We propose the Bayesian generalized method of moments (GMM), which is particularly useful when likelihood-based methods are difficult. By deriving the moments and concatenating them together, we build up a weighted quadratic objective function in the GMM framework. As in a normal density function, we take the negative GMM quadratic function divided by two and exponentiate it to substitute for the usual likelihood. After specifying the prior distributions, we apply the Markov chain Monte Carlo procedure to sample from the posterior distribution. We carry out simulation studies to examine the proposed Bayesian GMM procedure, and illustrate it with a real data example.

In credibility theory, the premium charged to a policyholder is computed on the basis of his/her own past claims and the accumulated past claims of the corresponding portfolio of policyholders. In order to obtain an appropriate formula for this, various methodologies have been proposed in actuarial literature, most of them in the field of Bayesian decision methodology.

In this paper, following the robust Bayesian paradigm, a procedure based on the posterior regret $\Gamma$-minimax principle is applied to derive, in a straightforward way, new credibility formula, making use of simple classes of distributions. This methodology is applied to the most commonly used premium calculation principles in insurance, namely the net, Esscher and variance principles.

This paper defines a class of univariate product partition models for which a novel deterministic search algorithm is guaranteed to find the maximum a posteriori (MAP) clustering or the maximum likelihood (ML) clustering. While the number of possible clusterings of $n$ items grows exponentially according to the Bell number, the proposed mode-finding algorithm exploits properties of the model to provide a search requiring only $n(n+1)$ computations. No Monte Carlo is involved. Thus, the algorithm finds the MAP or ML clustering for potentially tens of thousands of items, whereas it can only be approximated through a stochastic search. Integrating over the model parameters in a Dirichlet process mixture (DPM) model leads to a product partition model. A simulation study explores the quality of the clustering estimates despite departures from the assumptions. Finally, applications to three specific models --- clustering means, probabilities, and variances --- are used to illustrate the variety of applicable models and mode-finding algorithm.

A grade of membership (GoM) model is an individual level mixture model which allows individuals have partial membership of the groups that characterize a population. A GoM model for rank data is developed to model the particular case when the response data is ranked in nature. A Metropolis-within-Gibbs sampler provides the framework for model fitting, but the intricate nature of the rank data models makes the selection of suitable proposal distributions difficult. `Surrogate' proposal distributions are constructed using ideas from optimization transfer algorithms. Model fitting issues such as label switching and model selection are also addressed.

The GoM model for rank data is illustrated through an analysis of Irish election data where voters rank some or all of the candidates in order of preference. Interest lies in highlighting distinct groups of voters with similar preferences (i.e. `voting blocs') within the electorate, taking into account the rank nature of the response data, and in examining individuals' voting bloc memberships. The GoM model for rank data is fitted to data from an opinion poll conducted during the Irish presidential election campaign in 1997.

We discuss Bayesian modelling and computational methods in analysis of indirectly observed spatial point processes. The context involves noisy measurements on an underlying point process that provide indirect and noisy data on locations of point outcomes. We are interested in problems in which the spatial intensity function may be highly heterogenous, and so is modelled via flexible nonparametric Bayesian mixture models. Analysis aims to estimate the underlying intensity function and the abundance of realized but unobserved points. Our motivating applications involve immunological studies of multiple fluorescent intensity images in sections of lymphatic tissue where the point processes represent geographical configurations of cells. We are interested in estimating intensity functions and cell abundance for each of a series of such data sets to facilitate comparisons of outcomes at different times and with respect to differing experimental conditions. The analysis is heavily computational, utilizing recently introduced MCMC approaches for spatial point process mixtures and extending them to the broader new context here of unobserved outcomes. Further, our example applications are problems in which the individual objects of interest are not simply points, but rather small groups of pixels; this implies a need to work at an aggregate pixel region level and we develop the resulting novel methodology for this. Two examples with with immunofluorescence histology data demonstrate the models and computational methodology.

Gibbs random fields (GRF) are polymorphous statistical models that can be used to analyse different types of dependence, in particular for spatially correlated data. However, when those models are faced with the challenge of selecting a dependence structure from many, the use of standard model choice methods is hampered by the unavailability of the normalising constant in the Gibbs likelihood. In particular, from a Bayesian perspective, the computation of the posterior probabilities of the models under competition requires special likelihood-free simulation techniques like the Approximate Bayesian Computation (ABC) algorithm that is intensively used in population genetics. We show in this paper how to implement an ABC algorithm geared towards model choice in the general setting of Gibbs random fields, demonstrating in particular that there exists a sufficient statistic across models. The accuracy of the approximation to the posterior probabilities can be further improved by importance sampling on the distribution of the models. The practical aspects of the method are detailed through two applications, the test of an iid Bernoulli model versus a first-order Markov chain, and the choice of a folding structure for two proteins.

A large literature concerns the epidemiology of single pathogens on single hosts. Yet in some environmental applications, such as fungal pathogens of forest tree seedlings, the "one host-one pathogen" paradigm may not be applicable. Multiple potential pathogens are often found in a single individual and/or multiple hosts share the same pathogens. Understanding diversity requires techniques to infer how multiple pathogens might regulate multiple hosts and to predict how impacts might vary with the environment. Here we present a hierarchical framework for the case where there is detection information based on multiple sources (cultures, gene sequencing, and survival observations), and the inference problem includes not only parameters that describe environmental influences on pathogen incidence, infection, and host survival, but also on latent states themselves--pathogen incidence at a site and infection statuses of hosts. Due to the large size of the model space, we develop a reversible jump Markov chain Monte Carlo approach to select models, estimate posterior distributions, and predict environmental influences on host survival. We demonstrate with application to a data set involving fungal pathogens on tree hosts, where data include host survival and fungal detection using cultures and DNA sequencing.

In this paper we address the problem of obtaining a single clustering estimate $\hat{c}$ based on an MCMC sample of clusterings $c^{(1)},c^{(2)}\ldots,c^{(M)}$ from the posterior distribution of a Bayesian cluster model. Methods to derive $\hat{c}$ when the number of groups $K$ varies between the clusterings are reviewed and discussed. These include the maximum a posteriori (MAP) estimate and methods based on the posterior similarity matrix, a matrix containing the posterior probabilities that the observations $i$ and $j$ are in the same cluster. The posterior similarity matrix is related to a commonly used loss function by Binder (1978). Minimization of the loss is shown to be equivalent to maximizing the Rand index between estimated and true clustering. We propose new criteria for estimating a clustering, which are based on the posterior expected adjusted Rand index. The criteria are shown to possess a shrinkage property and outperform Binder's loss in a simulation study and in an application to gene expression data. They also perform favorably compared to other clustering procedures.

Computer model evaluation studies build statistical models of deterministic simulation-based predictions of field data to then assess and criticize the computer model and suggest refinements. Computer models are often expensive computationally: statistical models that adequately emulate their key features can be very much more efficient. Gaussian process models are often used as emulators, but the resulting computations lack the ability to scale to higher-dimensional, time-dependent or functional outputs. For some such problems, especially for contexts of time series outputs, building emulators using dynamic linear models provides a computationally attractive alternative as well as a flexible modelling approach capable of emulating a broad range of stochastic structures underlying the input-output simulations. We describe this here, combining Bayesian multivariate dynamic linear models with Gaussian process modelling in an effective manner, and illustrate the approach with data from a hydrological simulation model. The general strategy will be useful for other computer model evaluation studies with time series or functional outputs.