The marginal posterior probability density function (pdf) for the mean of a stationary pth order Gaussian autoregressive process is derived using the conditional likelihood function. While the posterior pdf provides a small sample analysis, the pdf is not well known and must be analyzed numerically. This is relatively easy since it is a function of only one variable. Two sets of examples are presented. The first set involves synthetic data generated by computer, and the second set deals with energy expenditure data on a bum patient.