Neuroscience aims to understand how complex pattern of neural activity in the human brain relate to the functional processes that allow for intelligent behavior. Novel recording techniques that can measure the activity patterns across many neurons or brain regions are generating novel highly multivariate dataset. In this talk, I will focus on two statistical approaches currently used to analyze the information content of brain activity patterns: Pattern Component Modeling (PCM) is a hierarchical Bayesian approach that models the probability distribution of the activity data directly, enabling model comparison using approximate marginal likelihoods. In Representational Similarity Analysis (RSA), inferences are based on similarity measures between activity patterns as a sufficient statistic. I will show new results that improve inference in the latter approach, which links it theoretically to the centered kernel alignment.