While there have been few theoretical contributions on the Markov Chain Monte Carlo
(MCMC) methods in the past decade, current understanding and application of MCMC to the …

The use of the Gibbs sampler as a method for calculating Bayesian marginal posterior and
predictive densities is reviewed and illustrated with a range of normal data models, including …

Kendall's Advanced Theory of Statistics and Kendall's Library of Statistics The development
of modern statistical theory in the past fifty years is reflected in the history of the late Sir …

Tierney and Kadane (1986) presented a simple second-order approximation for posterior
expectations of positive functions. They used Laplace's method for asymptotic evaluation of …

We present methods for justifying heuristic derivations of asymptotic expansions for
predictive densities, odds factors, marginal posterior densities, and posterior moments given …

The key quantity needed for Bayesian hypothesis testing and model selection is the
integrated, or marginal, likelihood of a model. We describe a way to use posterior simulation …

This paper is a survey of the major techniques and approaches available for the numerical
approximation of integrals in statistics. We classify these into five broad categories; namely …

SUMMARY A fully Bayesian analysis of linear and non‐linear population models has
previously been unavailable, as a consequence of the seeming impossibility of performing …

An exact Bayesian analysis of finite mixture distributions is often computationally infeasible,
because the number of terms in the posterior density grows exponentially with the sample …

This paper presents Bayesian estimation of the survival function of the Pareto distribution of
the second kind using the methods of Lindley (1980) and Tierney and Kadane (1986). A …