On Empirical Bayes Selection Rules for Negative Binomial Populations

1988 ◽  
Author(s):  
Shanti S. Gupta ◽  
TaChen Liang
Keyword(s):  
Empirical Bayes ◽  
Negative Binomial ◽  
Selection Rules ◽  
Binomial Populations

A Novel Technique to Identify Hot Zones for Active Commuters’ Crashes

2018 ◽  
Vol 2672 (38) ◽  
pp. 266-276 ◽  
Author(s):  
Ahmed Osama ◽  
Tarek Sayed ◽  
Emanuele Sacchi
Keyword(s):  
Mahalanobis Distance ◽  
Empirical Bayes ◽  
Negative Binomial ◽  
Active Transportation ◽  
Spatial Effects ◽  
Distance Method ◽  
Crash Data ◽  
Safety Improvement ◽  
Pedestrian Crashes ◽  
Psi Method

This paper presents an approach to identify and rank accident-prone (hot) zones for active transportation modes. The approach aims to extend the well-known empirical Bayes (EB) potential for safety improvement (PSI) method to cases where multiple crash modes are modeled jointly (multivariate modeling). In this study, crash modeling was pursued with a multivariate model, incorporating spatial effects, using the full Bayes (FB) technique. Cyclist and pedestrian crash data for the City of Vancouver (British Columbia, Canada) were analyzed for 134 traffic analysis zones (TAZs) to detect active transportation hot zones. The hot zones identification (HZID) process was based on the estimation of the Mahalanobis distance, which can be considered an extension to the PSI method in the context of multivariate analysis. In addition, a negative binomial model was developed for cyclist and pedestrian crashes, where the EB PSI for each mode crash was quantified. The cyclist and pedestrian PSIs were combined to detect active transportation hot zones. Overall, the Mahalanobis distance method is found to outperform the PSI method in terms of consistency of results; and discrepancy is observed between the hot zones identified using both approaches.

On the empty cells of Poisson histograms

1993 ◽  
Vol 30 (03) ◽  
pp. 561-574
Author(s):  
Wilfrid S. Kendall
Keyword(s):  
Cell Size ◽  
Poisson Distribution ◽  
Finite Groups ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Empirical Bayes ◽  
Negative Binomial ◽  
Almost Sure Convergence ◽  
Unit Cell Size ◽  
Independent Observations

This paper considers the histogram of unit cell size built up from m independent observations on a Poisson (μ) distribution. The following question is addressed: what is the limiting probability of the event that there are no unoccupied cells lying to the left of occupied cells of the histogram? It is shown that the probability of there being no such isolated empty cells (or isolated finite groups of empty cells) tends to unity as the number m of observations tends to infinity, but that the corresponding almost sure convergence fails. Moreover this probability does not tend to unity when the Poisson distribution is replaced by the negative binomial distribution arising when μ is randomized by a gamma distribution. The relevance to empirical Bayes statistical methods is discussed.

On the empty cells of Poisson histograms

1993 ◽  
Vol 30 (3) ◽  
pp. 561-574
Author(s):  
Wilfrid S. Kendall
Keyword(s):  
Cell Size ◽  
Poisson Distribution ◽  
Finite Groups ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Empirical Bayes ◽  
Negative Binomial ◽  
Almost Sure Convergence ◽  
Unit Cell Size ◽  
Independent Observations

This paper considers the histogram of unit cell size built up from m independent observations on a Poisson (μ) distribution. The following question is addressed: what is the limiting probability of the event that there are no unoccupied cells lying to the left of occupied cells of the histogram? It is shown that the probability of there being no such isolated empty cells (or isolated finite groups of empty cells) tends to unity as the number m of observations tends to infinity, but that the corresponding almost sure convergence fails. Moreover this probability does not tend to unity when the Poisson distribution is replaced by the negative binomial distribution arising when μ is randomized by a gamma distribution. The relevance to empirical Bayes statistical methods is discussed.

scholarly journals A Copula-Based Approach for Accommodating the Underreporting Effect in Wildlife‒Vehicle Crash Analysis

2019 ◽  
Vol 11 (2) ◽  
pp. 418 ◽  
Author(s):  
Yajie Zou ◽  
Xinzhi Zhong ◽  
Jinjun Tang ◽  
Xin Ye ◽  
Lingtao Wu ◽  
...  
Keyword(s):  
Regression Model ◽  
Empirical Bayes ◽  
Negative Binomial ◽  
Washington State ◽  
Gaussian Copula ◽  
Copula Model ◽  
Crash Analysis ◽  
Vehicle Collisions ◽  
Vehicle Collision

Wildlife‒vehicle collision (WVC) data usually contain two types: the reported WVC data and carcass removal data. Previous studies often found a discrepancy between the number of reported WVC and carcass removal data, and the quality of both datasets is affected by underreporting. Underreporting means the number of WVCs is not fully recorded in the database; neglecting the underreporting in WVC data may result in biased parameter estimation results. In this study, a copula regression model linking wildlife‒vehicle collisions and the underreporting outcome was proposed to consider the underreporting in WVC data. The WVC data collected from 10 highways in Washington State were analyzed using the copula regression model and the Negative Binomial (NB) model. The main findings from this study are as follows: (1) the Gaussian copula model can provide different modeling results when compared with the conventional modeling approach; (2) the hotspot identification results indicate that the Gaussian copula-based Empirical Bayes (EB) method can more accurately identify hotspots than the NB-based EB method. Thus, the proposed copula model may be a better alternative to the conventional NB model for modeling underreported WVC data.

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