Skip to content

Instantly share code, notes, and snippets.

@AustinRochford
Last active December 13, 2020 21:22
Show Gist options
  • Star 3 You must be signed in to star a gist
  • Fork 0 You must be signed in to fork a gist
  • Save AustinRochford/e67cb0c628b3692ecc669190fe86990c to your computer and use it in GitHub Desktop.
Save AustinRochford/e67cb0c628b3692ecc669190fe86990c to your computer and use it in GitHub Desktop.
Capture-Recapture Models in Python with PyMC3
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"title: Capture-Recapture Models in Python with PyMC3\n",
"tags: Bayesian Statistics, PyMC3, Ecology\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Recently, a project at work has led me to learn a bit about [capture-recapture](https://en.wikipedia.org/wiki/Mark_and_recapture) models for estimating the size and dynamics of populations that cannot be fully enumerated. These models often arise in ecological statistics when estimating the size, birth, and survival rates of animal populations in the wild. This post gives examples of implementing three capture-recapture models in Python with [PyMC3](https://github.com/pymc-devs/pymc3) and is intended primarily as a reference for my future self, though I hope it may serve as a useful introduction for others as well.\n",
"\n",
"We will implement three Bayesian capture-recapture models:\n",
"* the [Lincoln-Petersen](https://en.wikipedia.org/wiki/Mark_and_recapture#Lincoln%E2%80%93Petersen_estimator) model of abundance,\n",
"* the Cormack-Jolly-Seber model of survival, and\n",
"* the Jolly-Seber model of abundance and survival."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import logging"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"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",
"from pymc3.distributions.dist_math import binomln, bound, factln\n",
"import scipy as sp\n",
"import seaborn as sns\n",
"import theano\n",
"from theano import tensor as tt"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"sns.set()\n",
"\n",
"PCT_FORMATTER = StrMethodFormatter('{x:.1%}')"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"SEED = 518302 # from random.org, for reproducibility\n",
"\n",
"np.random.seed(SEED)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"# keep theano from complaining about compile locks\n",
"(logging.getLogger('theano.gof.compilelock')\n",
" .setLevel(logging.CRITICAL))\n",
"\n",
"# keep theano from warning about default rounding mode changes\n",
"theano.config.warn.round = False"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Lincoln-Petersen model\n",
"\n",
"The simplest model of abundace, that is, the size of a population, is the Lincoln-Petersen model. While this model is a bit simple for most practical applications, it will introduce some useful modeling concepts and computational techniques.\n",
"\n",
"The idea of the Lincoln-Petersen model is to visit the observation site twice to capture individuals from the population of interest. The individuals captured during the first visit are marked (often with tags, radio collars, microchips, etc.) and then released. The number of individuals captured, marked, and released is recorded as $n_1$. On the second visit, the number of captured individuals is recorded as $n_2$. If enough individuals are captured on the second visit, chances are quite high that several of them will have been marked on the first visit. The number of marked individuals recaptured on the second visit is recorded as $n_{1, 2}$.\n",
"\n",
"The Lincoln-Petersen model assumes that:\n",
"1. each individuals has an equal probability to be captured on both visits (regardless of whether or not they were marked),\n",
"2. no marks fall off or become illedgible, and\n",
"3. the population is closed, that is, no individuals are born, die, enter, or leave the site between visits.\n",
"\n",
"The third assumption is quite restrictive, and will be relaxed in the two subsequent models. The first two assumptions can be relaxed in various ways, but we will not do so in this post. First we derive a simple analytic estimator for the total population size given $n_1$, $n_2$, and $n_{1, 2}$, then we fit a Bayesian Lincoln-Petersen model using PyMC3 to set the stage for the (Cormack-)Jolly-Seber models.\n",
"\n",
"Let $N$ denote the size of the unknown total population, and let $p$ denote the capture probability. We have that\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"n_1, n_2\\ |\\ N, p\n",
" & \\sim \\textrm{Bin}(N, p) \\\\\n",
"n_{1, 2}\\ |\\ n_1, p\n",
" & \\sim \\textrm{Bin}(n_1, p).\n",
"\\end{align*}\n",
"$$\n",
"\n",
"Therefore $\\frac{n_2}{N}$ and $\\frac{n_{1, 2}}{n_1}$ are unbiased estimates of $p$. The Lincoln-Peterson estimator is derived by equating these estimators\n",
"\n",
"$$\\frac{n_2}{\\hat{N}} = \\frac{n_{1, 2}}{n_1}$$\n",
"\n",
"and solving for\n",
"\n",
"$$\\hat{N} = \\frac{n_1 n_2}{n_{1, 2}}.$$\n",
"\n",
"We now simulate a data set where $N = 1000$ and the capture probability is $p = 0.1$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"N_LP = 1000\n",
