Recentered importance sampling with applications to Bayesian model validation

Since its introduction in the early 1990s, the idea of using importance sampling (IS) with Markov chain Monte Carlo (MCMC) has found many applications. This article examines problems associated with its application to repeated evaluation of related posterior distributions with a particular focus on Bayesian model validation. We demonstrate that, in certain applications, the curse of dimensionality can be reduced by a simple modification of IS. In addition to providing new theoretical insight into the behavior of the IS approximation in a wide class of models, our result facilitates the implementation of computationally intensive Bayesian model checks. We illustrate the simplicity, computational savings, and potential inferential advantages of the proposed approach through two substantive case studies, notably computation of Bayesian p-values for linear regression models and simulation-based model checking. Supplementary materials including the Appendix and the R code for Section 3.1.2 are available online

Estimation and Simulation of the Reisz-Bessel Distribution

In this paper, further properties of the Riesz-Bessel distribution are provided. These properties allow for the simulation of random variables from the Riesz-Bessel distribution. Estimation is addressed by nonlinear generalized least squares regression on the empirical characteristic function. The estimator is seen to approximate the maximum likelihood estimator. The distribution is illustrated with financial data

A Bayesian-Decision Theoretic Approach to Model Error Modeling

This paper takes a Bayesian-decision theoretic approach to transfer function estimation, nominal model estimation, and quantification of the resulting model error. Consistency of the nonparametric estimate of the transfer function is proved together with a rate of convergence. The required quantities can be computed routinely using reversible jump Markov chain Monte Carlo methods. The proposed methodology has connections with set membership identification which has been extensively studied for this problem

Gates' Bidding Model

In evaluating closed-bid competitive procurement auctions, the most crucial issue is to determine the probability of placing a winning bid for a given mark-up level. There has long been disagreement on how this should be done due to the absence of a mathematical derivation of one of the main evaluation techniques – Gates' method. Gates' method is shown in this paper to be valid if, and only if, bids can be described using the proportional hazards family of statistical distributions. When mark-up values are included in Gates' method, it is seen that the underlying statistical distribution required for the method to work is closely related to the Weibull distribution. Likelihood based methods are suggested for parameter estimation and an illustrative example is provided by analysis of Shaffer and Micheau's (1971) construction contract bidding data

Optimising prediction error among completely monotone covariance sequences

We provide a characterisation of Gaussian time series which optimise the one-step prediction error subject to the covariance sequence being completely monotone with the first m covariances specified