No-U-turn sampling for fast Bayesian inference in ADMB and TMB: Introducing the adnuts and tmbstan R packages

Statistical inference is a widely-used, powerful tool for learning about natural processes in diverse fields. The statistical software platforms AD Model Builder (ADMB) and Template Model Builder (TMB) are particularly popular in the ecological literature, where they are typically used to perform frequentist inference of complex models. However, both lack capabilities for flexible and efficient Markov chain Monte Carlo (MCMC) integration. Recently, the no-U-turn sampler (NUTS) MCMC algorithm has gained popularity for Bayesian inference through the software Stan because it is efficient for high dimensional, complex hierarchical models. Here, we introduce the R packages adnuts and tmbstan, which provide NUTS sampling in parallel and interactive diagnostics with ShinyStan. The ADMB source code was modified to provide NUTS, while TMB models are linked directly into Stan. We describe the packages, provide case studies demonstrating their use, and contrast performance against Stan. For TMB models, we show how to test the accuracy of the Laplace approximation using NUTS. For complex models, the performance of ADMB and TMB was typically within +/-50% the speed of Stan. In one TMB case study we found inaccuracies in the Laplace approximation, potentially leading to biased inference. adnuts provides a new method for estimating hierarchical ADMB models which previously were infeasible. TMB users can fit the same model in both frequentist and Bayesian paradigms, including using NUTS to test the validity of the Laplace approximation of the marginal likelihood for arbitrary subsets of parameters. These software developments extend the available statistical methods of the ADMB and TMB user base with no additional effort by the user.