Direct Estimation of Inhomogeneous Markov Interval Models of Spike Trains

Direct Estimation of Inhomogeneous Markov Interval Models of Spike Trains

A necessary ingredient for a quantitative theory of neural coding is appropriate "spike kinematics": a precise description of spike trains. While summarizing experiments by complete spike time collections is clearly inefficient and probably unnecessary, the most common probabilistic model used in neurophysiology, the inhomogeneous Poisson process, often seems too crude. Recently a more general ...

Statistical models of spike trains∗

Inhomogeneous Parsimonious Markov Models

We introduce inhomogeneous parsimonious Markov models for modeling statistical patterns in discrete sequences. These models are based on parsimonious context trees, which are a generalization of context trees, and thus generalize variable order Markov models. We follow a Bayesian approach, consisting of structure and parameter learning. Structure learning is a challenging problem due to an over...

Fitting Neuron Models to Spike Trains

Computational modeling is increasingly used to understand the function of neural circuits in systems neuroscience. These studies require models of individual neurons with realistic input-output properties. Recently, it was found that spiking models can accurately predict the precisely timed spike trains produced by cortical neurons in response to somatically injected currents, if properly fitte...

Markov Chain Monte Carlo Methods for Decoding Neural Spike Trains

Stimulus reconstruction or decoding methods provide an important tool for understanding how sensory and motor information is represented in neural activity. We address Bayesian decoding methods based on an encoding generalized linear model (GLM) [1, 2] that accurately describes how stimuli are transformed into the spike trains of a group of neurons. The log-concave GLM likelihood is combined wi...