For the Paper “ a Spatio - Temporal Nonparametric Bayesian Model of Multi - Subject Fmri Data ”

MCMC algorithm. We describe the MCMC algorithm in detail here. For updating the selection parameters γiν and regression coefficients βiν , i = 1, . . . , N, ν = 1, . . . , V , we first generate number of subjects n from from Poisson distribution with mean parameter N/2, with N the total number of subjects. If 0 < n ≤ N , then we stop and select n subjects with simple random sampling method without replacement; If n = 0 or n > N , then we resample until 0 < n ≤ N . We then update the values of γiν and βiν , ν = 1, . . . , V for each of the selected subjects with a combination of add-delete-swap moves and the sampling algorithm for HDP models proposed by Teh et al. (2006). The updates on delay parameters λiν , innovation variance parameters ψiν , and long memory parameters αiν , ν = 1, . . . , V are for all subjects. To give the details of equations involved in MCMC steps, we introduce the following notations: