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.

Letters: Rejoinder to ‘Ahmed, M.S. (1998). A note on regression‐type estimators using multiple auxiliary information.’

Abstract: In the estimators t 3 , t 4 , t 5 of Mukerjee, Rao & Vijayan (1987), b yx and b yz are partial regression coefficients of y on x and z, respectively, based on the smaller sample. With the above interpretation of b yx and b yz in t 3 , t 4 , t 5 , all the calculations in Mukerjee at al.(1987) are correct. In this connection, we also wish to make it explicit that b xz in t 5 is an ordinary and not a partial regression coefficient. The 'corrected' MSEs of t 3 , t 4 , t 5 , as given in Ahmed (1998 Section 3) are computed assuming that our b yx and b yz are ordinary and not partial regression coefficients. Indeed, we had no intention of giving estimators using the corresponding ordinary regression coefficients which would lead to estimators inferior to those given by Kiregyera (1984). We accept responsibility for any notational confusion created by us and express regret to readers who have been confused by our notation. Finally, in consideration of the above, it may be noted that Tripathi & Ahmed's (1995) estimator t 0 , quoted also in Ahmed (1998), is no better than t 5 of Mukerjee at al.(1987).

Variance Analysis of Multiple Importance Sampling Schemes

Abstract: : Multiple importance sampling (MIS) is an increasingly used methodology where several proposal densities are used to approximate integrals, generally involving target probability density functions. The use of several proposals allows for a large variety of sampling and weighting schemes. Then, the practitioner must choose a given scheme, i.e., sampling mechanism and weighting function. A variance analysis has been proposed in Elvira et al (2019, Statistical Science 34 , 129-155), showing the superiority of the balanced heuristic estimator with respect to other competing schemes in some scenarios. However, some of their results are valid only for two proposals. In this paper, we extend and generalize these results, providing novel proofs that allow to determine the variance relations among MIS schemes.

Causal Inference from Strip-Plot Designs in a Potential Outcomes Framework

Abstract: Strip-plot designs are very useful when the treatments have a factorial structure and the factors levels are hard-to-change. We develop a randomization-based theory of causal inference from such designs in a potential outcomes framework. For any treatment contrast, an unbiased estimator is proposed, an expression for its sampling variance is worked out, and a conservative estimator of the sampling variance is obtained. This conservative estimator has a nonnegative bias, and becomes unbiased under between-block additivity, a condition milder than Neymannian strict additivity. A minimaxity property of this variance estimator is also established. Simulation results on the coverage of resulting confidence intervals lend support to theoretical considerations.

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.