Markov Chain Monte Carlo (MCMC), the most widely used algorithm in Bayesian statistics, can fail to converge. Although convergence is tested by various diagnostics, these can only reveal failure, never success. To avoid these difficulties, this paper suggests a recipe for using Bayesian network propagation (BNP) to compute posterior results for fish stock assessment. Bayesian networks employ discrete random variables and specify relationships between them with conditional probability tables. Therefore, the recipe uses a new technique called "fuzzy discretization" to convert a continuous Bayesian model into a discrete Bayesian network. The technique is illustrated on a Schaefer assessment model by showing how model equations can be converted to probability tables. Posterior density estimates for carrying capacity (K) from both MCMC and BNP were compared with exact results (obtained by analytic integration and grid search) under three scenarios. BNP outperformed MCMC (as implemented in WinBUGS) in all scenarios, though MCMC diagnostics previously deemed sufficient reported no problems. Tightening the grid resolution of discrete numeric variables over regions of high posterior probability greatly improved BNP performance, so a grid selection heuristic is included in the recipe. In summary, this recipe may provide an effective alternative to MCMC for similar Bayesian problems.
Accounting for correlated observations in an age-based state-space stock assessment model
