notebooks/diagnostics_and_criticism/model_averaging.ipynb

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    "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"
   ]
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    "RANDOM_SEED = 8927\n",
    "np.random.seed(RANDOM_SEED)\n",
    "az.style.use(\"arviz-darkgrid\")"
   ]
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  {
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    "# 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 [in this notebook](model_comparison.ipynb) and this other [example](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 PyMC3 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, 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 PyMC3 is know as _stacking of predictive distributions_ and it has been recently [proposed](https://arxiv.org/abs/1704.02030). We want to combine several models in a metamodel in order to minimize the diverge between the meta-model and the _true_ generating model, when using a logarithmic scoring rule this is equivalently 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. PyMC3 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 PyMC3 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 and 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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       "<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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.47</td>\n",
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       "      <td>0.158913</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.56</td>\n",
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       "      <td>0.181513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.89</td>\n",
       "      <td>0.064118</td>\n",
       "      <td>-0.579032</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.92</td>\n",
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       "   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"
      ]
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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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   "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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   "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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   "source": [
    "And finally the third model using the `neocortex` and `log_mass` variables"
   ]
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   "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)"
   ]
  },
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   "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."
   ]
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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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 plots (by default 95% credible intervals) grouped by variable names together with a point estimate (by default the mean)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-29T12:14:55.317577Z",
     "iopub.status.busy": "2020-11-29T12:14:55.315811Z",
     "iopub.status.idle": "2020-11-29T12:14:57.865674Z",
     "shell.execute_reply": "2020-11-29T12:14:57.866265Z"
    },
    "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": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1656x552 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_density(traces, var_names=[\"alpha\", \"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 PyMC3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-29T12:14:58.096083Z",
     "iopub.status.busy": "2020-11-29T12:14:58.095174Z",
     "iopub.status.idle": "2020-11-29T12:14:58.271990Z",
     "shell.execute_reply": "2020-11-29T12:14:58.272778Z"
    },
    "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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/arviz/stats/stats.py:150: UserWarning: \n",
      "The scale is now log by default. Use 'scale' argument or 'stats.ic_scale' rcParam if you rely on a specific value.\n",
      "A higher log-score (or a lower deviance) indicates a model with better predictive accuracy.\n",
      "  \"\\nThe scale is now log by default. Use 'scale' argument or \"\n",
      "/opt/conda/lib/python3.7/site-packages/arviz/stats/stats.py:684: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.\n",
      "  \"Estimated shape parameter of Pareto distribution is greater than 0.7 for \"\n"
     ]
    },
    {
     "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>8.10432</td>\n",
       "      <td>3.4365</td>\n",
       "      <td>0</td>\n",
       "      <td>0.881318</td>\n",
       "      <td>1.522</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>log</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_1</th>\n",
       "      <td>1</td>\n",
       "      <td>4.30275</td>\n",
       "      <td>2.15052</td>\n",
       "      <td>3.80157</td>\n",
       "      <td>0.0495761</td>\n",
       "      <td>2.02596</td>\n",
       "      <td>1.79232</td>\n",
       "      <td>False</td>\n",
       "      <td>log</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_0</th>\n",
       "      <td>2</td>\n",
       "      <td>3.49421</td>\n",
       "      <td>2.01803</td>\n",
       "      <td>4.61011</td>\n",
       "      <td>0.0691055</td>\n",
       "      <td>2.61444</td>\n",
       "      <td>2.5605</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 warning  \\\n",
       "model_2    0  8.10432   3.4365        0   0.881318    1.522        0    True   \n",
       "model_1    1  4.30275  2.15052  3.80157  0.0495761  2.02596  1.79232   False   \n",
       "model_0    2  3.49421  2.01803  4.61011  0.0691055  2.61444   2.5605   False   \n",
       "\n",
       "        loo_scale  \n",
       "model_2       log  \n",
       "model_1       log  \n",
       "model_0       log  "
      ]
     },
     "execution_count": 10,
     "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 [this notebook](model_comparison.ipynb) for a more detailed discussing 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 do not overinterpret these `weights`. \n",
    "\n",
    "Now we are going to use copmuted `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 PyMC3 we can call the `sample_posterior_predictive_w` function as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-29T12:14:58.524574Z",
     "iopub.status.busy": "2020-11-29T12:14:58.514166Z",
     "iopub.status.idle": "2020-11-29T12:15:29.907362Z",
     "shell.execute_reply": "2020-11-29T12:15:29.906569Z"
    },
    "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",
       "    <div>\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",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='1000' class='' max='1000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [1000/1000 00:25<00:00]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ppc_w = pm.sample_posterior_predictive_w(\n",
    "    traces,\n",
    "    1000,\n",
    "    [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": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-29T12:15:32.303974Z",
     "iopub.status.busy": "2020-11-29T12:15:30.150544Z",
     "iopub.status.idle": "2020-11-29T12:15:55.286893Z",
     "shell.execute_reply": "2020-11-29T12:15:55.286194Z"
    },
    "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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/pymc3/sampling.py:1692: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample\n",
      "  \"samples parameter is smaller than nchains times ndraws, some draws \"\n"
     ]
    }
   ],
   "source": [
    "ppc_2 = pm.sample_posterior_predictive(trace_2, 1000, 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": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-29T12:15:55.533847Z",
     "iopub.status.busy": "2020-11-29T12:15:55.531792Z",
     "iopub.status.idle": "2020-11-29T12:15:55.764004Z",
     "shell.execute_reply": "2020-11-29T12:15:55.763252Z"
    },
    "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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/arviz/stats/stats.py:487: FutureWarning: hdi currently interprets 2d data as (draw, shape) but this will change in a future release to (chain, draw) for coherence with other functions\n",
      "  FutureWarning,\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_w = ppc_w[\"kcal\"].mean()\n",
    "hpd_w = az.hdi(ppc_w[\"kcal\"]).mean(0)\n",
    "\n",
    "mean = ppc_2[\"kcal\"].mean()\n",
    "hpd = az.hdi(ppc_2[\"kcal\"]).mean(0)\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",
     "exception": false,
     "start_time": "2020-11-29T12:15:55.824995",
     "status": "completed"
    },
    "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 it's degree of bias, a number between 0 and 1 being 0.5 equal chance of head and tails. We could think of two separated 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": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-29T12:16:06.337708Z",
     "iopub.status.busy": "2020-11-29T12:16:06.336912Z",
     "iopub.status.idle": "2020-11-29T12:16:06.392050Z",
     "shell.execute_reply": "2020-11-29T12:16:06.391147Z"
    },
    "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: Sun Nov 29 2020\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.7.6\n",
      "IPython version      : 7.13.0\n",
      "\n",
      "pymc3     : 3.9.3\n",
      "pandas    : 1.1.4\n",
      "matplotlib: 3.2.1\n",
      "numpy     : 1.18.5\n",
      "arviz     : 0.10.0\n",
      "\n",
      "Watermark: 2.1.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  }
 ],
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