Multi-state capture-recapture data comprise individual-specific sighting histories together with information on individuals' states related, for example, to breeding status, infection level, or geographical location. Such data are often analysed using the Arnason-Schwarz model, where transitions between states are modelled using a discrete-time Markov chain, making the model most easily applicable to regular time series. When time intervals between capture occasions are not of equal length, more complex time-dependent constructions may be required, increasing the number of parameters to estimate, decreasing interpretability, and potentially leading to reduced precision. Here we develop a novel continuous-time multi-state model that can be regarded as an analogue of the Arnason-Schwarz model for irregularly sampled data. Statistical inference is carried out by regarding the capture-recapture data as realisations from a continuous-time hidden Markov model, which allows the associated efficient algorithms to be used for maximum likelihood estimation and state decoding. To illustrate the feasibility of the modelling framework, we use a long-term survey of bottlenose dolphins where capture occasion are not regularly spaced through time. Here we are particularly interested in seasonal effects on the movement rates of the dolphins along the Scottish east coast. The results reveal seasonal movement patterns between two core areas of their range, providing information that will inform conservation management.
We develop some new strategies for building and fitting new flexible classes of parametric capture-recapture models for closed populations which can be used to address a better understanding of behavioural patterns. We first rely on a conditional probability parameterization and review how to regard a large subset of standard capture-recapture models as a suitable partitioning in equivalence classes of the full set of conditional probability parameters. We then propose the use of new suitable quantifications of the conditioning binary partial capture histories as a device for enlarging the sco…
Capture-recapture (CRC) surveys are used to estimate the size of a population whose members cannot be enumerated directly. CRC surveys have been used to estimate the number of Covid-19 infections, people who use drugs, sex workers, conflict casualties, and trafficking victims. When $k$ capture samples are obtained, counts of unit captures in subsets of samples are represented naturally by a $2^k$ contingency table in which one element -- the number of individuals appearing in none of the samples -- remains unobserved. In the absence of additional assumptions, the population size is not identif…
We consider mark-recapture-recovery (MRR) data of animals where the model parameters are a function of individual time-varying continuous covariates. For such covariates, the covariate value is unobserved if the corresponding individual is unobserved, in which case the survival probability cannot be evaluated. For continuous-valued covariates, the corresponding likelihood can only be expressed in the form of an integral that is analytically intractable and, to date, no maximum likelihood approach that uses all the information in the data has been developed. Assuming a first-order Markov proces…
We apply the splitting method to three well-known counting problems, namely 3-SAT, random graphs with prescribed degrees, and binary contingency tables. We present an enhanced version of the splitting method based on the capture-recapture technique, and show by experiments the superiority of this technique for SAT problems in terms of variance of the associated estimators, and speed of the algorithms.
Estimation of population size using incomplete lists (also called the capture-recapture problem) has a long history across many biological and social sciences. For example, human rights and other groups often construct partial and overlapping lists of victims of armed conflicts, with the hope of using this information to estimate the total number of victims. Earlier statistical methods for this setup either use potentially restrictive parametric assumptions, or else rely on typically suboptimal plug-in-type nonparametric estimators; however, both approaches can lead to substantial bias, the fo…
We propose a modern method to estimate population size based on capture-recapture designs of K samples. The observed data is formulated as a sample of n i.i.d. K-dimensional vectors of binary indicators, where the k-th component of each vector indicates the subject being caught by the k-th sample, such that only subjects with nonzero capture vectors are observed. The target quantity is the unconditional probability of the vector being nonzero across both observed and unobserved subjects. We cover models assuming a single constraint (identification assumption) on the K-dimensional distribution …
A capture-recapture hidden Markov model framework for register-based inference of population size and dynamics
University of Kent（肯特大学）；Queen Mary University of London（伦敦大学玛丽女王学院）；Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院）；Stockholm University（斯德哥尔摩大学）；Umeå University（于默奥大学）
Capture-recapture methods aim to estimate the size of a closed population on the basis of multiple incomplete enumerations of individuals. In many applications, the individual probability of being recorded is heterogeneous in the population. Previous studies have suggested that it is not possible to reliably estimate the total population size when capture heterogeneity exists. Here we approach population estimation in the presence of capture heterogeneity as a latent length biased nonparametric density estimation problem on the unit interval. We show that in this setting it is generally imposs…
Doubly Robust Machine Learning for Population Size Estimation with Missing Covariates: Application to Gaza Conflict Mortality
Center for Data Science New York University（纽约大学数据科学中心）；Department of Statistics & Data Science Carnegie Mellon University（卡内基梅隆大学统计与数据科学系）；Department of Medical Statistics London School of Hygiene and Tropical Medicine（伦敦卫生与热带医学院医学统计学系）
We propose a general and flexible capture-recapture model in continuous time. Our model incorporates time-heterogeneity, observed and unobserved individual heterogeneity, and behavioral response to capture. Behavioral response can possibly have a delayed onset and a finite-time memory. Estimation of the population size is based on the conditional likelihood after use of the EM algorithm. We develop an application to the estimation of the number of adult cannabinoid users in Italy.
