, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the sup-

, inhomogeneous Poisson, and inhomogeneou s Markov interval models of neural spike trains from the sup-Neural Computation 14, 325–346 (2001)

space. Rather than computing estimates directly from time series, the system is modelled as a nite state Markov chain to extract stationary behaviour in the form of invariant measures and average absorption times. Ergodic-theoretic formulae are then applied to produce the estimates without the need

We propose a Markov process model for spike-frequency adapting neural en-sembles which synthesizes existing mean-adaptation approaches, population density methods, and inhomogeneous renewal theory, resulting in a unied and tractable framework which goes beyond renewal and mean-adaptation theories

We demonstrate the efficacy of a new spike-sorting method based on a Markov Chain Monte Carlo (MCMC) algorithm by applying it to real data recorded from Purkinje cells (PCs) in young rat cerebellar slices. This algorithm is unique in its capability to estimate and make use of the firing statistics

, statistical methods based on point process models of spike trains provide a wide range of data-analytical techniques. Two simplified point process models have been introduced in the literature: the time-rescaled renewal process (TRRP) and the multiplicative inhomogeneous Markov interval (m-IMI) model

A paradigm for constructing and analyzing non-Poisson stimulus-response models of neural spike train activity is presented. Inhomogeneous gamma (IG) and inverse Gaussian (IIG) probability models are constructed by generalizing the derivation of the inhomogeneous Poisson (IP) model from

these approximations, but that nonetheless retain the computational efficiency of the approximate methods. We discuss a variety of examples, applying these direct optimization techniques to problems in spike train smoothing, stimulus decoding, parameter estimation, and inference of synaptic properties. Along the way

model, slice normalized dynamic Markov logic networks (SN-DMLN), that suffers from none of these issues. It supports efficient online inference, and can directly model influences between variables within a time slice that do not have a causal direction, in contrast with fully directed models (e.g., DBNs

on a doubly stochastic inhomogeneous Poisson process model in which the rate functions are drawn from a low variance Gaussian process. It is found that, in contrast to continuous processes, the variance of the estimators cannot be reduced by smoothing beyond a scale which is set by the number of point