"P_LP = 0.1\n",
"\n",
"x_lp = sp.stats.bernoulli.rvs(P_LP, size=(2, N_LP))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The rows of `x_lp` correspond to site visits and the columns to individuals. The entry `x_lp[i, j]` is one if the $j$-th individuals was captured on the $i$-th site visit, and zero otherwise."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[0, 0, 0, ..., 0, 0, 0],\n",
" [0, 0, 0, ..., 0, 1, 0]])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x_lp"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We construct $n_1$, $n_2$, and $n_{1, 2}$ from `x_lp`."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"n1, n2 = x_lp.sum(axis=1)\n",
"n12 = x_lp.prod(axis=0).sum()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(109, 95, 10)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n1, n2, n12"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Lincoln-Petersen estimate of $N$ is therefore"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1035.5"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"N_lp = n1 * n2 / n12\n",
"\n",
"N_lp"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now give a Bayesian formulation of the Lincoln-Petersen model. We use the priors\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"p\n",
" & \\sim U(0, 1) \\\\\n",
"\\pi(N)\n",
" & = 1 \\textrm{ for } N \\geq n_1 + n_2 - n_{1, 2}.\n",
"\\end{align*}\n",
"$$\n",
"\n",
"Note that the prior on $N$ is improper."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"with pm.Model() as lp_model:\n",
" p = pm.Uniform('p', 0., 1.)\n",
" N_ = pm.Bound(pm.Flat, lower=n1 + n2 - n12)('N')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now implement the likelihoods of the data given above during the derivation of the Lincoln-Petersen estimator."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"with lp_model:\n",
" n1_obs = pm.Binomial('n1_obs', N_, p, observed=n1)\n",
" n2_obs = pm.Binomial('n2_obs', N_, p, observed=n2)\n",
" n12_obs = pm.Binomial('n12_obs', n1, p, observed=n12)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that the model is fully specified, we sample from its posterior distribution."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"NJOBS = 3\n",
"\n",
"SAMPLE_KWARGS = {\n",
" 'draws': 1000,\n",
" 'njobs': NJOBS,\n",
" 'random_seed': [SEED + i for i in range(NJOBS)],\n",
" 'nuts_kwargs': {'target_accept': 0.9}\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (3 chains in 3 jobs)\n",
"NUTS: [N_lowerbound__, p_interval__]\n",
"100%|██████████| 1500/1500 [00:06<00:00, 230.30it/s]\n",
"The number of effective samples is smaller than 25% for some parameters.\n"
]
}
],
"source": [
"with lp_model:\n",
" lp_trace = pm.sample(**SAMPLE_KWARGS)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First we examine a few sampling diagnostics. The Bayesian fraction of missing information (BFMI) and energy plot give no cause for concern."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0584389661341544"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.bfmi(lp_trace)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAcwAAAE5CAYAAAAdhBAsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\neVBgioiI5EGBKSIikgcFpoiISB7+f2X/LcCvpwqQAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fbc21533128>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.energyplot(lp_trace);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Gelman-Rubin statistics are close to one, indicating convergence."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0040982739011743"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(lp_trace).values())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since there are no apparent sampling problems, we examine the estimate of the population size."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAjkAAAGACAYAAABPxnNNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fbc02055080>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.plot_posterior(\n",
" lp_trace, varnames=['N'],\n",
" ref_val=N_LP,\n",
" lw=0., alpha=0.75\n",
");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The true population size is well within the 95% credible interval. The posterior estimate of $N$ could become more accurate by substituting a reasonable upper bound for the prior on $N$ for the uninformative prior we have used here out of convenience."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Cormack-Jolly-Seber model\n",
"\n",
"The Cormack-Jolly-Seber model estimates the survival dynamics of individuals in the population by relaxing the third assumption of the Lincoln-Petersen model, that the population is closed. Note that here \"survival\" does not necessarily correspond to the individual's death, as it includes individuals that leave the observation area during the study. Despite this subtlety, we will use the convenient terminology of \"alive\" and \"dead\" throughout.\n",
"\n",
