Conjunction analysis and propositional logic in fMRI data analysis using Bayesian statistics - Rudert, Thomas; Lohmann, Gabriele (Journal of magnetic resonance imaging, 2008)
Purpose To evaluate logical expressions over different effects in data analyses using the general linear model (GLM) and to evaluate logical expressions over different posterior probability maps (PPMs). Materials and Methods In functional magnetic resonance imaging (fMRI) data analysis, the GLM was applied to estimate unknown regression parameters. Based on the GLM, Bayesian statistics can be used to determine the probability of conjunction, disjunction, implication, or any other arbitrary logical expression over different effects or contrast. For second‐level inferences, PPMs from individual sessions or subjects are utilized. These PPMs can be combined to a logical expression and its probability can be computed. The methods proposed in this article are applied to data from a STROOP experiment and the methods are compared to conjunction analysis approaches for test‐statistics. Results The combination of Bayesian statistics with propositional logic provides a new approach for data analyses in fMRI. Two different methods are introduced for propositional logic: the first for analyses using the GLM and the second for common inferences about different probability maps. Conclusion The methods introduced extend the idea of conjunction analysis to a full propositional logic and adapt it from test‐statistics to Bayesian statistics. The new approaches allow inferences that are not possible with known standard methods in fMRI. J. Magn. Reson. Imaging 2008;28:1533–1539. © 2008 Wiley‐Liss, Inc.