A Bayesian autoregressive three-state hidden Markov model for identifying switching monotonic regimes in Microarray time course data

When modeling time course microarray data special interest may reside in identifying time frames in which gene expression levels follow a monotonic (increasing or decreasing) trend. A trajectory may change its regime because of the reaction to treatment or of a natural developmental phase, as in our motivating example about identification of genes involved in embryo development of mice with the 22q11 deletion. To this aim we propose a new flexible Bayesian autoregressive hidden Markov model based on three latent states, corresponding to stationarity, to an increasing and to a decreasing trend. In order to select a list of genes, we propose decision criteria based on the posterior distribution of the parameters of interest, taking into account the uncertainty in parameter estimates. We also compare the proposed model with two simpler models based on constrained formulations of the probability transition matrix.