Modeling clustered non-stationary Poisson processes for stochastic simulation inputs

Abstract

A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the random inputs vary over time in such a way that the functional forms of the distributions and/or their parameters depend on time. This paper answers the question whether a sequence of observations from a process follow the same statistical distribution, and if not, where the exact change points are, so that observations within two consecutive change points follow the same distribution. We propose two different methods based on likelihood ratio test and cluster analysis to detect multiple change points when observations follow non-stationary Poisson process with diverse occurrence rates over time. Results from a comprehensive Monte Carlo study indicate satisfactory performance for the proposed methods. A well-known example is also considered to show the application of our findings in real world cases.

Optimized combinatorial clustering for stochastic processes

“…Multiple comparisons with the best (MCB) [31] is one of the most widely used MCPs. To apply MCB in a discrete-event simulation, the simulation runs must be independently seeded and the simulation output must be normally distributed, or averaged so that the estimators used are somewhat normally distributed [31,36,38]. There are four R&S-MCB procedures having normally distributed data, but do not require known or equal variance: Nelson and Matejciks Procedure (Procedure NM) [31], two-stage procedure (Procedure B) [1,6], Watanabe (Procedure W) [40], and Frey and Dueck Procedure (Procedure FD) [10].…”

“…Numerous authors have studied this approach for specific data mining tasks such as clustering [10,18,37,38], association rule discovery [35], and decision tree induction [4]. When these approaches are implemented, one of the most challenging issues is determining a sample size that improves the performance of the algorithm without sacrificing the solution quality.…”

Predicting patient risk of readmission with frailty models in the Department of Veteran Affairs

“…Besides, they have not directly incorporated this effect into their modeling framework to control the variations of repeated rehospitalization and its marginal influence on each patient's admission/discharge profile [7,8]. To overcome this shortcoming, in the next part, we explain our proposed approach, which also allows additional clinical and demographic covariates being included into modeling structure.…”

“…The approximate variance matrix for is the inverse Hessian matrix evaluated at θ, and that for ! is an approximation to the conditional mean squared error of prediction described in [24]. Based on this approach, we also compute empirical Bayes estimate of the baseline readmission hazard, pdf of readmission time, and survivor function for all patients but for sake of brevity these are not presented here.…”