Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we s...

Cortical neurons in the waking brain fire highly irregular spike trains that have more in common with the ticking of a Geiger counter than of a clock. What is the source of this irregular firing? Softky and Koch1 noted a theoretical conundrum posed by the irregularity of cortical neurons firing at a constant average rate in vivo. If each cortical neuron were providing independent input to the o...

Retinal prosthesis offers a potential treatment for individuals suffering from photoreceptor degeneration diseases. Establishing biological retinal models and simulating how the biological retina convert incoming light signal into spike trains that can be properly decoded by the brain is a key issue. Some retinal models have been presented, ranking from structural models inspired by the layered...

Introduction Several coding stages occur in the nervous system when an internal decision is reached to enact a certain movement. The desired movement is coded into spike trains of a large number of neurons in prefrontal, premotor and suplementary motor cortices as well as in other areas such as the basal ganglia and cerebellum. These spike trains can be assembled in a column vector x(t), each e...

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 the exponential probability density. The resultant spike train models have Markov dependence. Quantile-quantil...

We present a unified approach to unsupervised Bayesian learning of factor models for binary data with binary and spike-and-slab latent factors. We introduce a non-negative constraint in the spike-and-slab prior that eliminates the usual sign ambiguity present in factor models and lowers the generalization error on the datasets tested here. For the generative models we use probit functions, whic...

To understand neural activity, two broad categories of models exist: statistical and dynamical. While statistical models possess rigorous methods for parameter estimation and goodness-of-fit assessment, dynamical models provide mechanistic insight. In general, these two categories of models are separately applied; understanding the relationships between these modeling approaches remains an area...