Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Below are our clarifications for the questions raised. The stability of the factorization under other kernels will be important to study in future work. Therefore, it may not make sense to compare LFP channels of different rats. In Section 3.3, the horseshoe prior is used on the loadings as an illustration of the methodology when The effective sample size is 276 (median) for the loadings but falls short for the length scales. Bayesian hypothesis testing in general and the null hypothesis formulation in this case are not well-defined.

A Bayesian nonparametric model known as the Wishart process has been shown to be effective in this situation, but its inference remains highly challenging. In this work, we introduce a Sequential Monte Carlo (SMC) sampler for the Wishart process, and show how it compares to conventional inference approaches, namely MCMC and variational inference. Using simulations we show that SMC sampling results in the most robust estimates and out-of-sample predictions of dynamic covariance. SMC especially outperforms the alternative approaches when using composite covariance functions with correlated parameters. We demonstrate the practical applicability of our proposed approach on a dataset of clinical depression (n = 1), and show how using an accurate representation of the posterior distribution can be used to test for dynamics on covariance.