医疗费用预测的贝叶斯多项式混合效应模型

医疗费用预测是健康保险费率厘定的前提和基础。对于多年期的医疗费用数据,通常使用线性混合效应模型对其进行拟合,但线性混合效应模型对非线性关系的纵向数据建模具有一定的局限性。本文对线性混合效应模型进行扩展,根据医疗费用数据中变量之间的非线性关系,建立了多项式混合效应模型,并将其应用于一组医疗费用数据进行实证研究。结果表明,多项式混合效应模型对住院医疗费用的拟合效果显著优于通常使用的线性混合模型,在医疗费用管理和健康保险的费率厘定中具有重要的应用价值。     

混合贝塔分布随机波动模型及其贝叶斯分析

为了更准确地揭示金融资产收益率数据的真实数据生成过程,提出了基于混合贝塔分布的随机波动模型,讨论了混合贝塔分布随机波动模型的贝叶斯估计方法,并给出了一种Gibbs抽样算法。以上证A股综指简单收益率为例,分别建立了基于正态分布和混合贝塔分布的随机波动模型,研究表明,基于混合贝塔分布的随机波动模型更准确地描述了样本数据的真实数据生成过程,而正态分布的随机波动模型将高峰厚尾等现象归结为波动冲击,从而低估了收益率的平均波动水平,高估了波动的持续性和波动的冲击扰动。     

混合效应模型的非参数贝叶斯分位回归方法研究

本文对混合效应模型提出了一种非参数贝叶斯分位回归方法,通过引进一种新的分层有限正态混合分布,将分位回归建模时对随机误差项的假定放宽至仅有分位点约束之下.通过对混合比例参数假设广泛灵活的Stick-Breaking先验,使得模型捕捉复杂数据分布信息的能力更强.在建立的非参数贝叶斯分层分位回归模型中引入潜变量,使模型参数估计的Gibbs抽样算法中原来每次需要计算(2M)N项函数值变为每次只需计算N项即可.蒙特卡罗模拟显示,在误差分布函数变得较为复杂时,非参数贝叶斯分位回归方法比参数方法在估计效果上有更大的优势.     

半参数混合模型下的贝叶斯方法与应用

极端值估计是损失评估的重要研究部分,文章在贝叶斯方法的基础上,用半参数混合模型来拟合损失.在确定模型参数的过程中,运用贝叶斯方法对参数建模,将参数转化成随机变量,并基于马尔卡夫蒙特卡罗(MCMC)抽样得到参数的估计值.该方法的特点是参数数量少,通过抽样把参数转化成随机变量,给出所有参数可能取值的频率分布图.实证结果表明模型结果既考虑了参数的不确定性,又兼顾了损失的厚尾性.     

基于Gamma随机效应分层贝叶斯模型的汽车延保定价

汽车延保在中国方兴未艾,相应保险产品的推出更是必然趋势,但相关精算定价研究仍为空白。假设系统故障过程为更新过程,将故障分析问题转换为生存分析问题,对存在左截断和右删失的选择性样本进行分析;模型构建上,假设汽车系统寿命服从两参数威布尔分布,构造多层贝叶斯模型,基于MCMC方法估计后验参数;在第二层模型中引入地区、车型、系统等因子作为协变量建立威布尔混合效应模型,并假设随机效应服从Gamma分布,考虑到系统内部件存在竞争风险,对系统寿命分布参数进行调整,把系统寿命的建模分析转换为指定时间内故障次数的分析,并据此给出延保产品精算定价;通过实证研究,基于某4S店真实数据给出两年期延保定价,结果表明基于Gibbs抽样的贝叶斯MCMC方法估计结果收敛性较好,最终定价也贴合实际情况。     

基于贝叶斯偏态线性混合模型的费率厘定

线性混合模型是非寿险费率厘定的主要方法之一。通常的线性混合模型假设随机误差项服从正态分布,而保险损失数据往往具有右偏特征,这使得该模型在非寿险费率厘定中的应用受到一定影响。在通常的线性混合模型基础上,假设随机误差项服从偏态分布,即可建立偏态线性混合模型,从而改善费率厘定结果的合理性。基于一组实际的保险损失数据,应用贝叶斯MCMC方法建立几个不同的偏态线性混合模型,并与正态分布假设下的线性混合模型进行对比,实证检验偏态线性混合模型在非寿险费率厘定中的优越性。     

