Microarrays measure gene expression typically from a mixture of cell populations during different stages of a biological process. However, the specific effects of the distinct or pure populations on measured gene expression are difficult or impossible to determine. The ability to deconvolve measured gene expression into the contributions from pure populations is critical to maximizing the potential of microarray analysis for investigating complex biological processes. In this paper, we describe a novel approach called the multinomial hidden Markov model (MHMM) that produces: (i) a maximum a posteriori estimate of the fraction represented by each pure population and (ii) gene expression values for each pure population. Our method uses an unsupervised, probabilistic approach for handling missing data points and clusters genes based on expression in pure populations. MHMM, used with several yeast datasets, identified statistically significant temporal dynamics. This method, unlike the linear decomposition models used previously for deconvolution, can extract information from different types of data, does not require a priori identification of pure gene expression, exploits the temporal nature of time series data, and is less affected by missing data.