A method to adjust a prior distribution in Bayesian second-level fMRI analysis

Abstract

Previous research has shown the potential value of Bayesian methods in fMRI (functional magnetic resonance imaging) analysis. For instance, the results from Bayes factor-applied second-level fMRI analysis showed a higher hit rate compared with frequentist second-level fMRI analysis, suggesting greater sensitivity. Although the method reported more positives as a result of the higher sensitivity, it was able to maintain a reasonable level of selectivity in term of the false positive rate. Moreover, employment of the multiple comparison correction method to update the default prior distribution significantly improved the performance of Bayesian second-level fMRI analysis. However, previous studies have utilized the default prior distribution and did not consider the nature of each individual study. Thus, in the present study, a method to adjust the Cauchy prior distribution based on a priori information, which can be acquired from the results of relevant previous studies, was proposed and tested. A Cauchy prior distribution was adjusted based on the contrast, noise strength, and proportion of true positives that were estimated from a meta-analysis of relevant previous studies. In the present study, both the simulated images and real contrast images from two previous studies were used to evaluate the performance of the proposed method. The results showed that the employment of the prior adjustment method resulted in improved performance of Bayesian second-level fMRI analysis.

A Novel Method to Use Coordinate Based Meta-Analysis to Determine a Prior Distribution for Voxelwise Bayesian Second-Level fMRI Analysis

“…Although Bayes factors have the aforementioned methodological merits, one fundamental issue should be considered and addressed while employing Bayesian inference in fMRI analysis. To estimate a posterior probability, P(H|D), and Bayes factor, BF, researchers need to determine a prior probability, P(H), which is updated with data, D. Given a change in P(H) significantly impacts the resultant P(H|D) [18][19][20], determination of P(H) is critical, and, thus, should not be arbitrary. As a possible way to address this issue, in the previous study that first employed multiple comparison correction in Bayesian second-level fMRI analysis [15], one of the most widely used noninformative prior distributions, the default Cauchy prior distribution, Cauchy (x0 = 0, σ = 0.707), was used [7][8][9].…”

“…As even slight changes in prior distributions may significantly alter the outcomes of Bayesian analysis [18,19], prior distributions should be carefully determined. The prior distributions employed in the previous study [20] were in fact default Cauchy prior distributions, which were not actually informed by the previous information. In fact, there have been concerns regarding the potential arbitrariness existing in default priors [21].…”

“…Researchers who applied the aforementioned approach to determine prior distributions have reported that the use of informative priors resulted in fewer biased outcomes and improved analysis performance [22][23][24]. In addition, in the case of voxelwise Bayesian fMRI analysis, when prior distributions were determined based on the results from the Bayesian image-based meta-analyses of relevant previous fMRI studies, the performance was significantly improved in terms of sensitivity and selectivity [20].…”

“…Although the concerns regarding Bayesian fMRI analysis, those associated with multiple comparison correction and the determination of prior distributions, can be addressed by determining prior distributions based on meta-analysis [15,20], a major practical issue may hinder the wide employment of the method in the field. In a previous study [20], the determination of informed prior distributions was performed with results from imagebased fMRI meta-analyses that could not be easily performed in ordinary cases. To perform image-based meta-analysis, researchers must have access to statistical images produced by relevant previous studies conducted by other researchers.…”

“…To perform image-based meta-analysis, researchers must have access to statistical images produced by relevant previous studies conducted by other researchers. Although there are several open repositories to share such images (e.g., NeuroVault, OpenfMRI), it is difficult to acquire large scale image data for every research topic [20,25]. Of course, compared with coordinatebased meta-analysis, which is more accessible to researchers and has been widely employed in the field, image-based meta-analysis possesses methodological advantages [25,26].…”