Choosing the observational likelihood in state-space stock assessment models

Abstract

Data used in stock assessment models result from combinations of biological, ecological, fishery, and sampling processes. Since different types of errors propagate through these processes it can be difficult to identify a particular family of distributions for modelling errors on observations a priori. By implementing several observational likelihoods, modelling both numbers-and proportions-at-age, in an age based state-space stock assessment model, we compare the model fit for each choice of likelihood along with the implications for spawning stock biomass and average fishing mortality. We propose using AIC intervals based on fitting the full observational model for comparing different observational likelihoods. Using data from four stocks, we show that the model fit is improved by modelling the correlation of observations within years. However, the best choice of observational likelihood differs for different stocks, and the choice is important for the short-term conclusions drawn from the assessment model; in particular, the choice can influence total allowable catch advise based on reference points.

Model-based estimates of reference points in an age-based state-space stock assessment model

“…Reference point estimation was implemented in the age-based state-space stock assessment model SAM (we refer to Nielsen and Berg, 2014;Berg and Nielsen, 2016;Albertsen et al, 2017;and Albertsen et al, 2018, for full details) using the R-package Template Model Builder (Kristensen et al, 2016). The source codes can be found at https://github.com/ fishfollower/SAM/tree/reference_points (commit b56f2ec).…”

“…The SAM model currently allows for three types of recruitment: random walk on log-scale, Ricker, and Beverton-Holt stock-recruitment functions. Recently, SAM has been extended to consider several observational models (Berg and Nielsen, 2016;Albertsen et al, 2017) and to model several stocks (Albertsen et al, 2018). In the SAM model, reference points cannot be expressed explicitly from model parameters.…”

A time‐series model for estimating temporal variation in phenotypic selection on laying dates in a Dutch great tit population

“…Thanks to the new techniques such as TMB for fast likelihood computation for non‐Gaussian and nonlinear models, the use of state‐space models for analysing ecological systems is increasing (for example Cadigan, ; Albertsen, Nielsen & Thygesen, ; Auger‐Méthé et al., ). The conditional independence structure in state‐space models yield a sparse precision matrix for the joint distribution of the data and the random effects (Kristensen et al., ) and TMB takes maximal advantage of this sparseness structure (through automatic sparsity detection) in its computation of the Laplace approximation.…”

Bayesian inference with tmbstan for a state-space model with VAR(1) state equation

“…Both frequentist and Bayesian statistical inference have been used for investigating ecological processes. In the frequentist framework, Template model builder (TMB, Kristensen et al, 2016), an R package developed for fast fitting complex linear or nonlinear mixed models, has gained the popularity recently, especially in the field of ecology which usually involves in modeling complicated ecological processes (for example Cadigan, 2015;Albertsen et al, 2016;Auger-Méthé et al, 2017). The combination of reverse-mode automatic differentiation and Laplace approximation for high-dimension integrals makes parameter estimation with TMB very efficient even for non-Gaussian and complex hierarchical models.…”

“…To gain more insights on these issues, in this paper we conduct simulation studies and a case study in the context of modeling fluctuating and auto-correlated selection with state-space models (SSM). These forms of models are more generally increasingly used in ecology to model time-series such as animal movement paths and population dynamics (for example Cadigan, 2015;Albertsen et al, 2016;Auger-Méthé et al, 2017). Furthermore, following Cao, Visser, and Tufto (2019), we also use order-1 vector autoregressive model (VAR(1)) to model the unobserved states, which in our study are temporally fluctuating and potentially auto-correlated height, width and location of a Gaussian fitness function.…”