Latent class recapture models with flexible behavioural response

Recapture models based on conditional capture probabilities are explored. These encompass all possible forms of time-dependence and behavioural response to capture. Covariates are used to deal with observed heterogeneity, while unobserved heterogeneity is modeled through flexible random effects with a finite number of support points

Information matrix for hidden Markov models with covariates

For a general class of hidden Markov models that may include time-varying covariates, we illustrate how to compute the observed information matrix, which may be used to obtain standard errors for the parameter estimates and check model identifiability. The proposed method is based on the Oakes’ identity and, as such, it allows for the exact computation of the information matrix on the basis of the output of the expectation-maximization (EM) algorithm for maximum likelihood estimation. In addition to this output, the method requires the first derivative of the posterior probabilities computed by the forward-backward recursions introduced by Baum and Welch. Alternative methods for computing exactly the observed information matrix require, instead, to differentiate twice the forward recursion used to compute the model likelihood, with a greater additional effort with respect to the EM algorithm. The proposed method is illustrated by a series of simulations and an application based on a longitudinal dataset in Health Economics

S-estimation of hidden Markov models

A method for robust estimation of dynamic mixtures of multivariate distributions is proposed. The EM algorithm is modified by replacing the classical M-step with high breakdown S-estimation of location and scatter, performed by using the bisquare multivariate S-estimator. Estimates are obtained by solving a system of estimating equations that are characterized by component specific sets of weights, based on robust Mahalanobis-type distances. Convergence of the resulting algorithm is proved and its finite sample behavior is investigated by means of a brief simulation study and n application to a multivariate time series of daily returns for seven stock markets

Heterogeneity and behavioral response in continuous time capture-recapture, with application to street cannabis use in Italy

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.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS672 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Generalized Augmentation for Control of the k-Familywise Error Rate

When performing many hypothesis tests at once a correction for multiplicity is needed to both keep under control the number of false discoveries and be able to detect the true departures from the null hypotheses. A recently introduced method which has been proved to be useful in genomics, neuroimaging and other fields consists in probabilistically controlling that the number of falsely rejected hypotheses does not exceed a pre-specified (low) . We introduce a new multiple testing procedure which is based on the idea of generalized augmentation: at first a number of hypotheses is rejected without any correction, then this number is adjusted by adding or removing rejections. The procedure is shown to keep under control the probability of or more false rejections. We show a small simulation study which suggests that the new procedure is very powerful, especially when the number of tests at stake is large. We conclude with an illustration on a benchmark data set on classification of colon cancer

Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data

We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits (local, global, continuation or reverse continuation), generalised log-odds ratios and similar higher-order interactions. For each constrained model, the prior distribution of the model parameters is formulated following the encompassing prior approach. Then, model selection is performed by using Bayes factors which are estimated by an importance sampling method. The approach is illustrated through three applications involving some datasets, which also include explanatory variables. In connection with one of these examples, a sensitivity analysis to the prior specification is also considered