"For the Cormack-Jolly-Seber and Jolly-Seber models, we follow the notation of [_Analysis of Capture-Recapture Data_](http://capturerecapture.co.uk/) by McCrea and Morgan. Additionally, we will use a [cormorant](https://en.wikipedia.org/wiki/Cormorant) data set from the book to illustrate these two models. This data set involves eleven site visits where individuals were given individualized identifying marks. The data are defined below in the form of an $M$-array."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"T = 10\n",
"\n",
"R = np.array([30, 157, 174, 298, 470, 421, 413, 514, 430, 181])\n",
"\n",
"M = np.zeros((T, T + 1))\n",
"M[0, 1:] = [10, 4, 2, 2, 0, 0, 0, 0, 0, 0]\n",
"M[1, 2:] = [42, 12, 16, 1, 0, 1, 1, 1, 0]\n",
"M[2, 3:] = [85, 22, 5, 5, 2, 1, 0, 1]\n",
"M[3, 4:] = [139, 39, 10, 10, 4, 2, 0]\n",
"M[4, 5:] = [175, 60, 22, 8, 4, 2]\n",
"M[5, 6:] = [159, 46, 16, 5, 2]\n",
"M[6, 7:] = [191, 39, 4, 8]\n",
"M[7, 8:] = [188, 19, 23]\n",
"M[8, 9:] = [101, 55]\n",
"M[9, 10] = 84"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here `T` indicates the number of revisits to the site so there were $T + 1 = 11$ total visits. The entries of `R` indicate the number of animals captured and released on each visit."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 30, 157, 174, 298, 470, 421, 413, 514, 430, 181])"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"R"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The entry `M[i, j]` indicates how many individuals captured on visit $i$ were first recaptured on visit $j$. The diagonal of `M` is entirely zero, since it is not possible to recapture an individual on the same visit as it was released."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0., 10., 4., 2.],\n",
" [ 0., 0., 42., 12.],\n",
" [ 0., 0., 0., 85.],\n",
" [ 0., 0., 0., 0.]])"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M[:4, :4]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Of the thirty individuals marked and released on the first visit, ten were recaptured on the second visit, four were recapture on the third visit, and so on.\n",
"\n",
"Capture-recapture data is often given in the form of encounter histories, for example\n",
"\n",
"$$1001000100,$$\n",
"\n",
"which indicates that the individual was first captured on the first visit and recaptured on the fourth and eigth visits. It is straightforward to convert a series of encounter histories to an $M$-array. We will discuss encounter histories again at the end of this post.\n",
"\n",
"The parameters of the Cormack-Jolly-Seber model are $p$, the capture probability, and $\\phi_i$, the probability that an individual that was alive during the $i$-th visit is still alive during the $(i + 1)$-th visit. The capture probability can vary over time in the Cormack-Jolly-Seber model, but we use a constant capture probability here for simplicity.\n",
"\n",
"We again place a uniform prior on $p$."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"with pm.Model() as cjs_model:\n",
" p = pm.Uniform('p', 0., 1.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We also place a uniform prior on $\\phi_i$."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"with cjs_model:\n",
" ϕ = pm.Uniform('ϕ', 0., 1., shape=T)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If $\\nu_{i, j}$ is the probability associated with `M[i, j]`, then\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\nu_{i, j}\n",
" & = P(\\textrm{individual that was alive at visit } i \\textrm{ is alive at visit } j) \\\\\n",
" & \\times P(\\textrm{individual was not captured on visits } i + 1, \\ldots, j - 1) \\\\\n",
" & \\times P(\\textrm{individual is captured on visit } j).\n",
"\\end{align*}\n",
"$$\n",
"\n",
"From our parameter definitions,\n",
"\n",
"$$P(\\textrm{individual that was alive at visit } i \\textrm{ is alive at visit } j) = \\prod_{k = i}^{j - 1} \\phi_k,$$"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"def fill_lower_diag_ones(x):\n",
" return tt.triu(x) + tt.tril(tt.ones_like(x), k=-1)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"with cjs_model:\n",
" p_alive = tt.triu(\n",
" tt.cumprod(\n",
" fill_lower_diag_ones(np.ones_like(M[:, 1:]) * ϕ),\n",
" axis=1\n",
" )\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$P(\\textrm{individual was not captured at visits } i + 1, \\ldots, j - 1) = (1 - p)^{j - i - 1},$$"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"i = np.arange(T)[:, np.newaxis]\n",
"j = np.arange(T + 1)[np.newaxis]\n",
"\n",
"not_cap_visits = np.clip(j - i - 1, 0, np.inf)[:, 1:]"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"with cjs_model:\n",
" p_not_cap = tt.triu(\n",
" (1 - p)**not_cap_visits\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and\n",
"\n",
"$$P(\\textrm{individual is captured on visit } j) = p.$$"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"with cjs_model:\n",
" ν = p_alive * p_not_cap * p"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The likelihood of the observed recaptures is then"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"triu_i, triu_j = np.triu_indices_from(M[:, 1:])"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"with cjs_model:\n",
