Showing papers by "Rahul Mukerjee published in 2002"

Uniformity in Fractional Factorials

Abstract: The issue of uniformity is crucial in quasi-Monte Carlo methods and in the design of computer experiments. In this paper we study the role of uniformity in fractional factorial designs. For fractions of two- or three-level factorials, we derive results connecting orthogonality, aberration and uniformity and show that these criteria agree quite well. This provides further justification for the criteria of orthogonality or minimum aberration in terms of uniformity. Our results refer to several natural measures of uniformity and we consider both regular and nonregular fractions. The theory developed here has the potential of significantly reducing the complexity of computation for searching for minimum aberration designs.

On an exact probability matching property of right‐invariant priors

Abstract: SUMMARY The paper considers priors which are right invariant with respect to the Haar measure. It is shown that the posterior coverage probabilities of certain invariant Bayesian predictive regions exactly match the corresponding frequentist probabilities. Several examples are given to illustrate the main result.

Optimal main effect plans with non‐orthogonal blocking

Abstract: The current literature on fractional factorial plans in block designs centres around orthogonal blocking which may not, however, always be attainable because of practical restrictions on the block size. For general factorials, including asymmetric ones, sufficient conditions are indicated in this paper for a main effect plan to be universally optimal under possibly non-orthogonal blocking. A construction procedure is given using generalised Youden designs in conjunction with orthogonal arrays. We also illustrate how the procedure can be applied to obtain optimal main effect plans in the practically important situation where each factor has two or three levels and the block size is small.

On the positive definiteness of the information matrix under the binary and poisson mixed models

Abstract: Binary and Poisson generalized linear mixed models are used to analyse over/under-dispersed proportion and count data, respectively. As the positive definiteness of the information matrix is a required property for valid inference about the fixed regression vector and the variance components of the random effects, this paper derives the relevant necessary and sufficient conditions under both these models. It is found that the conditions for the positive definiteness are not identical for these two nonlinear mixed models and that a mere analogy with the usual linear mixed model does not dictate these conditions.