now try with the other two methods for computing weights `stacking` (the default and recommended method) and `pseudo-BMA`.\n",
    "\n",
    "**Final notes:** \n",
    "\n",
    "There are other ways to average models such as, for example, explicitly building a meta-model that includes all the models we have. We then perform parameter inference while jumping between the models. One problem with this approach is that jumping between models could hamper the proper sampling of the posterior.\n",
    "\n",
    "Besides averaging discrete models we can sometimes think of continuous versions of them. 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 towards tails. We could fit both separate models and then average them using, for example, IC-derived weights. An alternative, is to build a hierarchical model to estimate the prior distribution, instead of contemplating two discrete models we will be computing a continuous model that includes these 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#411](https://github.com/pymc-devs/pymc-examples/pull/411))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
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     "end_time": "2020-11-29T12:16:06.392237",
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     "start_time": "2020-11-29T12:16:06.264642",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sat Aug 06 2022\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.10.5\n",
      "IPython version      : 8.4.0\n",
      "\n",
      "numpy     : 1.22.1\n",
      "pandas    : 1.4.3\n",
      "pymc3     : 3.11.5\n",
      "arviz     : 0.12.1\n",
      "matplotlib: 3.5.2\n",
      "\n",
      "Watermark: 2.3.1\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  }
 ],
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