基于随机波动模型的沪深股市波动分析——以06,07年度沪深股指为例

基于马尔科夫链蒙特卡罗(MCMC)模拟的贝叶斯(Bayes)分析方法,应用随机波动(SV)模型实证分析06、07年度中国股票市场指数的波动性,并对比沪市与深市的股指,对不同形式的SV模型的参数进行估计,对结论作出合理的解释.     

0-1序列中变点的贝叶斯分析

对于0-1(伯努利)序列中的变点问题,本文提出了一个确定变点的个数和位置的贝叶斯方法。首先借助于二分法把变点个数的确定问题转化为一系列对没有变点和仅有一个变点的模型进行比较的问题,然后通过贝叶斯因子进行模型比较。本文得到了贝叶斯因子和未知变点的后验分布的显式表达式。最后,通过对上证指数数据的实证分析阐释了所提方法的有效性。     

国内主要城市空气质量统计分析

我国目前评价城市空气质量所用的空气污染指数法中仅以首要污染指数来反映空气质量状况,而忽视了次要污染物对空气质量的影响,这将会使评价结果的准确性产生偏差.本文在空气污染指数模型的基础上引入次要污染物,建立了新的空气质量评价模型,再利用该模型对我国近三年主要城市空气质量状况进行了评价及分析.     

基于MCMC模拟的贝叶斯厚尾金融随机波动模型分析

针对现有金融时间序列模型建模方法难以刻画模型参数的渐变性问题,利用贝叶斯分析方法构建贝叶斯厚尾SV模型。首先对反映波动性特征的厚尾金融随机波动模型(SV-T)进行贝叶斯分析,构造了基于Gibbs抽样的MCMC数值计算过程进行仿真分析,并利用DIC准则对SV-N模型和SV-T模型进行优劣比较。研究结果表明:在模拟我国股市的波动性方面,SV-T模型比SV-N模型更优,更能反应我国股市的尖峰厚尾的特性,并且证明了我国股市具有很强的波动持续性。     

利用贝叶斯网络提高港口国检查效率

提高港口国监控(PSC)的检查效率,本文研究了船舶固有属性(船舶年龄、船旗、船级社、船舶尺度)、港口国检查缺陷项与船舶事故间的影响关系。本文所使用的数据主要来自于英国劳氏船级社(LR)、国际海事组织(IMO)和东京谅解备忘录(Tokyo MOU)三个数据库,共5478条干散货船数据。利用贝叶斯网络(BN)构建模型,并分别采用Bayesian Network (BN)和Greedy thick thinning(GTT)算法构建网络模型。同时利用K-折交叉验证、对数似然函数(LL)、赤池信息量准则(AIC)和贝叶斯信息准则(BIC)对模型进行评估。结果表明船舶的固有属性和关键检查缺陷项对船舶事故均有较高的直接影响,而大多数的港口国监控检查缺陷之间具有相互影响,并且通过关键检查缺陷项对船舶事故产生间接影响。因此可以利用关键检查缺陷项优化港口国检验制度,提高检验效率。     

基于PSOGSA-LSTM模型的长江经济带空气质量指数预测研究

本文以长江经济带100个地级及以上城市的空气质量指数(AQI)为研究对象,选取了六大污染物和11个影响空气质量指数的气象因子作为影响因素。针对空气质量相关数据的特性,将粒子群算法和万有引力算法结合的混合算法(PSOGSA)与长短期记忆(LSTM)神经网络进行组合,建立PSOGSA-LSTM组合预测模型,对模型的预测精度进行了三个方面的检验,并与传统的LSTM模型的预测结果进行比较,最后将其应用于长江经济带100个城市未来7天的空气质量指数预测。研究结果表明,PSOGSA-LSTM模型相比传统的LSTM模型具有更高的预测精度和较强的稳定性。     

基于贝叶斯ARFIMA-WRV模型高频数据长记忆性研究

考虑到高频时间序列波动率的长记忆性问题,构建了赋权已实现波动分数整合自回归移动平均(ARFIMA-WRV)模型对其进行了研究.利用贝叶斯统计方法对模型做了相应的贝叶斯分析,并对我国中小板股市收益波动率的长记忆性特征进行了实证分析.实证结果表明我国中小板股市收益波动率存在长记忆性特征;采用消除日历效应影响的赋权已实现波动作为波动度量和贝叶斯参数估计方法,很大程度上提高了模型的参数精度.     