" recap_obs = pm.Binomial(\n",
" 'recap_obs',\n",
" M[:, 1:][triu_i, triu_j],\n",
" ν[triu_i, triu_j],\n",
" observed=M[:, 1:][triu_i, triu_j]\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, some individual released on each occasion are not recaptured again,"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 12., 83., 53., 94., 199., 193., 171., 284., 274., 97.])"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"R - M.sum(axis=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The probability of this event is\n",
"\n",
"$$\\chi_i = P(\\textrm{released on visit } i \\textrm{ and not recaptured again}) = 1 - \\sum_{j = i + 1}^T \\nu_{i, j}.$$"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"with cjs_model:\n",
" χ = 1 - ν.sum(axis=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The likelihood of the individual that were not recaptured again is"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"with cjs_model:\n",
" no_recap_obs = pm.Binomial(\n",
" 'no_recap_obs',\n",
" R - M.sum(axis=1), χ,\n",
" observed=R - M.sum(axis=1)\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that the model is fully specified, we sample from its posterior distribution."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (3 chains in 3 jobs)\n",
"NUTS: [ϕ_interval__, p_interval__]\n",
"100%|██████████| 1500/1500 [00:05<00:00, 272.61it/s]\n"
]
}
],
"source": [
"with cjs_model:\n",
" cjs_trace = pm.sample(**SAMPLE_KWARGS)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again, the BFMI and energy plot are reasonable."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"0.97973424667749842"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.bfmi(cjs_trace)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAcwAAAE5CAYAAAAdhBAsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nbcfqAwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fbc04c55c18>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.energyplot(cjs_trace);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Gelman-Rubin statistics also indicate convergence."
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0009026695355843"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(cjs_trace).values())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"McCrea and Morgan's book includes a table of maximum likelihood estimates for $\\phi_i$ and $p$. We verify that our Bayesian estimates are close to these."
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"ϕ_mle = np.array([0.8, 0.56, 0.83, 0.86, 0.73, 0.69, 0.81, 0.64, 0.46, 0.99])"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAg0AAAF1CAYAAABrgdmlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngIhoAAAiogEAiIgGACAiGgCAiGgAACI/BYfDCiNsZkEAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fbbe6358f98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"t_plot = np.arange(T) + 1\n",
"low, high = np.percentile(cjs_trace['ϕ'], [5, 95], axis=0)\n",
"\n",
"ax.fill_between(\n",
" t_plot, low, high,\n",
" alpha=0.5, label=\"90% interval\"\n",
");\n",
"ax.plot(\n",
" t_plot, cjs_trace['ϕ'].mean(axis=0),\n",
" label=\"Posterior expected value\"\n",
");\n",
"\n",
"ax.scatter(\n",
" t_plot, ϕ_mle,\n",
" zorder=5,\n",
" c='k', label=\"Maximum likelihood estimate\"\n",
");\n",
"\n",
"ax.set_xlim(1, T);\n",
"ax.set_xlabel(\"$t$\");\n",
"\n",
"ax.yaxis.set_major_formatter(PCT_FORMATTER);\n",
"ax.set_ylabel(r\"$\\phi_t$\");\n",
"\n",
"ax.legend(loc=2);"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [],
"source": [
"p_mle = 0.51"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAjQAAAGACAYAAAC6OPj9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nR6EBAADGo9AAAADj/X9TB2cBvOdznAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fbc08b43f28>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax = pm.plot_posterior(\n",
" cjs_trace, varnames=['p'],\n",
" ref_val=p_mle,\n",
" lw=0., alpha=0.75\n",
")\n",
"\n",
"ax.set_title(\"$p$\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Jolly-Seber Model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Jolly-Seber model is an extension of the Cormack-Jolly-Seber model (the fact that the extension is named after fewer people is a bit counterintuitive) that estimates abundance and birth dynamics, in addition to the survival dynamics estimated by the Cormack-Jolly-Seber model. As with the Cormack-Jolly-Seber model where \"death\" included leaving the site, \"birth\" includes not just the actual birth of new individuals, but individuals that arrive at the site during the study from elsewhere. Again, despite this subtlety, we will use the convenient terminology of \"birth\" and \"born\" throughout.\n",
"\n",
"In order to estimate abundance and birth dynamics, the Jolly-Seber model adds likelihood terms for the first time an individual is captured to the recapture likelihood of the Cormack-Jolly-Seber model. We use the same uniform priors on $p$ and $\\phi_i$ as in the Cormack-Jolly-Seber model."
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [],
"source": [
"with pm.Model() as js_model:\n",
" p = pm.Uniform('p', 0., 1.)\n",
