A robust Bayesian two-sample test for detecting intervals of differential gene expression in microarray time series.

Understanding the regulatory mechanisms that are responsible for an organism's response to environmental change is an important issue in molecular biology. A first and important step towards this goal is to detect genes whose expression levels are affected by altered external conditions. A range of methods to test for differential gene expression, both in static as well as in time-course experiments, have been proposed. While these tests answer the question whether a gene is differentially expressed, they do not explicitly address the question when a gene is differentially expressed, although this information may provide insights into the course and causal structure of regulatory programs. In this article, we propose a two-sample test for identifying intervals of differential gene expression in microarray time series. Our approach is based on Gaussian process regression, can deal with arbitrary numbers of replicates, and is robust with respect to outliers. We apply our algorithm to study the response of Arabidopsis thaliana genes to an infection by a fungal pathogen using a microarray time series dataset covering 30,336 gene probes at 24 observed time points. In classification experiments, our test compares favorably with existing methods and provides additional insights into time-dependent differential expression.

Reversible jump sampler for autoregressive time series

We use reversible jump Markov chain Monte Carlo (MCMC) methods to address the problem of model order uncertainty in autoregressive (AR) time series within a Bayesian framework. Efficient model jumping is achieved by proposing model space moves from the full conditional density for the AR parameters, which is obtained analytically. This is compared with an alternative method, for which the moves are cheaper to compute, in which proposals are made only for new parameters in each move. Results are presented for both synthetic and audio time series.

Bayesian model selection for time series using Markov chain Monte Carlo

We present a stochastic simulation technique for subset selection in time series models, based on the use of indicator variables with the Gibbs sampler within a hierarchical Bayesian framework. As an example, the method is applied to the selection of subset linear AR models, in which only significant lags are included. Joint sampling of the indicators and parameters is found to speed convergence. We discuss the possibility of model mixing where the model is not well determined by the data, and the extension of the approach to include non-linear model terms.