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.

Development of Research in Experimental Design in India

Abstract: Resume Cet article presente un panorama de la recherche indienne des 70 dernieres annees dans le domaine des plans d’experiences. Le travail accompli dans ce cadre est considerable, tant par le volume que par l'importance des contributions, et nous nous sommes attaches a en presenter un historique coherent. Les sujets traites incluent les carres latins mutuellement orthogonaux, les plans en blocs incomplets, les plans factoriels, les plans factoriels fractionnaires, les surfaces de reponse, les plans mixtes, les plans ligne-colonne et les etudes croisees. Summary This paper presents an account of research done in India over the last 70 years or so in the field of experimental design. This body of work is substantial, both in terms of depth and volume, and we have attempted to present a coherent history of the various developments in this area. The topics covered include mutually orthogonal Latin squares, incomplete block designs, factorial designs, fractional factorial plans, response surface and mixture designs, and row-column and crossover designs.

Central limit theorems for four new types of U-designs

Abstract: Orthogonal array (OA)-based Latin hypercube designs, also called U-designs, have been popularly adopted in designing a computer experiment. Nested U-designs, sliced U-designs, strong OA-based U-designs and correlation controlled U-designs are four types of extensions of U-designs for different applications in computer experiments. Their elaborate multi-layer structure or multi-dimensional uniformity, which makes them desirable for different applications, brings difficulty in analysing the related statistical properties. In this paper, we derive central limit theorems for these four types of designs by introducing a newly constructed discrete function. It is shown that the means of the four samples generated from these four types of designs asymptotically follow the same normal distribution. These results are useful in assessing the confidence intervals of the gross mean. Two examples are presented to illustrate the closeness of the simulated density plots to the corresponding normal distributions.

Probability matching priors for two-sided tolerance intervals in balanced one-way and two-way nested random effects models

Abstract: We consider two-sided Bayesian tolerance intervals, with approximate frequentist validity, for a future observation in balanced one-way and two-way nested random effects models Probability matching conditions, specific to this problem, are derived in either case via a technique that involves inversion of approximate posterior characteristic functions In addition to yielding probability matching priors for the present problem, these conditions are useful in evaluating certain other priors that have received attention in the literature

A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions

Abstract: The study of good nonregular fractional factorial designs has received significant attention over the last two decades Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard The present paper shows how a trigonometric approach can facilitate a systematic understanding of such QC designs and lead to new theoretical results covering hitherto unexplored situations We focus attention on one-eighth and one-sixteenth fractions of two-level factorials and show that optimal QC designs often have larger generalized resolution and projectivity than comparable regular designs Moreover, some of these designs are found to have maximum projectivity among all designs

Approximate theory-aided robust efficient factorial fractions under baseline parametrization

Abstract: With reference to a baseline parametrization, we explore highly efficient fractional factorial designs for inference on the main effects and, perhaps, some interactions. Our tools include approximate theory together with certain carefully devised discretization procedures. The robustness of these designs to possible model misspecification is investigated using a minimaxity approach. Examples are given to demonstrate that our technique works well even when the run size is quite small.

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.