1,721,048 research outputs found
A new Bayesian method for nonparametric capture-recapture models in presence of heterogeneity
No full textCapture-recapture models are among the oldest and most popular methods for estimating how large a wild animal population is, though the usefulness of these models goes beyond zoological matters having been applied, among others, to epidemiological studies, socio-demographic investigations and even to software reliability problems. The intrinsic heterogeneity of individuals has been recognized as a potential source of bias in the estimation procedures. To account for this heterogeneity in the model a hierarchical structure has been proposed where the probabilities that each animal is caught in a single occasion are modeled as i.i.d. draws from a common unknown distribution F .
There is general agreement since the work by Burnham and Overton (1978) that modelling F with a simple parametric curve may lead to unsatisfactory results. Hence other nonparametric solutions have been developed (Smith and van Belle 1984, Chao 1989, Norris and Pollock 1996). Recently Basu (1998) proposed a Bayesian nonparametric solution that uses a Dirichlet process prior for F. Here we propose an alternative Bayesian approach that relies on a different parameterization which still maintains no assumptions on the shape of F but drives the problem back to a finite-dimensional setting. Our approach avoids some identifiablity problems related to such recapture models and, at the same time, allows for a formal Bayesian default analysis. Results of analyses conducted on computer simulations as well as on on-field experiments and other real data sets show good performance of this method in comparison with some of the estimators commonly used in the classical capture-recapture literature
A canonical moment approach to the analysis of binomial mixtures
No full textMixture of binomial distributions are often considered as a flexible model for count data which can account for sources of heterogeneity in the population and also as a device to deal with exchangeable binary sequences. For instance they are routinely used in a wide range of applied context such as psychological testing as well as in industrial sampling or in toxicological experiments, just to mention some of them. Different param- eterizations are presented in order to build up a convenient methodological framework for developing a default Bayesian analysis when no parametric form of the mixing distribu- tion is assumed. This approach can be exploited for estimation and prediction purposes. Also in this paper a first attempt to investigate its usefulness in model selection problems is carried out
Metodologie Cattura-Ricattura per la ricerca sociale: determinazione della consistenza di popolazioni e sottopopolazioni elusive e controllo della mancata copertura di un’indagine
No full textQuesto lavoro intende presentare alcune linee essenziali delle metodologie cattura-ricattura e illustrarne, anche attraverso alcune applicazioni a problemi reali, l’u- tilizzo nell’ambito della ricerca sociale. A tale scopo, dopo aver introdotto i modelli principali, si sofferma l’attenzione sulle ipotesi collegate a tali modelli e sulla loro pos- sibile (in)adeguatezza nelle applicazioni nel contesto sociale. In secondo luogo verranno discussi alcuni aspetti critici inerenti il problema inferenziale, che ancora oggi stimolano la ricerca metodologica in tale ambito rendendo possibili importanti avanzamenti per l’ot- tenimento di buone proprieta` inferenziali dei metodi utilizzati per questo tipo di modelli particolarmente difficili. Si passeranno in rassegna alcune nuove strategie d’analisi indi- viduate nella recente letteratura che richiedono ipotesi meno stringenti piu` aderenti alla realta`. Infine verranno svolte considerazioni critiche su quale possibile spazio possa an- cora essere rimasto per l’investigazione e l’uso dei metodi di cattura-ricattura nell’ambito della ricerca sociale
A note on estimating the diameter of a truncated moment class
No full textThe k-truncated moment class Gamma (m(k)) = {pi is an element of P: m(i) = integral (l)x(i)pi (dx), i = 1,...,k} of all probability distributions pi on a compact interval I of the real line which have the same first k moments is considered. This paper derives some remarkable properties of the ranges of (k + h)th moments which allow to provide bounds for the diameter of Gamma (m(k)) for a suitable probability metric. (C) 2001 Elsevier Science B.V. All rights reserved
A Bayesian hierarchical model for comparing ovalbumin epitopes in allergic patients before and after oral specific desensitization.
No full textConsistency in nonparametrics: a revisitation and some recent developments.
