Improving inference for nonlinear state-space models of animal population dynamics given biased sequential life stage data

TL;DR

This paper investigates inference challenges in nonlinear stage-structured state-space models of animal populations with biased data, highlighting the importance of covariates and external variance estimates for reliable parameter inference.

Contribution

It demonstrates that including covariates and using externally estimated observation variances improves inference accuracy in nonlinear ecological SSMs.

Findings

Covariates are necessary for parameter identifiability.

Using external estimates of observation variance reduces bias and standard error.

Estimating both process and observation variances jointly can lead to implausible estimates.

Abstract

State-space models (SSMs) are a popular tool for modeling animal abundances. Inference difficulties for simple linear SSMs are well known, particularly in relation to simultaneous estimation of process and observation variances. Several remedies to overcome estimation problems have been studied for relatively simple SSMs, but whether these challenges and proposed remedies apply for nonlinear stage-structured SSMs, an important class of ecological models, is less well understood. Here we identify improvements for inference about nonlinear stage-structured SSMs fit with biased sequential life stage data. Theoretical analyses indicate parameter identifiability requires covariates in the state processes. Simulation studies show that plugging in externally estimated observation variances, as opposed to jointly estimating them with other parameters, reduces bias and standard error of estimates. In contrast to previous results for simple linear SSMs, strong confounding between jointly estimated process and observation variance parameters was not found in the models explored here. However, when observation variance was also estimated in the motivating case study, the resulting process variance estimates were implausibly low (near-zero). As SSMs are used in increasingly complex ways, understanding when inference can be expected to be successful, and what aids it, becomes more important. Our study illustrates (i) the need for relevant process covariates and (ii) the benefits of using externally estimated observation variances for inference for nonlinear stage-structured SSMs.