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Bayesian Parametric Survival Analysis with PyMC3
{
"cells": [
{
"cell_type": "markdown",
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"source": [
"---\n",
"title: Bayesian Parametric Survival Analysis with PyMC3\n",
"tags: Bayesian Statistics, PyMC3\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Survival analysis](https://en.wikipedia.org/wiki/Survival_analysis) studies the distribution of the time between when a subject comes under observation and when that subject experiences an event of interest. One of the fundamental challenges of survival analysis (which also makes is mathematically interesting) is that, in general, not every subject will experience the event of interest before we conduct our analysis. In more concrete terms, if we are studying the time between cancer treatment and death (as we will in this post), we will often want to analyze our data before every subject has died. This phenomenon is called <a href=\"https://en.wikipedia.org/wiki/Censoring_(statistics)\">censoring</a> and is fundamental to survival analysis.\n",
"\n",
"I have previously [written](http://austinrochford.com/posts/2015-10-05-bayes-survival.html) about Bayesian survival analysis using the [semiparametric](https://en.wikipedia.org/wiki/Semiparametric_model) [Cox proportional hazards model](https://en.wikipedia.org/wiki/Proportional_hazards_model#The_Cox_model). Implementing that semiparametric model in PyMC3 involved some fairly complex `numpy` code and nonobvious probability theory equivalences. This post illustrates a parametric approach to Bayesian survival analysis in PyMC3. Parametric models of survival are simpler to both implement and understand than semiparametric models; statistically, they are also more [powerful](https://en.wikipedia.org/wiki/Statistical_power) than non- or semiparametric methods _when they are correctly specified_. This post will not further cover the differences between parametric and nonparametric models or the various methods for chosing between them.\n",
"\n",
"As in the previous post, we will analyze [mastectomy data](https://vincentarelbundock.github.io/Rdatasets/doc/HSAUR/mastectomy.html) from `R`'s [`HSAUR`](https://cran.r-project.org/web/packages/HSAUR/index.html) package. First, we load the data."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from matplotlib import pyplot as plt\n",
"from matplotlib.ticker import StrMethodFormatter\n",
"import numpy as np\n",
"import pymc3 as pm\n",
"import scipy as sp\n",
"import seaborn as sns\n",
"from statsmodels import datasets\n",
"from theano import shared, tensor as tt"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sns.set()\n",
"blue, green, red, purple, gold, teal = sns.color_palette()\n",
"\n",
"pct_formatter = StrMethodFormatter('{x:.1%}')"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df = (datasets.get_rdataset('mastectomy', 'HSAUR', cache=True)\n",
" .data\n",
" .assign(metastized=lambda df: 1. * (df.metastized == \"yes\"),\n",
" event=lambda df: 1. * df.event))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>time</th>\n",
" <th>event</th>\n",
" <th>metastized</th>\n",
" </tr>\n",
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"text/plain": [
" time event metastized\n",
"0 23 1.0 0.0\n",
"1 47 1.0 0.0\n",
"2 69 1.0 0.0\n",
"3 70 0.0 0.0\n",
"4 100 0.0 0.0"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The column `time` represents the survival time for a breast cancer patient after a mastectomy, measured in months. The column `event` indicates whether or not the observation is censored. If `event` is one, the patient's death was observed during the study; if `event` is zero, the patient lived past the end of the study and their survival time is censored. The column `metastized` indicates whether the cancer had [metastized](https://en.wikipedia.org/wiki/Metastasis) prior to the mastectomy. In this post, we will use Bayesian parametric survival regression to quantify the difference in survival times for patients whose cancer had and had not metastized."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Accelerated failure time models\n",
"\n",
"[Accenterated failure time models](https://en.wikipedia.org/wiki/Accelerated_failure_time_model) are the most common type of parametric survival regression models. The fundamental quantity of survival analysis is the [survival function](https://en.wikipedia.org/wiki/Survival_function); if $T$ is the random variable representing the time to the event in question, the survival function is $S(t) = P(T > t)$. Accelerated failure time models incorporate covariates $\\mathbf{x}$ into the survival function as\n",
"\n",
"$$S(t\\ |\\ \\beta, \\mathbf{x}) = S_0\\left(\\exp\\left(\\beta^{\\top} \\mathbf{x}\\right) \\cdot t\\right),$$\n",
"\n",
"where $S_0(t)$ is a fixed baseline survival function. These models are called \"accelerated failure time\" because, when $\\beta^{\\top} \\mathbf{x} > 0$, $\\exp\\left(\\beta^{\\top} \\mathbf{x}\\right) \\cdot t > t$, so the effect of the covariates is to accelerate the _effective_ passage of time for the individual in question. The following plot illustrates this phenomenon using an exponential survival function."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"S0 = sp.stats.expon.sf"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
