Bayesian inference for zero-and-one-inflated geometric distribution regression model using Pólya-Gamma latent variables

Abstract

In the fields of internet financial transactions and reliability engineering, there could be more zero and one observations simultaneously. In this paper, considering that it is beyond the range where the conventional model can fit, zero-and-one-inflated geometric distribution regression model is proposed. Ingeniously introducing Pólya-Gamma latent variables in the Bayesian inference, posterior sampling with high-dimensional parameters is converted to latent variables sampling and posterior sampling with lower-dimensional parameters, respectively. Circumventing the need for Metropolis-Hastings sampling, the sample with higher sampling efficiency is obtained. A simulation study is conducted to assess the performance of the proposed estimation for various sample sizes. Finally, a doctoral dissertation data set is analyzed to illustrate the practicability of the proposed method, research shows that zero-and-one-inflated geometric distribution regression model using Pólya-Gamma latent variables can achieve better fitting results.     

面板数据的贝叶斯Elastic Net分位数回归方法及其应用研究

本文首次将Elastic Net这种用于高度相关变量的惩罚方法用于面板数据的贝叶斯分位数回归,并基于非对称Laplace先验分布推导所有参数的后验分布,进而构建Gibbs抽样。为了验证模型的有效性,本文将面板数据的贝叶斯Elastic Net分位数回归方法(BQR. EN)与面板数据的贝叶斯分位数回归方法(BQR)、面板数据的贝叶斯Lasso分位数回归方法(BLQR)、面板数据的贝叶斯自适应Lasso分位数回归方法(BALQR)进行了多种情形下的全方位比较,结果表明BQR. EN方法适用于具有高度相关性、数据维度很高和尖峰厚尾分布特征的数据。进一步地,本文就BQR. EN方法在不同扰动项假设、不同样本量的情形展开模拟比较,验证了新方法的稳健性和小样本特性。最后,本文选取互联网金融类上市公司经济增加值(EVA)作为实证研究对象,检验新方法在实际问题中的参数估计与变量选择能力,实证结果符合预期。     

环境信息披露的污染减排效应评估

本文利用我国2008年正式实施环境信息披露制度这一外生冲击构造准自然实验,基于2004-2017年我国285个城市的面板数据,通过双重差分法系统评估环境信息披露对工业污染物排放的影响。克服环境信息披露的测量困难与内生性问题,首次考察环境信息披露的污染减排效果,并借助数理模型对其影响机制进行规范阐释。研究发现,环境信息披露能够显著降低工业污染物排放水平,且该影响具有一定的时滞性和长期性;同时,减排作用会随地区环境污染程度和环境规制力度的增强而呈现递增规律;此外,机制分析的结果表明,其传导机制主要来自于产业结构转型和减排技术进步。为验证研究结论的稳健性,本文提供了平行趋势、工具变量、安慰剂等多种方法的检验结果。本文的研究在经验上丰富了环境信息披露与环境污染治理之间关系的相关讨论,为提升我国环境污染治理水平、打赢污染防治攻坚战提供有益的政策启示。     

贝叶斯决策理论视域下的经济逻辑及其研究范式转向--兼析习近平经济思想

经济逻辑学是经济学和逻辑学的交叉学科,它的产生有其必然性,我们可以从经济学的基本假设、经济学的研究方法、经济学研究的确定性以及逻辑学的发展等几个角度给予论证。从贝叶斯决策理论的视角看,它是研究经济活动中理性决策和策略推理的科学。在理论驱动力和现实驱动力的双重作用下,经济逻辑的研究已开始了由形式逻辑范式向科学逻辑范式的转向。     

中国上市 ITO 企业经营效率评价及影响因素分析

运用基于规模报酬可变的投入导向的超效率DEA模型,对在沪深两市上市的具有代表性的30家中国ITO企业的经营效率进行实证研究,结果表明中国上市ITO公司整体运营效率不高,且各企业之间存在显著差异性。为分析企业规模、员工素质、研发投入等因素对中国上市ITO企业效率的影响,采用Tobit模型发现企业规模、员工素质、政府支持等因素对企业运营效率有着积极地影响,而研发投入对企业运营效率的影响并不显著。     