" ϕ = pm.Uniform('ϕ', 0., 1., shape=T)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As with the Lincoln-Petersen model, the Jolly-Seber model estimates the size of the population, including all individuals ever alive during the study period, $N$. We use the Schwarz-Arnason formulation of the Jolly-Seber model, where each individual has probability $\\beta_i$ of being born into the population between visits $i$ and $i + 1$. We place a $\\operatorname{Dirichlet}(1, \\ldots, 1)$ prior on these parameters."
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [],
"source": [
"with js_model:\n",
" β = pm.Dirichlet('β', np.ones(T), shape=T)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let $\\Psi_i$ denote the probability that a given individual is alive on visit $i$ and has not yet been captured before visit $i$. Then $\\Psi_1 = \\beta_0$, since no individuals can have been captured before the first visit, and\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\Psi_{i + 1}\n",
" & = P(\\textrm{the individual was alive and unmarked during visit } i \\textrm{ and survived to visit } i + 1) \\\\\n",
" & + P(\\textrm{the individual was born between visits } i \\textrm{ and } i + 1) \\\\\n",
" & = \\Psi_i (1 - p) \\phi_i + \\beta_i.\n",
"\\end{align*}\n",
"$$\n",
"\n",
"After writing out the first few terms, we see that this recursion has the closed-form solution\n",
"\n",
"$$\\Psi_{i + 1} = \\sum_{k = 0}^i \\left(\\beta_k (1 - p)^{i - k} \\prod_{\\ell = 1}^{i - k} \\phi_{\\ell} \\right).$$"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [],
"source": [
"never_cap_surv_ix = sp.linalg.circulant(np.arange(T))\n",
"\n",
"with js_model:\n",
" p_never_cap_surv = tt.concatenate((\n",
" [1], tt.cumprod((1 - p) * ϕ)[:-1]\n",
" ))\n",
"\n",
" Ψ = tt.tril(\n",
" β * p_never_cap_surv[never_cap_surv_ix]\n",
" ).sum(axis=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The probability that an unmarked individual that is alive at visit $i$ is captured on visit $i$ is then $\\Psi_i p$. The probability that an individual is alive at the end of the study period and never captured is \n",
"$$1 - \\sum_{i = 1}^T \\Psi_i p.$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Therefore, the likelihood of the observed first captures is a $(T + 1)$-dimensional multinomial, where the first $T$ probabilities are $\\Psi_1 p, \\ldots, \\Psi_T p$, and the corresponding first $T$ counts are the observed number of unmarked individuals captured at each visit, $u_i$. The final probability is\n",
"\n",
"$$1 - \\sum_{i = 1}^T \\Psi_i p$$\n",
"\n",
"and corresponds to the unobserved number of individuals never captured. Since PyMC3 does not implement such an \"incomplete multinomial\" distribution, we give a minimal implementation here."
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [],
"source": [
"class IncompleteMultinomial(pm.Discrete):\n",
" def __init__(self, n, p, *args, **kwargs):\n",
" \"\"\"\n",
" n is the total frequency\n",
" p is the vector of probabilities of the observed components\n",
" \"\"\"\n",
" super(IncompleteMultinomial, self).__init__(*args, **kwargs)\n",
" self.n = n\n",
" self.p = p\n",
" self.mean = n * p.sum() * p,\n",
" self.mode = tt.cast(tt.round(n * p), 'int32')\n",
" \n",
" def logp(self, x):\n",
" \"\"\"\n",
" x is the vector of frequences of all but the last components\n",
" \"\"\"\n",
" n = self.n\n",
" p = self.p\n",
" \n",
" x_last = n - x.sum()\n",
" \n",
" return bound(\n",
" factln(n) + tt.sum(x * tt.log(p) - factln(x)) \\\n",
" + x_last * tt.log(1 - p.sum()) - factln(x_last),\n",
" tt.all(x >= 0), tt.all(x <= n), tt.sum(x) <= n,\n",
" n >= 0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As in the Lincoln-Petersen model, we place an improper flat prior (with the appropriate lower bound) on $N$."
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [],
"source": [
"u = np.concatenate(([R[0]], R[1:] - M[:, 1:].sum(axis=0)[:-1]))"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [],
"source": [
"with js_model:\n",
" N = pm.Bound(pm.Flat, lower=u.sum())('N')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The likelihood of the observed first captures is therefore"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [],
"source": [
"with js_model:\n",
" unmarked_obs = IncompleteMultinomial(\n",
" 'unmarked_obs', N, Ψ * p,\n",
" observed=u\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The recapture likelihood for the Jolly-Seber model is the same as for the Cormack-Jolly-Seber model."
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [],
"source": [
"with js_model:\n",
" p_alive = tt.triu(\n",
" tt.cumprod(\n",
" fill_lower_diag_ones(np.ones_like(M[:, 1:]) * ϕ),\n",
" axis=1\n",
" )\n",
" )\n",
" p_not_cap = tt.triu(\n",
" (1 - p)**not_cap_visits\n",
" )\n",
" ν = p_alive * p_not_cap * p\n",
" \n",
" recap_obs = pm.Binomial(\n",
" 'recap_obs',\n",
" M[:, 1:][triu_i, triu_j], ν[triu_i, triu_j],\n",
" observed=M[:, 1:][triu_i, triu_j]\n",
" )"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [],
"source": [
"with js_model:\n",
