Analysis of Ozone Behaviour in the City of Puebla-Mexico Using Non-Homogeneous Poisson Models with Multiple Change-Points

In this work, some non-homogeneous Poisson models are considered to study the behaviour of ozone in the city of Puebla, Mexico. Several functions are used as the rate function for the non-homogeneous Poisson process. In addition to their dependence on time, these rate functions also depend on some parameters that need to be estimated. In order to estimate them, a Bayesian approach will be taken. The expressions for the distributions of the parameters involved in the models are very complex. Therefore, Markov chain Monte Carlo algorithms are used to estimate them. The methodology is applied to the ozone data from the city of Puebla, Mexico.

Comparing the Adequacy of Some Non-Homogeneous Poisson Models to Estimate Ozone Exceedances in Mexico City

We consider some non-homogeneous Poisson models to estimate the mean number of times that a given environmental threshold of interest is surpassed by a given pollutant. Seven different rate functions for the Poisson processes describing the models are taken into account. The rate functions considered are the Weibull, exponentiated-Weibull, and their generalisation the Beta-Weibull rate function. We also use the Musa-Okumoto, the Goel-Okumoto, a generalised Goel- Okumoto and the Weibull-geometric rate functions. Whenever thought justifiable, the model allowing the presence of change-points is also going to be considered. The different models are applied to the daily maximum ozone measurements data provided by the monitoring network of the Metropolitan Area of Mexico City. The aim is to compare the adjustment of different rate functions to the data. Even though, some of the rate functions have been considered before, now we are applying them to the same data set. In previous works they were used in different data sets and therefore a comparison of the adequacy of those models were not possible. The measurements considered here were obtained after a series of environmental measures were implemented in Mexico City. Hence, the data present a different behaviour from that of earlier studies.

Using Poisson Modeling and Queuing Theory to Optimize Staffing and Decrease Patient Wait Time in the Emergency Department

Introduction: Studies have shown Emergency Department (ED) crowding contributes to reduced quality of patient care, delays in starting treatments, and increased number of patients leaving without being seen. This analysis shows how to theoretically and optimally align staffing to demand. Methods: The ED value stream was identified and mapped. Patients were stratified into three resource-driven care flow cells based on the severity indices. Time observations were conducted for each of the key care team members and the manual cycle times and service rate were calculated and stratified by severity indices. Using X32 Healthcare’s Online Staffing Optimization (OSO) tool, staffing inefficiencies were identified and an optimal schedule was created for each provider group. Results: Lower Severity Indices (higher acuity patient) led to longer times for providers, nurses, patient care assistants, and clerks. The patient length of stay varied from under one hour to over five hours. The flow of patients varied considerably over the 24 hours’ period but was similar by day of the week. Using flow data, we showed that we needed more nurses, more care team members during peak times of patient flow. Eight hour shifts would allow better flexibility. We showed that the additional salary hours added to the budget would be made up for by increased revenue recognized by decreasing the number of patients who leave without being seen. Conclusion: If implemented, these changes will improve ED flow by using lean tools and principles, ultimately leading to timeliness of care, reduced waits, and improved patient experience.

Asymptotic Comparison of Method of Moments Estimators and Maximum Likelihood Estimators of Parameters in Zero-Inflated Poisson Model

This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.

A Note on the Characterization of Zero-Inflated Poisson Model

Zero-Inflated Poisson model has found a wide variety of applications in recent years in statistical analyses of count data, especially in count regression models. Zero-Inflated Poisson model is characterized in this paper through a linear differential equation satisfied by its probability generating function [1] [2].

Accounting for Heterogeneity in Stop Frequency Models of Work Tours Using Latent Class Poisson Models

Stop frequency models, as one of the elements of activity based models, represent an important part of travel behavior. Unobserved heterogeneity across the travelers should be taken into consideration to prevent biasedness and inconsistency in the estimated parameters in the stop frequency models. Additionally, previous studies on the stop frequency have mostly been done in larger metropolitan areas and less attention has been paid to the areas with less population. This study addresses these gaps by using 2012 travel data from a medium sized U.S. urban area using the work tour for the case study. Stop in the work tour were classified into three groups of outbound leg, work based subtour, and inbound leg of the commutes. Latent Class Poisson Regression Models were used to analyze the data. The results indicate the presence of heterogeneity across the commuters. Using latent class models significantly improves the predictive power of the models compared to regular one class Poisson regression models. In contrast to one class Poisson models, gender becomes insignificant in predicting the number of tours when unobserved heterogeneity is accounted for. The commuters are associated with increased stops on their work based subtour when the employment density of service-related occupations increases in their work zone, but employment density of retail employment does not significantly contribute to the stop making likelihood of the commuters. Additionally, an increase in the number of work tours was associated with fewer stops on the inbound leg of the commute. The results of this study suggest the consideration of unobserved heterogeneity in the stop frequency models and help transportation agencies and policy makers make better inferences from such models.

