Bayesian Inference For Exponential Distribution Based On Upper Record Range

This paper deals with Bayesian estimations of scale parameter of the exponential distribution based on upper record range (Rn). This has been done in two steps; point and interval. In the first step the quadratic, squared error and absolute error, loss functions have been considered to obtain Bayesian-point estimations. Also in the next step the shortest Bayes interval (Hight Posterior Density interval) and Bayes interval with equal tails based on upper record range have been found. Therefore, the Homotopy Perturbation Method(HPM) has been applied to obtain the limits of Hight Posterior Density intervals. Moreover, efforts have been made to meet the admissibility conditions for linear estimators based on upper record range of the form mRn+d by obtained Bayesian point estimations. So regarding the consideration of loss functions, the prior distribution between the conjunction family has been chosen to be able to produce the linear estimations from upper record range statistics. Finally, some numerical examples and simulations have been presented

Modeling the Effect of a Road Construction Project on Transportation System Performance

Road construction projects create physical changes on roads that result in capacity reduction and travel time escalation during the construction project period. The reduction in the posted speed limit, the number of lanes, lane width and shoulder width at the construction zone makes it difficult for the road to accommodate high traffic volume. Therefore, the goal of this research is to model the effect of a road construction project on travel time at road link-level and help improve the mobility of people and goods through dissemination or implementation of proactive solutions. Data for a resurfacing construction project on I-485 in the city of Charlotte, North Carolina (NC) was used evaluation, analysis, and modeling. A statistical t-test was conducted to examine the relationship between the change in travel time before and during the construction project period. Further, travel time models were developed for the freeway links and the connecting arterial street links, both before and during the construction project period. The road network characteristics of each link, such as the volume/ capacity (V/C), the number of lanes, the speed limit, the shoulder width, the lane width, whether the link is divided or undivided, characteristics of neighboring links, the time-of-the-day, the day-of-the-week, and the distance of the link from the road construction project were considered as predictor variables for modeling. The results obtained indicate that a decrease in travel time was observed during the construction project period on the freeway links when compared to the before construction project period. Contrarily, an increase in travel time was observed during the construction project period on the connecting arterial street links when compared to the before construction project period. Also, the average travel time, the planning time, and the travel time index can better explain the effect of a road construction project on transportation system performance when compared to the planning time index and the buffer time index. The influence of predictor variables seem to vary before and during the construction project period on the freeway links and connecting arterial street links. Practitioners should take the research findings into consideration, in addition to the construction zone characteristics, when planning a road construction project and developing temporary traffic control and detour plans

Adaptive methods for Bayesian time-to-event point-of-care clinical trials

Point-of-care clinical trials are randomized clinical trials designed to maximize pragmatic design features. The goal is to integrate research into standard care such that the burden of research is minimized for patient and physician, including recruitment, randomization and study visits. When possible, these studies employ Bayesian adaptive methods and data collection through the medical record. Due to the passive and adaptive nature of these trials, a number of unique challenges may arise over the course of a study. In this dissertation, adaptive methodology for Bayesian time-to-event clinical trials is developed and evaluated for studies with limited censoring. Use of a normal approximation to the study parameter likelihood is proposed for trials in which the likelihood is not normally distributed and assessed with respect to frequentist type I and II errors. A previously developed method for choosing a normal prior distribution for analysis is applied with modifications to allow for adaptive randomization. This method of prior selection in conjunction with the normal parameter likelihood is used to estimate future data for the purpose of prediction of study success. A previously published method for future event estimation is modified to allow for adaptive randomization and inclusion of prior information. Accuracy of this method is evaluated against final study numbers under a range of study designs and parameter likelihood assumptions. With these future estimates, we predict study conclusions by calculating predicted probabilities of study outcome and compare them to actual study conclusions. Reliability of this method is evaluated considering prior distribution choice, study design, and use of an incorrect likelihood for analysis. The normal approximation to non-normally distributed data performs well here and is reliable when the underlying likelihood is known. The choice of analytic prior distribution agrees with previously published results when equal allocation is forced, but changes depending on the severity of adaptive allocation. Performance of event estimation and prediction vary, but can provide reliable estimates after only 25 subjects have been observed. Analysis and prediction can reliably be carried out in point-of-care studies when care is taken to ensure assumptions are reasonable