非线性模型中VaR估测的正态性改进

VaR风险测度技术已经被学界和业界广泛使用,但其局限性也是显而易见的,国内外学者对其进行了一系列的改进.由线性模型扩展为非线性模型以及由正态假定转换到非正态性均源于风险测度的精确化.探讨依数据特征改进和扩展VaR估测方法,使用Johnson转换方法与Cornish-Fisher扩展方法这两种正态性改进方法改善VaR估值,一方面利用正态假定成熟理论结果简化VaR估测方法的推演,另一方面从实证分析角度论证了正态性改进方法在VaR估测中的准确性与有效性.     

基于Copula贝叶斯估计的行业风险差异分析

通过对常替代弹性资本资产定价模型中投资标度问题的分析,提出了Copula贝叶斯估计方法用以获得系统风险β与投资标度比λ的联合后验分布.Copula贝叶斯估计方法针对数据非正态特征及强相关性特征而构建,采用Copula函数取代原有普通贝叶斯估计方法中的正态假设.传统贝叶斯估计方法假设了正态的似然函数,忽略了数据可能存在尖峰后尾等在金融实证数据分析中普遍存在的非正态情况.Copula贝叶斯估计算法采用半相依回归法处理数据的强相关性问题,将原有函数依照数据形式假设为非正态结构.针对来自6个工业产业24组公司数据的系统风险参数β与其对应的投资标度参数比λ进行估计,获得不同行业中系统风险参数与投资标度之间的动态关系并进行分析,为业界投资及相关研究提供有效参考建议.     

关于贝叶斯推断中的计算问题

本文讨论了贝叶斯推断中的估计模型，给出了正态总体中贝叶斯估计的简单计算公式，从而简化了贝叶斯推断中的计算问题，使贝叶斯推断的方法应用更为简明方便．     

小批量生产的贝叶斯质量控制模型

本应用贝叶斯统计推断方法，研究了基于正态共轭先验分布和正态——逆伽玛共轭先验分布的小批量生产下的质量控制模型问题，根据不同控制对象的预报分布密度函数，分别构造了方差已知时的贝叶斯均值控制图和方差未知时的贝叶斯均值——标准差控制图，并与经典质量控制模型进行了比较。     

具有测量误差的非线性模型的Bayes估计

测量中大量的函数模型都是非线性回归模型．当回归变量含有一定的测量误差时，我们得到非线性测量误差模型．本讨论了这种模型中未知参数具有正态先验分布时的参数Bayes估计方法，并对这种估计进行了影响分析，证明了删除模型与均值漂移模型中参数的Bayes估计相同，利用Cook统计量给出了删除模型下参数的Bayes估计的影响度量．     

非线性贝叶斯动态模型的重要性再抽样(英文)

本文研究了非线性贝叶斯动态模型的随机模拟.在更宽泛的先验分布假设下.利用重要性再抽样的方法,以"样本"代替"分布",实现了对模型的后验推断、预测和模型选择,扩张了贝叶斯动态模型的应用领域.     

非正态总体控制图和预防维修策略耦合优化的研究

主要探讨非正态有偏总体的过程监控和预防维修耦合优化问题。假定设备故障率随时间递增,设备发生异常前在正常状态的停留时间服从威布尔分布,一旦发生异常将导致过程均值漂移。采用赋权方差法构造X控制图,将过程监控和预防维修策略联系起来,结合生产不合格品损失、抽样成本及维修成本等,构建综合损失模型,提出动态抽样方案、控制图参数和预防维修间隔的确定方法。最后对模型进行了灵敏度分析。     

非线性再生散度随机效应模型的贝叶斯分析

非线性再生散度随机效应模型是一类非常广泛的统计模型，包括了线性随机效应模型、非线性随机效应模型、广义线性随机效应模型和指数族非线性随机效应模型等．本文研究非线性再生散度随机效应模型的贝叶斯分析．通过视随机效应为缺失数据以及应用结合Gibbs抽样技术和Metropolis-Hastings算法（简称MH算法）的混合算法获得了模型参数与随机效应的同时贝叶斯估计．最后，用一个模拟研究和一个实际例子说明上述算法的可行眭．     

模型监控在预测中的应用

本文利用贝叶斯因子法讨论了一类贝叶斯动态模型的监控问题。     

核实数据下非线性半参数EV模型的估计（英文）

本文研究了核实数据下的协变量带有测量误差的非线性半参数EV模型.在不假定测量误差结构的情形下,利用最小二乘方法和核光滑技术,构造了非线性函数中未知参数的两种估计,证明了未知参数估计的渐近正态性.通过数值模拟说明所提估计方法在有限样本下的有效性.     

Bayesian estimation of linear functionals in the case of multidimensional normal distribution

In this paper we describe an approach for the construction of the substitutional method of obtaining Bayesian estimators H_B(f) for H(f). This method is used to obtain Bayesian estimators for the characteristic function, for moments of fixed orders and for the probability of linear inequalities in the case of a multivariate normal distribution. Reported at the XVI Seminar on Stability Problems for Stochastic Models, Eger, Hungary, 29 August — 3 September 1994. Received by the Editorial Board 15 April, 1995. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russian, 1995, Part II.     

Chain ladder method: Bayesian bootstrap versus classical bootstrap

The intention of this paper is to estimate a Bayesian distribution-free chain ladder (DFCL) model using approximate Bayesian computation (ABC) methodology. We demonstrate how to estimate quantities of interest in claims reserving and compare the estimates to those obtained from classical and credibility approaches. In this context, a novel numerical procedure utilizing a Markov chain Monte Carlo (MCMC) technique, ABC and a Bayesian bootstrap procedure was developed in a truly distribution-free setting. The ABC methodology arises because we work in a distribution-free setting in which we make no parametric assumptions, meaning we cannot evaluate the likelihood point-wise or in this case simulate directly from the likelihood model. The use of a bootstrap procedure allows us to generate samples from the intractable likelihood without the requirement of distributional assumptions; this is crucial to the ABC framework. The developed methodology is used to obtain the empirical distribution of the DFCL model parameters and the predictive distribution of the outstanding loss liabilities conditional on the observed claims. We then estimate predictive Bayesian capital estimates, the value at risk (VaR) and the mean square error of prediction (MSEP). The latter is compared with the classical bootstrap and credibility methods.     

