Reference priors of nuisance parameters in Bayesian sequential population analysis

TL;DR

This paper discusses the derivation of noninformative priors for nuisance parameters in Bayesian fishery population models, proposing Berger and Bernardo's method over Jeffreys to avoid paradoxes in multiparameter settings.

Contribution

It introduces a new approach for eliciting priors for nuisance parameters in Bayesian sequential population analysis, improving upon Jeffreys' method.

Findings

Berger and Bernardo's priors avoid Jeffreys' paradoxes in multiparameter models.

Derived benchmark priors for observational parameters in fishery models.

Enhanced robustness of Bayesian inference in population analysis.

Abstract

Prior distributions elicited for modelling the natural fluctuations or the uncertainty on parameters of Bayesian fishery population models, can be chosen among a vast range of statistical laws. Since the statistical framework is defined by observational processes, observational parameters enter into the estimation and must be considered random, similarly to parameters or states of interest like population levels or real catches. The former are thus perceived as nuisance parameters whose values are intrinsically linked to the considered experiment, which also require noninformative priors. In fishery research Jeffreys methodology has been presented by Millar (2002) as a practical way to elicit such priors. However they can present wrong properties in multiparameter contexts. Therefore we suggest to use the elicitation method proposed by Berger and Bernardo to avoid paradoxical results raised by Jeffreys priors. These benchmark priors are derived here in the framework of sequential population analysis.