In this chapter we enlarge the sampling information considered so far by adding to the data of cost and effectiveness of every patient a set of patient covariates. The covariates indicate certain deterministic physical characteristics of the patient such as age, sex, health status, and semiological variables of the disease. The optimal treatment for the whole patient population is typically suboptimal for subgroups, and hence the adaptation of the cost-effectiveness analysis to this situation is of interest and yields the cost-effectiveness analysis for subgroups. Since the definition of patient subgroups is made in terms of the set of covariates it is important to exclude those covariates that do not have an influence on the disease. This means that for carrying out a cost-effectiveness analysis for subgroups a previous step should be the statistical detection of the influential covariates from the original set of them. A …

Summary 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.

This presidential address explores how statisticians can exploit their skills and expertise effectively to ensure that development strategies are pro poor and pro equity. Many papers in statistical journals have addressed the work of national official statisticians but few have examined the work of statisticians in international, supranational or bilateral agencies. This paper attempts to redress this imbalance by highlighting some of the dilemmas facing international statisticians. It aims to raise consciousness of the role of statisticians employed in an international context, to explain some of the constraints under which they work, to address principles which ought to govern the activities of statisticians generally and to evaluate the relevance of such principles to international statisticians in particular.

Dawid (1973,Biometrika60, 664–666) stated conditions in the univariate location model with known scale parameter needed for there to be either vanishing likelihood or prior influence on the posterior distribution when there is a conflict between likelihood and prior. More recently, Pericchi and Sansó (1995,Biometrika82, 223–225) noted that there are distributions that partially satisfy Dawid's conditions but have bounded rather than vanishing influence on the posterior distribution. In this paper, we present the extension of these results for the location and scale model using the multivariatev-spherical distributions. We show that when thev(·)=‖·‖ function is a norm, the ‖‖-spherical distributions, exponential power, and logistic power provide a robust analysis for the location model with known scale parameter, whereas Student's powertprovides a robust analysis for the location and scale model. Robust analyses are illustrated for normal-gamma prior location and scale models. Numerical computations are implemented via the Gibbs sampler.

A quadruplex system for determining the genetic profile of an individual at four short tandem repeat (STR) loci has recently been introduced into forensic casework by the Forensic Science Service (FSS), primarily for the purposes of forensic identification. Data have been collected under this system from the three racial groups of most relevance in casework in the UK: Caucasian. Afro-Caribbean and Asian (from the Indian subcontinent). These data are utilized in calculations to quantify the evidential strength of a DNA match between suspect and crime scene sample, say, through the evaluation of a likelihood ratio (LR). Previous papers (1,2) have studied the databases via classical statistical methods. However, we focus on a Bayesian approach (3) to validation of the data for LR evaluation in two main cases: when individuals being compared are either (i) completely unrelated, or (ii) members of the same racial group subpopulation. Empirical studies are conducted to establish the robustness of proposed models and obtain efficient and adequate approximations to the LR calculations. This involves the use of statistical simulation methods to determine the suitability of the product rule and Bayesian inference for coancestry coefficients in the absence of subpopulation data.

Bayesian approaches to model choice are reviewed from an historical perspective and then discussed in terms of possible desiderata and principles. Particular focus is given to issues of conformity with a decision-theoretic formulation and to the issue of model choice when none of the available models is regarded as true.

We present a Bayesian analysis of variance component models via simulation. In particular, we study the 2-component hierarchical design model under balanced and unbalanced experiments. Also, we consider 2-factor additive random effect models and mixed models in a cross-classified design. We assess the sensitivity of inference to the choice of prior by a sampling/resampling technique. Finally, attention is given to non-normal error distributions such as the heavy-tailed t distribution.

Freeman and Morgan (1992, Biometrics 48, 217-235) recently proposed a strategy for analysing recovery data from birds ringed as nestlings. In this paper we consider a Bayesian reanalysis of their models, using Markov chain Monte Carlo methods to perform inferences conditional on models and a combination of simulation and graphical diagnostics to compare models.

