A gentle tutorial of accelerated parameter and confidence interval estimation for Hidden Markov Models using Template Model Builder

Timothée Bacri timothee.bacri@uib.no

Jan Bulla jan.bulla@uib.no

Geir Berentsen geir.berentsen@nhh.no

Sondre Hølleland sondre.hoelleland@hi.no

1 Introduction

Welcome !

This website aims to accompany the reader of https://doi.org/10.1002/bimj.202100256.

The files used in this repository are available in https://github.com/timothee-bacri/HMM_with_TMB.

For a description of the files and the directory structure, please read Directory Structure.
Note that only the folders code/, functions/, and data/ contain files used in the article. The other folders and files relate to this Gitbook and are not described in Directory Structure.

For a description of the functions in functions/utils.R and their parameters and return objects, please take a look at functions/utils.R-explanation.R.

Additionally, as a by-product of using TMB, we can derive standard errors and hence confidence intervals for smoothing probabilities (as defined in Section 11).

1.1 Other article

A preprint version of https://doi.org/10.1080/00949655.2023.2226788 that is published can be found along with the code of its results in the folder paper2-github-preprint/.

This article looks at HMM optimization using popular optimization functions, compares their performance along with their robustness to bad initial parameters, and presents and analyzes smoothing probabilities confidence intervals. Its code is organized in a similar fashion to the article that this repository accompanies.