Joint Monitoring of Several Types of Shocks in Normal Dynamic Linear Models: A Bayesian Decision Theoretic Approach

In this article we consider the sequential monitoring process in normal dynamic linear models as a Bayesian sequential decision problem. We use this approach to build a general procedure that jointly analyzes the existence of outliers, level changes, variance changes, and the development of local correlations. In addition, we study the frequentist performance of this procedure and compare it with the monitoring algorithm proposed in an earlier article.     

Statistical Bayesian classifiers of normal populations and their comparative analysis

In the present paper, direct and substitutional Bayesian classification rules for normal populations are described and their properties are compared. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part III     

Locally averaged Bayesian Dirichlet metrics for learning the structure and the parameters of Bayesian networks

The marginal likelihood of the data computed using Bayesian score metrics is at the core of score+search methods when learning Bayesian networks from data. However, common formulations of those Bayesian score metrics rely on free parameters which are hard to assess. Recent theoretical and experimental works have also shown that the commonly employed BDe score metric is strongly biased by the particular assignments of its free parameter known as the equivalent sample size. This sensitivity means that poor choices of this parameter lead to inferred BN models whose structure and parameters do not properly represent the distribution generating the data even for large sample sizes. In this paper we argue that the problem is that the BDe metric is based on assumptions about the BN model parameters distribution assumed to generate the data which are too strict and do not hold in real settings. To overcome this issue we introduce here an approach that tries to marginalize the meta-parameter locally, aiming to embrace a wider set of assumptions about these parameters. It is shown experimentally that this approach offers a robust performance, as good as that of the standard BDe metric with an optimum selection of its free parameter and, in consequence, this method prevents the choice of wrong settings for this widely applied Bayesian score metric.     

Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors

We consider the problem of estimating the density of a random variable when precise measurements on the variable are not available, but replicated proxies contaminated with measurement error are available for sufficiently many subjects. Under the assumption of additive measurement errors this reduces to a problem of deconvolution of densities. Deconvolution methods often make restrictive and unrealistic assumptions about the density of interest and the distribution of measurement errors, for example, normality and homoscedasticity and thus independence from the variable of interest. This article relaxes these assumptions and introduces novel Bayesian semiparametric methodology based on Dirichlet process mixture models for robust deconvolution of densities in the presence of conditionally heteroscedastic measurement errors. In particular, the models can adapt to asymmetry, heavy tails, and multimodality. In simulation experiments, we show that our methods vastly outperform a recent Bayesian approach based on estimating the densities via mixtures of splines. We apply our methods to data from nutritional epidemiology. Even in the special case when the measurement errors are homoscedastic, our methodology is novel and dominates other methods that have been proposed previously. Additional simulation results, instructions on getting access to the dataset and R programs implementing our methods are included as part of online supplementary materials.     

基于Jeffreys验前的Bayes方差估计修正

分析了基于Jeffreys验前的经典Bayes方差估计以及考虑验前信息可信度情况下Bayes方差估计存在的问题,在一般情况下,其方差估计要大于验前子样和验后子样的方差,这显然是不合理的.这是采用Jeffreys验前和正态共轭分布假设时存在的固有问题.为了解决这一问题,提出了方差估计的修正公式,经过计算验证,其值在验前子样和验后子样方差之间,说明修正公式是合理的.     

非线性Bayes动态模型预测的数值算法

本文用一阶样条函数分段逼近密度函数的方法给出了非线性 Bayes动态模型预测的一个数值算法     

Supporting reliability engineers in exploiting the power of Dynamic Bayesian Networks

In this paper, we present an approach to reliability modeling and analysis based on the automatic conversion of a particular reliability engineering model, the Dynamic Fault Tree (DFT), into Dynamic Bayesian Networks (DBN). The approach is implemented in a software tool called RADYBAN (Reliability Analysis with DYnamic BAyesian Networks). The aim is to provide a familiar interface to reliability engineers, by allowing them to model the system to be analyzed with a standard formalism; however, a modular algorithm is implemented to automatically compile a DFT into the corresponding DBN. In fact, when the computation of specific reliability measures is requested, classical algorithms for the inference on Dynamic Bayesian Networks are exploited, in order to compute the requested parameters. This is performed in a totally transparent way to the user, who could in principle be completely unaware of the underlying Bayesian Network. The use of DBNs allows the user to be able to compute measures that are not directly computable from DFTs, but that are naturally obtainable from DBN inference. Moreover, the modeling capabilities of a DBN, allow us to extend the basic DFT formalism, by introducing probabilistic dependencies among system components, as well as the definition of specific repair policies that can be taken into account during the reliability analysis phase. We finally show how the approach operates on some specific examples, by describing the advantages of having available a full inference engine based on DBNs for the requested analysis tasks.     

泊松逆高斯回归模型的贝叶斯统计推断

本文研究泊松逆高斯回归模型的贝叶斯统计推断.基于应用Gibbs抽样,Metropolis-Hastings算法以及Multiple-Try Metropolis算法等MCMC统计方法计算模型未知参数和潜变量的联合贝叶斯估计,并引入两个拟合优度统计量来评价提出的泊松逆高斯回归模型的合理性.若干模拟研究与一个实证分析说明方...