Petros Dellaportas

Bayesian Inference for Generalized Linear and Proportional Hazards Models via Gibbs Sampling

It is shown that Gibbs sampling, making systematic use of an adaptive rejection algorithm proposed by Gilks and Wild, provides a straightforward computational procedure for Bayesian inferences in a wide class of generalized linear and proportional hazards models.

Full Bayesian Inference for GARCH and EGARCH Models

A full Bayesian analysis of GARCH and EGARCH models is proposed consisting of parameter estimation, model selection, and volatility prediction. The Bayesian paradigm is implemented via Markov-chain Monte Carlo methodologies. We provide implementation details and illustrations using the General Index of the Athens stock exchange.

BAYESIAN ANALYSIS OF ERRORS-IN-VARIABLES REGRESSION MODELS

SUMMARY Use of errors-in-variables models is appropriate in many practical experimental problems. However, inference based on such models is by no means straightforward. In previous analyses, simplifying assumptions have been made in order to ease this intractability, but assumptions of this nature are unfortunate and restrictive. In this paper, we analyse errors-in-variables models in full generality under a Bayesian formulation. In order to compute the necessary posterior distributions, we utilize various computational techniques. Two specific non-linear errors-in-variables regression examples are considered; the first is a re-analysed Berkson-type model, and the second is a classical errors-in-variables model. Our analyses are compared and contrasted with those presented elsewhere in the literature.

Multivariate mixtures of normals with unknown number of components

We present full Bayesian analysis of finite mixtures of multivariate normals with unknown number of components. We adopt reversible jump Markov chain Monte Carlo and we construct, in a manner similar to that of Richardson and Green (1997), split and merge moves that produce good mixing of the Markov chains. The split moves are constructed on the space of eigenvectors and eigenvalues of the current covariance matrix so that the proposed covariance matrices are positive definite. Our proposed methodology has applications in classification and discrimination as well as heterogeneity modelling. We test our algorithm with real and simulated data.

Bayesian variable and link determination for generalised linear models

In this paper, we describe full Bayesian inference for generalised linear models where uncertainty exists about the structure of the linear predictor, the linear parameters and the link function. Choice of suitable prior distributions is discussed in detail and we propose an efficient reversible jump Markov chain Monte-Carlo algorithm for calculating posterior summaries. We illustrate our method with two data examples.

An Introduction to MCMC

Markov chain Monte Carlo (MCMC) algorithms are now widely used in virtually all areas of statistics. In particular, spatial applications featured very prominently in the early development of the methodology (Geman & Geman 1984), and they still provide some of the most challenging problems for MCMC techniques. It is not of a great surprise that most modern introductions to the subject emphasise the flexibility and generality of MCMC. We will do that here too, but we also have more targeted aims in supporting the other chapters in this book covering different areas of spatial statistics.

Bayesian Modelling of Outstanding Liabilities Incorporating Claim Count Uncertainty

Abstract This paper deals with the prediction of the amount of outstanding automobile claims that an insurance company will pay in the near future. We consider various competing models using Bayesian theory and Markov chain Monte Carlo methods. Claim counts are used to add a further hierarchical stage in the model with log-normally distributed claim amounts and its corresponding state space version. This way, we incorporate information from both the outstanding claim amounts and counts data resulting in new model formulations. Implementation details and illustrations with real insurance data are provided.

Bayesian analysis of mortality data

Congdon argued that the use of parametric modelling of mortality data is necessary in many practical demographical problems. In this paper, we focus on a form of model introduced by Heligman and Pollard in 1980, and we adopt a Bayesian analysis, using Markov chain Monte Carlo simulation, to produce the posterior summaries required. This opens the way to richer, more flexible inference summaries and avoids the numerical problems that are encountered with classical methods. Particular methodologies to cope with incomplete life-tables and a derivation of joint lifetimes, median times to death and related quantities of interest are also presented.

Stochastic search variable selection for log-linear models

We develop a Markov chain Monte Carlo algorithm, based on ‘stochastic search variable selection’ (George and McCuUoch, 1993), for identifying promising log-linear models. The method may be used in the analysis of multi-way contingency tables where the set of plausible models is very large.

Bayesian analysis of extreme values by mixture modeling

Modeling of extreme values in the presence of heterogeneity is still a relatively unexplored area. We consider losses pertaining to several related categories. For each category, we view exceedances over a given threshold as generated by a Poisson process whose intensity is regulated by a specific location, shape and scale parameter. Using a Bayesian approach, we develop a hierarchical mixture prior, with an unknown number of components, for each of the above parameters. Computations are performed using Reversible Jump MCMC. Our model accounts for possible grouping effects and takes advantage of the similarity across categories, both for estimation and prediction purposes. Some guidance on the specification of the prior distribution is provided, together with an assessment of inferential robustness. The method is illustrated throughout using a data set on large claims against a well-known insurance company over a 15-year period.