Bayesian state space models for inferring and predicting temporal gene expression profiles

Prediction of gene dynamic behavior is a challenging and important problem in genomic research while estimating the temporal correlations and non-stationarity are the keys in this process. Unfortunately, most existing techniques used for the inclusion of the temporal correlations treat the time course as evenly distributed time intervals and use stationary models with time-invariant settings. This is an assumption that is often violated in microarray time course data since the time course expression data are at unequal time points, where the difference in sampling times varies from minutes to days. Furthermore, the unevenly spaced short time courses with sudden changes make the prediction of genetic dynamics difficult. In this paper, we develop two types of Bayesian state space models to tackle this challenge for inferring and predicting the gene expression profiles associated with diseases. In the univariate time-varying Bayesian state space models we treat both the stochastic transition matrix and the observation matrix time-variant with linear setting and point out that this can easily be extended to nonlinear setting. In the multivariate Bayesian state space model we include temporal correlation structures in the covariance matrix estimations. In both models, the unevenly spaced short time courses with unseen time points are treated as hidden state variables. Bayesian approaches with various prior and hyper-prior models with MCMC algorithms are used to estimate the model parameters and hidden variables. We apply our models to multiple tissue polygenetic affymetrix data sets. Results show that the predictions of the genomic dynamic behavior can be well captured by the proposed models.