Bayesian Modeling of Skewed Spatio-Temporal Data Using a Flexible Random Field with Matérn Correlation and Adaptive Hamiltonian Algorithm

Omid Karimi

Spatio-temporal data often exhibit skewed distributions, which pose challenges for accurate modeling. Skew Gaussian random fields are among the common approaches for analyzing such data, although some existing models suffer from computational complexity and identifiability issues. In this paper, a Bayesian framework is proposed for modeling skewed spatio-temporal data based on a flexible closed skew Gaussian random field, which possesses desirable properties such as identifiability and closure under marginalization and conditioning. By employing the Matérn correlation function, the proposed model provides adequate flexibility for capturing spatio-temporal dependence structures. Bayesian inference is performed using the Hamiltonian Monte Carlo algorithm, and a simulation study is conducted to compare its performance with conventional Markov Chain Monte Carlo methods. Finally, the performance of the proposed model was also evaluated using observed PM-10 air pollution data.

An Estimation of the Minimum Average Waiting Time for Two Queueing Models under Steady-State Conditions in an $M/M/1$ System

Shahram Yaghoobzadeh

In classical queueing systems, customers wait in line to receive service. However, some customers prefer to join multiple queues simultaneously for the same service to obtain it as quickly as possible. Once a customer receives service from one of the queues, they immediately leave the others, thereby minimizing their waiting time. Based on this concept, this paper considers two $M/M/1$ queueing models with arrival and service rates $(lambda_1, mu_1)$ for the first model and $(lambda_2, mu_2)$ for the second. The minimum average waiting time in these two models is estimated using Bayesian, $E$-Bayesian, and Hierarchical Bayesian approaches under the General Entropy Loss Function. Furthermore, Monte Carlo simulations and a real dataset are employed to evaluate and identify the most appropriate estimator.

Journal of Statistical Sciences

Bayesian Modeling of Skewed Spatio-Temporal Data Using a Flexible Random Field with Matérn Correlation and Adaptive Hamiltonian Algorithm

An Estimation of the Minimum Average Waiting Time for Two Queueing Models under Steady-State Conditions in an $M/M/1$ System