" χ = 1 - ν.sum(axis=1)\n",
" \n",
" no_recap_obs = pm.Binomial(\n",
" 'no_recap_obs',\n",
" R - M.sum(axis=1), χ,\n",
" observed=R - M.sum(axis=1)\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again we sample from the posterior distribution of this model."
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (3 chains in 3 jobs)\n",
"NUTS: [N_lowerbound__, β_stickbreaking__, ϕ_interval__, p_interval__]\n",
"100%|██████████| 1500/1500 [00:29<00:00, 50.24it/s]\n"
]
}
],
"source": [
"with js_model:\n",
" js_trace = pm.sample(**SAMPLE_KWARGS)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again, the BFMI and energy plot are reasonable."
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"0.93076073875335852"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.bfmi(js_trace)"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAcwAAAE5CAYAAAAdhBAsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nWvD/DY0zglB483cAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fbbe2426a90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.energyplot(js_trace);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Gelman-Rubin statistics also indicate convergence."
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0051087141503718"
]
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(js_trace).values())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The posterior expected survival rates are, somewhat surprisingly, still quite similar to the maximum likelihood estimates under the Cormack-Jolly-Seber model."
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAg0AAAF1CAYAAABrgdmlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAUJF3PxFxRoOAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fbbd9fdc198>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"low, high = np.percentile(js_trace['ϕ'], [5, 95], axis=0)\n",
"\n",
"ax.fill_between(\n",
" t_plot, low, high,\n",
" alpha=0.5, label=\"90% interval\"\n",
");\n",
"ax.plot(\n",
" t_plot, js_trace['ϕ'].mean(axis=0),\n",
" label=\"Posterior expected value\"\n",
");\n",
"\n",
"ax.scatter(\n",
" t_plot, ϕ_mle,\n",
" zorder=5,\n",
" c='k', label=\"Maximum likelihood estimate (CJS)\"\n",
");\n",
"\n",
"ax.set_xlim(1, T);\n",
"ax.set_xlabel(\"$t$\");\n",
"\n",
"ax.yaxis.set_major_formatter(PCT_FORMATTER);\n",
"ax.set_ylabel(r\"$\\phi_t$\");\n",
"\n",
"ax.legend(loc=\"upper center\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following plot shows the estimated birth dynamics."
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAgUAAAF1CAYAAAB4VplRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/wTMTUS3naDTAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fbbd956c0f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"low, high = np.percentile(js_trace['β'], [5, 95], axis=0)\n",
"\n",
"ax.fill_between(\n",
" t_plot - 1, low, high,\n",
" alpha=0.5, label=\"90% interval\"\n",
");\n",
"ax.plot(\n",
" t_plot - 1, js_trace['β'].mean(axis=0),\n",
" label=\"Posterior expected value\"\n",
");\n",
"\n",
"ax.set_xlim(0, T - 1);\n",
"ax.set_xlabel(\"$t$\");\n",
"\n",
"ax.yaxis.set_major_formatter(PCT_FORMATTER);\n",
"ax.set_ylabel(r\"$\\beta_t$\");\n",
"\n",
"ax.legend(loc=2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The posterior expected population size is about 30% larger than the number of distinct individuals marked."
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.2951923918464066"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"js_trace['N'].mean() / u.sum()"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAjUAAAGACAYAAABV+pPDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBgAAGIFSAwAAjPD/AYwaffYv8GKEAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fbbd9e18198>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.plot_posterior(\n",
" js_trace, varnames=['N'],\n",
" lw=0., alpha=0.75\n",
");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we have estimated these three models, we return briefly to the topic of $M$-arrays versus encounter histories. While $M$-arrays are a convienent summary of encounter histories, they do not lend themselves to common extensions of these models to include individual random effects, trap-dependent recapture, etc. as readily as encounter histories. Two possibile approaches to include such effects are:\n",
"1. Use likelihoods for the (Cormack-)Jolly-Seber models based on encounter histories, which are a bit more complex than those based on $M$-arrays.\n",
"2. Individual $M$-arrays: transform each individual's account history into an $M$-array an stack them into a three-dimensional array of $M$-arrays.\n",
"We may explore one (or both) of these approaches in a future post.\n",
"\n",
"Thanks to [Eric Heydenberk](http://heydenberk.com/) for his feedback on a early draft of this post.\n",
"\n",
"This post is available as a Jupyter notebook [here](http://nbviewer.jupyter.org/gist/AustinRochford/e67cb0c628b3692ecc669190fe86990c)."
]
}
],
"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": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
@Edderic
Copy link