The Random Distribution of the Loading and Unloading Response Ratio Under the Assumptions of Poisson Models

This paper discussed the random distribution of the loading and unloading response ratio（LURR） of different definitions（Y1～Y5）using the assumptions that the earthquakes occurfollowing the Poisson process and their magnitudes obey the Gutenberg-Richter law.Theresults show that Y1～Y5 are quite stable or concentrated when the expected number of eventsin the calculation time window is relatively large（】40）;but when this occurrence ratebecomes very small,Y2～Y5 become quite variable or unstable.That is to say,a high value ofthe LURR can be produced not only from seismicity before a large earthquake,but also from arandom sequence of earthquakes that obeys a Poisson process when the expected number ofevents in the window is too small.To check the influence of randomness in the catalogue tothe LURR,the random distribution of the LURR under Poisson models has been calculated bysimulation.90%,95% and 99% confidence ranges of Y1 and Y3 are given in this paper,which is helpful to quantify the random

Zero Truncated Bivariate Poisson Model: Marginal-Conditional Modeling Approach with an Application to Traffic Accident Data

A new covariate dependent zero-truncated bivariate Poisson model is proposed in this paper employing generalized linear model. A marginal-conditional approach is used to show the bivariate model. The proposed model with estimation procedure and tests for goodness-of-fit and under (or over) dispersion are shown and applied to road safety data. Two correlated outcome variables considered in this study are number of cars involved in an accident and number of casualties for given number of cars.

有向Poisson网络模型的渐近性理论

研究了有向Poisson网络模型极大似然估计量的渐近性理论.考虑当网络顶点的个数趋于无穷大时,推导出有向Poisson网络模型极大似然估计量线性组合的中心极限定理.此外,通过数值模拟对理论结果进行了验证,期望能够为有向加权网络模型的统计推断提供坚实的理论基础.

Statistical inference for zero-and-one-inflated poisson models

In this paper, a zero-and-one-inflated Poisson (ZOIP) model is studied. The maximum likelihoodestimation and the Bayesian estimation of the model parameters are obtained based on dataaugmentation method. A simulation study based on proposed sampling algorithm is conductedto assess the performance of the proposed estimation for various sample sizes. Finally, two realdata-sets are analysed to illustrate the practicability of the proposed method.

A censored-Poisson model based approach to the analysis of RNA-seq data

Background:With the recent advance of sequencing technology,the collction of RNA expression(RNA-seq)data has been growing rapidly.RNA-seq data are statistically count-type measurements.Poisson distribution is a basic probability distribution for modeling count-type data.With Poisson regression models,various experimental factors,GC content as well as alternative splicing isoforms can be flexibly considered in RNA-seq data analysis.Due to the biochemical and technical limitations of sequencing technology,the biases among RNA-seq data have been recognized.Methods:In this study,an artificial censoring approach has been proposed to an isoform-specific Poisson regression model for analy zing RNA-seq data.Low expression values can be grouped(censored)into one probability category,and high expression values can also be grouped(censored)into another probability category.We have implemented the related Newton-Raphson numeric computing procedure to achieve the maximum likelihood estimation for our censored-Poisson regression model.The related mathematical simplifications have been derived for the consideration of stable and convenient numerical computing.Results:The advantages of our artificial censoring approach have been demonstrated in both simulation studies and application analysis of experimental data.Conclusions:Our proposed artificial censoring approach allows us to focus on the majority of data.As the extreme values(tails)of data are artificially censored,more efficient analysis results can be obtained,even from relatively simple Poisson regression models.Our proposed artificial censoring approach can certainly be considered for other well-developed models or methods for RNA-seq data analysis.

