Despite significant advances in software testing research, the ability to produce reliable software products for a variety of critical applications remains an open problem. The key challenge has been the fact that each program or soft-ware product is unique, and existing methods are predominantly not capable of adapting to the observations made during program analysis. This paper makes the following claim: Bayesian reasoning methods provide an ideal research paradigm for achieving reliable and effcient software testing and program analysis. A brief overview of some popular Bayesian reasoning methods is provided, along with a justification of why they are applicable to software testing. Furthermore, some practical challenges to the widespread use of Bayesian methods are discussed, along with possible solutions to these challenges.