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W9wqK84shAbpGBbbpFAWAwTuc0B63oDpt5KZtwGEra5PrCiGEEK0lSUMN+qqk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x96TQ2W+oZiF68sXNnQSpKEt8rOmk11LFlRRTJp0NMxxsVzQ7Qe6SISSuCusGK1iXtMsiUOZoUh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\n+f87VyKK4pue6wAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f83ee43b278>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"t = np.linspace(0, 10, 100)\n",
"\n",
"ax.plot(t, S0(5 * t),\n",
" label=r\"$\\beta^{\\top} \\mathbf{x} = \\log\\ 5$\");\n",
"ax.plot(t, S0(2 * t),\n",
" label=r\"$\\beta^{\\top} \\mathbf{x} = \\log\\ 2$\");\n",
"ax.plot(t, S0(t),\n",
" label=r\"$\\beta^{\\top} \\mathbf{x} = 0$ ($S_0$)\");\n",
"ax.plot(t, S0(0.5 * t),\n",
" label=r\"$\\beta^{\\top} \\mathbf{x} = -\\log\\ 2$\");\n",
"ax.plot(t, S0(0.2 * t),\n",
" label=r\"$\\beta^{\\top} \\mathbf{x} = -\\log\\ 5$\");\n",
"\n",
"ax.set_xlim(0, 10);\n",
"ax.set_xlabel(r\"$t$\");\n",
"\n",
"ax.yaxis.set_major_formatter(pct_formatter);\n",
"ax.set_ylim(-0.025, 1);\n",
"ax.set_ylabel(r\"Survival probability, $S(t\\ |\\ \\beta, \\mathbf{x})$\");\n",
"\n",
"ax.legend(loc=1);\n",
"ax.set_title(\"Accelerated failure times\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Accelerated failure time models are equivalent to log-linear models for $T$,\n",
"\n",
"$$Y = \\log T = \\beta^{\\top} \\mathbf{x} + \\varepsilon.$$\n",
"\n",
"A choice of distribution for the error term $\\varepsilon$ determines baseline survival function, $S_0$, of the accelerated failure time model. The following table shows the correspondence between the distribution of $\\varepsilon$ and $S_0$ for several common accelerated failure time models.\n",
"\n",
"<center>\n",
"<table border=\"1\">\n",
" <tr>\n",
" <th>Log-linear error distribution ($\\varepsilon$)</th>\n",
" <th>Baseline survival function ($S_0$)</th>\n",
" </tr>\n",
" <tr>\n",
" <td>[Normal](https://en.wikipedia.org/wiki/Normal_distribution)</td>\n",
" <td>[Log-normal](https://en.wikipedia.org/wiki/Log-normal_distribution)</td>\n",
" </tr>\n",
" <tr>\n",
" <td>Extreme value ([Gumbel](https://en.wikipedia.org/wiki/Gumbel_distribution))</td>\n",
" <td>[Weibull](https://en.wikipedia.org/wiki/Weibull_distribution)</td>\n",
" </tr>\n",
" <tr>\n",
" <td>[Logistic](https://en.wikipedia.org/wiki/Logistic_distribution)</td>\n",
" <td>[Log-logistic](https://en.wikipedia.org/wiki/Log-logistic_distribution)</td>\n",
" </tr>\n",
"</table>\n",
"</center>\n",
"\n",
"Accelerated failure time models are conventionally named after their baseline survival function, $S_0$. The rest of this post will show how to implement Weibull and log-logistic survival regression models in PyMC3 using the mastectomy data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Weibull survival regression\n",
"\n",
"In this example, the covariates are $\\mathbf{x}_i = \\left(1\\ x^{\\textrm{met}}_i\\right)^{\\top}$, where\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"x^{\\textrm{met}}_i\n",
" & = \\begin{cases}\n",
" 0 & \\textrm{if the } i\\textrm{-th patient's cancer had not metastized} \\\\\n",
" 1 & \\textrm{if the } i\\textrm{-th patient's cancer had metastized}\n",
" \\end{cases}.\n",
"\\end{align*}\n",
"$$\n",
"\n",
"We construct the matrix of covariates $\\mathbf{X}$."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"n_patient, _ = df.shape\n",
"\n",
"X = np.empty((n_patient, 2))\n",
"X[:, 0] = 1.\n",
"X[:, 1] = df.metastized"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We place independent, vague normal prior distributions on the regression coefficients,\n",
"\n",
"$$\\beta \\sim N(0, 5^2 I_2).$$"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"VAGUE_PRIOR_SD = 5."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"with pm.Model() as weibull_model:\n",
" β = pm.Normal('β', 0., VAGUE_PRIOR_SD, shape=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The covariates, $\\mathbf{x}$, affect value of $Y = \\log T$ through $\\eta = \\beta^{\\top} \\mathbf{x}$."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"X_ = shared(X)\n",
"\n",
"with weibull_model:\n",
" η = β.dot(X_.T)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For Weibull regression, we use\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" \\varepsilon\n",
" & \\sim \\textrm{Gumbel}(0, s) \\\\\n",
" s\n",
" & \\sim \\textrm{HalfNormal(5)}.\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"with weibull_model:\n",
" s = pm.HalfNormal('s', 5.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are nearly ready to specify the likelihood of the observations given these priors. Before doing so, we transform the observed times to the log scale and standardize them."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"y = np.log(df.time.values)\n",
"y_std = (y - y.mean()) / y.std()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The likelihood of the data is specified in two parts, one for uncensored samples, and one for censored samples. Since $Y = \\eta + \\varepsilon$, and $\\varepsilon \\sim \\textrm{Gumbel}(0, s)$, $Y \\sim \\textrm{Gumbel}(\\eta, s)$. For the uncensored survival times, the likelihood is implemented as"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cens = df.event.values == 0."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"cens_ = shared(cens)\n",
"\n",
"with weibull_model:\n",
" y_obs = pm.Gumbel(\n",
" 'y_obs', η[~cens_], s,\n",
