Overcoming long Bayesian run times in integrated fisheries stock assessments

Bayesian inference is an appealing alternative to maximum likelihood estimation, but estimation can be prohibitively long for integrated fisheries stock assessments. Here, we investigated potential causes of long run times including high dimensionality, complex model structure, and inefficient Bayesian algorithms for four US assessments written in AD Model Builder (ADMB), both custom built and Stock Synthesis models. The biggest culprit for long run times was overparameterization and they were reduced from months to days by adding priors and turning off estimation for poorly-informed parameters (i.e. regularization), especially for selectivity parameters. Thus, regularization is a necessary step in converting assessments from frequentist to Bayesian frameworks. We also tested the usefulness of the no-U-turn sampler (NUTS), a Bayesian algorithm recently added to ADMB, and the R package adnuts that allows for easy implementation of NUTS and parallel computation. These additions further reduced run times and better sampled posterior distributions than existing Bayesian algorithms in ADMB, and for both of these reasons we recommend using NUTS for inference. Between regularization, a faster algorithm, and parallel computation, we expect models to run 50-50 000 times faster for most current stock assessment models, opening the door to routine usage of Bayesian methods for management of fish stocks.