Bayesian Inference Using Gibbs Sampling in Applications and Curricula of Decision Analysis

Applications and curricula of decision analysis currently do not include methods to compute Bayes’ rule and obtain posteriors for non-conjugate prior distributions. The current convention is to force the decision maker’s belief to take the form of a conjugate distribution, leading to a suboptimal decision. BUGS software, which uses MCMCmethods, is numerically capable of obtaining posteriors for non-conjugate priors. By using the decision maker’s true non-conjugate belief, the problems explored suggest that BUGS is able to produce a posterior distribution which leads to optimal decision making. Other methods exist which can use nonconjugate priors, but they must be implemented ad hoc as they do not have any supporting software. BUGS offers the distinct advantage of being implemented in existing software. This software has a gradual learning curve, and with simple coding can solve a wide range of decision analysis problems. BUGS is useful in making optimal decisions, and it is reasonably easy to learn and implement, therefore there is value in including BUGS in decision analysis curricula.