Page 377 - Special Topic Session (STS) - Volume 3

STS551 Yousif Alyousifi et al.
nitrogen dioxide (NO2) and ozone (O3) (Gass et al. 2015). The US model is
used to determine the API data in Malaysian where the concentration of each
pollutant is transformed into a numerical scale which ranged between 0 and
infinity (DOE 2000). The API value of less than 100 indicates a moderate air
quality while the API value that is more than 100 shows a higher level of air
pollution.
More specifically, several researchers have also utilized Markov chain in
their studies on air pollution. For example, Hoyos et al. (2010) have proposed
a finite Markov chain for modeling the levels of air pollution in Mexico City for
the purpose of evaluating how far the control policies on air pollution are
effective. Rodrigues & Achcar (2012) employed a Markov chain model on
ozone air pollution using the daily maximum measurements. They applied the
Bayesian method to estimate the parameters of the first order Markov Matrix
and found that the Markov model to be adequate to explain the classification
of the different level of air pollution. Alyousifi et al. (2017) have employed a
Markov chain model to predict and investigate the occurrences of air pollution
in Peninsular Malaysia. They have estimated the count matrix using the
maximum likelihood method. Although, the Markov model appear to be quite
flexible in representing the transitions between the different air pollution
states, the resultant Markov matrix is found to include some zero probabilities,
indicating no possibility of going from certain state to another. It has been
argued by the authors that the results are not surprisingly due to the persistent
occurrences of dry months during the period of the study. Meanwhile, the
empirical Bayes approach has been suggested by several authors such as
(Fienberg & Holland 1973; Meshkani & Billard 1992; Rodrigues & Achcar 2012;
Seal & Hossain 2013,2015; Sanusi et al.2013; Agresti & Chuang 1989), which
offers a solution for addressing the problem of zero probabilities in the
transition matrix of the Markov chain found based on maximum likelihood
method. In this study, the empirical Bayesian method is applied for smoothing
the zero probability in the transition matrix and to estimate the parameters of
Markov chain model based on hourly API data to describe air pollution
characteristics of seven cities located in the central region of Peninsular
Malaysia. For each particular state of air pollution, the characteristics of
interest are air pollution persistence, probability of air pollution and air
pollution duration, which will be obtained by determining the mean residence
time, the steady-state probability and the mean recurrence time of the air
pollution respectively.

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