Addressing potential prior‐data conflict when using informative priors in proof‐of‐concept studies

Bayesian methods are increasingly used in proof‐of‐concept studies. An important benefit of these methods is the potential to use informative priors, thereby reducing sample size. This is particularly relevant for treatment arms where there is a substantial amount of historical information such as placebo and active comparators. One issue with using an informative prior is the possibility of a mismatch between the informative prior and the observed data, referred to as prior‐data conflict. We focus on two methods for dealing with this: a testing approach and a mixture prior approach. The testing approach assesses prior‐data conflict by comparing the observed data to the prior predictive distribution and resorting to a non‐informative prior if prior‐data conflict is declared. The mixture prior approach uses a prior with a precise and diffuse component. We assess these approaches for the normal case via simulation and show they have some attractive features as compared with the standard one‐component informative prior. For example, when the discrepancy between the prior and the data is sufficiently marked, and intuitively, one feels less certain about the results, both the testing and mixture approaches typically yield wider posterior‐credible intervals than when there is no discrepancy. In contrast, when there is no discrepancy, the results of these approaches are typically similar to the standard approach. Whilst for any specific study, the operating characteristics of any selected approach should be assessed and agreed at the design stage; we believe these two approaches are each worthy of consideration. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparison of Interval Estimators of Pr(X < Y) in the Two-parameter Exponential Distribution

We consider confidence intervals for the stress–strength reliability Pr(X< Y) in the two-parameter exponential distribution. We have derived the Bayesian highest posterior density interval using non-informative prior distributions. We have compared its performance with the intervals based on the generalized pivot variable intervals in terms of their coverage probabilities and expected lengths. Our simulation study shows that the Bayesian interval performs better according to the criteria used, especially when the sample sizes are very small. An example is given.     

Mixed-effects Models with Skewed Distributions for Time-varying Decay Rate in HIV Dynamics

After initiation of treatment, HIV viral load has multiphasic changes, which indicates that the viral decay rate is a time-varying process. Mixed-effects models with different time-varying decay rate functions have been proposed in literature. However, there are two unresolved critical issues: (i) it is not clear which model is more appropriate for practical use, and (ii) the model random errors are commonly assumed to follow a normal distribution, which may be unrealistic and can obscure important features of within- and among-subject variations. Because asymmetry of HIV viral load data is still noticeable even after transformation, it is important to use a more general distribution family that enables the unrealistic normal assumption to be relaxed. We developed skew-elliptical (SE) Bayesian mixed-effects models by considering the model random errors to have an SE distribution. We compared the performance among five SE models that have different time-varying decay rate functions. For each model, we also contrasted the performance under different model random error assumptions such as normal, Student-t, skew-normal, or skew-t distribution. Two AIDS clinical trial datasets were used to illustrate the proposed models and methods. The results indicate that the model with a time-varying viral decay rate that has two exponential components is preferred. Among the four distribution assumptions, the skew-t and skew-normal models provided better fitting to the data than normal or Student-t model, suggesting that it is important to assume a model with a skewed distribution in order to achieve reasonable results when the data exhibit skewness.     

Temporal Disaggregation: Methods,Information Loss,and Diagnostics

This research provides a generalized framework to disaggregate lower-frequency time series and evaluate the disaggregation performance. The proposed framework combines two models in separate stages: a linear regression model to exploit related independent variables in the first stage and a state–space model to disaggregate the residual from the regression in the second stage. For the purpose of providing a set of practical criteria for assessing the disaggregation performance, we measure the information loss that occurs during temporal aggregation while examining what effects take place when aggregating data. To validate the proposed framework, we implement Monte Carlo simulations and provide two empirical studies. Supplementary materials for this article are available online.