Hidden Markov Model Based on Logistic Regression

Abstract

A hidden Markov model (HMM) is a useful tool for modeling dependent heterogeneous phenomena. It can be used to find factors that affect real-world events, even when those factors cannot be directly observed. HMMs differ from traditional methods by using state variables and mixture distributions to model the hidden states. This allows HMMs to find relationships between variables even when the variables cannot be directly observed. HMM can be extended, allowing the transition probabilities to depend on covariates. This makes HMMs more flexible and powerful, as they can be used to model a wider range of sequential data. Modeling covariates in a hidden Markov model is particularly difficult when the dimension of the state variable is large. To avoid these difficulties, Markovian properties are achieved by implanting the previous state variables to the logistic regression model. We apply the proposed method to find the factors that affect the hidden state of matsutake mushroom growth, in which it is hard to find covariates that directly affect matsutake mushroom growth in Korea. We believe that this method can be used to identify factors that are difficult to find using traditional methods.

Keywords

• Bayesian analysis
• hidden Markov model
• hierarcical modeling
• logistic regression