## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 8, Number 3 (2014), 1800-1824.

### A Bayesian hierarchical spatial point process model for multi-type neuroimaging meta-analysis

Jian Kang, Thomas E. Nichols, Tor D. Wager, and Timothy D. Johnson

#### Abstract

Neuroimaging meta-analysis is an important tool for finding consistent effects over studies that each usually have 20 or fewer subjects. Interest in meta-analysis in brain mapping is also driven by a recent focus on so-called “reverse inference”: where as traditional “forward inference” identifies the regions of the brain involved in a task, a reverse inference identifies the cognitive processes that a task engages. Such reverse inferences, however, require a set of meta-analysis, one for each possible cognitive domain. However, existing methods for neuroimaging meta-analysis have significant limitations. Commonly used methods for neuroimaging meta-analysis are not model based, do not provide interpretable parameter estimates, and only produce null hypothesis inferences; further, they are generally designed for a single group of studies and cannot produce reverse inferences. In this work we address these limitations by adopting a nonparametric Bayesian approach for meta-analysis data from multiple classes or types of studies. In particular, foci from each type of study are modeled as a cluster process driven by a random intensity function that is modeled as a kernel convolution of a gamma random field. The type-specific gamma random fields are linked and modeled as a realization of a common gamma random field, shared by all types, that induces correlation between study types and mimics the behavior of a univariate mixed effects model. We illustrate our model on simulation studies and a meta-analysis of five emotions from 219 studies and check model fit by a posterior predictive assessment. In addition, we implement reverse inference by using the model to predict study type from a newly presented study. We evaluate this predictive performance via leave-one-out cross-validation that is efficiently implemented using importance sampling techniques.

#### Article information

**Source**

Ann. Appl. Stat., Volume 8, Number 3 (2014), 1800-1824.

**Dates**

First available in Project Euclid: 23 October 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1414091235

**Digital Object Identifier**

doi:10.1214/14-AOAS757

**Mathematical Reviews number (MathSciNet)**

MR3271354

**Zentralblatt MATH identifier**

1304.62133

**Keywords**

Bayesian spatial point processes classification hierarchical model random intensity measure neuorimage meta-analysis

#### Citation

Kang, Jian; Nichols, Thomas E.; Wager, Tor D.; Johnson, Timothy D. A Bayesian hierarchical spatial point process model for multi-type neuroimaging meta-analysis. Ann. Appl. Stat. 8 (2014), no. 3, 1800--1824. doi:10.1214/14-AOAS757. https://projecteuclid.org/euclid.aoas/1414091235

#### Supplemental materials

- Supplementary material: Supplement to “A Bayesian hierarchical spatial point process model for multi-type neuroimaging meta-analysis”. In this online supplemental article, we provide (1) proofs of main theorems for the HPGRF model, (2) details on posterior computations, (3) additional figures to assess the posterior variabilities of intensity functions in simulation studies and data application, (4) sensitivity analysis, and (5) details of a Bayesian spatial point process classifier.Digital Object Identifier: doi:10.1214/14-AOAS757SUPP