" observed=y_std[~cens]\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For censored observations, we only know that their true survival time exceeded the total time that they were under observation. This probability is given by the survival function of the Gumbel distribution,\n",
"\n",
"$$P(Y \\geq y) = 1 - \\exp\\left(-\\exp\\left(-\\frac{y - \\mu}{s}\\right)\\right).$$\n",
"\n",
"This survival function is implemented below."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def gumbel_sf(y, μ, σ):\n",
" return 1. - tt.exp(-tt.exp(-(y - μ) / σ))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now specify the likelihood for the censored observations."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"with weibull_model:\n",
" y_cens = pm.Bernoulli(\n",
" 'y_cens', gumbel_sf(y_std[cens], η[cens_], s),\n",
" observed=np.ones(cens.sum())\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now sample from the model."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"SEED = 845199 # from random.org, for reproducibility\n",
"\n",
"SAMPLE_KWARGS = {\n",
" 'njobs': 3,\n",
" 'tune': 1000,\n",
" 'random_seed': [\n",
" SEED,\n",
" SEED + 1,\n",
" SEED + 2\n",
" ]\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"100%|██████████| 1500/1500 [00:04<00:00, 322.90it/s]\n",
"INFO (theano.gof.compilelock): Waiting for existing lock by process '21392' (I am process '21393')\n",
"INFO (theano.gof.compilelock): To manually release the lock, delete /home/jovyan/.theano/compiledir_Linux-4.9-moby-x86_64-with-debian-stretch-sid-x86_64-3.6.2-64/lock_dir\n"
]
}
],
"source": [
"with weibull_model:\n",
" weibull_trace = pm.sample(**SAMPLE_KWARGS)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The energy plot and Bayesian fraction of missing information give no cause for concern about poor mixing in NUTS."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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FbWkafgaxKjYcijHb7AWD2Y/thq1jVhBLxxmNjxlyPSFEfiQwRVHLjTDLDBph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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f83df73c588>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.energyplot(weibull_trace);"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0189285246960067"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.bfmi(weibull_trace)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Gelman-Rubin statistics also indicate convergence."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0077500079163573"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(weibull_trace).values())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below we plot posterior distributions of the parameters."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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07f2WZRVD62jz6qU6dfyA0tPTFXnykO7u9rRN65npekqS4mMzJq1ITkpQxLH9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\nIiIyABZXREREREREBvAf3Pv/q956rXoAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f83d9138cf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.plot_posterior(weibull_trace, lw=0, alpha=0.5);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These are somewhat interesting (espescially the fact that the posterior of $\\beta_1$ is fairly well-separated from zero), but the posterior predictive survival curves will be much more interpretable.\n",
"\n",
"The advantage of using [`theano.shared`](http://deeplearning.net/software/theano_versions/dev/library/compile/shared.html) variables is that we can now change their values to perform posterior predictive sampling. For posterior prediction, we set $X$ to have two rows, one for a subject whose cancer had not metastized and one for a subject whose cancer had metastized. Since we want to predict actual survival times, none of the posterior predictive rows are censored."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"X_pp = np.empty((2, 2))\n",
"X_pp[:, 0] = 1.\n",
"X_pp[:, 1] = [0, 1]\n",
"X_.set_value(X_pp)\n",
"\n",
"cens_pp = np.repeat(False, 2)\n",
"cens_.set_value(cens_pp)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 1500/1500 [00:00<00:00, 2789.50it/s]\n"
]
}
],
"source": [
"with weibull_model:\n",
" pp_weibull_trace = pm.sample_ppc(\n",
" weibull_trace, samples=1500, vars=[y_obs]\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The posterior predictive survival times show that, on average, patients whose cancer had not metastized survived longer than those whose cancer had metastized."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"t_plot = np.linspace(0, 230, 100)\n",
"\n",
"weibull_pp_surv = (np.greater_equal\n",
" .outer(np.exp(y.mean() + y.std() * pp_weibull_trace['y_obs']),\n",
" t_plot))\n",
"weibull_pp_surv_mean = weibull_pp_surv.mean(axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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BA3vJzMxg+vQpmJtb4OvbBhsbW9q2bc/8+XNYuvTfAKSlpbJpUyitW/uxd+8u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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f83dfd7f160>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"\n",
"ax.plot(t_plot, weibull_pp_surv_mean[0],\n",
" c=blue, label=\"Not metastized\");\n",
"ax.plot(t_plot, weibull_pp_surv_mean[1],\n",
" c=red, label=\"Metastized\");\n",
"\n",
"ax.set_xlim(0, 230);\n",
"ax.set_xlabel(\"Weeks since mastectomy\");\n",
"\n",
"ax.set_ylim(top=1);\n",
"ax.yaxis.set_major_formatter(pct_formatter);\n",
"ax.set_ylabel(\"Survival probability\");\n",
"\n",
"ax.legend(loc=1);\n",