Asymptotically Optimal Dividend Policy for Regime-Switching Compound Poisson Models

This work develops asymptotically optimal dividend policies to maximize the expected present value of dividends until ruin.Compound Poisson processes with regime switching are used to model the surplus and the switching（a continuous-time controlled Markov chain） represents random environment and other economic conditions.Assuming the switching to be fast varying together with suitable conditions,it is shown that the system has a limit that is an average with respect to the invariant measure of a related Markov chain.Under simple conditions,the optimal policy of the limit dividend strategy is a threshold policy.Using the optimal policy of the limit system as a guide,feedback control for the original surplus is then developed.It is demonstrated that the constructed dividend policy is asymptotically optimal.

On two actuarial quantities for the compound Poisson risk model with tax and a threshold dividend strategy

In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability function for the total number of taxation periods over the lifetime of the surplus process is derived. Second, analytical expression of the expected accumulated discounted dividends paid between two consecutive taxation periods is provided. In addition, explicit expressions are also given for the exponential individual claims.

Optimal Dividend Problem for a Compound Poisson Risk Model

In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generalized Poisson process. This model includes the classical risk model and the Pólya-Aeppli risk model as special cases. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that under some conditions the optimal dividend strategy is formed by a barrier strategy. Moreover, two conjectures are proposed.

基于DP算法的Poisson回归模型的变量选择

利用已有的DP算法,对Poisson回归模型的似然函数进行优化估计出模型的参数,分别写出Lasso、Adaptive Lasso、SCAD、MCP 4种惩罚似然函数,用DP算法进行求解,实现变量选择.为了实现算法的自动变量选择,在对惩罚参数的选择上,使用了AIC、BIC信息准则.为了验证DP算法的可行性,通过随机模拟的方式生成数据进行求解.在各项指标下,将DP算法与已有的相关算法进行对比.

Comparison of Ruin Probabilities in Compound Poisson Risk Model

Compound Poisson risk model has been simulated. It has started with exponential claim sizes. The simulations have checked for infinite ruin probabilities. An appropriate time window has been chosen to estimate and compare ruin probabilities. The infinite ruin probabilities of two-compound Poisson risk process have estimated and compared them with standard theoretical results.

Dividend Payments with a Hybrid Strategy in the Compound Poisson Risk Model

In this paper, a hybrid dividend strategy in the compound Poisson risk model is considered. In the absence of dividends, the surplus of an insurance company is modelled by a compound Poisson process. Dividends are paid at a constant rate whenever the modified surplus is in a interval;the premium income no longer goes into the surplus but is paid out as dividends whenever the modified surplus exceeds the upper bound of the interval, otherwise no dividends are paid. Integro-differential equations with boundary conditions satisfied by the expected total discounted dividends until ruin are derived;for example, closed-form solutions are given when claims are exponentially distributed. Accordingly, the moments and moment-generating functions of total discounted dividends until ruin are considered. Finally, the Gerber-Shiu function and Laplace transform of the ruin time are discussed.

带有测量误差Poisson回归模型的变量选择

Poisson回归模型是一种特殊的广义线性模型,被广泛用于计数数据的建模.然而在很多应用中,模型中的协变量很难被精确测量,在进行变量选择和参数估计时,这些测量误差通常难以处理,特别是当维数较高时.针对这一问题,本文提出了一种惩罚的偏差校正方法以确定带有测量误差的Poisson回归模型(MPR)的真实结构.该方法惩罚了专门设计用于处理测量误差的目标函数,并在一个有界的区域内利用复合梯度下降算法给出回归参数的估计.通过随机模拟验证了本文所提出方法的有限样本性质.

广义混合Poisson线性模型的贝叶斯推断

该文在贝叶斯框架下研究广义混合Poisson线性模型的变量估计和变量选择问题.首先结合广义Poisson线性模型和GMM模型,构造混合广义Poisson线性模型,并给出似然函数,然后构造未知参数的先验,给出后验似然函数,随后通过后验似然与先验的乘积得到未知参数的满条件分布,用Gibbs算法和M-H抽样算法抽取未知参数得到参数的估计值,并运用二元潜变量标记活跃变量,假设未知先验,给出后验似然,通过Gibbs算法和M-H抽样算法挑选出回归系数,最后进行数值模拟验证贝叶斯估计的有效性和变量选择的准确性.