Bayesian decision theory is increasingly applied to support decision-making processes under environmental variability and uncertainty. Researchers from application areas like psychology and biomedicine have applied these techniques successfully. However, in the area of software engineering and specifically in the area of self-adaptive systems (SASs), little progress has been made in the application of Bayesian decision theory. We believe that techniques based on Bayesian Networks (BNs) are useful for systems that dynamically adapt themselves at runtime to a changing environment, which is usually uncertain. In this paper, we discuss the case for the use of BNs, specifically Dynamic Decision Networks (DDNs), to support the decision-making of self-adaptive systems. We present how such a probabilistic model can be used to support the decision-making in SASs and justify its applicability. We have applied our DDN-based approach to the case of an adaptive remote data mirroring system. We discuss results, implications and potential benefits of the DDN to enhance the development and operation of self-adaptive systems, by providing mechanisms to cope with uncertainty and automatically make the best decision.