## Bayesian Analysis

- Bayesian Anal.
- Volume 13, Number 1 (2018), 29-58.

### Bayesian Inference and Testing of Group Differences in Brain Networks

Daniele Durante and David B. Dunson

**Full-text: Open access**

#### Abstract

Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or high creative reasoning group. It is of paramount importance to develop statistical methods for testing of global and local changes in the structural interconnections among brain regions across groups. We develop a general Bayesian procedure for inference and testing of group differences in the network structure, which relies on a nonparametric representation for the conditional probability mass function associated with a network-valued random variable. By leveraging a mixture of low-rank factorizations, we allow simple global and local hypothesis testing adjusting for multiplicity. An efficient Gibbs sampler is defined for posterior computation. We provide theoretical results on the flexibility of the model and assess testing performance in simulations. The approach is applied to provide novel insights on the relationships between human brain networks and creativity.

#### Article information

**Source**

Bayesian Anal. Volume 13, Number 1 (2018), 29-58.

**Dates**

First available in Project Euclid: 15 November 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.ba/1479179031

**Digital Object Identifier**

doi:10.1214/16-BA1030

**Keywords**

brain network mixture model multiple testing nonparametric Bayes

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Durante, Daniele; Dunson, David B. Bayesian Inference and Testing of Group Differences in Brain Networks. Bayesian Anal. 13 (2018), no. 1, 29--58. doi:10.1214/16-BA1030. https://projecteuclid.org/euclid.ba/1479179031

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#### Supplemental materials

- Supplement A: Supplementary Materials for “Bayesian Inference and Testing of Group Differences in Brain Networks”. The online supplementary material contains proofs of the Propositions 1, 2 and 3, providing theoretical support for our methodology.Digital Object Identifier: doi:10.1214/16-BA1030SUPP

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