Parameterizations and Fitting of Bi-directed Graph Models to Categorical Data

Abstract.  We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi-directed graph models, under the global Markov property. Such models are useful data analytic tools especially if used in combination with other graphical models. The first parameterization, in the saturated case, is also known as thenation multivariate logistic transformation, the second is a variant that allows, in some (but not all) cases, variation-independent parameters. An algorithm for maximum likelihood fitting is proposed, based on an extension of the Aitchison and Silvey method.     

Focused Information Criterion for Capture–Recapture Models for Closed Populations

Abstract. We propose a criterion for selecting a capture–recapture model for closed populations, which follows the basic idea of the focused information criterion (FIC) of Claeskens and Hjort. The proposed criterion aims at selecting the model which, among the available models, leads to the smallest mean‐squared error (MSE) of the resulting estimator of the population size and is based on an index which, up to a constant term, is equal to the asymptotic MSE of the estimator. Two alternative approaches to estimate this FIC index are proposed. We also deal with multimodel inference; in this case, the population size is estimated by using a weighted average of the estimates coming from different models, with weights chosen so as to minimize the MSE of the resulting estimator. The proposed model selection approach is compared with more common approaches through a series of simulations. It is also illustrated by an application based on a dataset coming from a live‐trapping experiment.