Bayesian nonparametric (non-)renewal processes for analyzing neural spike train variability Supplementary Material A Point process theory

From the conditional intensity function (CIF) defined in Eq. 1, we can obtain the survival function The terms over-or underdispersion describe empirical quantile distributions that do not match the point process model. A.3 Renewal processes A.3.1 Firing rates and ISIs The law of large numbers for renewal processes [24] shows that for a Markov renewal process lim Below we give the parametric densities for renewal processes used in the paper. To evaluate the CIF for renewal processes, we need to compute the hazard function as discussed above. Gamma The cumulative density function is C ( τ) = 1 Γ(α) γ ( α,τ) (32) where γ (,) denotes the lower incomplete Gamma function. B.1 Sparse variational Gaussian processes B.1.1 Gaussian processes as priors over functions In addition, closed-form inference and prediction are not possible for non-Gaussian likelihoods as used in this paper.