We estimate the number of fatal victims of the Peruvian internal armed conflict between 1980-2000 using stratified seven-list Capture-Recapture methods based on Dirichlet process mixtures, which we extend to accommodate incomplete stratification information. We use matched data from six sources, originally analyzed by the Peruvian Truth and Reconciliation Commission in 2003, together with a new large dataset, originally published in 2006 by the Peruvian government. We deal with missing stratification labels by developing a general framework and estimation methods based on MCMC sampling for joi…
Spatial Capture-Recapture With Penalized Regression Splines to Flexibly Model Wildlife Density and Distribution
Utrecht University（乌得勒支大学）；University of Glasgow（格拉斯哥大学）；University of St Andrews（圣安德鲁斯大学）；World Wide Fund for Nature（世界自然基金会）；University of Auckland（奥克兰大学）
Species distribution models (SDMs) are increasingly used in ecology, biogeography, and wildlife management to learn about the species-habitat relationships and abundance across space and time. Distance sampling (DS) and capture-recapture (CR) are two widely collected data types to learn about species-habitat relationships and abundance; still, they are seldomly used in SDMs due to the lack of spatial coverage. However, data fusion of the two data sources can increase spatial coverage, which can reduce parameter uncertainty and make predictions more accurate, and therefore, can be used for spec…
Traditional analyses of capture-recapture data are based on likelihood functions that explicitly integrate out all missing data. We use a complete data likelihood (CDL) to show how a wide range of capture-recapture models can be easily fitted using readily available software JAGS/BUGS even when there are individual-specific time-varying covariates. The models we describe extend those that condition on first capture to include abundance parameters, or parameters related to abundance, such as population size, birth rates or lifetime. The use of a CDL means that any missing data, including uncert…
In this paper, we consider capture-recapture experiments with heterogenous catchability. In the setting we consider, the widespread Huggins-Alho estimator is not very suitable and we introduce and study a new generalized Horvitz-Thompson estimator. Our motivation is Respondent Driven Sampling (RDS), a prime example for such a setting where the capture probability is dependent on both the unknown population size as well as on an observable covariate, the network degree of an individual, due to peer recruitment. After discussing the theoretical properties of the new estimator, with full details …
Passive acoustic monitoring is a promising method for surveying wildlife populations that are easier to detect acoustically than visually. When animal vocalisations can be uniquely identified on an array of sensors, the potential exists to estimate population density through acoustic spatial capture-recapture (ASCR). However, sound classification is imperfect, and in some situations a high proportion of sounds detected on just a single sensor ('singletons') are not from the target species. We present a case study of bowhead whale calls (Baleana mysticetus) collected in the Beaufort Sea in 2010…
Heterogeneity of response patterns is important in estimating the size of a closed population from multiple recapture data when capture patterns are different over time and location. In this paper, we extend the non-parametric one layer latent class model for multiple recapture data proposed by Manrique-Vallier (2016) to a nested latent class model with the first layer modeling individual heterogeneity and the second layer modeling location-time differences. Location-time groups with similar recording patterns are in the same top layer latent class and individuals within each top layer class a…
Advances in field techniques have lead to an increase in spatially-referenced capture-recapture data to estimate a species' population size as well as other demographic parameters and patterns of space usage. Statistical models for these data have assumed that the number of individuals in the population and their spatial locations follow a homogeneous Poisson point process model, which implies that the individuals are uniformly and independently distributed over the spatial domain of interest. In many applications there is reason to question independence, for example when species display terri…
Spatially explicit capture recapture (SECR) models have gained enormous popularity to solve abundance estimation problems in ecology. In this study, we develop a novel Bayesian SECR model that disentangles the process of animal movement through a detector from the process of recording data by a detector in the face of imperfect detection. We integrate this complexity into an advanced version of a recent SECR model involving partially identified individuals (Royle, 2015). We assess the performance of our model over a range of realistic simulation scenarios and demonstrate that estimates of popu…
