AD Model Builder Research Articles

Overcoming long Bayesian run times in integrated fisheries stock assessments

Abstract 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.

Population dynamics of eastern oysters in the Choptank River Complex, Maryland during 1989–2015

The eastern oyster (Crassostrea virginica) fishery in the Choptank River Complex (CRC), Maryland supports a large fishery. The CRC is also host to some of the largest oyster restoration projects in the world. Yet the relative effects of harvest and restoration on the population dynamics of eastern oyster in the CRC have not been assessed. We developed stage-based population models for each region of the CRC in AD Model Builder using dredge survey and harvest data provided by Maryland Department of Natural Resources from 1989 to 2015. Patterns in exploitation rates over time varied among regions. Abundance generally decreased during 1989–2003 and increased thereafter. Recruitment was greatest in the late 1990s, 2010, and 2012, which led to increases in abundance. Natural mortality was low across all regions during 2004-2015. Habitat, recruitment, and abundance declined 50–70% during 1989–2015, but fishery effort increased in years with higher abundance.

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.

Performing statistical population reconstruction using Program PopRecon 2.0

ABSTRACTStatistical population reconstruction develops an integrated likelihood model that incorporates age‐at‐harvest composition, harvest totals, hunter effort, and auxiliary data on survival, harvest, or abundance to model demographics of harvested populations. Each statistical population reconstruction model is handcrafted to account for varying levels of available demographic data, hunting regulations, sampling of the harvest process, and biology of the harvested species. PopRecon 2.0 is a software program that facilitates the creation and analysis of these unique demographic models and capable of analyzing either full or pooled age‐at‐harvest data using either fixed or random effects on the annual survival and harvest processes. The program produces annual estimates of abundance, harvest probabilities, natural survival, and recruitment using a user‐friendly, interactive computing environment and AD Model Builder analytical software. Program PopRecon 2.0 is demonstrated using 23 years (1993–2015) of harvest data on greater sage‐grouse (Centrocercus urophasianus) from Oregon, USA. © 2017 The Wildlife Society.

TMB: Automatic Differentiation and Laplace Approximation

TMB is an open source R package that enables quick implementation of complex nonlinear random effect (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, admb-project.org). In addition, it offers easy access to parallel computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (~10^6) and parameters (~10^3). Computation times using ADMB and TMB are compared on a suite of examples ranging from simple models to large spatial models where the random effects are a Gaussian random field. Speedups ranging from 1.5 to about 100 are obtained with increasing gains for large problems. The package and examples are available at http://tmb-project.org.

Comparison of the accuracy and consistency of likelihood‐based estimation routines for genetic stock identification

Summary Genetic stock identification (GSI) frequently is used to assess spawning/breeding population contributions to mixtures of individuals. Although multiple estimation routines are available for conducting GSI, their performance may vary depending on characteristics of assessed source populations and mixtures and of employed genetic markers. We conducted simulations to compare performance of several likelihood‐based GSI estimation routines. Estimation routines were implemented in SPAM, ONCOR and AD Model Builder (ADMB). Two ADMB routines were evaluated, one based on conditional maximum likelihood estimation (ADMB‐MLE), similar to SPAM and ONCOR, and one based on conditional penalized maximum likelihood estimation (ADMB‐PMLE). The simulations examined how performance varied by number of source populations, population divergence levels, number of evaluated loci, and source population and mixture sample sizes. Evaluations included scenarios with many loci with low levels of polymorphism for assessing performance when single nucleotide polymorphism (SNP) markers are incorporated in analyses. Mixture sample size and source population genetic divergence accounted for most of the explained variability in simulation results. Overall, routines based on conditional maximum likelihood estimation (SPAM, ONCOR and ADMB‐MLE) had similar levels of accuracy, including scenarios mimicking SNP markers, with SPAM having slightly better accuracy than ONCOR and ADMB‐MLE. The accuracy of the ADMB‐PMLE routine in many scenarios was noticeably poorer than the other routines, although in some instances accuracy of the ADMB‐PMLE estimates approached the other routines with large mixture sample sizes. SPAM, ONCOR and ADMB‐MLE also generally had similar levels of performance with respect to consistency, whereas ADMB‐PMLE varied widely in consistency due in part to poor accuracy. Because SPAM and ONCOR typically performed better than the ADMB‐MLE routine, there appears to be little need for users to program their own likelihood‐based estimation routines for standard GSI analyses, although for specialized applications (e.g. modelling contributions as functions of ecological or demographic features), it may be necessary for users to program their own routines. Given the performance of the ADMB‐PMLE routine, additional research is needed to determine an appropriate configuration (e.g. penalty, optimization algorithm) for a penalized maximum likelihood GSI estimator.

Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS

Summary Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open‐source model fitting tools and discusses general strategies for defining and fitting models. R is convenient and (relatively) easy to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. Our model‐fitting suggestions range from general cultural advice (where possible, use the tools and models that are most common in your subfield) to specific suggestions about how to change the mathematical description of models to make them more amenable to parameter estimation. A companion web site (https://groups.nceas.ucsb.edu/non-linear-modeling/projects) presents detailed examples of application of the three tools to a variety of typical ecological estimation problems; each example links both to a detailed project report and to full source code and data.

A review of integrated analysis in fisheries stock assessment

Limited data, and the requirement to provide science-based advice for exploited populations, have led to the development of statistical methods that combine several sources of information into a single analysis. This approach, “integrated analysis”, was first formulated by Fournier and Archibald in 1982. Contemporary use of integrated analysis involves using all available data, in as raw a form as appropriate, in a single analysis. Analyses that were traditionally carried out independently are now conducted simultaneously through likelihood functions that include multiple data sources. For example, the traditional analysis of converting catch-at-length data into catch-at-age data for use in an age-structured population dynamics models can be avoided by including the basic data used in this conversion, length-frequency and conditional age-at-length data, in the likelihood function. This allows for consistency in assumptions and permits the uncertainty associated with both data sources to be propagated to final model outputs, such as catch limits under harvest control rules. The development of the AD Model Builder software has greatly facilitated the use of integrated analyses, and there are now several general stock assessment models (e.g., Stock Synthesis) that allow many data types and model assumptions to be analyzed simultaneously. In this paper, we define integrated analysis, describe its history and development, give several examples, and describe the advantages of and problems with integrated analysis.

AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models

Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem. Automatic Differentiation Model Builder (ADMB) is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number of parameters. The benefits of using AD are computational efficiency and high numerical accuracy, both crucial in many practical problems. We describe the basic components and the underlying philosophy of ADMB, with an emphasis on functionality found in no other statistical software. One example of such a feature is the generic implementation of Laplace approximation of high-dimensional integrals for use in latent variable models. We also review the literature in which ADMB has been used, and discuss future development of ADMB as an open source project. Overall, the main advantages of ADMB are flexibility, speed, precision, stability and built-in methods to quantify uncertainty.

Estimation methods for nonlinear state-space models in ecology

The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance for all three methods was largely identical, however with BUGS providing overall wider credible intervals for parameters than HMM and ADMB confidence intervals.

EVALUATING NONLINEAR CROSSED RANDOM EFFECTS MODELS FOR COMPARING TEMPERATURE OF FEEDING PIGS UNDER DIFFERENT THERMAL ENVIRONMENTS

The thermal environment plays a large role in an animal’s ability to convert feed into weight gain. A better understanding of a pig’s metabolism will help swine producers select environmental specifications for optimizing feed conversion. The objectives of this study are to 1) characterize the thermoregulatory responses of pigs during a feeding event 2) compare those responses for three thermal environmental treatments applied in a Latin Square design 3) investigate different procedures for fitting nonlinear mixed-effect models with crossed random effects (NLME function in R, %NLINMIX macro in SAS, random effects modeling in AD Model Builder: ADMB-RE). We found that the threeparameter first-order compartment model provides a reasonable representation of the tympanic temperatures of feeding pigs during feeding events. The thermal environmental treatments (28ºC + High air speed) and (18ºC + Low air speed) are significantly different from the reference treatment (28ºC + Low air speed), at the 5% level. Both NLME and ADMB-RE successfully fit the nonlinear mixed-effects model and produce similar results. The %NLINMIX macro did not converge unless restrictions were placed on the model. The estimates of fixed and random effects from the restricted model using %NLINMIX macro were generally different from those from NLME and ADMB-RE.

Population viability analysis based on combining Bayesian, integrated, and hierarchical analyses

Abstract Several methods used in fisheries stock assessment models that can be applied to population viability analysis are presented. (1) Integrated analysis allows the use of all information on a particular population, and ensures that all model assumptions and parameter are consistent throughout the analysis, that uncertainty is propagated throughout the analysis, and that the correlation among parameters is preserved. (2) Bayesian analysis allows for the inclusion of prior information, and is a convenient way to represent uncertainty. (3) Random-effects models based on hierarchical modeling allow information to be shared among parameter estimates and allow the separation of process error from estimation error. (4) Non-parametric representation of parameters allows for a more flexible relationship among the parameters. (5) Robust likelihood functions provide an automatic method to reduce the influence of outliers when the data sets are large. These methods are applied to artificial data sets provided by the Extinction Risk Working Group of the National Center for Ecological Analysis and Synthesis (NCEAS) using AD Model Builder software (Otter Research™).