Introduction To motivate the methods described in this chapter, consider the following inference problem in astronomy (Soubiran, 1993). Until fairly recently, it has been believed that the Galaxy consists of two stellar populations, the disk and the halo. More recently, it has been hypothesized that there are in fact three stellar populations, the old (or thin) disk, the thick disk, and the halo, distinguished by their spatial distributions, their velocities, and their metallicities. These hypotheses have different implications for theories of the formation of the Galaxy. Some of the evidence for deciding whether there are two or three populations is shown in Figure 1, which shows radial and rotational velocities for n = 2; 370 stars. A natural model for this situation is a mixture model with J components, namely y i = J X j=1 ae j

A new approach to cluster analysis has been introduced based on parsimonious geometric modelling of the within-group covariance matrices in a mixture of multivariate normal distributions, using hierarchical agglomeration and iterative relocation. It works well and is widely used via the MCLUST software available in S-PLUS and StatLib. However, it has several limitations: there is no assessment of the uncertainty about the classification, the partition can be suboptimal, parameter estimates are biased, the shape matrix has to be specified by the user, prior group probabilities are assumed to be equal, the method for choosing the number of groups is based on a crude approximation, and no formal way of choosing between the various possible models is included. Here, we propose a new approach which overcomes all these difficulties. It consists of exact Bayesian inference via Gibbs sampling, and the calculation of Bayes factors (for choosing the model and the number of groups) from the output using the Laplace-Metropolis estimator. It works well in several real and simulated examples.

This thesis addresses a number of issues concerned with the restoration of one type of image sequence, namely archived black and white motion pictures. These are often a valuable historical record, but because of the physical nature of the film they can suffer from a variety of degradations which reduce their usefulness. The main visual defects are `dirt and sparkle' due to dust and dirt becoming attached to the film, or abrasion removing the emulsion, and `line scratches' due to the film running against foreign bodies in the camera or projector. For an image

`Publication bias' is a relatively new statistical phenomenon that only arises when one attempts through a meta-analysis to review all studies, significant or insignificant, in order to provide a total perspective on a particular issue. This has recently received some notoriety as an issue in the evaluation of the relative risk of lung cancer associated with passive smoking, following legal challenges to a 1992 EPA analysis which concluded that such exposure is associated with significant excess risk of lung cancer. We introduce a Bayesian approach which estimates and adjusts for publication bias. Estimation is based on a data augmentation principle within a hierarchical model, and the number and outcomes of unobserved studies are simulated using Gibbs sampling methods. This technique yields a quantitative adjustment for the passive smoking meta-analysis. We estimate that there may be both negative and positive but insignificant studies omitted, and that failing to allow for these woul...

We are grateful to Melissa Hughes of Signal Corporation and EPA Rhode Island and to Tony Olsen of EPA Corvallis for making these data available to us, to Wendy Meiring for a careful reading of the paper and many valuable suggestions, and to two anonymous referees for helpful comments. This research had partial support from the United States Environmental Protection Agency under a cooperative agreement withthe University ofWashington. This document has not undergone Agency review, and re ects in no way o cial Agency policy. 1 Biological monitoring of aquatic biota is used to assess the impact of changes in the environment. Critical to the development of a sound biological monitoring protocol is the judicious selection of organisms and organism characteristics to be monitored. Accurate interpretations of change necessitate description of the natural variability of the system. We introduce a state-space model for compositional monitoring data, and illustrate how one can incorporate spatial structure and covariates to assess natural variability. The methods are illustrated on benthic survey data from Delaware Bay, and applied to proportional composition at the genus level. The distribution of benthic macroinvertebrates in Delaware Bay depends signi cantly on salinity. There is residual spatial dependence in the data after accounting for the salinity e ect. Key Words: Biological monitoring � benthic invertebrates � spatial model � statespace model 1.

Multivariate event time data arises frequently in both medical and industrial settings. In such data sets: event times may be associated with quite different occurrences, event times can not be considered as independent - the distribution of time to occurrence of one event may change after the occurrence of another, events can occur simultaneously, available covariate information may provide useful explanation. Censoring in some of the observations, both partial and complete, occurs. Focusing on the bivariate case, we formulate models rich enough to accommodate these features. In the spirit of fatal shock models our classes are built using latent waiting times which are assumed to follow general proportional hazards or accelerated life models. We adopt a Bayesian perspective for inference using simulation based fitting which routinely handles censoring. Since a wide range of model specifications can be introduced, we propose a generic model selection criterion for choosing among bivari...

This research was supported by O ceofNaval Research contract no. N-00014-91-J-1074 and by INRIA, France. The authors are grateful to Jean Diebolt for helpful discussions and to Caroline Ban eld and Raftery (1993) introduced a new approach to cluster analysis based on parsimonious geometric modeling of the within-group covariance matrices in a mixture of multivariate normal distributions, using hierarchical agglomeration and iterative relocation. It works well and is widely used via the MCLUST software available in S-PLUS and StatLib. However, it has several limitations: there is no assessment of the uncertainty about the classi cation, the partition can be suboptimal, parameter estimates are biased, the shape matrix has to be speci ed by the user, prior group probabilities are assumed to be equal, the method for choosing the number of groups is based on a crude approximation, and no formal way of choosing between the various possible models is included. We propose a new approach whichovercomes these di culties. It consists of exact Bayesian inference via Gibbs sampling, and the calculation of Bayes factors (for choosing the model and the number of groups) from the output using the Laplace-Metropolis estimator.

diagnostic for a set of (not-necessarily independent) MCMC sampers. It combines the estimate error-bounding approach of Raftery and Lewis with evaulate between verses within chain approach of Gelman and Rubin.

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One of the most influential results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent work has shown that while these generative models do have the right degree distribution, they are not good models for real life networks due to their differences on other important metrics like conductance. We believe this is, in part, because many of these real-world networks have very different joint degree distributions, i.e. the probability that a randomly selected edge will be between nodes of degree k and l. Assortativity is a sufficient statistic of the joint degree distribution, and it has been previously noted that social networks tend to be assortative, while biological and technological networks tend to be disassortative. We suggest that the joint degree distribution of graphs is an interesting avenue of study for further research into network structure. We provide a simple greedy algorithm for constructing simple graphs from a given joint degree distribution, and a Monte Carlo Markov Chain method for sampling them. We also show that the state space of simple graphs with a fixed degree distribution is connected via endpoint switches. We empirically evaluate the mixing time of this Markov Chain by using experiments based on the autocorrelation of each edge.