This chapter centers on developing best practices for fitting non-linear state-space models such as that described in Millar and Meyer (2000). This model was originally fit in BUGS, but a translation to Stan reveals some underlying problems, namely divergence transitions when using the NUTS sampler. These divergences have been shown to result in biased inferences, but reparameterizations can often eliminate them.
This project compares potential reparameterizations in order to evaluate which tend to eliminate divergent transitions, and which reduce the computational burden. So far, comparisons have been made between the model originally specified in Millar and Meyer (2000) and multiple reparameterized models. Improvements have already been shown, but more work is necessary to consider the effects of more robust parameterizations.
These non-linear state-space models are commonly used in stock assessments. This work has the potential to make many assessments more reliable. Comparing the results of an existing stock assessment that used the standard version would make the results particularly impactful.
This will be chapter 4 of my PhD Dissertation.