Flexible estimation of the state dwell-time distribution in hidden semi-Markov models

TL;DR

This paper introduces a flexible, data-driven method for estimating dwell-time distributions in hidden semi-Markov models, overcoming limitations of parametric choices, demonstrated through muskox movement data analysis.

Contribution

It proposes a penalised maximum likelihood approach for nonparametric dwell-time estimation in hidden semi-Markov models, implemented in the R-package PHSMM.

Findings

Effective modeling of muskox movement data.

Flexible estimation without restrictive distributional assumptions.

Available implementation in R package PHSMM.

Abstract

Hidden semi-Markov models generalise hidden Markov models by explicitly modelling the time spent in a given state, the so-called dwell time, using some distribution defined on the natural numbers. While the (shifted) Poisson and negative binomial distribution provide natural choices for such distributions, in practice, parametric distributions can lack the flexibility to adequately model the dwell times. To overcome this problem, a penalised maximum likelihood approach is proposed that allows for a flexible and data-driven estimation of the dwell-time distributions without the need to make any distributional assumption. This approach is suitable for direct modelling purposes or as an exploratory tool to investigate the latent state dynamics. The feasibility and potential of the suggested approach is illustrated by modelling muskox movements in northeast Greenland using GPS tracking data. The proposed method is implemented in the R-package PHSMM which is available on CRAN.