Advancing Bayesian methods in fisheries stock assessment
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Inference is the process of drawing conclusions from data about unobserved quantities. Bayesian inference is one type of statistical inference and is widely applied in diverse fields. In fisheries, it has many advantages, notably a statistically rigorous way of including information from other studies (through prior distributions) and making probabilistic statements about key management quantities such as sustainable future levels of catch (in the estimated posterior distributions). Despite these advantages, it is rarely applied for integrated stock assessments due to computational hurdles (i.e., long run times). The goal of this dissertation is to advance computation methods for integrated models so that these methods can be more widely applied. In chapter 1, I explore the potential of a new algorithm, the no-U-turn sampler (NUTS), to more efficiently sample the posterior distribution. Here, I compared the recently-developed Bayesian software Stan, which uses NUTS, to the most commonly used, JAGS, which belongs to the BUGS family of software. I found that NUTS was substantially more efficient, particularly as model size and complexity increased. However, hierarchical models were more sensitive to the parameterization with NUTS. I conclude that NUTS has high potential and should be incorporated in the software framework most commonly used in fisheries stock assessments, AD Model Builder (ADMB), and tested for stock assessments. In my second chapter, I implemented NUTS into the source code of ADMB and compared the efficiency of NUTS against the current Bayesian algorithm in ADMB, random walk Metropolis-Hastings (RWM) for six stock assessments, including an idealized, simulated model, four age-structured Stock Synthesis models, a custom-built, length-structured model, and a length- and age-based model used for research. I found that the main obstacle to fast run times was poorly parameterized models. One of the main causes of poor parameterization was overparameterized fishery selectivity curves, causing selectivity parameters to be near bounds, have long tails, and exhibit extreme correlation with other parameters. Most selectivity parameters are nuisance parameters that had no impact on management quantities, and so constraining the posterior with more informative priors and fixing parameters to the value at the bounds reduced run time by orders of magnitude while having negligible effect on model posterior distributions. An additional, and even more problematic, cause of poor parameterization was correlated early recruitment deviations, whose geometric shape challenged both NUTS and RWM algorithms. Most alarmingly, when models displayed these kinds of pathologies, the default RWM algorithm did not fully explore the posterior space even when apparently converged, which resulted in biased posterior samples. Even worse, this bias would not be detectable using traditional diagnostics, and longer RWM chains with more thinning would not help. In these cases, NUTS fared better, in that it was able to avoid the bias, but with greater accuracy came much slower run times. The end result of these explorations was a set of guidelines and the development of a software package designed to achieve run times 10-1000 times faster for most current stock assessment models. In my last chapter, I examined the effect of hook spacing on Pacific halibut longline catch rates (CPUE) in commercial catch data. I found clear evidence for a hook spacing effect (i.e., hooks were less effective closer together) at the population level, using a spatially-explicit (geospatial) model with both non-parametric and parametric relationships. However, accounting for space had a greater impact on CPUE trends than did hook spacing, likely due to the relatively constant average hook spacing over time. Nevertheless, since constant hook spacing is likely unusual in most fisheries over time, historical and future trends in hook spacing in commercial data can have important impacts on longline CPUE standardization. Accounting for hook spacing effects in other fisheries may improve the estimates of relative abundance trends, leading to better inference and thus management.