We propose a Bayesian approach for predicting the number of failures in a piece of software, using the logarithmic-Poisson model, a nonhomogeneous Poisson process (NHPP) commonly used for describing software failures. A similar approach can be applied to other forms of the NHPP. The key feature of the approach is that now we are able to use, in a formal manner, expert knowledge on software testing, as for example, published information on the empirical experiences of other researchers. This is accomplished by treating such information as expert opinion in the construction of a likelihood function which leads us to a joint distribution. The procedure is computationally intensive, but for the case of the logarithmic-Poisson model has been codified for use on a personal computer. We illustrate the working of the approach via some real live data on software testing. The aim is not to propose another model for software reliability assessment. Rather, we present a methodology that can be invoked with existing software reliability models.>