We discuss the semiparametric modeling of mark-recapture-recovery data where the temporal and/or individual variation of model parameters is explained via covariates. Typically, in such analyses a fixed (or mixed) effects parametric model is specified for the relationship between the model parameters and the covariates of interest. In this paper, we discuss the modeling of the relationship via the use of penalized splines, to allow for considerably more flexible functional forms. Corresponding models can be fitted via numerical maximum penalized likelihood estimation, employing cross-validatio…
As noninvasive sampling techniques for animal populations have become more popular, there has been increasing interest in the development of capture-recapture models that can accommodate both imperfect detection and misidentification of individuals (e.g., due to genotyping error). However, current methods do not allow for individual variation in parameters, such as detection or survival probability. Here we develop misidentification models for capture-recapture data that can simultaneously account for temporal variation, behavioral effects and individual heterogeneity in parameters. To facilit…
There lies a latent danger in utilizing some known mathematical results in ecology. Some results do not apply to the problem at hand. We identify one such trend. Based on a couple of theorems in mathematical statistics, Link (2013) cautions ecologists about the inappropriateness of using the discrete uniform prior in their analysis under certain conditions and instead recommends the routine use of the scale prior during analysis. This recommendation is been absorbed immediately and widely among ecologists. In this study, we consider the two fundamental capture-recapture models used widely in e…
The paper describes a new class of capture-recapture models for closed populations when individual covariates are available. The novelty consists in combining a latent class model for the distribution of the capture history, where the class weights and the conditional distributions given the latent may depend on covariates, with a model for the marginal distribution of the available covariates as in \cite{Liu2017}. In addition, any general form of serial dependence is allowed when modeling capture histories conditionally on the latent and covariates. A Fisher-scoring algorithm for maximum like…
Understanding space usage and resource selection is a primary focus of many studies of animal populations. Usually, such studies are based on location data obtained from telemetry, and resource selection functions (RSF) are used for inference. Another important focus of wildlife research is estimation and modeling population size and density. Recently developed spatial capture-recapture (SCR) models accomplish this objective using individual encounter history data with auxiliary spatial information on location of capture. SCR models include encounter probability functions that are intuitively …
Spatial capture-recapture (SCR) models are now widely used for estimating density from repeated individual spatial encounters. SCR accounts for the inherent spatial autocorrelation in individual detections by modelling detection probabilities as a function of distance between the detectors and individual activity centres. However, additional spatial heterogeneity in detection probability may still creep in due to environmental or sampling characteristics. if unaccounted for, such variation can lead to pronounced bias in population size estimates. Using simulations, we describe and test three B…
Hierarchical modeling of abundance in space or time using closed-population mark-recapture under heterogeneity (model M$_{h}$) presents two challenges: (i) finding a flexible likelihood in which abundance appears as an explicit parameter and (ii) fitting the hierarchical model for abundance. The first challenge arises because abundance not only indexes the population size, it also determines the dimension of the capture probabilities in heterogeneity models. A common approach is to use data augmentation to include these capture probabilities directly into the likelihood and fit the model using…
A vast amount of ecological knowledge generated recently has hinged upon the ability of model selection methods to discriminate among various ecological hypotheses. The last decade has seen the rise of Bayesian hierarchical models in ecology. Consequently, popular tools, such as the AIC, become largely inapplicable and other tools are not universally applicable. We focus on a class of competing Bayesian spatially explicit capture recapture (SECR) models and first apply some of the recommended Bayesian model selection tools: (1) Bayes Factor - using (a) Gelfand-Dey (b) harmonic mean methods, (2…
