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.

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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.

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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

It is shown that an inequality among parameters of a non-symmetric strongly resolvable design, conjectured by A Beutelspacher and U Porta [1], is valid in general

An inequality for strongly resolvable designs

We propose a new unequal probability scheme for shared key operations. It is seen that this scheme improves upon the values of anonymity measures, as quantified via appropriate conditional probabilities, over the existing ones, which are based on equal probability selection.

An Unequal Probability Scheme for Improving Anonymity in Shared Key Operations

The present paper obtains necessary and sufficient conditions for factorial orthogonality in the presence of covariates. In particular, when interactions are absent, combinatorial characterizations of the conditions, as natural generalizations of the well-known equal and proportional frequency criteria, have been derived.

Factorial orthogonality in the presence of covariates

Key predistribution schemes for distributed sensor networks have received significant attention in the recent literature. In this paper we propose a new construction method for these schemes based on combinations of duals of standard block designs. Our method is a broad spectrum one which works for any intersection threshold. By varying the initial designs, we can generate various schemes and this makes the method quite flexible. We also obtain explicit algebraic expressions for the metrics for local connectivity and resiliency. These schemes are quite efficient with regard to connectivity and resiliency and at the same time they allow a straightforward shared-key discovery.

Key Predistribution Schemes for Distributed Sensor Networks

We consider the problem of comparing predictive intervals for a future observation via their expected lengths at a given confidence level. A higher order asymptotic theory is developed. This yields an explicit formula for expected length comparison and associated admissibility results. Illustrative examples are given.

Rahul Mukerjee

Papers

An inequality for strongly resolvable designs

An Unequal Probability Scheme for Improving Anonymity in Shared Key Operations

Factorial orthogonality in the presence of covariates

Key Predistribution Schemes for Distributed Sensor Networks

On Expected Lengths of Predictive Intervals