[Show abstract][Hide abstract] ABSTRACT: This letter considers how a number of modern Markov chain Monte Carlo (MCMC) methods can be applied for parameter estimation and inference in state-space models with point process observations. We quantified the efficiencies of these MCMC methods on synthetic data, and our results suggest that the Reimannian manifold Hamiltonian Monte Carlo method offers the best performance. We further compared such a method with a previously tested variational Bayes method on two experimental data sets. Results indicate similar performance on the large data sets and superior performance on small ones. The work offers an extensive suite of MCMC algorithms evaluated on an important class of models for physiological signal analysis.
[Show abstract][Hide abstract] ABSTRACT: We present a variational Bayesian (VB) approach for the state and parameter inference of a state-space model with point-process observations, a physiologically plausible model for signal processing of spike data. We also give the derivation of a variational smoother, as well as an efficient online filtering algorithm, which can also be used to track changes in physiological parameters. The methods are assessed on simulated data, and results are compared to expectation-maximization, as well as Monte Carlo estimation techniques, in order to evaluate the accuracy of the proposed approach. The VB filter is further assessed on a data set of taste-response neural cells, showing that the proposed approach can effectively capture dynamical changes in neural responses in real time.
[Show abstract][Hide abstract] ABSTRACT: Physiological signals such as neural spikes and heartbeats are discrete events in time, driven by continuous underlying systems. A recently introduced data-driven model to analyze such a system is a state-space model with point process observations, parameters of which and the underlying state sequence are simultaneously identified in a maximum likelihood setting using the expectation-maximization (EM) algorithm. In this note, we observe some simple convergence properties of such a setting, previously un-noticed. Simulations show that the likelihood is unimodal in the unknown parameters, and hence the EM iterations are always able to find the globally optimal solution.