Some subjective bayesian considerations in the selection of models

Some considerations relating to the post-data selection of models are discussed. These include some difficulties with orthodox theory, implementation of the likelihood principle, and Bayesian tests of hypotheses.     

The evaluation of DNA evidence in pedigrees requiring population inference

Summary. The evaluation of nuclear DNA evidence for identification purposes is performed here taking account of the uncertainty about population parameters. Graphical models are used to detail the hypotheses being debated in a trial with the aim of obtaining a directed acyclic graph. Graphs also clarify the set of evidence that contributes to population inferences and they also describe the conditional independence structure of DNA evidence. Numerical illustrations are provided by re-examining three case-studies taken from the literature. Our calculations of the weight of evidence differ from those given by the authors of case-studies in that they reveal more conservative values.     

On the efficiency of affine minimax rules in estimating a bounded multivariate normal mean

Problems involving bounded parameter spaces, for example T-minimax and minimax esyimation of bounded parameters, have received much attention in recent years. The existing literature is rich. In this paper we consider T-minimax estimation of a multivariate bounded normal mean by affine rules, and discuss the loss of efficiency due to the use of such rules instead of optimal, unrestricted rules. We also investigate the behavior of 'probability restricted' affine rules, i.e., rules that have a guaranteed large probability of being in the bounded parameter space of the problem.     

An alternative competing risk model to the Weibull distribution for modelling aging in lifetime data analysis

A simple competing risk distribution as a possible alternative to the Weibull distribution in lifetime analysis is proposed. This distribution corresponds to the minimum between exponential and Weibull distributions. Our motivation is to take account of both accidental and aging failures in lifetime data analysis. First, the main characteristics of this distribution are presented. Then, the estimation of its parameters are considered through maximum likelihood and Bayesian inference. In particular, the existence of a unique consistent root of the likelihood equations is proved. Decision tests to choose between an exponential, Weibull and this competing risk distribution are presented. And this alternative model is compared to the Weibull model from numerical experiments on both real and simulated data sets, especially in an industrial context.     

Robust Bayesian inference in STAR models with neighbourhood effects

In this paper we propose a robust Bayesian procedure of estimation, testing, validation and selection of spatio-temporal autoregressive models (STAR) with neighbourhood effects applied to the appraisal of dwelling prices. The methodology does not depend on asymptotic results and, unlike previously procedures proposed in the literature, takes into account the uncertainty associated to the estimation of the neighbourhood parameters of the model, giving more realism to the analysis. Moreover, a sequential algorithm to elaborate fast on-line forecast, is provided. The methodology is illustrated by means of a practical case of the real estate market of Zaragoza.     

Bayesian measures of model complexity and fit

Summary. We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure p _D for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest. In general p _D approximately corresponds to the trace of the product of Fisher's information and the posterior covariance, which in normal models is the trace of the 'hat' matrix projecting observations onto fitted values. Its properties in exponential families are explored. The posterior mean deviance is suggested as a Bayesian measure of fit or adequacy, and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. Adding p _D to the posterior mean deviance gives a deviance information criterion for comparing models, which is related to other information criteria and has an approximate decision theoretic justification. The procedure is illustrated in some examples, and comparisons are drawn with alternative Bayesian and classical proposals. Throughout it is emphasized that the quantities required are trivial to compute in a Markov chain Monte Carlo analysis.