半参数双重Tweedie复合泊松回归模型的贝叶斯分析

为了分析健康保险行业中出现的半连续卫生保健费用数据,本文提出一类半参数双重Tweedie复合泊松回归模型.在分析中,首先采用修正鞍点逼近的数值方法去近似Tweedie复合泊松分布的密度函数;其次,利用Gibbs抽样技术和Metropolis-Hastings(MH)算法的混合算法获得了模型参数的联合贝叶斯估计;最后,给出了几个模拟研究以及把这些方法用来分析兰德健康保险实验中的卫生保健费用数据.     

基于Keras的LSTM模型在空气质量指数预测的应用

为了高精度预测空气质量指数(AQI),针对大气环境复杂多变性、不确定性,以2014年至2017年的太原市空气污染物监测数据为基础,首先采用python3.5.2中的相关性分析函数对污染物与AQI指数进行了相关性分析,然后建立基于深度学习库Keras(一种高层神经网络API)的长短期记忆循环神经网络(LSTM)模型,对太原市空气质量指数(AQI)进行仿真预测.实验结果表明:模型的均方根误差为4.875,具有预测精度高、范围广等优点,为大气污染防治工作提供了科学合理的理论依据和新的预测方法.     

基于贝叶斯网络的工程项目进度完工概率分析

针对传统计划评审技术(Program Evaluation and Review Technique,PERT)在计算完工概率时假设条件的局限性(假设条件与工程实际存在偏差,导致完工概率偏大),提出了基于贝叶斯网络的施工进度完工概率分析方法.首先,分析了贝叶斯网络与进度计划网络之间的相似性,将两者结合起来构建了贝叶斯进度网络;在此基础上,综合考虑贝叶斯网络在节点取值及概率计算方面的优越性,并结合工程项目的不确定性及复杂性特点,建立了基于贝叶斯网络的施工进度完工概率分析模型.最后,将该模型应用于具体工程进行实例分析,验证了模型的可行性与有效性.研究结果表明:基于贝叶斯网络的进度完工概率模型充分考虑了工程施工中的风险因素,其结果能更客观地反映工程实际,可为工程项目决策者提供可靠的依据.     

Improved Diffusion Monte Carlo

We propose a modification, based on the RESTART (repetitive simulation trials after reaching thresholds) and DPR (dynamics probability redistribution) rare event simulation algorithms, of the standard diffusion Monte Carlo (DMC) algorithm. The new algorithm has a lower variance per workload, regardless of the regime considered. In particular, it makes it feasible to use DMC in situations where the “naïve” generalization of the standard algorithm would be impractical due to an exponential explosion of its variance. We numerically demonstrate the effectiveness of the new algorithm on a standard rare event simulation problem (probability of an unlikely transition in a Lennard‐Jones cluster), as well as a high‐frequency data assimilation problem. © 2014 Wiley Periodicals, Inc.     

Forecasting seasonal time series data: a Bayesian model averaging approach

A flexible Bayesian periodic autoregressive model is used for the prediction of quarterly and monthly time series data. As the unknown autoregressive lag order, the occurrence of structural breaks and their respective break dates are common sources of uncertainty these are treated as random quantities within the Bayesian framework. Since no analytical expressions for the corresponding marginal posterior predictive distributions exist a Markov Chain Monte Carlo approach based on data augmentation is proposed. Its performance is demonstrated in Monte Carlo experiments. Instead of resorting to a model selection approach by choosing a particular candidate model for prediction, a forecasting approach based on Bayesian model averaging is used in order to account for model uncertainty and to improve forecasting accuracy. For model diagnosis a Bayesian sign test is introduced to compare the predictive accuracy of different forecasting models in terms of statistical significance. In an empirical application, using monthly unemployment rates of Germany, the performance of the model averaging prediction approach is compared to those of model selected Bayesian and classical (non)periodic time series models.     

Semiparametric Bayesian optimal replacement policies: application to railroad tracks

We present a Bayesian decision theoretic approach for developing replacement strategies. In so doing, we consider a semiparametric model to describe the failure characteristics of systems by specifying a nonparametric form for cumulative intensity function and by taking into account effect of covariates by a parametric form. Use of a gamma process prior for the cumulative intensity function complicates the Bayesian analysis when the updating is based on failure count data. We develop a Bayesian analysis of the model using Markov chain Monte Carlo methods and determine replacement strategies. Adoption of Markov chain Monte Carlo methods involves a data augmentation algorithm. We show the implementation of our approach using actual data from railroad tracks. Copyright © 2016 John Wiley & Sons, Ltd.     