真实固定效应空间随机前沿模型的贝叶斯估计

忽略个体效应和空间效应会严重干扰效率测算,其中忽略个体效应使得技术无效率项发生偏移,忽略空间相关性导致估计量有偏且不一致。本文基于真实固定效应随机前沿模型（引入了个体效应）,引入因变量和双边误差项的空间滞后项,构建了适用性更佳的真实固定效应空间随机前沿模型。对模型进行组内变化以消除额外参数,使用贝叶斯方法（需推导未知参数的后验分布并执行MCMC抽样）估计参数和技术效率。该方法真正克服了额外参数问题,比同类方法直观、简便。数值模拟结果表明,本文方法对参数、个体截距项及技术无效率项的估计精度均较高,且增加样本容量,估计精度变优。     

基于贝叶斯推断的HIV非线性混合效应联合模型研究

 在纵向数据研究中,混合效应模型的随机误差通常采用正态性假设。而诸如病毒载量和CD4细胞数目等病毒性数据通常呈现偏斜性,因此正态性假设可能影响模型结果甚至导致错误的结论。在HIV动力学研究中,病毒响应值往往与协变量相关,且协变量的测量值通常存在误差,为此论文中联立协变量过程建立具有偏正态分布的非线性混合效应联合模型,并用贝叶斯推断方法估计模型的参数。由于协变量能够解释个体内的部分变化,因此协变量过程的模型选择对病毒载量的拟合效果有重要的影响。该文提出了一次移动平均模型作为协变量过程的改进模型,比较后发现当协变量采用移动平均模型时,病毒载量模型的拟合效果更好。该结果对协变量模型的研究具有重要的指导意义。     

混合频率FA-MIDAS类模型构建及其应用

文章构建了一类能够直接将大量不同频率指标放入同一模型的混频数据因子（FA-MIDAS）模型,深入挖掘了FA-MIDAS类模型的内部结构及驱动机制,推导出了FA-MIDAS类模型非线性最小二乘估计方法。在此基础上,引入多个高频宏观经济影响因素对我国经济增长进行了预测和监测研究。结果表明：非线性最小二乘估计方法能迅速找到FA-MIDAS类模型的收敛解;FA-MIDAS-AR模型在对经济增长的短期预测上具有领先优势,组合模型FA-MIDAS-AR-BIC对新时期经济增长的预测具有较高的时效性及精确性;按照各因子对经济增长的动力程度由高到低依次为高频消费因子、高频投资因子。     

交互效应动态面板模型的非线性工具变量估计

文章针对交互效应动态面板数据模型的参数估计难题,提出了一种非线性工具变量估计方法.通过Monte Carlo仿真发现:这种非线性工具变量估计法具有较好的有限样本性质,特别是针对非平稳的数据,该方法表现出了非常好的有限样本估计特征.     

The Use of Working Variables in the Bayesian Modeling of Mean and Dispersion Parameters in Generalized Nonlinear Models with Random Effects

This article is aimed at reviewing a novel Bayesian approach to handle inference and estimation in the class of generalized nonlinear models. These models include some of the main techniques of statistical methodology, namely generalized linear models and parametric nonlinear regression. In addition, this proposal extends to methods for the systematic treatment of variation that is not explicitly predicted within the model, through the inclusion of random effects, and takes into account the modeling of dispersion parameters in the class of two-parameter exponential family. The methodology is based on the implementation of a two-stage algorithm that induces a hybrid approach based on numerical methods for approximating the likelihood to a normal density using a Taylor linearization around the values of current parameters in an MCMC routine.     

Dirichlet Processes in Nonlinear Mixed Effects Models

In this article, we use two efficient approaches to deal with the difficulty in computing the intractable integrals when implementing Gibbs sampling in the nonlinear mixed effects model (NLMM) based on Dirichlet processes (DP). In the first approach, we compute the Laplace's approximation to the integral for its high accuracy, low cost, and ease of implementation. The second approach uses the no-gaps algorithm of MacEachern and Müller (1998 MacEachern , S. , Müller , P. ( 1998 ). Estimating mixtures of Dirichlet process models . Journal of Computational and Graphical Statistics 7 : 223 – 238 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) to perform Gibbs sampling without evaluating the difficult integral. We apply both approaches to real problems and simulations. Results show that both approaches perform well in density estimation and prediction and are superior to the parametric analysis in that they can detect important model features, such as skewness, long tails, and multimodality, whereas the parametric analysis cannot.     

