Discrete-Time Markov Chain Modelling of the Ontario Air Quality Health Index

Abstract

The Air Quality Health Index (AQHI) is an aggregate indicator of air pollution used to communicate to Canadians the health impact of short-term exposure to current air pollutant levels. Understanding the stochastic behaviour of the AQHI can aid public health officials in predicting air pollution levels, determining the likelihood and duration of air quality advisories, and planning for increased strain on the health care system during periods of higher air pollution. Previous research has applied discrete-time Markov chains to investigate stochastic behaviour of air pollution indices but only in a handful of regions and none with the same climatic characteristics as Canadian regions. In this study, we investigated the stochastic behaviour of AQHI risk categories in Ontario (34 air monitoring stations) for 5 years from 2015 to 2019. We employed discrete-time Markov chains using three of the AQHI risk categories (Low Risk, Moderate Risk, High Risk) as states to determine (1) the transition probabilities between these states, (2) the long-run proportion of time spent in each state, and (3) the mean persistence time of each state. These results were then used to assess spatial trends in the stochastic behaviour of AQHI risk categories and the likelihood and duration of air quality advisories. Overall, the air quality (as characterised by the AQHI) in Ontario tends to decrease as population density increases. Urban areas spent a greater proportion of time in higher risk categories, and tended to remain in the higher risk categories for longer before transitioning.

Examining Air Pollution Continuity in Tehran Province using Markov Chain Model

“…Building upon these insights, Holmes and Hassini [14] employed the Air Quality Health Index (AQHI) in eastern Canada, highlighting that urban areas spent more time in high-risk categories and tended to remain in these categories for extended durations before transitioning.…”

“…Holmes and Hassini. [14] examined the random behavior of AQHI risk categories in Ontario (34 air monitoring stations) over five years from 2015 to 2019. They determined discrete-time Markov chains using three AQHI risk categories (low risk, moderate risk, high risk) as states for transition probabilities.…”

Measurement of Cooling Load-Based Occupant Behavior in Under-Actuated Zones: A Time-Variance Approach

“…Each of these approaches provides distinct advantages and faces specific limitations that shape their applicability in capturing the complexity of occupant behavior. The Bernoulli method focuses on independent and memoryless conditions, where (Holmes and Hassini, 2021) occupants make binary decisions based on fixed probabilities. However, it falls short of capturing the complexity of occupant behavior, influenced by external factors, past experiences, and contextual elements (Yan et al, 2015).…”

“…Deep learning survival models (Dai et al, 2020;Yang et al, 2019) and Survival regression models (George et al, 2014). In contrast to Bernoulli and Markov chain models, which primarily focus on predicting event probabilities at specific time instants (Holmes and Hassini, 2021); survival analysis considers the time taken for an event to occur. Specifically, it examines the duration between the initiation of an event and its completion.…”

Application of Spatiotemporal Data Mining to Air Quality Data

“…Essentially, Markov chains model how a system transitions between states (e.g., different levels of air quality) over time in a "memoryless" manner. Many studies have used Markov chains (e.g., Holmes and Hassini, 2021;Asadollahfardi et al, 2016;Caraka et al, 2019) and their spatial variant (e.g., Alyousifi et al, 2020;Biancardi et al, under review) to gain insight into the dynamics, spatial relationships, seasonality, and intradaily patterns of air pollution. Markov chains offer a simple approach with metrics that are easy to understand and compare.…”