Work

Advanced Posterior Analyses of Hidden Markov Models: Finite Markov Chain Imbedding and Hybrid Decoding

Year: 2026

Type: article

Abstract: ABSTRACT Two major tasks in applications of hidden Markov models are to (i) compute distributions of summary statistics of the hidden state sequence, and (ii) decode the hidden state sequence. We describe finite Markov chain imbedding (FMCI) and hybrid decoding to solve each of these two tasks. In the first part of our paper, we use FMCI to compute posterior distributions of summary statistics such as the number of visits to a hidden state, the total time spent in a hidden state, the sojourn time in a hidden state, and the longest run length. We use samples generated from the posterior distribution of the hidden state sequence, conditional on the observed sequence, to establish the FMCI framework. In the second part of our paper, we apply hybrid segmentation for improved decoding of an HMM. We demonstrate that hybrid decoding shows increased performance compared to Viterbi or Posterior decoding (often also referred to as global or local decoding), and we introduce a novel procedure for choosing the tuning parameter in the hybrid procedure. Furthermore, we provide an alternative derivation of the hybrid loss function based on weighted geometric means. We demonstrate and apply FMCI and hybrid decoding on various classical data sets and supply accompanying code for reproducibility.

Source: Scandinavian Journal of Statistics

DOI: 10.1111/sjos.70088

Authors: Zenia Elise Damgaard Bæk, Moisès Coll Macià, Laurits Skov, Asger Hobolth

Institutions: Aarhus University, University of Copenhagen

Language: English

Topic: Bayesian Methods and Mixture Models

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,500

Funders: Danish Data Science Academy, Novo Nordisk Fonden