Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic...

Area of Science:

• Statistics
• Epidemiology
• Computational Biology

Background:

• Hidden Markov Models (HMMs) are stochastic models where unobservable Markov chains govern mixture distribution parameters.
• Poisson-hidden Markov models (PHMMs) are used when observations follow a mixture of Poisson distributions.
• Estimating transition probabilities and state durations in PHMMs is crucial for understanding underlying processes.

Purpose of the Study:

• To explain and apply methods for estimating Poisson-hidden Markov models.
• To analyze monthly Vibrio cholerae counts over an 11-year period.
• To identify hidden states, estimate transition probabilities, and analyze environmental risk factors.

Main Methods:

• Application of Poisson-hidden Markov models to Vibrio cholerae count data.
• Utilizing the Viterbi algorithm to determine the most likely state sequence and transition probability matrix.
• Estimating mean passage times and their confidence intervals via Monte Carlo simulation.
• Employing Markov ordinal logistic regression to investigate environmental risk factors.

Main Results:

• Three hidden states were identified and labeled: 'Low' (mean count 1.4), 'Moderate' (mean count 6.6), and 'High' (mean count 20.2).
• Estimated average durations of stay in these states were 3, 3, and 4 months, respectively.
• No significant association was found between disease severity levels and climate components.

Conclusions:

• The study successfully applied PHMMs to model Vibrio cholerae dynamics, revealing distinct disease states.
• The Viterbi algorithm and Monte Carlo simulations provided robust estimates for model parameters and state durations.
• Environmental risk factors, specifically climate components, did not show a significant link to Vibrio cholerae severity levels in this dataset.