EMPIRICAL BAYES SELECTION FOR THE HIGHEST SUCCESS PROBABILITY IN BERNOULLI PROCESSES WITH NEGATIVE BINOMIAL SAMPLING

1991 ◽  
Vol 9 (3) ◽  
Author(s):  
TaChen Liang
Keyword(s):  
Empirical Bayes ◽  
Negative Binomial ◽  
Success Probability ◽  
Binomial Sampling ◽  
Selection For ◽  
Bernoulli Processes

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.

scholarly journals Spike-Based Winner-Take-All Computation: Fundamental Limits and Order-Optimal Circuits

2019 ◽  
Vol 31 (12) ◽  
pp. 2523-2561 ◽  
Author(s):  
Lili Su ◽  
Chia-Jung Chang ◽  
Nancy Lynch
Keyword(s):  
Lower Bound ◽  
Waiting Time ◽  
Success Probability ◽  
Spike Trains ◽  
Decision Time ◽  
Text Input ◽  
Bernoulli Processes ◽  
Winner Take All ◽  
Input Spike ◽  
Take All

Winner-take-all (WTA) refers to the neural operation that selects a (typically small) group of neurons from a large neuron pool. It is conjectured to underlie many of the brain's fundamental computational abilities. However, not much is known about the robustness of a spike-based WTA network to the inherent randomness of the input spike trains. In this work, we consider a spike-based [Formula: see text]–WTA model wherein [Formula: see text] randomly generated input spike trains compete with each other based on their underlying firing rates and [Formula: see text] winners are supposed to be selected. We slot the time evenly with each time slot of length 1 ms and model the [Formula: see text] input spike trains as [Formula: see text] independent Bernoulli processes. We analytically characterize the minimum waiting time needed so that a target minimax decision accuracy (success probability) can be reached. We first derive an information-theoretic lower bound on the waiting time. We show that to guarantee a (minimax) decision error [Formula: see text] (where [Formula: see text]), the waiting time of any WTA circuit is at least [Formula: see text]where [Formula: see text] is a finite set of rates and [Formula: see text] is a difficulty parameter of a WTA task with respect to set [Formula: see text] for independent input spike trains. Additionally, [Formula: see text] is independent of [Formula: see text], [Formula: see text], and [Formula: see text]. We then design a simple WTA circuit whose waiting time is [Formula: see text]provided that the local memory of each output neuron is sufficiently long. It turns out that for any fixed [Formula: see text], this decision time is order-optimal (i.e., it matches the above lower bound up to a multiplicative constant factor) in terms of its scaling in [Formula: see text], [Formula: see text], and [Formula: see text].

Stochastic variable selection strategies for zero-inflated models

2017 ◽  
Vol 18 (1) ◽  
pp. 3-23 ◽  
Author(s):  
Eva Cantoni ◽  
Marie Auda
Keyword(s):  
Variable Selection ◽  
Count Data ◽  
Negative Binomial ◽  
Stochastic Search ◽  
Simulation Studies ◽  
Stochastic Variable ◽  
Selection Strategies ◽  
Selection For ◽  
A Chain ◽  
Zero Counts

When count data exhibit excess zero, that is more zero counts than a simpler parametric distribution can model, the zero-inflated Poisson (ZIP) or zero-inflated negative binomial (ZINB) models are often used. Variable selection for these models is even more challenging than for other regression situations because the availability of p covariates implies 4 p possible models. We adapt to zero-inflated models an approach for variable selection that avoids the screening of all possible models. This approach is based on a stochastic search through the space of all possible models, which generates a chain of interesting models. As an additional novelty, we propose three ways of extracting information from this rich chain and we compare them in two simulation studies, where we also contrast our approach with regularization (penalized) techniques available in the literature. The analysis of a typical dataset that has motivated our research is also presented, before concluding with some recommendations.

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.

Sign in / Sign up

Export Citation Format

Share Document