Sequential change-point detection for time series models: assessing the functional dynamics of neuronal networks

This paper illustrates a sequential method to detect significant parameter changes for time series models. Rather than relying on an explicit state equation, the parameters’ dynamics are assessed as a change-point problem by combining Bayesian estimation with a nonparametric test of hypothesis. The Kullback-Leibler divergence between the posterior probability densities given two different sets of data is proposed as a test statistic. Markov chain Monte Carlo posterior simulation is used to approximate in general the value of the Kullback-Leibler statistic and its critical region under the null hypothesis. For exponential family models we show that the statistic has a closed form. We also report the results of a simulation study demonstrating empirically that for the Bernoulli model the power of the change-point test is not affected by the difference in the sample Research fellow, CRiSM, Department of Statistics, University of Warwick; [email protected]