"ax.set_title(\"Weibull survival regression model\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Log-logistic survival regression\n",
"\n",
"Other accelerated failure time models can be specificed in a modular way by changing the prior distribution on $\\varepsilon$. A log-logistic model corresponds to a [logistic](https://en.wikipedia.org/wiki/Logistic_distribution) prior on $\\varepsilon$. Most of the model specification is the same as for the Weibull model above."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"X_.set_value(X)\n",
"cens_.set_value(cens)\n",
"\n",
"with pm.Model() as log_logistic_model:\n",
" β = pm.Normal('β', 0., VAGUE_PRIOR_SD, shape=2)\n",
" η = β.dot(X_.T)\n",
" \n",
" s = pm.HalfNormal('s', 5.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We use the prior $\\varepsilon \\sim \\textrm{Logistic}(0, s)$. The survival function of the logistic distribution is\n",
"\n",
"$$P(Y \\geq y) = 1 - \\frac{1}{1 + \\exp\\left(-\\left(\\frac{y - \\mu}{s}\\right)\\right)},$$\n",
"\n",
"so we get the likelihood "
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def logistic_sf(y, μ, s):\n",
" return 1. - pm.math.sigmoid((y - μ) / s)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"with log_logistic_model:\n",
" y_obs = pm.Logistic(\n",
" 'y_obs', η[~cens_], s,\n",
" observed=y_std[~cens]\n",
" )\n",
" y_cens = pm.Bernoulli(\n",
" 'y_cens', logistic_sf(y_std[cens], η[cens_], s),\n",
" observed=np.ones(cens.sum())\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now sample from the log-logistic model."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"100%|██████████| 1500/1500 [00:05<00:00, 291.48it/s]\n"
]
}
],
"source": [
"with log_logistic_model:\n",
" log_logistic_trace = pm.sample(**SAMPLE_KWARGS)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All of the sampling diagnostics look good for this model."
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
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RI4cmzB7vuOM7fO5zX2LDhlP45Cf/dcLtJWNjozz33DM88MCvSKVS/P73v+Fv/ubtU359\nx/e7VRSFb37zezz77NP85Cd3cfXV/3bS/yfV1TUl/VoKJXuYomKNBOPc88c2LCaVvzp3RS4sAexW\nI2993SrsFiMPPnWErsGpm2wcGT1KJBVlpWt5Xsu3k1l1rKfsbt++WX28qExdXZ0T9i9vvfWW3Puy\n12fV1zcSDoc4cGAfPT3dXHPNR7jmmo8QiYQZGMg0Is9eX9XZeZTTTjsDgPPPvyB3c8ab3vQWnnji\nUXw+Lw6Hk9raqX/pamlZTlVVNTB+DdjVV1814Rqwya6w2r79Uq699uP8+tf/x5vedPLtJidqbd3P\nmWeeA2R64vb0dAPgcDhYv34DkLk6LBSaeEVWf39/rp/siY3a3e4qVqxYxWc+cx2PP/5H3vzmt077\n9R3vrLMyY9mypbCrvor5WgolM0xRsX71TDvJlMZFZzRT5TSf9H6H1cRFr2nm4Re6+eFv9/P5923D\naDj5d8BXvZmQW1VEI/UVrmXQn3nWpSsvmvkDREHesf6KomaDszXdHuaJ10QZjSbOP/8Crr/+sxNe\n9/LLL+X25nRdRz22R378dVWXXfZX3Hjj9VitNt74xr+adkzZq7imuwZssiusPvnJG+js7OCJJx7l\nmms+wp133j3t51GUiVdkZa/tOv7Zxz8/6/glzckaxX3969+ira2VRx99mIcf/h233z7xhpXxq8ZO\nGtGEsZ34y+10133N9msplMwwRUXq9YZ4enc/NS4Lp6w4+bfRrJWNLjatrKbHG+bJV06ultN1nVe9\n+zCrJpocDbMej81oo8FWR/toB8FEaS+lFQvDxo2b2bnzZWKxGLqu841vfI14PDbhNZnrvvYD8OKL\nz+eupKqpqcHtdvPII7/nDW+4+KRnn3h9FRR2DVgoFOJ//ucHrFq1mve//8O4XFVEIuNV3ZNdt7Vp\n0xZeeSVz1Grv3j2sWbMur+9DXV09XV0d6LrOK69MPG7V39/Hz39+Hxs3buLqq69ldHR0yq/vRLt3\nvwLAvn17WLVqDXa7g5GRYXRdx+/30dfXU/KvpVAywxQV6Q8vdKHrsG1zw4TLayezbXMD7X1j/OrZ\no7xuaxN26/hvsD2hPkbiAdZWrUJVivv9cKVrOUNRH3t9Bzh/2bainiUqQ3ZJ9ngf//i/TvrapqYm\nrrzy3fzLv3wYVVW56KLtWCzWCa953etez+9+92s+9rEPcuaZZ+N2j7df3L79Up599mnsdsdJz57s\n+qpCrgFzOp0EAiN8+MPvxWazs3Xr6RM+99atp3HzzV+kurom97Yrr3w3X/7yTfzrv34UTdO47rpP\nT/etyrnqqo9z442fpqmpmYaGxgnvq6urZ+/eV3n88T9iMpl461v/ZsqvbzLXX/9vDA0N8rnP/Sdu\nt5tzzjk39/Vn9x5L+bUUSpqvi4oTiia57jvP4LCauPKSmStgAXYd8vHigSEuf+1K/m77+tzb/3D0\ncX579BG2t1zAmqqpC4PyMRoP8ssjv+W0ui189PT3FfUssTiNjY2yc+cOtm+/FK93iE984mPce2+m\nAOfmm7/AW97y17m9OlG55HovsWA8u6efVFpn8+qavIt0tq6tZe/RYZ54uZfLz1uF05aZZbaOHATI\nXRBdjCqLi2qLm9bhQyTTSbnBRJzEbnfwxBOPce+996DrGtdccx3xeJxrrvkImzdvkbBc4CQwRUXR\ndZ0nX+nFoCqcsmLq20ROZDSonL7Ow/P7BnlsRzdve/1aYqkY7aOd1FlrsRotJRlfi6OZfcNtHBnt\nYFPthpI8UyweRqOR//zPkw/j33nnj+d/MKLkpOhHVJSj/UEGR6KsaXZjNRf2+9zmVTVYzQYe29FD\nNJ7iUKAdTddY5mwq2fhanM0AHBg+WLJnCiEWBglMUVFeah0EYF2Lu+CPNRlVtq6pJRJP8dzeAVqH\nDwGZWWGpNNrrMSiqBKYQS5AEpqgYuq6zo9WL2aiyvP7kSsJ8bF5dg6oqPP5yDweGD2JUjSXtzGNU\njTTaG+gN9TMal6I4IZYSCUxRMY72B/GPxVjV5MIwSQOCfNgsRtYuczMY8jMY8dJkb8Cg5N9sPR/L\nHJkl3laZZQqxpEhgioqxo20IgLXLCl+OPd7WNTWo7mEAlpWgOvZELcf2RGVZVoilRQJTVIw9R/wY\nDQots1yOzaqvtmH3ZDqMuKgrxdAmqLFUYzNaaR05VHSrLSHEwiGBKSrC8FiMXl+YZo9j0n6whVAU\nBYM7gJ4y0nPUVqIRTnx+s72RYCLEQGSo5M8XQlQmCUxREfYezSyhrmgobnYJEEmHiCtj6OEaDhxK\nkkqVfhaYbYTQNnK45M8WQlQmCUxREfa2+wFY3uAs+llDiUwTdrehhnhc53BHouhnnigbmIdGjpT8\n2UKIyiSBKcourWns6xjGZTdR5Tj5Gq9CDSUzgbmsKnNZ9IGDpQ9Mp8mB0+Tg4MgRNF0r+fOFEJVH\nAlOUXcdAkGg8TUu9Y9YXPB9vKNGDikqdo5raWugfSjEcmP5qoUIpikKzo4FIKkpvqL+kzxZCVCYJ\nTFF2B7szt8gvqyt+/zKuxRhJ+XAZqlEVleXLMwF84GC86GefqMmeWZY9KMuyQiwJEpii7A52ZQKz\nudZe9LN8yT4A3MbMcmx9PZhM0HYkQTpd2uKf7D7mQSn8EWJJkMAUZaVpOgd7ArjtZhy24q/L8iYy\ny6MuQzUAqqqwbBnE4jrtncmin388h8mOy+zkSKBD9jGFWAIkMEVZ9XhDRONpmuuKn10C+JIDwHhg\nArS0ZJZl9x8q/bJso62eaDpGf3iw5M8WQlQWCUxRVm0lXI7VdR1fsh+b6sCkjlfbOhwKNTXQ259i\ndKy0xT+N9noAjgQ6SvpcIUTlkcAUZXWwJxOYTZ7iA3MsPUxST+A8bnaZlZtllrj4JxeYo0dL+lwh\nROWRwBRlo+s6h3tHsVuMuOyl2790TxKYDQ1gMkLr4QRprXTFP26zC6vBIjNMIZYACUxRNiPBOKOh\nBA01tpKcv/QljxX8GE8OTINBoakZojGdju7SFf8oikKDvZ6ReIDh2EjJniuEqDwSmKJsjvSNAdBQ\nU5oG6b7kACoqdtU16fvn6kxmoz1zI0q7zDKFWNQkMEXZHOnNXMHVWFt8YCa1BIGUD6ehClWZ/Mfa\n6VSoqoKu3hRjwdIV/zTasvuYHSV7phCi8khgirI50jeKokBdVfGB6U8OoqNPOE4ymWzxT+vh0vWX\nrbXVYFAMso8pxCIngSnKIpnS6BwI4nFbMRmL/zGcbv/yeE1NYDTCgUNxtBIV/xgUA/U2D33hfiLJ\naEmeKYSoPBKYoix6vCFSab2E+5cTO/xMxWBQaGqCcESnq7d0xT+N9np04OhYZ8meKYSoLBKYoiw6\nBoIA1FcXH5i