Bayesian tolerance intervals with probability matching priors / Dharini a/p Pathmanathan - Pathmanathan, Dharini (2014)
A review on statistical tolerance intervals shows that the derivation of two-sided tolerance intervals is far more challenging than that of their one-sided counterparts. Much of the existing construction of two-sided tolerance intervals are through a numerical approach. This study addresses the problems of constructing two-sided tolerance intervals in balanced one-way random effects models and for a general family of distributions. The Bayesian tolerance interval developed by Ong and Mukerjee (2011) using probability matching priors (PMP) is compared via Monte Carlo simulation with the modified large sample (MLS) tolerance interval of Krishnamoorthy and Mathew (2009) for normal and non-normal experimental errors with respect to coverage probabilities and expected widths. Data generated from normal and nonnormal experimental errors were studied to see the effects on the tolerance intervals since real data may not necessarily follow the normal distribution. Results show that the PMP tolerance interval appears to be less conservative for data with moderate and large number of classes while the MLS tolerance interval is preferable for smaller sample sizes. For the second part of the study, the PMP as well as frequentist two-sided tolerance intervals are constructed for a general family of parametric models. Simulation studies show that the asymptotic results are well-reflected in finite sample sizes. The findings are then applied to real data. The results obtained in this research are a contribution to the area of statistical tolerance regions.