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 nonconjugate 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. Bayesian inference using Gibbs sampling BUGS software, which uses Markov chain Monte Carlo methods, numerically obtains posteriors for nonconjugate priors. By using the decision maker's true nonconjugate belief, the problems explored suggest that BUGS can produce a posterior distribution that leads to optimal decision making. Other methods exist that can use nonconjugate priors, but they must be implemented ad hoc because they do not have any supporting software. BUGS offers the distinct advantage of being implemented in existing software, and with simple coding can solve a wide range of decision analysis problems. BUGS is useful in making optimal decisions, and it is easy to learn and implement; therefore, including BUGS in decision analysis curricula is valuable.