Estimates of population size for hidden and hard-to-reach individuals are of particular interest to health officials when health problems are concentrated in such populations. Efforts to derive these estimates are often frustrated by a range of factors including social stigma or an association with illegal activities that ordinarily preclude conventional survey strategies. This paper builds on and extends prior work that proposed a method to meet these challenges. Here we describe a rigorous formalization of a one-step, network-based population estimation procedure that can be employed under c…
Estimating spatially-varying density and time-varying demographics with open population spatial capture-recapture: a photo-ID case study on bottlenose dolphins in Barataria Bay, Louisana, USA
University of St Andrews（圣安德鲁斯大学）；Centre for Research into Ecological and Environmental Modelling（生态与环境建模研究中心）；National Marine Mammal Foundation（国家海洋哺乳动物基金会）；National Marine Fisheries Service（国家海洋渔业局）；Department of Fisheries and Oceans（渔业与海洋部）；Marine Mammal Commission（海洋哺乳动物委员会）
We develop a multi-state model to estimate the size of a closed population from ecological capture-recapture studies. We consider the case where capture-recapture data are not of a simple binary form, but where the state of an individual is also recorded upon every capture as a discrete variable. The proposed multi-state model can be regarded as a generalisation of the commonly applied set of closed population models to a multi-state form. The model permits individuals to move between the different discrete states, whilst allowing heterogeneity within the capture probabilities. A closed-form e…
Link et al. (2010) define a general framework for analyzing capture-recapture data with potential misidentifications. In this framework, the observed vector of counts, $y$, is considered as a linear function of a vector of latent counts, $x$, such that $y = A x$, with $x$ assumed to follow a multinomial distribution conditional on the model parameters, $θ$. Bayesian methods are then applied by sampling from the joint posterior distribution of both $x$ and $θ$. In particular, Link et al. (2010) propose a Metropolis-Hastings algorithm to sample from the full conditional distribution of $x$, wher…
Connected vehicles (CVs) can capture and transmit detailed data such as vehicle position and speed through vehicle-to-vehicle and vehicle-to-infrastructure communications. The wealth of CV data provides new opportunities to improve safety and mobility of transportation systems. However, it is likely to overburden storage and communication systems. To mitigate this issue, we propose a compressive sensing (CS) approach that allows CVs to capture and compress data in real-time and later recover the original data accurately and efficiently. The approach is evaluated using two case studies. In the …
In recent literature, the Gaussian Graphical model (GGM; Lauritzen, 1996),a network of partial correlation coefficients, has been used to capture potential dynamic relationships between observed variables. The GGM can be estimated using regularization in combination with model selection using the extended Bayesian Information Criterion (Foygel and Drton, 2010). I term this methodology GeLasso, and asses its performance using a plausible psychological network structure with both continuous and ordinal datasets.Simulation results indicate that GeLasso works well as an out-of-the-box method to es…
Connected vehicles (CVs) can capture and transmit detailed data like vehicle position, speed and so on through vehicle-to-vehicle and vehicle-to-infrastructure communications. The wealth of CV data provides new opportunities to improve the safety, mobility, and sustainability of transportation systems. However, the potential data explosion likely will overburden storage and communication systems. To solve this issue, we design a real-time compressive sensing (CS) approach which allows CVs to collect and compress data in real-time and can recover the original data accurately and efficiently whe…
Growth mixture models (GMMs) incorporate both conventional random effects growth modeling and latent trajectory classes as in finite mixture modeling; therefore, they offer a way to handle the unobserved heterogeneity between subjects in their development. GMMs with Gaussian random effects dominate the literature. When the data are asymmetric and/or have heavier tails, more than one latent class is required to capture the observed variable distribution. Therefore, a GMM with continuous non-elliptical distributions is proposed to capture skewness and heavier tails in the data set. Specifically,…
We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process assumes that the dwell time in each state (i.e., the duration of a stay in a given state) has a geome…
