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## Perfect simulation for Reed-Frost epidemic models

### Statistics and Computing (2003-02-01) 13: 37-44 , February 01, 2003

The Reed-Frost epidemic model is a simple stochastic process with parameter *q* that describes the spread of an infectious disease among a closed population. Given data on the final outcome of an epidemic, it is possible to perform Bayesian inference for *q* using a simple Gibbs sampler algorithm. In this paper it is illustrated that by choosing latent variables appropriately, certain monotonicity properties hold which facilitate the use of a perfect simulation algorithm. The methods are applied to real data.

## Bayesian detection of structural changes

### Annals of the Institute of Statistical Mathematics (1991-03-01) 43: 77-93 , March 01, 1991

A Bayesian solution is given to the problem of making inferences about an unknown number of structural changes in a sequence of observations. Inferences are based on the posterior distribution of the number of change points and on the posterior probabilities of possible change points. Detailed analyses are given for binomial data and some regression problems, and numerical illustrations are provided. In addition, an approximation procedure to compute the posterior probabilities is presented.

## Bayesian multivariate Poisson mixtures with an unknown number of components

### Statistics and Computing (2007-06-01) 17: 93-107 , June 01, 2007

In this paper we present Bayesian analysis of finite mixtures of multivariate Poisson distributions with an unknown number of components. The multivariate Poisson distribution can be regarded as the discrete counterpart of the multivariate normal distribution, which is suitable for modelling multivariate count data. Mixtures of multivariate Poisson distributions allow for overdispersion and for negative correlations between variables. To perform Bayesian analysis of these models we adopt a reversible jump Markov chain Monte Carlo (MCMC) algorithm with birth and death moves for updating the number of components. We present results obtained from applying our modelling approach to simulated and real data. Furthermore, we apply our approach to a problem in multivariate disease mapping, namely joint modelling of diseases with correlated counts.

## Parallelizing MCMC for Bayesian spatiotemporal geostatistical models

### Statistics and Computing (2007-12-01) 17: 323-335 , December 01, 2007

When MCMC methods for Bayesian spatiotemporal modeling are applied to large geostatistical problems, challenges arise as a consequence of memory requirements, computing costs, and convergence monitoring. This article describes the parallelization of a reparametrized and marginalized posterior sampling (RAMPS) algorithm, which is carefully designed to generate posterior samples efficiently. The algorithm is implemented using the Parallel Linear Algebra Package (PLAPACK). The scalability of the algorithm is investigated via simulation experiments that are implemented using a cluster with 25 processors. The usefulness of the method is illustrated with an application to sulfur dioxide concentration data from the Air Quality System database of the U.S. Environmental Protection Agency.

## Acute Middle Ear Infection in Small Children: A Bayesian Analysis Using Multiple Time Scales

### Lifetime Data Analysis (1998-06-01) 4: 121-137 , June 01, 1998

The study is based on a sample of 965 children living in Oulu region (Finland), who were monitored for acute middle ear infections from birth to the age of two years. We introduce a nonparametrically defined intensity model for ear infections, which involves both fixed and time dependent covariates, such as calendar time, current age, length of breast-feeding time until present, or current type of day care. Unmeasured heterogeneity, which manifests itself in frequent infections in some children and rare in others and which cannot be explained in terms of the known covariates, is modelled by using individual frailty parameters. A Bayesian approach is proposed to solve the inferential problem. The numerical work is carried out by Monte Carlo integration (Metropolis-Hastings algorithm).

## Numerical Bayesian inference with arbitrary prior

### Statistical Papers (2000-10-01) 41: 437-451 , October 01, 2000

The purpose of the paper, is to explain how recent advances in Markov Chain Monte Carlo integration can facilitate the routine Bayesian analysis of the linear model when the prior distribution is completely user dependent. The method is based on a Metropolis-Hastings algorithm with a Student-t source distribution that can generate posterior moments as well as marginal posterior densities for model parameters. The method is illustrated with numerical examples where the combination of prior and likelihood information leads to multimodal posteriors due to prior-likelihood conflicts, and to cases where prior information can be summarized by symmetric stable Paretian distributions.

## A comparison of centring parameterisations of Gaussian process-based models for Bayesian computation using MCMC

### Statistics and Computing (2017-11-01) 27: 1491-1512 , November 01, 2017

Markov chain Monte Carlo (MCMC) algorithms for Bayesian computation for Gaussian process-based models under default parameterisations are slow to converge due to the presence of spatial- and other-induced dependence structures. The main focus of this paper is to study the effect of the assumed spatial correlation structure on the convergence properties of the Gibbs sampler under the default non-centred parameterisation and a rival centred parameterisation (CP), for the mean structure of a general multi-process Gaussian spatial model. Our investigation finds answers to many pertinent, but as yet unanswered, questions on the choice between the two. Assuming the covariance parameters to be known, we compare the exact rates of convergence of the two by varying the strength of the spatial correlation, the level of covariance tapering, the scale of the spatially varying covariates, the number of data points, the number and the structure of block updating of the spatial effects and the amount of smoothness assumed in a Matérn covariance function. We also study the effects of introducing differing levels of geometric anisotropy in the spatial model. The case of unknown variance parameters is investigated using well-known MCMC convergence diagnostics. A simulation study and a real-data example on modelling air pollution levels in London are used for illustrations. A generic pattern emerges that the CP is preferable in the presence of more spatial correlation or more information obtained through, for example, additional data points or by increased covariate variability.

## Bayesian estimation in the class of bisexual branching processes with population-size dependent mating

### TEST (2008-05-01) 17: 179-196 , May 01, 2008

This paper deals with the class of bisexual branching processes with population-size dependent mating introduced in Molina et al. (2002, Bisexual Galton–Watson branching process with population-size dependent mating. *J Appl Probab* 39:479–490). We determine Bayes estimators for the main moments of such processes in both situations: assuming offspring distribution belonging to the bivariate power series family and considering that no assumption is made about the underlying offspring distribution. As illustration we provide several examples, in particular, considering some classical offspring distributions, we explicitly determine the proposed Bayes estimators and, through simulation, we show the evolution of their estimates and of the corresponding high posterior density credibility sets.

## Multivariate mixtures of normals with unknown number of components

### Statistics and Computing (2006-01-01) 16: 57-68 , January 01, 2006

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 factor analysis for spatially correlated data: application to cancer incidence data in Scotland

### Statistical Methods & Applications (2012-03-01) 21: 49-74 , March 01, 2012

A hierarchical Bayesian factor model for multivariate spatially correlated data is proposed. Multiple cancer incidence data in Scotland are jointly analyzed, looking for common components, able to detect etiological factors of diseases hidden behind the data. The proposed method searches factor scores incorporating a dependence within observations due to a geographical structure. The great flexibility of the Bayesian approach allows the inclusion of prior opinions about adjacent regions having highly correlated observable and latent variables. The proposed model is an extension of a model proposed by Rowe (2003a) and starts from the introduction of separable covariance matrix for the observations. A Gibbs sampling algorithm is implemented to sample from the posterior distributions.