# Asymptotic theory of dependent Bayesian multiple testing procedures under possible model misspecification

@article{Chandra2020AsymptoticTO, title={Asymptotic theory of dependent Bayesian multiple testing procedures under possible model misspecification}, author={N. K. Chandra and Sourabh Bhattacharya}, journal={Annals of the Institute of Statistical Mathematics}, year={2020} }

We study asymptotic properties of Bayesian multiple testing procedures and provide sufficient conditions for strong consistency under general dependence structure. We also consider a novel Bayesian multiple testing procedure and associated error measures that coherently accounts for the dependence structure present in the model. We advocate posterior versions of FDR and FNR as appropriate error rates and show that their asymptotic convergence rates are directly associated with the Kullback…

## 5 Citations

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## References

SHOWING 1-10 OF 44 REFERENCES

High-dimensional Asymptotic Theory of Bayesian Multiple Testing Procedures Under General Dependent Setup and Possible Misspecification

- Mathematics, Computer Science
- 2020

This article investigates strong consistency of the procedures and asymptotic properties of different versions of false discovery and false non-discovery rates under the high dimensional setup, and focuses on the setup where the number of hypotheses increases at a faster rate compared to the sample size.

Dynamics of Bayesian Updating with Dependent Data and Misspecified Models

- Mathematics
- 2009

This work establishes sufficient conditions for posterior convergence when all hypotheses are wrong, and the data have complex dependencies, and derives a kind of large deviations principle for the posterior measure, extending in some cases to rates of convergence, and discusses the advantages of predicting using a combination of models known to be wrong.

Large-scale multiple testing under dependence

- Mathematics
- 2009

Summary. The paper considers the problem of multiple testing under dependence in a compound decision theoretic framework. The observed data are assumed to be generated from an underlying two‐state…

Dependency and false discovery rate: Asymptotics

- Mathematics
- 2007

Some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step-up procedure (LSU) for testing n hypotheses when test…

Non-marginal decisions: A novel Bayesian multiple testing procedure

- Computer ScienceElectronic Journal of Statistics
- 2019

This article develops a novel Bayesian multiple testing procedure that substantially enhances efficiency by judicious exploitation of the dependence structure among the hypotheses, and proves theoretical results on the relevant error probabilities, establishing the coherence and usefulness of the method.

A Bayesian discovery procedure

- Computer Science, MathematicsJournal of the Royal Statistical Society. Series B, Statistical methodology
- 2009

It is shown that, under a coherent decision theoretic framework, a loss function combining true positive and false positive counts leads to a decision rule that is based on a threshold of the posterior probability of the alternative.

The positive false discovery rate: a Bayesian interpretation and the q-value

- Computer Science
- 2003

This work introduces a modified version of the FDR called the “positive false discovery rate” (pFDR), which can be written as a Bayesian posterior probability and can be connected to classification theory.

On the false discovery rate and an asymptotically optimal rejection curve

- Mathematics
- 2009

In this paper we introduce and investigate a new rejection curve for asymptotic control of the false discovery rate (FDR) in multiple hypotheses testing problems. We first give a heuristic motivation…

Bayesian variable selection with shrinking and diffusing priors

- Mathematics
- 2014

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as…

Multiple hypotheses testing and expected number of type I. errors

- Mathematics
- 2002

The performance of multiple test procedures with respect to error control is an old issue. Assuming that all hypotheses are true we investigate the behavior of the expected number of type I errors…