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

Two-level minimum aberration designs in N =2 (mod 4) runs

In a multiparameter set-up, this paper characterizes priors which ensure frequentist validity, up to o(n-1), of confidence regions based on the highest posterior density. The role of Jeffreys' prior in this regard has also been investigated.

/pdf/corrections-to-frequentist-validity-of-highest-posterior-38vq2jmvyp.pdf

Corrections to “Frequentist validity of highest posterior density regions in the multiparameter case”

Anti-collusion digital fingerprinting codes have been of significant current interest in the context of deterring unauthorized use of multimedia content by a coalition of users In this article, partially cover-free families of sets are considered and these are employed to obtain such codes Compared to the existing methods of construction, our methods ensure gains in terms of accommodating more users and/or reducing the number of basis vectors

Anti-Collusion Digital Fingerprinting Codes via Partially Cover-Free Families

Since X -m and X -m-1 are consecutive integers, the inequality (I) follows considering the expectation of the nonnegative quantity (x-m)(x-m-1). The simple inequaliy \\(1) is useful in proving nonexistence results on symmetric rothogonal arrays. For ease in reference, recall that a symmetric orthogonal array LN(sn), of strenths two, is an Nxn array, with entries from a set of s (~ 2) distinct symbols such that all the s2 possible ordered pairs of symbols appear equally often as row vectors in every N x 2 subarray thereof. In LN(sn), let x; be the number of positions in which the 1st and the ith rows have indentical entries (2 ::; i ::; N). Also, let X be an integer-valued random variable assuming values x2 , ... , XN, each with probaility l/(N -1). Then, from the definition of LN(sn), it is not hard to see that

http://csa.sagepub.com/content/48/1-2/119.full.pdf

On Multivariate Extension of an Inequality with a Potential Application

SYNOPTIC ABSTRACTWe consider the problem of nonparametric estimation of the optimal ordering strategy in a one-period inventory situation where both the supply and the (customer) demand are random variables with unknown distributions. Almost sure convergence of the proposed estimator to its true value has been established.

Rahul Mukerjee

Papers

Two-level minimum aberration designs in N =2 (mod 4) runs

Corrections to “Frequentist validity of highest posterior density regions in the multiparameter case”

Anti-Collusion Digital Fingerprinting Codes via Partially Cover-Free Families

On Multivariate Extension of an Inequality with a Potential Application

Optimal Ordering Strategy Under Risk and its Nonparametric Estimation