Rahul Mukerjee

Bio: Rahul Mukerjee is an academic researcher from Indian Institute of Management Calcutta. The author has contributed to research in topics: Frequentist inference & Prior probability. The author has an hindex of 30, co-authored 206 publications receiving 3507 citations. Previous affiliations of Rahul Mukerjee include Siemens & Chiba University.

D-optimal designs for covariate models

Abstract: The problem of finding D-optimal or D-efficient designs in the presence of covariates is considered under a completely randomized design set-up with v treatments, k covariates and N experimental units. In contrast to Lopes Troya [Lopes Troya, J., 1982, Optimal designs for covariates models. Journal of Statistical Planning and Inference, 6, 373–419.], who considered this problem in the equireplicate case, we do not assume that N/v is an integer, and this allows us to study situations where no equireplicate design exists. Even when N/v is an integer, it is seen quite counter-intuitively that there are situations where a non-equireplicate design outperforms the best equireplicate design under the D-criterion.

Optimal (2, n) visual cryptographic schemes

Abstract: In (2,n) visual cryptographic schemes, a secret image(text or picture) is encrypted into n shares, which are distributed among n participants. The image cannot be decoded from any single share but any two participants can together decode it visually, without using any complex decoding mechanism. In this paper, we introduce three meaningful optimality criteria for evaluating different schemes and show that some classes of combinatorial designs, such as BIB designs, PBIB designs and regular graph designs, can yield a large number of black and white (2,n) schemes that are optimal with respect to all these criteria. For a practically useful range of n, we also obtain optimal schemes with the smallest possible pixel expansion.

Optimal estimation of a finite population mean in the presence of linear trend

Abstract: SUMMARY Postulating different superpopulation models for a finite population with linear trend, we suggest optimal sampling strategies for estimating the finite population mean within some classes of unbiased strategies.

Bayesian Experimental Design: A Review

Abstract: 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.

The Selection of Prior Distributions by Formal Rules

Abstract: 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...

Design and Analysis of Cross-Over Trials

Abstract: 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.

Experimental design

Abstract: 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.

Uniform Design: Theory and Application

Abstract: 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.