6ruNN9mNWLFjUmZ83fiazdMuy0sBAiMVPAlOUReexwKyrshb9rIgWJKZFZpxdZrnd\nCi4XdPYkCYVL0wO23laHgiINDIRYxCQwRVl0DgYxqAo1LkvRz8o1XDfW5P0xy5cr6Dq0Hi7NEROz\nwUSNtYrOsW6SWqokzxRCVBYJTDHvUmmNXm+IWrcFVS1hw4I8Z5iQKf4xqHDgUAJdL03xT6OtnqSW\nojvYW5LnCSEqiwSmmHd9vjCptF6S4ySQvaFEwWlw5/0xRqNCYxMEQxrdfaWZETbk9jFlWVaIxUgC\nU8y7Uu5fpvU0/uQgDtWFQTEW9LGl7vwz3oi9oyTPE0JUFglMMe86Bo8FZnXxgRlI+dBIz3j+cjJu\nNzid0N6VJBItvvjHYbLjMNnpGO0q2TKvEKJySGCKedc1GERVKEnBjz+ZubjZaagq+GMVRaGlJVP8\n01aizj/1tjqCyRD+2HBJnieEqBwSmGJeabpOz1CIKqcFo6H4Hz9/cgAA1ywCE6C5GVQV9h+Kl2RW\n2GDzAHB0tKvoZwkhKosEpphXvkCUeFLD4y5+ORYyM8zMDSXOWX28yaTQ2AijYxp9A8UX/9TbMjeX\nSMcfIRYfCUwxr7qHQgDUuotfjk3pSQIpPw6DG2WKG0rykev8c6j4ZVmPtQZVUWWGKcQiJIEp5lU2\nMD0lqJAdSfrQ0Wa1f3m86mpwOKC9I0EsVlzxj0E14LHW0BPqI5EuXa9aIUT5SWCKeZULzBLMMIeL\nKPg5nqIoLFumkNag7Ujxs8x6Wx2artEV7Cn6WUKIyiGBKeZVjzeE1WzAZinszORk/KnSBCbAsmWg\nKLD/YPHFPw3ZfcxR2ccUYjGRwBTzJhpP4Q3EqHVbUJTiW+L5kwOoGGZd8HM8s1mhoQFGRjUGvOmi\nnlVvz1TKdozJPqYQi4kEppg3vd4wQEkqZJNaktHUME6DuyThC+PFP8V2/nEY7diNNtpHO6WBgRCL\niASmmDc9vsz+ZU0J9i9HUkPo6CVZjs2qrQWbDQ4dTRBPzD7oFEWh3uZhLBFkJB4o2fiEEOUlgSnm\nTd+xGWatq/gZZjEdfqaS7fyTTsOh9uJmmfWyjynEoiOBKeZNry8TmNUuc9HPmovAhPHin30Hi7v2\nq8GebWAg+5hCLBYSmGLe9PnCOG0mzEZD0c/yJwcxYMSmOkowsnEWi0J9PfiH03j9sy/+8VhrUFCk\ngYEQi4gEppgXoWiS0XCiJA3Xk1qCsXRpC36Ol+v8U0Txj1E14rHW0B3sJamV5r5NIUR5SWCKedF3\nbDm2FIE5nBoCSr8cm+XxgNUKh9oTJJOzX5att9eR1tN0B3tLODohRLlIYIp5UcrAnKv9y6xs559k\nKlMxO1v1x24u6ZDCHyEWBQlMMS96SxqYmSu95iowAVpaMn8eODT7Zdlcxx8p/BFiUZDAFPOi1DNM\nI0asqr3oZ03FalWorYVBb5rR4OyKf5wmBxaDhc4x6SkrxGIggSnmRZ8/UyFrMhb3I5fQYgTTAZzG\nqjkp+Dlec3Pm+YfaZ7csqygKddZa/LFhgolQKYcmhCgDCUwx56LxFKOhBNXOUpy/nNuCn+M1NICq\nwsH22Z/JzO5jys0lQix8Ephizg0MRwCoclbOlV75MBoV6uogMKrhG57dsmydrRaAzrHuUg5NCFEG\nEphizmUDsyQzzBJe6ZWP7LLswVkuy0pgCrF4SGCKOTeYm2GWYkl2AKNiwqLYin5WPurqwGjM7GNq\nWuHLsjajDYfJTudYj9xcIsQCJ4Ep5tz4DLO4Jdm4FiWUHsNpmPuCnyxVVWhshEhUp29wdh176qwe\ngskQwzG5uUSIhUwCU8y5fn8Eo0HBYTUW9ZxswwLXPC3HZjU1FbcsW59dlg3KsqwQC5kEpphTmq4z\nOByhymEuelY41x1+plJTAxYLtHcmSacLX1aty1bKynlMIRY0CUwxpwLBOImUVpIK2XIFpqIoNDRA\nIqHTO1D4sqzHmplhdkjHHyEWNAlMMaf6S1ghO5wcxKRYMCvFX0BdqMbGzOz4SEfhy7Jmg4kqs5uu\nYC+arpV6aEKIeSKBKebUYInOYEbTEcJacM6u9JpJdTWYzXC0Kzmratk6Wy3xdJyhiHcORieEmA8S\nmGJODfhLM8McnufzlyfKLsvG4jr9s6iWzd1cIucxhViwJDDFnMp1+XEUF5jlqpA9XkPDsWXZzmTB\nH5st/JFG7EIsXBKYYk4NDEewWYyYTYainlOugp/j1dSAyQTtnYX3lq21VKMqqnT8EWIBk8AUcyaR\nTOMfjZWo6foAZsWKWZ3/gp8sVVWor880MRgYKqy3rEE1UGuppifUR0qbXQMEIUR5SWCKOTMUiKJT\nfEu8SDpEVAuXdXaZlauW7Sy8WrbOVktaT9Mb6i/1sIQQ80ACU8yZ8YKf4ipkK2E5Nqu2NtNbdjbL\nsuP7mLIsK8RCJIEp5kypbikZroCCnyxVzVz5FQrr+Au88qvOKoU/QixkEphizpSsQjZ3pMRd9JhK\nob4+syx7tLuwatkqiwuTapSOP0IsUBKYYs4MDEdQFQWXffaBqes6/uQgFsWKSS2+vV4peDygKNBR\nYGCqiorHWstgxEssFZuj0Qkh5ooEppgzA8MR3A4Tqjr7zjwRLUhMi1TE/mWWyaRQUwNef5pQuLBW\nd3W2WnR0uoO9czQ6IcRckcAUcyIUTRKJpXCXqGGB01BdimGVTHZZtrOnsFlmnXT8EWLBksAUc8Ib\niAIUHZikEaHrAAAgAElEQVS+5AAALmPlzDAB6uszfx7tLux4SZ01ezemFP4IsdBIYIo5MTRSmsCs\npCMlx7PZFJxO6O1LkUzmf7zEaXJgNVjolMIfIRYcCUwxJ4ayM0y7adbPyBT8DGBV7RiV2T9nrtTX\nQ1qD7r78l2UVRaHO5mE4FiCYCM3h6IQQpSaBKeaEtwQzzGA6QFJP4Kqw/cus7D5modWydbZjy7Ky\njynEgiKBKebEUCCKAkUdKfEf27+stOXYLLc7c0dmR3dhd2SONzCQwBRiIZHAFHPCOxLFYTNhKOJI\nia9C9y+zFCXT9ScW1/EW0PUnO8PsksIfIRYUCUxRcolkmpFQHLejuH3H4WRldfiZTF1d5heCrgKO\nl9iMVhwmO51jPQX3oxVClI8Epii5Uhwp0XQNf3IQu+rCoBhLNbSSq63NdP3p6i1wH9PqIZgMMRIP\nzNHIhBClJoEpSm68Qnb2gTma8pMmVREN16djMilUVcGQL00snn/Xn/HCH1mWFWKhkMAUJVeKCtlK\nPX85GY9HQdehuy//i6GlUlaIhUcCU5RcboZZxB7mQgrMurrMn90FLMtKxx8hFh4JTFFypViS9ScH\nUFBxGFylGtaccbnAZMrsY+ZbxGM2mKkyu+ga60bTC2vgLoQoDwlMUXLekShWswGzyTCrj0/rKUZS\nXhwGF6oyu2fMp+zxkkhUxz9SyPESD7F0HG/UP4ejE0KUigSmKClN0/GNxoravwykfGhoC2I5Nsvj\nyR4vyX8f02OVfUwhFhIJTFFSw2Mx0ppeVA/ZbMOCSq+QPZ4n07ynoOMluQYGUikrxIIggSlKaqgE\nZzDHW+JVZg/ZyZjNCm439A+lSCTy28f0WGtQUOgMygxTiIVAAlOUVGkKfgZRMWBXHaUa1ryoqwNd\nh57+/GaZRtVIjaWK7mAfaS3/vU8hRHlIYIqSKvYMZlJLMpry4zS4UZSF9eOZ28csaFnWQ1JL0h8e\nnKthCSFKZGH9jSQqXrFnMEdSQ+joC6rgJ8vtBqMRunpTeR8vkUbsQiwcEpiipLwjUYwGBZtldv1f\nF1LDghOpqoLHA6GwxshofmcrpVJWiIVDAlOUjK7rDAWiuO1mFGV213r5jhX8VOql0TPJ3V6S57Js\nrbUag6JKxx8hFgAJTFEywWiSWCKNq8gKWaNiwqraSziy+VPo8RJVUam11tAb6ieZLuzGEyHE/JLA\nFCXjH40B4JrlGcyEFiOYDhwr+Jn9xdPlZLEoOJ3QP5gilcpzH9Nai6Zr9IT653h0QohiSGCKksnd\ngznLwPQnh4CFuX95PI8H0mnoG8yv60+dLTMtlfOYQlQ2CUxRMtkZpnOWZzAXYsOCyWSPl3T35bfE\nKh1/hFgYJDBFyXiPBebsZ5gLryXeZKqrQVXzv+7LbXZhUo1S+CNEhZPAFCXjO7Yk65x1YA5gUiyY\nFWsphzXvDAaFmhoYDmiEwjMfL1EVFY+1lsHwELFUbB5GKISYDQlMUTK+0VjmWi9j4VdyRdMRwlpw\nQRf8HG82y7I6Ot3B3rkclhCiCBKYoiQ0Xcc3Gp11hax/gZ+/PFH2eEm+y7J11mzhjyzLClGpJDBF\nSYyFE6TSOk7bLAMztXA7/EzG4QCLBbr7U2jazMdLsoU/0vFHiMolgSlKwhfInsEstkJ2cQSmomTa\n5MXjOt7hmW8icZocWAwWOqVSVoiKJYEpSsI7OvszmLqu408OYlGsmFVLqYdWNrl9zDyWZRVFoc5a\ngz82TCgRnuuhCSFmQQJTlIQvdwaz8MCMaCFiWmTBn788UW1mlZXuvsIaGMjNJUJUJglMURK+Ii6O\nzhX8GBfHcmyW2azgdsPAUIpEopB9TAlMISqRBKYoiWJmmL5Ftn95PI8HdB16B2Zelh2vlJXCHyEq\nkQSmKAnfaBSbxYjRUPiP1EK+A3Mm2X3Mrt6Zl2XtJht2o10qZYWoUBKYomiapuMfi8/qDGam4GcA\nm+rAqMzuSEolq6oCo7GwBgZjiSCB+Ogcj0wIUSgJTFG0kWAcTdNnFZhj6RGSemJRzi4BVFWhthbG\nghqjYzMfL6mzynlMISqVBKYomu/YkZLZnMFcbB1+JlNbm3+bPLm5RIjKJYEpiuYr4uJo3xIIzLq6\nzJ/deexj5ipl5WiJEBVHAlMULXtx9GwC058cQEHBYXCVelgVw2ZTsNuhZyBJeoY2eRaDBZfZSedY\nD7o+81EUIcT8kcAURcteHO2yFbYkm9bTDCe9OAwuVKXwG04WEo8HkkkY9OYxy7TWEklF8EWH52Fk\nQoh8SWCKonlneQYzkPKhkV50HX4mM94mL59lWTmPKUQlksAURfMFojhsRgxqYfdYju9fLs4K2ePV\n1ICiQFcefWWlUlaIyiSBKYqSSmuMhOIFL8fC8TeULP4ZptGoUF0NXn+aaEyb9rUeWw0KirTIE6LC\nSGCKogyPxdD12VfIGjBgV51zMLLKk12W7ZmhGbtJNVFlcdMd7EXTpw9XIcT8kcAURZntkZKklmA0\n5cdpqEJRClvKXag8ma3J/M5jWmtJaAkGwkNzPCohRL4kMEVRxgOzsCXZ8f6xi385NsvlArMpE5gz\nHRkZL/yRZVkhKoUEpijKeJefwmaYi/VKr+koikKtB8IRneHA9Eut4x1/pPBHiEohgSmK4gvMbknW\nt4QKfo6XO14yw7JsraUaVVGl8EeICiKBKYriHY2iKuCwFj7DNClmLIp1jkZWmXL7mDMcLzGoBmos\n1fSE+khpM5/dFELMPQlMURRfIIbDZkIt4AxmNB0mrAVxGqqXTMFPlsWi4HRC32CKVGqmfcxa0nqa\n3lD/PI1OCDEdCUwxa4lkmtFwYtbLsUuhYcFkPB5IpzOhOZ36Y4U/R8e65mNYQogZSGCKWfOPzbZC\ndvHfUDKdfPcxG2yZa046RiUwhagEEphi1mZ7BnO8w8/SnGFWV4NBnXkf0212YTaYZYYpRIWQwBSz\n5gsUfnG0ruv4koNYVTsmtfB2eouBwaBQXQPDAY1QeOrjJYqiUG/z4Iv6CSZC8zhCIcRkJDDFrOVm\nmLb8Z5ih9CgJPbZk9y+zxtvk5bksK7NMIcpOAlPMWvZaL5cj/8BcqucvT5Q9XtI1Q2DmCn9kH1OI\nspPAFLPmH41iUBXsFmPeH7PUK2SzHA6wWDKN2KdrkzcemJ3zNTQhxBQkMMWseQMxnDZTQWcp/ckB\nFBQcSzwwFUXB44FYXMfrT0/5OrPBTLXFTcdYt9xcIkSZSWCKWYklUoSiyYIqZDU9zXByCLvqwqAY\n5nB0C0N2H3OmS6XrbXUktAT94cH5GJYQYgoSmGJWZnNLSSDlJ01qyR4nOVFtpr/6jPdjZgt/2mVZ\nVoiyksAUszKbpuu5/Uvj0i74yTKbFdxuGBhKkUjMvI8pDQyEKC8JTDErs7nWyy8FPyfxeEDToXdg\n6mXZKosbk2qSBgZClJkEppiV2SzJ+pMDqBiwq865GtaCM94mb+plWVVRqbfVMhgZIpyMzNfQhBAn\nkMAUs1JoW7ykliSQ8uM0uFEU+bHLqqoCozG/wh+ADrlQWoiykb+5xKz4AlGMBgWrOb9q1+HUIDr6\nkm9YcCJVVaithbGgxnBg6uMl4/uYUvgjRLlIYIpZ8Y5GcdnNeZ/B9CczRyJk//JkDQ2Z72F7Z2LK\n12RnmLKPKUT5SGCKgkViSaLxtFTIlkhdHSgKHO2aelnWarTgNrvoGOuSBgZClIkEpiiYdxZHSvzJ\nfoyKCYtim6thLVgmU2ZZ1utPMxacflk2mooxFPHO4+iEEFkSmKJguSMltvwqZGNahFB6DJehuqA2\nektJbll2mlnmeAMDWZYVohwkMEXBcjPMPG8pye5fSoefqTU0ZP6cfh/zWOHPmBT+CFEOEpiiYN5j\nM0x3nmcwx28okf3LqZjNCjU1MDCUJhyZfI+yxlqNUTHKVV9ClIkEpihYoW3xfIn+zOtlhjmt7LLs\nVMU/qqJSZ6ulPzxINBWbz6EJIZDAFLPgDUSxmg2YTTOfwdR1HV+yH6tqx6Ra5mF0C1duWbZr+mVZ\nHZ1OaWAgxLyTwBQF0XQd32g079llMB0gocdlOTYPVmumGXtvf4pobPJl2fGOP7IsK8R8k8AUBRkN\nJUil9bx7yHqT2eVYCcx8NDYq6Doc6Zh8lllvzxT+HJWOP0LMOwlMURBvoLBbSsb3LyUw89HcnPmz\n7cjkgWk32nCaHBwd7ULXp74STAhRehKYoiDZwMy/QrYfBRWHwT2Xw1o0LBYFjwcGvWkCo5M3MWiw\n1RFORRiK+uZ5dEIsbRKYoiCF3FKS0pOMpLw4DVWockNJ3pqbM9WyB9snn2U22I81MAh0zNeQhBBI\nYIoC5WaYjplnmP5k5oYSWY4tTEMDGAyZZdnJll0b7fUAHBntmOeRCbG0SWCKgvgCURTAaZt5huk7\nVvDjlobrBTEYFBoaIBjS6B86+WLpaksVJtVEuwSmEPNKAlMUxBuI4bCZUNWZe8JKwc/s5ZZlJyn+\nURWVBpuHwYiXYCI030MTYsmSwBR5S6bSjITiee1f6rqON9mPWbFgVqzzMLrFpbYWLBY4fDRBKnXy\nsmzDsWXZdjleIsS8kcAUecsW/OSzfxnRQkS1sNxQMkuKotDcDIkkHJmkIfv4PubR+R6aEEuWBKbI\nWyH3YGb3L+XC6Nlbvjzzi8be1vhJ76uzeVBQaA/IDFOI+SKBKfLmK+CWEm9u/7JmTse0mNlsCnV1\nmTOZXv/E4h+TasRjraEr2EMiPfUdmkKI0pHAFHkrpMtPZoap4JSGBUWZbpbZYK8nrafpCvbM97CE\nWJIkMEXexq/1mn6GmdbT+JODOFQXBsU4H0NbtOrqwGaDQ+0JYvGJDdlz+5gB2ccUYj5IYIq8eQNR\njAYFm2X6a70CKS8aadm/LAFFUVi+XCGVhrbDE4t/sh1/pIGBEPNDAlPkRdd1hgJRXHbzjFWvXjl/\nWVLLloGqwt62+ITOP3ajDZfZSftoB5o++XVgQojSkcAUeQnHUsQS6bz2L4eSfQC4peCnJMxmhcZG\nGB3T6OqdWPzTaKsnmooxEB4q0+iEWDokMEVe8q2Q1XUdb6IXk2LGqtrnY2hLwqpVmVn9zj2xCW+X\nZVkh5o8EpshLvmcww1qQiBbCbaiRhgUl5HJljpj0D6boGxw/RjJe+NNRppEJsXRIYIq8DA5HgJm7\n/AwlejOvM9bO+ZiWmjVrjs0yd4/PMqvMbiwGM+3S8UeIOSeBKfIyOJIJzCrn9IHpzQam7F+WXHW1\nQnU1dPWmco0MFEWhwVaPPzbCcGykzCMUYnGTwBR5GRzJXOs10xnMoWQvKgYc0rBgTuRmmcftZTY7\nGgA4NNJeljEJsVRIYIq8DA5HcNnNGKa51iuuxQik/LgM1aiK/GjNBY8HXC440pFkZDQNQJOjEYCD\ngSPlHJoQi578rSZmFImlCEaSVDmnL/jxJo4dJzHKcuxcURQlN8t8+dXMLLPWUo3ZYJYZphBzTAJT\nzCi7f+l2WKZ93VBS9i/nQ0MDOJ1w6GiCkUAaRVFosjfgjw3jj8o+phBzRQJTzChX8DNDhWx2humS\nGeacUhSFdesUdB12vJo5H9tkP7aPKcuyQswZCUwxo6HhzF/K01XIpvUUvmQ/DtWNURquz7n6+sxe\n5qGjSYYD6Vzhz8ERCUwh5ooEpphRPjNMf3IQDU3OX84TRVFYuzazl7ljV5QaSzUWg5lDAdnHFGKu\nSGCKGQ2ORFEVcNqmLvrJNiyokuXYeZOdZR7uSDIc0Gi0NzAcG8EfHS730IRYlCQwxYyyR0rUaY6U\nZBuuu6TgZ95k9zIhM8tstsuyrBBzSQJTTCsUTRKOpabdv8w0XO/DqtqxqNZ5HJ2oqwO3G450JrGm\nMo3YZVlWiLkhgSmmNX6kZOrAHE0Pk9BjMrssg+Nnma37zFgMFg6OHJ5wb6YQojQkMMW0chWy0wTm\nUKIn8xrZvywLjweqqqCjK0WNsY6R+Cj+mOxjClFqEphiWvlUyA4kujOvMUiFbDkcP8sMD2V+aTko\nXX+EKDkJTDGtwZHpz2Dqus5gogezYsGqOuZzaOI4tbVQXQ3eripACn+EmAsSmGJag8MRDKoy5ZGS\n0ZSfmBahyuiRC6PLKHsuU486UdJm2ccUYg5IYIop6brO4HAEt8M8ZRjmlmONnvkcmphEZpapkAzU\nMpoYYyAyVO4hCbGoSGCKKQUjSaKJ9LQVsoPHArNaArPssnuZ2mjmeMmB4YNlHpEQi4sEppjSTAU/\nuq4zkOjBotiwKLb5HJqYQm2tgkvJBObLffvLPBohFhcJTDGlwRmOlIykfCT0GFXGWtm/rCDrV9nQ\nIk46Qx0ktVS5hyPEoiGBKabU7w8DU1fIDsr+ZUWqqVEwJTzoSpqnD+8t93CEWDQkMMWU+nyZwKx1\nTX5xtBT8VK7lVZll2ccP7irzSIRYPCQwxZR6fWFsFgNWy8n3W2q6xmCiG6tqx6rK/mWlWVblAU1h\nWO+mxxsq93CEWBQkMMWk4ok0/tEYNVPMLkdSXpJ6Qrr7VCiDYsROLaojyG9ePFDu4QixKEhgikn1\nD4fRgWqnLMcuVI22zHVfuwYPEAjFyzwaIRY+CUwxqV7v9PuXUvBT+WpNmcBUqoZ4/OWeMo9GiIVP\nAlNMqu9YhWz1JIGZ2b/sxaY65P7LCmYzOLApDlS3nyd2dRFLyBETIYohgSkm1TfNDNOfHCSlJ6gy\nyv5lpas1NaAY0sTNQzyzu7/cwxFiQZPAFJPq809dIduf6ASg2lg338MSBcouyxprvDy6owdNGrIL\nMWsSmOIksUQKX2DqCtm+eAcggbkQuAw1GBUTZo8XbyDC3na5WFqI2ZLAFCfpHgqhAx73yfuTCS2O\nL9mPy1CNUZn8yi9ROVRFpdbYQNoQRXUGeGKnFP8IMVsSmOIkXYOZg+6eqpMDcyDRhY4us8sFpM7U\nDICr2c+eI/5cU30hRGEkMMVJuoeCANRNEpjZ5dgaY/18DkkUodrowYARqvvR0fnTzt5yD0mIBUkC\nU5ykczCEQVVOalqg6zp98U6MigmXoapMoxOFUhUDtaZGEkoYW3WIZ3b3E0+kyz0sIRYcCUwxQSqt\n0esNUeOyoKoTr+waS48Q1saoMnhQFPnRWUjqTE0A1K4cJhJP8fz+gTKPSIiFR/7WExMM+COk0vqk\ny7G98aMA1JhkOXahqTHWYcBI1NaNqug8/nIPuhwxEaIgEphigq5j+5eTFfz0xNsBqDU2zOuYRPFU\nxUCdqYmoHqJpVYweb5j2vrFyD0uIBUUCU0zQMTB5YCa0GEOJXpyGKszq5OczRWVrMC8HwNKQ6fjz\n5C4p/hGiEBKYYoIjvWOoinLSkmxfvBMdTWaXC5jbUINFseFTjuJyKLx4YIhILFnuYQmxYEhgipxE\nMk3nYJC6aitGw8Qfjd7scqxJAnOhUhSFBnMLKT1J09ogyZTGc3ul+EeIfElgipyOgSCaptNQY5vw\ndk3X6I0fxaxYcKjuMo1OlEKDqQWAuOsoqqLw5Cu9UvwjRJ4kMEXOkd5RAJpq7RPe7kv2E9djmZsv\nFGWyDxULhM3goMrgwZvqpWWFRp8/wqGe0XIPS4gFQQJT5Bw+FpgnzjC7YocA8Bib5n1MovSWWVYB\nYGnOXAL+lBT/CJEXCUwBZLr4HO4dxWE14rSZJry9K3YYA0aqjJ4yjlCUSq2xAYtiZZBDuF0KL7UO\nEYpK8Y8QM5HAFAAMDEcIRpI0nrAcO5waIqyNUWtqQJXuPouCoqg0mVeS0pPUr/WTSus8t0culxZi\nJvI3oABgz7F7Elc0OCe8Pbcca5Ll2MWkybwCFZWA9QCqQefJXX1S/CPEDCQwBQB72/0ALG9w5N6W\nWY49hIoqt5MsMibVQqN5JRE9SOPaYQaGI7R1Bco9LCEqmgSmIJFM09YdoNZtwWEd378MpPyMpUeo\nMdZjUAxlHKGYC8sta