Stochastic processes with independent increments play a central role in Bayesian nonparametric inference. The distributions of the increments of these processes, aside from fixed points of discontinuity, are infinitely divisible and their Laplace and/or Fourier transforms in the Levy representation are usually known. Conventional Bayesian inference in this context has been limited largely to providing point estimates of the random quantities of interest, although Markov chain Monte Carlo methods have been used to obtain a fuller analysis in the context of Dirichlet process priors. In this paper, we propose and implement a general method for simulating infinitely divisible random variates when their Fourier or Laplace transforms are available in the Levy representation. Theoretical justification is established by proving a convergence theorem that is a 'sampling form' of a classical theorem in probability. The results provide a method for implementing Bayesian nonparametric inference by using a wide range of stochastic processes as priors.

A fit of the Poisson-gamma model to the pump-failure data quoted by George et al. (Scand. J. Statist. 20, 147-156) using maximum conjugate likelihood gives pump effects that agree closely with the values obtained from a full Bayesian model. However, the model is a poor fit, because the estimates of the pump effects do not look like a sample from a gamma distribution. A split of the pumps into two subgroups does give an adequate fit.

We consider the problem of directly extracting high-level shape information from images of scenes involving faces. The approach adopted owes much to the work of Grenander and colleagues at Brown University on pattern analysis and involves designing stochastic deformable templates for objects in the underlying image scenes. A wide range of realistic object poses can be captured by imposing a prior probability distribution over the space of allowable deformations. We show how hierarchical models can be used to organize the prior information into a coherent structure. Markov chain Monte Carlo methods are exploited to recover the deformation given observed image data.

A fully Bayesian analysis of linear and non-linear population models has previously been unavailable, as a consequence of the seeming impossibility of performing the necessary numerical integrations in the complex multiparameter structures that typically arise in such models. It is demonstrated that, for a variety of linear and non-linear population models, a fully Bayesian analysis can be implemented in a straightforward manner by using the Gibbs sampler. The approach is illustrated with examples involving challenging problems of outliers and mean-variance relationships in population modelling.

An ANTIQUITY paper used the methods of Bayesian statistics to combine radiocarbon and stratigraphic information into a single considered view. But are they different kinds of information, more fairly kept separate?

Abstract We examine the problem of constructing thematic maps which show land-use patterns, given satellite data and deterministic prior information. The latter came from a road network. We make the simplifying assumption that the satellite observations are conditionally independent, given the scene. We specify a normal likelihood, the usual normal-inverse Wishart prior for the distributional parameters, and a Markov random field prior for the image together with the road information. Our results indicate that the Markov random field prior and road network information help improve classification, despite evidence that the assumption of normal likelihoods is suspect.

Markov chain Monte Carlo (MCMC) simulation methods are being used increasingly in statistical computation to explore and estimate features of likelihood surfaces and Bayesian posterior distributions. This paper presents simple conditions which ensure the convergence of two widely used versions of MCMC, the Gibbs sampler and Metropolis-Hastings algorithms.

The three-parameter Weibull density is commonly used to model the distribution of tree diameters in forest stands. We demonstrate, through likelihood profiles, that maximum likelihood estimation is often inappropriate for data from young trees due to negative estimates of the location parameter. We suggest a Bayesian model and fit it, using the Gibbs sampler, to three data sets. The latter model is easy to implement and guarantees a positive estimate for the location parameter. We illustrate some novel forms of model diagnostics, demonstrating that the Bayesian model is appropriate for two of the data sets, while it is dubious for the third. A sampling-resampling method shows that the lack of fit of the model for the latter data set is due to the likelihood, and not the prior specification.

The use of the Gibbs sampler for Bayesian computation is reviewed and illustrated in the context of some canonical examples. Other Markov chain Monte Carlo simulation methods are also briefly described, and comments are made on the advantages of sample-based approaches for Bayesian inference summaries.