No full textAll’interno della vasta letteratura sulla consistenza nell’inferenza non parametrica
il lavoro rivisita alcune analisi di consistenza per le stime di massima verosimiglianza
e per le procedure bayesiane con l’obiettivo di mettere in luce quali aspetti del problema
possono determinarne un comportamento parallelo talvolta rilevato ma non ancora completamente
sviluppato in ambito non parametrico
Bayesian mixture of Plackett-Luce models for partially ranked data
No full textThe Plackett-Luce model is one of the most popular and frequently applied parametric distributions to analyze partial top-rankings of a finite set of items. A Bayesian finite mixture of Plackett-Luce models is illustrated, that extends a Bayesian device recently introduced in the literature in order to account for unobserved sample heterogeneity. We describe an efficient way to incorporate the latent group structure in the data augmentation approach and how to interpret existing maximum likelihood procedures as special instances of the proposed Bayesian analysis. Bayesian inference is conducted with the combination of the Expectation-Maximization algorithm for maximum a posteriori estimation and the Gibbs sampling iterative procedure, with a focus on the identifiability problems that can affect the results of the MCMC technique. The novel Bayesian Plackett- Luce mixture is illustrated with an analysis of real preference partially ranked data, which discusses the application of several relabeling algorithms to solve the label-switching issue and the resulting posterior estimates
IDR for marginal likelihood in Bayesian phylogenetics
No full textIt is widely accepted that species diversified in a tree like pattern from a
common descendant and that the diversification is mainly due to changes in
the genetic codes of the species accumulating during the centuries. The main
aim of phylogenetics is to investigate the evolutionary relationships among
species, studying similarities and diFFerences of aligned genomic sequences.
From a statistical point of view, the problem of analyzing phylogenetic sequences is often formalized as follows: given a set of DNA sequences of different
species, we aim at inferring the tree that better represents the evolutionary
relationships using the variations occurred in the genetic codes. Since genes
evolve accumulating changes, the larger the number of differences in the genetic
code of two species, the larger the evolutionary distance between them is
likely to be. Alternative tree estimation methods such as parsimony methods
(Felsenstein (2004), chapter 7) and distance methods (Fitch and Margoliash,
1967; Cavalli-Sforza and Edwards, 1967) have been proposed. We consider
stochastic models for substitution rates in a fully Bayesian framework. We focus
on model selection issues and several estimation procedures of the Bayesian
model evidence will be rewived. We address within a fully Bayesian framework
proposing alternative model evidence estimation procedures
Identifiability and inferential issues in capture-recapture experiments with heterogeneous detection probabilities
No full textWe focus on a capture-recapture model in which capture probabilities arise from an unspecified distribution F. We show that model parameters are identifiable based on the unconditional likelihood. This is not true with the conditional likelihood. We also clarify that consistency and asymptotic equivalence of maximum likelihood estimators based on conditional and unconditional likelihood do not hold. We show that estimates of the undetected fraction of population based on the unconditional likelihood converge to the so-called estimable sharpest lower bound and we derive a new asymptotic equivalence result. We finally provide theoretical and simulation arguments in favor of the use of the unconditional likelihood rather than the conditional likelihood especially when one is willing to infer on the sharpest lower bound
Bayesian Plackett--Luce Mixture Models for Partially Ranked Data
Full text linkThe elicitation of an ordinal judgment on multiple alternatives is often required in many psychological
and behavioral experiments to investigate preference/choice orientation of a specific population. The
Plackett–Luce model is one of the most popular and frequently applied parametric distributions to analyze
rankings of a finite set of items. The present work introduces a Bayesian finite mixture of Plackett–Luce
models to account for unobserved sample heterogeneity of partially ranked data. We describe an efficient
way to incorporate the latent group structure in the data augmentation approach and the derivation of existing
maximum likelihood procedures as special instances of the proposed Bayesian method. Inference can
be conducted with the combination of the Expectation-Maximization algorithm for maximum a posteriori
estimation and the Gibbs sampling iterative procedure.We additionally investigate several Bayesian criteria
for selecting the optimal mixture configuration and describe diagnostic tools for assessing the fitness of
ranking distributions conditionally and unconditionally on the number of ranked items. The utility of the
novel Bayesian parametric Plackett–Luce mixture for characterizing sample heterogeneity is illustrated
with several applications to simulated and real preference ranked data. We compare our method with the
frequentist approach and a Bayesian nonparametric mixture model both assuming the Plackett–Luce model
as a mixture component. Our analysis on real datasets reveals the importance of an accurate diagnostic
check for an appropriate in-depth understanding of the heterogenous nature of the partial ranking data
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