CHING'S MARKOV CHAIN MODELS
HIGHWAY WINTER CRASH MODELING
A. G. B. Khaleghei, F. Z. G. Naderkhani, V. Makis and S. Nichol (2012). Highway Winter Crash Modeling with Stochastic Covariates and Missing Data, in Proceedings of the 2012 Industrial and Systems Engineering Research Conference, Orlando, Florida, USA.
In Khaleghei et al. (2012), the authors considered the problem of winter road safety. They provided a stochastic approach for modeling highway collision in the winter time and also identifying the most probable contributing factors.
In Khaleghei et al. (2012), the authors noticed traditional statistical models are not able to capture changes in crash frequencies and are consequently unable to help transportation and traffic decision makers to correctly assess and forecast driving conditions. Contrarily, the Markov process is capable to capture the crash process in collision data modeling during winter times in randomly changing environment. Therefore, it was suggested to be used to predict the collision data.
The weather process is defined as three categorical sequences called Good, Rainy and Snowy weather, in which each category is classified into four possible states according to weather type severity. The parsimonious multivariate Markov chain model Ching et al. (2002) was employed to estimate the coefficient. Following those estimation methods, the problem of estimating coefficients thus being reduced to a linear programming problem. The weather process can then be predicted efficiently.
The performance of the proposed model in Khaleghei et al. (2012) was evaluated by predicting the number of hours in which at least one collision occurs over a future interval of length 24, 168, 744 and 2928 hours. The predicted values are compared with actual 2007 winter collision data. The results show that the proposed model is able to predict future collision well and based on the Mean Absolute Deviation (MAD) criterion, its performance is comparable with logistic regression with non-stochastic covariates.
W. Ching, E. Fung, M. Ng, A multivariate Markov chain model for categorical data sequences and its applications in demand predictions, IMA Journal of Management Mathematics 13 (2002) 87–199.
https://ieeexplore.ieee.org/document/8142556