Lingbin Bian, Tiangang Cui, Adeel Razi, Jonathan KeithWe present a novel Bayesian method for identifying the change of dynamic network structure in working memory task fMRI data via model fitness assessment. Specifically, we detect dynamic community structure change- point(s) based on overlapped sliding window applied to multivariate time series. We use the weighted stochastic block model to quantify the likelihood of a network configuration, and develop a novel scoring criterion that we call posterior predictive discrepancy by evaluating the goodness of fit between model and observations within the sliding window. The parameters for this model include latent label vector assigning network nodes to interacting communities, and the block model parameter determining the weighted connectivity within and between communities. The GLM analyses were conducted in both subject level and group level and the contrast between 2-back, 0-back and baseline were used to localise the regions of interest in task fMRI data. The working memory task fMRI data in the HCP were pre-processed and GLM analyses were applied. With the extracted time series of regions of interest, we propose to use the Gaussian latent block model [1], also known as the weighted stochastic block model (WSBM), to quantify the likelihood of a network and Gibbs sampling to sample a posterior distribution derived from this model. The Gibbs sampling approach we adopt is based on the work of [1, 2] for finite mixture models. The proposed model fitness procedure draws parameters from the posterior distribution and uses them to generate a replicated adjacency matrix; then calculates a disagreement matrix to quantify the difference between the replicated adjacency matrix and realised adjacency matrix. For the evaluation of the model fitness, we define a parameter- dependent statistic called the posterior predictive discrepancy (PPD) by averaging the disagreement matrix. Then we compute the cumulative discrepancy energy (CDE) from PPD by applying another sliding window for smoothing and use CDE as a score criterion for change point detection. The CDE increases when change points are contained within the window, and can thus be used to assess whether a statistically significant change point exists within a period of time. We first applied the algorithm to the synthetic data simulated from the Multivariate Gaussian distribution for validation. We visualise the Gibbs iteration of sampled latent labels and the histogram of the block parameters reflecting the characterisation of the connectivity within and between communities. We then demonstrated the performance of the change point detection with different window sizes. In real working memory task fMRI data analyses, the fixed effects analyses are conducted to estimate the average effect size across runs within subjects at the subject level. At group level, the mixed effects analyses are conducted, where the subject effect size is considered to be random. In this work, we mainly focus on the memory load contrast (2-back vs 0-back, 2-back vs baseline, or 0-back vs baseline). References 1\. Wyse J, Friel N. Block clustering with collapsed latent block models. Statistics and computing, 2012, 22, 415-428. 2\. Nobile A, Fearnside A T. Bayesian finite mixtures with an unknown number of components: the allocation sampler. Statistics and Computing, 2007, 17, 147-162.
