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Summary form only given. We propose a Bayesian regression model to study the time course expression profile of a virus-gene using data from micro-array experiments. Since the time course expression level of a virus gene in a cell is typically constantly zero initially, increasing for a while, and then decreasing, we consider regression model in which the mean function satisfies the above shape restriction. The prior is introduced through Bernstein polynomials. We note that Bernstein polynomial provides an excellent tool to incorporate geometric information into priors for Bayesian inference. We use the Metropolis-Hastings-Green algorithm to generate the posterior distribution and use the posterior mode as the estimate. This method is illustrated in simulation studies and analysis of real datasets. In this extended abstract, we include the expression profile of one of the genes of Baculavirus, obtained from the Bayesian method of this work. In this paper, the author discussed applications of the expression profiles in the study of the virus genome.