Edderic commented Jul 11, 2019

Hey,

Thanks for this awesome tutorial! I'm planning to make use of it for calculating birth rates for whales, so thanks so much for writing this up!

I have one question. In the Jolly-Seber section, you mentioned the following:

Screenshot from 2019-07-11 09-26-01

I read the above expression as "everything other than detecting an individual who was alive in the study period" which involves scenarios where individual is alive up to the end of the study but never captured, like you said, but also involves scenarios where individual dies before the end of study. So the description "the probability that an individual is alive at the end of the study period but never captured" is not entirely correct, is it?

@AustinRochford
Copy link
Author

I think the probability that an individual is alive at the end of the study period but never captured" is correct - the definition of $\Psi$ includes the survival probability $\phi$.

@vaisvila
Copy link

vaisvila commented Sep 14, 2020

Hi,

I am new to Python and am trying to run the Jolly-Seber example as the building block of an analysis I want to do. I am having trouble when I try to run:

with js_model:
js_trace = pm.sample(**SAMPLE_KWARGS)

It gives me this traceback. I imagine it has to do with syntax changing since the example was produced but I am not sure how to diagnose given how new I am to python. This might be a silly problem, sorry!

Traceback (most recent call last):
File "", line 1, in
File "C:\Users\16307\anaconda3\lib\multiprocessing\spawn.py", line 116, in spawn_main
exitcode = _main(fd, parent_sentinel)
File "C:\Users\16307\anaconda3\lib\multiprocessing\spawn.py", line 126, in _main
self = reduction.pickle.load(from_parent)
AttributeError: Can't get attribute 'IncompleteMultinomial' on <module 'main' (built-in)>

EDIT: It seems that "njobs" has been deprecated in favor of "cores".

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment