This paper reviews the literature on Bayesian experimental design. A unified view of this topic is presented, based on a decision-theoretic approach. This framework casts criteria from the Bayesian literature of design as part of a single coherent approach. The decision-theoretic structure incorporates both linear and nonlinear design problems and it suggests possible new directions to the experimental design problem, motivated by the use of new utility functions. We show that, in some special cases of linear design problems, Bayesian solutions change in a sensible way when the prior distribution and the utility function are modified to allow for the specific structure of the experiment. The decision-theoretic approach also gives a mathematical justification for selecting the appropriate optimality criterion.

/pdf/bayesian-experimental-design-a-review-1z4pqf25ac.pdf

Bayesian Experimental Design: A Review

Subjectivism has become the dominant philosophical foundation for Bayesian inference. Yet in practice, most Bayesian analyses are performed with so-called “noninformative” priors, that is, priors constructed by some formal rule. We review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used. We give special emphasis to Jeffreys's rules and discuss the evolution of his viewpoint about the interpretation of priors, away from unique representation of ignorance toward the notion that they should be chosen by convention. We conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly: When sample sizes are small (relative to the number of parameters being estimated), it is dangerous to put faith in any “default” solution; but when asymptotics take over, Jeffreys's rules and their variants remain reasonable choices. We also provide an annotated b...

The Selection of Prior Distributions by Formal Rules

This chapter provides an overview of recent developments in the design and analysis of cross-over trials. We first consider the analysis of the trial that compares two treatments, A and B, over two periods and where the subjects are randomized to the treatment sequences AB and BA. We make the distinction between fixed and random effects models and show how these models can easily be fitted using modern software. Issues with fitting and testing for a difference in carry-over effects are described and the use of baseline measurements is discussed. Simple methods for testing for a treatment difference when the data are binary are also described. Various designs with two or more treatments but with three or four periods are then described and compared. These include the balanced and partially balanced designs for three or more treatments and designs for factorial treatment combinations. Also described are nearly balanced and nearly strongly balanced designs. Random subject-effects models for the designs with two or more treatments are described and methods for analysing non-normal data are also given. The chapter concludes with a description of the use of cross-over designs in the testing of bioequivalence.

/pdf/design-and-analysis-of-cross-over-trials-4ootbxi8hy.pdf

Design and Analysis of Cross-Over Trials

Maximizing data information requires careful selection, termed design, of the points at which data are observed. Experimental design is reviewed here for broad classes of data collection and analysis problems, including: fractioning techniques based on orthogonal arrays, Latin hypercube designs and their variants for computer experimentation, efficient design for data mining and machine learning applications, and sequential design for active learning. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.

Experimental design

A uniform design (UD) seeks design points that are uniformly scattered on the domain. It has been popular since 1980. A survey of UD is given in the first portion: The fundamental idea and construction method are presented and discussed and examples are given for illustration. It is shown that UD's have many desirable properties for a wide variety of applications. Furthermore, we use the global optimization algorithm, threshold accepting, to generate UD's with low discrepancy. The relationship between uniformity and orthogonality is investigated. It turns out that most UD's obtained here are indeed orthogonal.

Uniform Design: Theory and Application

SUMMARY This paper considers, in the multiparameter case, perturbed ellipsoidal and highest posterior density regions with both Bayesian and frequentist validity up to o (n-I).

On Perturbed Ellipsoidal and Highest Posterior Density Regions with

Shoutir Kishore Chatterjee was born in Ranchi, a small hill station in India, on November 6, 1934. He received his B.Sc. in statistics from the Presidency College, Calcutta, in 1954, and M.Sc. and Ph.D. degrees in statistics from the University of Calcutta in 1956 and 1962, respectively. He was appointed a lecturer in the Department of Statistics, University of Calcutta, in 1960 and was a member of its faculty until his retirement as a professor in 1997. Indeed, from the 1970s he steered the teaching and research activities of the department for the next three decades. Professor Chatterjee was the National Lecturer in Statistics (1985–1986) of the University Grants Commission, India, the President of the Section of Statistics of the Indian Science Congress (1989) and an Emeritus Scientist (1997–2000) of the Council of Scientific and Industrial Research, India. Professor Chatterjee, affectionately known as SKC to his students and admirers, is a truly exceptional person who embodies the spirit of eternal India. He firmly believes that “fulfillment in man’s life does not come from amassing a lot of money, after the threshold of what is required for achieving a decent living is crossed. It does not come even from peer recognition for intellectual achievements. Of course, one has to work and toil a lot before one realizes these facts.”

/pdf/a-conversation-with-shoutir-kishore-chatterjee-28lqm9pri1.pdf

A Conversation with Shoutir Kishore Chatterjee

Further results on optimal designs with circular string property

In this paper we shall consider the problem of judging how good an actual compromise allocation is compared to Neyman's optimum allocation for the case of stratified random sampling by obtaining a bound to the ratio of the corresponding variances. A solution to a more general version of the problem considered by COCHRAN (1977) and RAO (1983) has been obtained and the results have been empirically demonstrated.

Rahul Mukerjee

Papers

On Perturbed Ellipsoidal and Highest Posterior Density Regions with

A Conversation with Shoutir Kishore Chatterjee

Further results on optimal designs with circular string property

On a Problem of Allocation of Sample Size in Stratified Random Sampling

Optimal spatial sampling plans in the presence of linear trend