1BQiNe0Abp0/hFiBhKYgrbuAMmUdtJybEesFYA607JyDEvMMYtqo9G8nChj\nuJf5eLnNy1gkUe5hCVGxJDAFrx72ARP3L3Vd52i0FQMG6e6ziC23rENBQVnWRlpP86wU/wgxJQnM\nJS6Z0nhh/yA2i2FCwwJfsv9YdWyTLMcuYlbVTrN5FQk1hKmpi6d29aFJ8Y8Qk5LAXOJeOeQlHEux\nYXn1hAujjx5bjm2Q5dhFb4VlPQaMmFraGRob5UDnSLmHJERFksBc4p7ZnVmC27iyOvc2TdfojB3E\npJilWcESYFLNrLCuR1cTmJYf5qlXpPhHiMlIYC5h/f4w+44O01Bjo8Y1fsdlX7yDmBahztQszQqW\niGXmVdhUB8aGLl7pPcxoKF7uIQlRceRvwyVK13XueaQNHXjN+omzyCPRvQA0HrtwWCx+qmJgvW0r\nKGBctZcnX5VZphAnksBcgjRd59EdPbR2BVjZ6GRVkyv3vpgWoTvejkN1yVVeS0yV0UO9oQXVEeTx\nrqdIpbVyD0mIiiKBucREYilu+ckO7nv8ECajygWnNU24sqs9egAdjUbzCrnKawlaa9+MmraQqm/l\nkd17yz0cISqKBOYSk0ilCYQSrG9x846L1uKym3Pv03WdI9G9KKjUS3XskmRSzay1nIai6jwy+GsS\nKWlkIESWBOYSU+208Jl/OotLzl5OldM84X3eZB+BlB+PqQGTap7iCWKxa3I0YBpbSdo8xg9e+UW5\nhyNExZDAFDltkV0ANJtXlXkkotw2ujehhV3sD+7ihf6Xyz0cISqCBKYAIJIO0Rk7hF114jbUlns4\nosyqq4w4/K9BTxm5t/VBekPSMk8ICUwBwOHoHnQ0ms2rpNhHALBuhZNE+2mk9BR37r6bSDJa7iEJ\nUVYSmIK0nuZgZDcGjDSYW8o9HFEhqqsVagyNJPvW4IsNc8+BB+SSabGkSWAKjkYPENXCNJqXY1CM\n5R6OqCAbNiikejagRjzs9u3jkc4/lXtIQpSNBOYSp+kae8MvoaDQYllT7uGICuNyKTQ3q4RbT8eM\njd+2P8xe34FyD0uIspDAXOK644cJpkdoMLVgUW3lHo6oQOvXKxh0C/GDZ6IqBv5n370MhIfKPSwh\n5p0E5hKm6zp7Qy8CsNyytsyjEZXKalVYu1YhFnBTEzyDWDrOHXvuJpqSIiCxtEhgLmHd8cMMp4ao\nMzVjMzjLPRxRwVauBKcTuvc3sNy4gaGIlx/v+xmaLv1mxdIhgblEabrGruCzKCissmwo93BEhVNV\nhdNOU1BV6NyxjgZrI3v9rfzf4d+Ve2hCzBsJzCXqaKyV0fQwDaYWmV2KvDidCps2KSQSENh9Om6T\nmye6n+bPPc+Ve2hCzAsJzCUoqSV5NfgsCiorrDK7FPlraVFYtQpGAwa0I2djNVh54OCvpHJWLAkS\nmEvQXwafI6wFWWZehVUqY0WBNmxQaG4G74AF/ehZqIrKj/b9lO5gX7mHJsScksBcYgLxUZ4efBqT\nYmaFdX25hyMWIEVROPVUhRUrIDDgJnHkNOLpBP/96o/wR0fKPTwh5owE5hLz0OE/kNSSrLJuxKiY\nyj0csUApisLGjQpbtiikR5pIdG5iNDHG11/6PmPxYLmHJ8SckMBcQg4MH+SlwZ1Um2toNC0v93DE\nAqcoCi0tCq99rUKttppk3xpGUyPc+MS3+N2LBwnHkuUeohAlpejTdFP2euU3xcUink5wywu3MRwb\n4ZLmS4hHLOUeklhkRgIah0L7SLi60SJO0ofO5YxVLbz21EZOX1eHySi/n4uFob7eNenbJTCXiAcP\n/YYnup/mNM9mTnGdyuBIpNxDEouQruscCu9nKN2JEncQ2b8NklbsFiPbNjdw6VnLWd4gx5hEZZPA\nXMJahw/x7V0/wGV28ra1lxOJ6RKYYs7ouk5HrI3eRDs2xUXj8CV0dqeJxFIAnLbWwzsuWsuqpsn/\nUhKi3KYKTLnLaZELJcLcvf8+VBTe0PI6jKoRkL0lMXcURWG1dSMGxUBX/BCDnse5fN3bCA3b2H3E\nz572zD8XndHMu7avx2mT4jOxMMimwiKm6Rr3HLifsUSQMxtOp97mKfeQxBKhKAorrRtYY91EVAvx\nx5H7Mdb4uOJ1q3jL+SupdVn486v9fO6HL9DWJUdRxMIggbmI/a79j+z1t7LM0cRpns3lHo5Yglos\na9lkPxNNT/OnkYc4FN3D8non73jDWrZtbmAskuDWn73Cb5/rQJt6d0iIiiCBuUi9PPgqD3c+gcvk\nZPvy16EoSrmHJJaoOlMzWx3nYVRMvDD2GC8H/4yiwJkb6vjrC1Zjtxj55Z/b+ebPdxONp8o9XCGm\nJIG5CB0aOcJP9t+PSTVy6YrXYzHIERJRXm5jDac7zsemOtgf3sGfA78lpSdpqrXzzjesZXm9gz3t\nfm69dyejoXi5hyvEpCQwF5neUD/f3303mp7m4uUXUmOtLveQhADAZnBwuuN83IZauuKHeHT450TT\nYawWI28+byWbVlbTORjilnteZmBYqrhF5ZHAXER6Q/1865U7iaVjXNjyWlqczeUekhATmFQzWx3n\n0mBqwZcc4A/+nxFI+VFVhdef0czZG+vxjcb48j0v0zEwVu7hCjGBBOYi0R3s5Zs77yCUDHN+8zbW\nVa0u95CEmJSqqGywnc5KywbC2hgP+39Gf7wTRVE4e2M9rz+9mVA0ya33viIVtKKiSGAuAgeGD3L7\nzv8mnIpwQfO5bKqRW0hEZcseOznFdgYpPcXjI//H4cheADavruHSs1tIJNPc9sCr7D7iL/NohciQ\nwFzAdF3n6d7n+d6rPyKlpbh4+YWcUrOu3MMSIm8N5ha2Os7FoBj4y9gf2Rd+CYB1LVW86dwVaJrO\ntx7czYsHBss8UiGkNd6CFUvF+FnbL9kxuAuLwcylKy6i0V6f18eORZLSGk9UlEg6xN7wiyT0GKc6\nzuFM5+tRFIV+f5iHX+gmldL4f5dv4qIzlpV7qGIJkF6yi0hvqJ8f7rmHoaiPelsd25e/DqfJkffH\nS36GwbgAAAr1SURBVGCKShTTouwLv0hUC7PetpXz3JehKireQJQ/PN9FLJHmyovX8+bzVpZ7qGKR\nk8BcBDRd48nuZ/h1+8MktRRbPZs4u+EMVKWwlXUJTFGpklqcfZGXCKXHWGFZz+ur34JBMTISjPP7\nv3QSjqX469et5m2vXyPNOMSckcBc4LrGeriv7f/oDHZjMVi4cNl5rHS1zOpZEpiikqX0JAfCOxlN\n+2kyr2B79d9iUs2MhRP8/vkuxsIJ3vCaZfzjZafIHZtiTkhgLlCj8SC/bv8DL/S/jI7O2qpVnNd4\nFlajddbPlMAUlU7T07RGdjGcGsRjbOSS2rdjVe1EYkl+/3wXw2NxVjW6+Njbt9JQbSv3cMUiI4G5\nwMTTCZ7qfpaHOx8nnk5QY6nm3KYzWeZoKvrZEphiIdB1jcPRvQwme3Abaris9p04DG5SKY1n9w7Q\n1hXAajbwvss3sW1TgyzRipKRwFwgoqkoT/X8hSe6nyacDGM1WDiz4XROqV5b8F7lVCQwxUJx/GXU\ndtXJZbXvpMqYuabuYFeAZ/b0k0rrnLbWw5UXr6Ol3lnmEYvFQAKzwvmjwzzX9yJP9TxHNB3DrJrZ\nXLuBUz2bsBjMJf1cEphioemJH6Ej1oZFsXJxzduoN2eOlwRCcZ7dPUCvL4wCnL2xnkvOWs7GldUy\n4xSzJoFZgRLpBLu8e/lL/w4OjhwGwGqwcKpnE5tqNmA2zM1N9BKYYiEaSHRzOLoHFZVz3ZewwX46\nkJmFdg2GeLnNi280BkCt28KZ6+tZu8zN6mYXjbV2VAlQkScJzAoRTkbY529lt3cf+4fbiKcTADTa\n6tlQs5Y17pUYVeOcjkECUyxUgZSP1sgrpPQkG2ynsc19MQYl89+LrusMDkc50DlC50CQRErLfZzF\npFJfbaehxkZDtY364/70uC0YVKm2FeMkMMskraXpDHbTNnyY1pFDtAc60cj8h+wyO1njXsn6qrVU\nWSb/P2guSGCKhSymRTgQ3klYG6PO1MxF1W/FYXBPeE06reEdjeENRPGOxBgeizEWSZJKayc9T1UV\nPG4LjTV21i+vYsuqWlY3uzAaJESXKgnMeaLrOv3hQVpHDtE2fJhDgXbi6fELcettHla6WljpWk6V\n2V2WfRYJTLHQpfU0h6N78Cb7MClmznFtZ53t1Gn/e9J1nWg8zVgkwVj42D+RJMFj/x5NpHOvtZoN\nnLG+jvM2N7J1ba2E5xIjgTlHdF3HG/VzONBO28hh2kYOE0yEcu93m10sczTS7Gii2dGAxWAp42gz\nJDDFYqDrOkPJHtqjB0iTotG8gnNdF1NtqpvV82KJFH2+CH2+MN1DIYKRJAB2q5FzNtZz3uZGNq6s\nQVVlL3Sxk8AsgXg6gS/qxxv10x8a4OhYFx1jXYST4+FjM1ppdjSyzNFEs6OxoB6v80UCUywmMS3K\nkeg+RlJDKCj/f3v3ttvGccdx/DuzO3vkQZSl2EhlJG7rpIWLor0I2gK9K9D2pq/SZ+lj9KrPUxRG\ngsSWJTmyJJ72ODvTC1KUZFkOhdiRLP8/wmBmKXGxWIj748wOh/wifcJve3+8NEx7Hd57vj+peLo7\n5uvdCUVtARj1Yv7w5D5/evKAh5/IR1juqo86MJ13jOsJh+URR9UxhS2pbEVpK6quonWWznVYZ2m9\nxS7bneuw3mKdpbQVk+by+eiZnO30Hp+kW3zae3Bjw6zXIYEp7qKj9oBvqv9SujkazWfJl/wq/z33\nwvs/6jXpvGf/VcHT52O+fjFZTSba2c756tf3+d0vt9jZzm/9616s76MITOcdh+UrXsz22Z3v82K2\nz958n8PyiM53P7yDcxSKQGm0DtBojA7pRzn9qE/f9NiIB2ylm6Thh7cslwSmuKsWw7S7PK+/pnSL\nWyP9YMTnyRd8Gj9iyzz4UQuA2M7x3cGMp8/HfHcwwy0vn5uDmN88uscXD4c83tlga5hIgH7A7lRg\nOu84qccczL9nd77H3uyAF/M99uYvaV174W8jHTGI+vSjnJ5ZlCSMiXSECQyRNgQqQGtNoIJFSC7L\nXSWBKe467z0n9pCD9hlH7cvVzPSAkJHZZhhukuoemc5JgoxEZxgVESqDURFGRwSEbw29uul49nLG\ntwdTnh3MLnyMpZ8ZdrZ77Gz3+Nl2ztYwYWuYsDlIZALRB+DWB6bzjrprqGxFYUumzYxJM2XazFbl\npB5zWB1xXJ1c6jEGSjOMB4ziDUbxcFEnG2RhKu/0XiOBKT4mnbcc20NO7CETe0zpZniuvOydozDK\nEKoIcy5IjYpW7VT36QdDcj2gKRKOjh37rwoOx9Vq0tCFPSoY9WM2+wnDPGLYixj2YjZO23nMRi8i\nT40E6w268cB8VR7z7//9h7Kt6HyH8w7rLFVXU9mKumvW+idOgmTVWxxEfUbJBqN4g0HUu9O9wndJ\nAlN8zJzvqF1J42saV9P4GutbOm8XBUvnOzpvsavHFtuey5/jPM+omH4wpB+OyNUQ3fRwVY4tEoq5\nZlq0TIuGorZcfeVdSKOAPDXkqaF3WhJDnob0UkOWhKRxSBYv6rMS3MqFGLz3zG3BuJ5Qdw3OOz4b\nPMRcY6EW5z2zomVSNDSto2k78tS88wlYVwXm+11S5pxZO+Pp8TdYb1EotNIESmO0ITMpw3hApA1G\nG6LAkIQJaZCQhsmiHSakYXqtkyuEEK/TKiANeqRc/yLrvDsXoC21q6hcQeUKymV9bA85si/PnmSA\nIcQbKYNwxKNwRD/YIPEDtM3wTYqtDWXdUVSWsrZUjaVuOsracjKrsd06PeIzUahXAZrFIekqXAOS\n6HLIZvEinAd5RD8z1w5c6yzjesJJPeGkHjOux6v26rFmgnX2wvP+8fO/8ffP/7I8t55p0XI8rTie\n1BxNa47OtyfVlefiX//8M4Ps3a65/SY/6ZDs7myPvdn+O92nuD7pYQrx/njvqX1F5eaU3ZzSnZXK\nlfCGkTSNJgv65LpPGvRIdEqsE2KdEquUkBhvQzqrsa3CWoVtNbaF1kLbOhrbLXpdp3Xb0dhF7dbK\nWw/Kg+7IM00v1+QZpKkmThxhYlFhjQ9qWlVRu4KimzO1Ewr79utJrBIinWJICLoEb0PoIkbVl5Rz\nw/G0/sE3BlkckqcheWrI4pAw0ISB4vHOBn/96uE7vfV24z1MWMw8lfuJN0+jZCFqId4XpcjIyIIM\nzPaFXznvlr3R+bJnWlK7itqV1K5k1o3h8q3PyzQQLwvLayvqrKUWdbwsCoXH471fToBatE9/FmF5\n7jiBybKstFw6Nt8F+DbGN5v4JsY3yXI7wTcJtDG+jSn9m3uszyhQQJqEbPaT1XDz6TB0nhh6aUiW\nGIIrFox4vPPTfTPNrZn0I4QQHzvrLJNmyrwtmLXzs7qZU3U1jWtpu3ZZNzRdS+fdKgw9HvfatveL\nx5Ra3ApTyzfMCr2oL7Q1cWCIdEQURBht8F2AciGqi8FGdHWEtxHKxrRW0TbuwgzhU4FWREZjwoAo\n1JhQ088WQ779LGKQGfp5RC8xt271pFvRwxRCCHG1UIdsJiM2k9FNH4p4g9s3lUoIIYS4hSQwhRBC\niDVIYAohhBBrkMAUQggh1iCBKYQQQqxBAlMIIYRYgwSmEEIIsQYJTCGEEGINEphCCCHEGiQwhRBC\niDVIYAohhBBrkMAUQggh1iCBKYQQQqzhrV/vJYQQQogF6WEKIYQQa5DAFEIIIdYggSmEEEKsQQJT\nCCGEWIMEphBCCLEGCUwhhBBiDf8H27r+VZXwG0oAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f83d852bc18>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.energyplot(log_logistic_trace);"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.98805328946082049"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.bfmi(log_logistic_trace)"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0018938145216476"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(log_logistic_trace).values())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again, we calculate the posterior expected survival functions for this model."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 1500/1500 [00:00<00:00, 2526.82it/s]\n"
]
}
],
"source": [
"X_.set_value(X_pp)\n",
"cens_.set_value(cens_pp)\n",
"\n",
"with log_logistic_model:\n",
" pp_log_logistic_trace = pm.sample_ppc(\n",
" log_logistic_trace, samples=1500, vars=[y_obs]\n",
" )"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"log_logistic_pp_surv = (np.greater_equal\n",
" .outer(np.exp(y.mean() + y.std() * pp_log_logistic_trace['y_obs']),\n",
" t_plot))\n",
"log_logistic_pp_surv_mean = log_logistic_pp_surv.mean(axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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48FAuXPBh1KghbNu2GXt7B3R0dHFza8ewYQNZtGge1arZFftavmQS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AWvu1gcfG43ruPH8OTn4c7Px1NQQEXOGZw/HQRFISQ+HsstI4js0/eS5y+I6klbCDy1xEA2JhJC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\nXlJSUgCqvNcffviB9u3b+8866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"text/plain": [
"<matplotlib.figure.Figure at 0x7f83d80b1828>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"ax.plot(t_plot, weibull_pp_surv_mean[0],\n",
" c=blue, label=\"Weibull, not metastized\");\n",
"ax.plot(t_plot, weibull_pp_surv_mean[1],\n",
" c=red, label=\"Weibull, metastized\");\n",
"\n",
"ax.plot(t_plot, log_logistic_pp_surv_mean[0],\n",
" '--', c=blue, \n",
" label=\"Log-logistic, not metastized\");\n",
"ax.plot(t_plot, log_logistic_pp_surv_mean[1],\n",
" '--', c=red,\n",
" label=\"Log-logistic, metastized\");\n",
"\n",
"ax.set_xlim(0, 230);\n",
"ax.set_xlabel(\"Weeks since mastectomy\");\n",
"\n",
"ax.set_ylim(top=1);\n",
"ax.yaxis.set_major_formatter(pct_formatter);\n",
"ax.set_ylabel(\"Survival probability\");\n",
"\n",
"ax.legend(loc=1);\n",
"ax.set_title(\"Weibull and log-logistic\\nsurvival regression models\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This post has been a short introduction to implementing parametric survival regression models in PyMC3 with a fairly simple data set. The modular nature of probabilistic programming with PyMC3 should make it straightforward to generalize these techniques to more complex and interesting data set."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This post is available as a Jupyter notebook [here](https://gist.github.com/AustinRochford/4b8a163b66a11cdcbc430797b9b664fe)."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
@peadarcoylezopa

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peadarcoylezopa commented Oct 24, 2017

Hey Austin. I run into a bug on this around the \nu cens - TypeError: TensorType does not support boolean mask for indexing such as tensor[x==0]. Instead you can use non_zeros() such as tensor[(x == 0).nonzeros()].

Any suggestions. I tried doing n[(cens).nonzero()] but it leads to problems with alignment further on.

@AustinRochford

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Owner

AustinRochford commented Oct 31, 2017

@peadarcoylezopa what PyMC3 and Theano versions are you using?

@springcoil

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springcoil commented Nov 16, 2017

Hey Austin - the bug turned out to be fixed by a newer version of theano.

@AustinRochford

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Owner

AustinRochford commented Nov 16, 2017

Glad to hear it!

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