Markov chain modeling for air pollution index based on maximum a posteriori method

Air pollution is a major environmental problem, which brings about a threat to human health and the natural environment. Thus, determination and assessment of the level of air pollution is an important component in monitoring of the air quality. This study involves estimating the transition probability matrix of the Markov chain model based on maximum a posteriori (MAP) method using hourly data of air pollution index (API). The API data has been collected from seven air-monitoring stations in peninsular Malaysia. The estimated transition probability matrix is used to determine the characteristics of air pollution such as the steady-state probability and the expected return time. The transition probabilities of the Markov chain are fitted based on maximum a posteriori method under three different priors, which are Dirichlet, Jeffreys, and uniform. The results found show that the maximum a posteriori method under the Dirichlet prior produced the most precise estimates as compared with the other priors. In addition, for the areas considered in the study, the moderate state is more persistent as opposed to unhealthy states indicating that the problem of air quality is not very serious. In general, this study could provide important implications for developing proper strategies for managing air quality and for improving public health.