arXiv subjects

Abhyuday Mandal

Publications and source records attributed to Abhyuday Mandal.

25 records · Page 2Linked to original sources

arXiv2015

A two-component normal mixture alternative to the Fay-Herriot model

This article considers a robust hierarchical Bayesian approach to deal with random effects of small area means when some of these effects assume extreme values, resulting in outliers. In presence of outliers, the standard Fay-Herriot model, used for modeling area-level data, under normality assumptions of the random effects may overestimate random effects variance, thus provides less than ideal shrinkage towards the synthetic regression predictions and inhibits borrowing information. Even a small number of substantive outliers of random effects result in a large estimate of the random effects variance in the Fay-Herriot model, thereby achieving little shrinkage to the synthetic part of the model or little reduction in posterior variance associated with the regular Bayes estimator for any of the small areas. While a scale mixture of normal distributions with known mixing distribution for the random effects has been found to be effective in presence of outliers, the solution depends on the mixing distribution. As a possible alternative solution to the problem, a two-component normal mixture model has been proposed based on noninformative priors on the model variance parameters, regression coefficients and the mixing probability. Data analysis and simulation studies based on real, simulated and synthetic data show advantage of the proposed method over the standard Bayesian Fay-Herriot solution derived under normality of random effects.

stat.ME↗

arXiv2015

Optimal Designs for 2^k Factorial Experiments with Binary Response

We consider the problem of obtaining D-optimal designs for factorial experiments with a binary response and $k$ qualitative factors each at two levels. We obtain a characterization for a design to be locally D-optimal. Based on this characterization, we develop efficient numerical techniques to search for locally D-optimal designs. Using prior distributions on the parameters, we investigate EW D-optimal designs, which are designs that maximize the determinant of the expected information matrix. It turns out that these designs can be obtained very easily using our algorithm for locally D-optimal designs and are very good surrogates for Bayes D-optimal designs. We also investigate the properties of fractional factorial designs and study the robustness with respect to the assumed parameter values of locally D-optimal designs.

math.ST↗

arXiv2014

Maximin and maximin-efficient event-related fMRI designs under a nonlinear model

Previous studies on event-related functional magnetic resonance imaging experimental designs are primarily based on linear models, in which a known shape of the hemodynamic response function (HRF) is assumed. However, the HRF shape is usually uncertain at the design stage. To address this issue, we consider a nonlinear model to accommodate a wide spectrum of feasible HRF shapes, and propose efficient approaches for obtaining maximin and maximin-efficient designs. Our approaches involve a reduction in the parameter space and a search algorithm that helps to efficiently search over a restricted class of designs for good designs. The obtained designs are compared with traditional designs widely used in practice. We also demonstrate the usefulness of our approaches via a motivating example.

stat.AP↗

arXiv2013

D-optimal Factorial Designs under Generalized Linear Models

Generalized linear models (GLMs) have been used widely for modelling the mean response both for discrete and continuous random variables with an emphasis on categorical response. Recently Yang, Mandal and Majumdar (2013) considered full factorial and fractional factorial locally D-optimal designs for binary response and two-level experimental factors. In this paper, we extend their results to a general setup with response belonging to a single-parameter exponential family and for multi-level predictors.

math.ST↗

arXiv2010

Optimal Designs for Two-Level Factorial Experiments with Binary Response

We consider the problem of obtaining locally D-optimal designs for factorial experiments with qualitative factors at two levels each with binary response. Our focus is primarily on the 2^2 experiment. In this paper, we derive analytic results for some special cases and indicate how to handle the general case. The performance of the uniform design in examined and we show that this design is highly efficient in general. For the general 2^k case we show that the uniform design has a maximin property.

stat.ME↗

arXiv2010

Robustness of Optimal Designs for 2^2 Experiments with Binary Response

We consider an experiment with two qualitative factors at 2 levels each and a binary response, that follows a generalized linear model. In Mandal, Yang and Majumdar (2010) we obtained basic results and characterizations of locally D-optimal designs for special cases. As locally optimal designs depend on the assumed parameter values, a critical issue is the sensitivity of the design to misspecification of these values. In this paper we study the sensitivity theoretically and by simulation, and show that the optimal designs are quite robust. We use the method of cylindrical algebraic decomposition to obtain locally D-optimal designs in the general case.

stat.ME↗

arXiv2009

$\mathcal{G}$-SELC: Optimization by sequential elimination of level combinations using genetic algorithms and Gaussian processes

Identifying promising compounds from a vast collection of feasible compounds is an important and yet challenging problem in the pharmaceutical industry. An efficient solution to this problem will help reduce the expenditure at the early stages of drug discovery. In an attempt to solve this problem, Mandal, Wu and Johnson [Technometrics 48 (2006) 273--283] proposed the SELC algorithm. Although powerful, it fails to extract substantial information from the data to guide the search efficiently, as this methodology is not based on any statistical modeling. The proposed approach uses Gaussian Process (GP) modeling to improve upon SELC, and hence named $\mathcal{G}$-SELC. The performance of the proposed methodology is illustrated using four and five dimensional test functions. Finally, we implement the new algorithm on a real pharmaceutical data set for finding a group of chemical compounds with optimal properties.

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