Prediction–variance relation in a state-space fish stock assessment model

Casper W Berg,Sam Subbey,Olav Nikolai Breivik,Anders Nielsen

doi:10.1093/icesjms/fsab205

Casper W Berg, Sam Subbey + Show 2 more

Open Access

https://doi.org/10.1093/icesjms/fsab205

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Abstract

Abstract The state-space assessment model (SAM) is extended by allowing a functional relationship between observation variance and the corresponding prediction. An estimated relationship between observation variance and predicted value for each individual observation allows the model to assign smaller (or larger) variance to predicted larger log-observations. This relation is different from the usual assumption of constant variance of log-observations within age groups. The prediction–variance link is implemented and compared to the usual constant variance assumption for the official assessments of North East Arctic cod and haddock. For both of these stocks, the prediction–variance link is found to give a significant improvement.

Highlights

The state-space assessment model (SAM; Nielsen and Berg, 2014) is a frequently used assessment model for species being monitored by the International Council for the Exploration of the Sea (ICES)
We investigate how the current assessments of North East Arctic (NEA) cod and haddock are affected by the prediction–variance link extension
Both of these stocks are currently assessed with SAM (ICES, 2020a, 2021), and the following three different model configurations are compared: (1) Standard variance configuration for log-observations

Summary

Introduction

The state-space assessment model (SAM; Nielsen and Berg, 2014) is a frequently used assessment model for species being monitored by the International Council for the Exploration of the Sea (ICES). Several options are available in SAM to accommodate for observation variance structures in data. Variances can be estimated to be independent, correlated in different ways (Berg and Nielsen, 2016), separate or combined across ages. Externally estimated variance/covariance matrices can be assigned. We further expand SAM by allowing a functional relationship between observation variance and its associated prediction to be estimated. The link is similar to the relation that Taylor (1961) found to typically exist in survey data and to the link used in the assessment model Aanes (2016). The main difference is, that here the relationship is estimated within the assessment model, rather than being based on external variance estimates

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Conclusion