The Annals of Applied Statistics

Semi-parametric dynamic time series modelling with applications to detecting neural dynamics

Fabio Rigat and Jim Q. Smith

Full-text: Open access

Abstract

This paper illustrates novel methods for nonstationary time series modeling along with their applications to selected problems in neuroscience. These methods are semi-parametric in that inferences are derived by combining sequential Bayesian updating with a non-parametric change-point test. As a test statistic, we propose a Kullback–Leibler (KL) divergence between posterior distributions arising from different sets of data. A closed form expression of this statistic is derived for exponential family models, whereas standard Markov chain Monte Carlo output is used to approximate its value and its critical region for more general models. The behavior of one-step ahead predictive distributions under our semi-parametric framework is described analytically for a dynamic linear time series model. Conditions under which our approach reduces to fully parametric state-space modeling are also illustrated. We apply our methods to estimating the functional dynamics of a wide range of neural data, including multi-channel electroencephalogram recordings, longitudinal behavioral experiments and in-vivo multiple spike trains recordings. The estimated dynamics are related to the presentation of visual stimuli, to the evaluation of a learning performance and to changes in the functional connections between neurons over a sequence of experiments.

Article information

Source
Ann. Appl. Stat., Volume 3, Number 4 (2009), 1776-1804.

Dates
First available in Project Euclid: 1 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1267453964

Digital Object Identifier
doi:10.1214/09-AOAS275

Mathematical Reviews number (MathSciNet)
MR2752158

Zentralblatt MATH identifier
1184.62155

Keywords
Dynamic time series modeling change-point testing Bayesian statistics statistics for neural data

Citation

Rigat, Fabio; Smith, Jim Q. Semi-parametric dynamic time series modelling with applications to detecting neural dynamics. Ann. Appl. Stat. 3 (2009), no. 4, 1776--1804. doi:10.1214/09-AOAS275. https://projecteuclid.org/euclid.aoas/1267453964


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