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2019 Non-marginal decisions: A novel Bayesian multiple testing procedure
Noirrit Kiran Chandra, Sourabh Bhattacharya
Electron. J. Statist. 13(1): 489-535 (2019). DOI: 10.1214/19-EJS1535


In this paper, we consider the problem of multiple testing where the hypotheses are dependent. In most of the existing literature, either Bayesian or non-Bayesian, the decision rules mainly focus on the validity of the test procedure rather than actually utilizing the dependency to increase efficiency. Moreover, the decisions regarding different hypotheses are marginal in the sense that they do not depend upon each other directly. However, in realistic situations, the hypotheses are usually dependent, and hence it is desirable that the decisions regarding the dependent hypotheses are taken jointly.

In this article, we develop a novel Bayesian multiple testing procedure that coherently takes this requirement into consideration. Our method, which is based on new notions of error and non-error terms, substantially enhances efficiency by judicious exploitation of the dependence structure among the hypotheses. We show that our method minimizes the posterior expected loss associated with an additive “0-1” loss function; we also prove theoretical results on the relevant error probabilities, establishing the coherence and usefulness of our method. The optimal decision configuration is not available in closed form and we propose an efficient simulated annealing algorithm for the purpose of optimization, which is also generically applicable to binary optimization problems.

Extensive simulation studies indicate that in dependent situations, our method performs significantly better than some existing popular conventional multiple testing methods, in terms of accuracy and power control. Moreover, application of our ideas to a real, spatial data set associated with radionuclide concentration in Rongelap islands yielded insightful results.


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Noirrit Kiran Chandra. Sourabh Bhattacharya. "Non-marginal decisions: A novel Bayesian multiple testing procedure." Electron. J. Statist. 13 (1) 489 - 535, 2019.


Received: 1 June 2018; Published: 2019
First available in Project Euclid: 14 February 2019

zbMATH: 07021712
MathSciNet: MR3911692
Digital Object Identifier: 10.1214/19-EJS1535

Primary: 62F05 , 62F15
Secondary: 62C10

Keywords: Bayesian multiple testing , dependent hypotheses , False discovery rate , Kullback-Leibler , simulated annealing , TMCMC


Vol.13 • No. 1 • 2019
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