Multilevel Mixed Linear Models for Survival Data

For the analysis of correlated survival data mixed linear models are useful alternatives to frailty models. By their use the survival times can be directly modelled, so that the interpretation of the fixed and random effects is straightforward. However, because of intractable integration involved with the use of marginal likelihood the class of models in use has been severely restricted. Such a difficulty can be avoided by using hierarchical-likelihood, which provides a statistically efficient and fast fitting algorithm for multilevel models. The proposed method is illustrated using the chronic granulomatous disease data. A simulation study is carried out to evaluate the performance.     

Inference for nonconjugate Bayesian Models using the Gibbs sampler

A Bayesian approach to modeling a rich class of nonconjugate problems is presented. An adaptive Monte Carlo integration technique known as the Gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework. The result is a general strategy for obtaining marginal posterior densities under changing specification of the model error densities and related prior densities. We illustrate the approach in a nonlinear regression setting, comparing the merits of three candidate error distributions.     

Nonparametric Applications of Bayesian Inference

This article evaluates the usefulness of a nonparametric approach to Bayesian inference by presenting two applications. Our first application considers an educational choice problem. We focus on obtaining a predictive distribution for earnings corresponding to various levels of schooling. This predictive distribution incorporates the parameter uncertainty, so that it is relevant for decision making under uncertainty in the expected utility framework of microeconomics. The second application is to quantile regression. Our point here is to examine the potential of the nonparametric framework to provide inferences without relying on asymptotic approximations. Unlike in the first application, the standard asymptotic normal approximation turns out not to be a good guide.     

On the Functional Approach to Bayesian Efficient Designs for Nonlinear Regression Models

The present article is devoted to an extension of the functional approach elaborated in the book Melas (2006 Melas , V. B. ( 2006 ). Functional Approach to Optimal Experimental Design . Lecture Notes in Statistics , Vol. 184. Heidelberg : Springer . [Google Scholar]) for studying optimal designs in linear and nonlinear regression models. Here we consider Bayesian efficient designs for nonlinear models under the standard assumptions on the observational errors. Sufficient conditions for uniqueness of locally optimal and Bayesian efficient designs for common optimality criteria are given. L-efficient Bayesian designs are constructed and investigated for a special nonlinear regression model of a rational form as an illustration of our main results. This model is interesting in both a practical and a theoretical sense.     

Bayesian Inference for Skew-normal Linear Mixed Models

Linear mixed models (LMM) are frequently used to analyze repeated measures data, because they are more flexible to modelling the correlation within-subject, often present in this type of data. The most popular LMM for continuous responses assumes that both the random effects and the within-subjects errors are normally distributed, which can be an unrealistic assumption, obscuring important features of the variations present within and among the units (or groups). This work presents skew-normal liner mixed models (SNLMM) that relax the normality assumption by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in mixed models. The MCMC scheme is derived and the results of a simulation study are provided demonstrating that standard information criteria may be used to detect departures from normality. The procedures are illustrated using a real data set from a cholesterol study.     

Nonlinear mixed effects modelling for estimation of steady state attainment

Assessment of the time needed to attain steady state is a key pharmacokinetic objective during drug development. Traditional approaches for assessing steady state include ANOVA‐based methods for comparing mean plasma concentration values from each sampling day, with either a difference or equivalence test. However, hypothesis‐testing approaches are ill suited for assessment of steady state. This paper presents a nonlinear mixed effects modelling approach for estimation of steady state attainment, based on fitting a simple nonlinear mixed model to observed trough plasma concentrations. The simple nonlinear mixed model is developed and proposed for use under certain pharmacokinetic assumptions. The nonlinear mixed modelling estimation approach is described and illustrated by application to trough data from a multiple dose trial in healthy subjects. The performance of the nonlinear mixed modelling approach is compared to ANOVA‐based approaches by means of simulation techniques. Copyright © 2005 John Wiley & Sons, Ltd.