Efficiency of Monte Carlo EM and Simulated Maximum Likelihood in Two-Stage Hierarchical Models

Likelihood estimation in hierarchical models is often complicated by the fact that the likelihood function involves an analytically intractable integral. Numerical approximation to this integral is an option but it is generally not recommended when the integral dimension is high. An alternative approach is based on the ideas of Monte Carlo integration, which approximates the intractable integral by an empirical average based on simulations. This article investigates the efficiency of two Monte Carlo estimation methods, the Monte Carlo EM (MCEM) algorithm and simulated maximum likelihood (SML). We derive the asymptotic Monte Carlo errors of both methods and show that, even under the optimal SML importance sampling distribution, the efficiency of SML decreases rapidly (relative to that of MCEM) as the missing information about the unknown parameter increases. We illustrate our results in a simple mixed model example and perform a simulation study which shows that, compared to MCEM, SML can be extremely inefficient in practical applications.     

On Markov chain Monte Carlo Algorithms for Computing Conditional Expectations Based on Sufficient Statistics

Much work has focused on developing exact tests for the analysis of discrete data using log linear or logistic regression models. A parametric model is tested for a dataset by conditioning on the value of a sufficient statistic and determining the probability of obtaining another dataset as extreme or more extreme relative to the general model, where extremeness is determined by the value of a test statistic such as the chi-square or the log-likelihood ratio. Exact determination of these probabilities can be infeasible for high dimensional problems, and asymptotic approximations to them are often inaccurate when there are small data entries and/or there are many nuisance parameters. In these cases Monte Carlo methods can be used to estimate exact probabilities by randomly generating datasets (tables) that match the sufficient statistic of the original table. However, naive Monte Carlo methods produce tables that are usually far from matching the sufficient statistic. The Markov chain Monte Carlo method used in this work (the regression/attraction approach) uses attraction to concentrate the distribution around the set of tables that match the sufficient statistic, and uses regression to take advantage of information in tables that “almost” match. It is also more general than others in that it does not require the sufficient statistic to be linear, and it can be adapted to problems involving continuous variables. The method is applied to several high dimensional settings including four-way tables with a model of no four-way interaction, and a table of continuous data based on beta distributions. It is powerful enough to deal with the difficult problem of four-way tables and flexible enough to handle continuous data with a nonlinear sufficient statistic.     

Bayesian Variable Selection via Particle Stochastic Search

We focus on Bayesian variable selection in regression models. One challenge is to search the huge model space adequately, while identifying high posterior probability regions. In the past decades, the main focus has been on the use of Markov chain Monte Carlo (MCMC) algorithms for these purposes. In this article, we propose a new computational approach based on sequential Monte Carlo (SMC), which we refer to as particle stochastic search (PSS). We illustrate PSS through applications to linear regression and probit models.     

Integrated structural approach to Credit Value Adjustment

This paper proposes an integrated pricing framework for Credit Value Adjustment of equity and commodity products. The given framework, in fact, generates dependence endogenously, allows for calibration and pricing to be based on the same numerical schemes (up to Monte Carlo simulation), and also allows the inclusion of risk mitigation clauses such as netting, collateral and initial margin provisions. The model is based on a structural approach which uses correlated Lévy processes with idiosyncratic and systematic components; the pricing numerical scheme, instead, efficiently combines Monte Carlo simulation and Fourier transform based methods. We illustrate the tractability of the proposed framework and the performance of the proposed numerical scheme by means of a case study on a portfolio of commodity swaps using real market data.     

Compound negative binomial shared frailty models for bivariate survival data

In this paper, we introduce a new shared frailty model called the compound negative binomial shared frailty model with three different baseline distributions namely, Weibull, generalized exponential and exponential power distribution. To estimate the parameters involved in these models we adopt Markov Chain Monte Carlo (MCMC) approach. Also we apply these three models to a real life bivariate survival data set of McGrilchrist and Aisbett (1991) related to kidney infection and suggest a better model for the data.     

Dynamic Detection of Change Points in Long Time Series

We consider the problem of detecting change points (structural changes) in long sequences of data, whether in a sequential fashion or not, and without assuming prior knowledge of the number of these change points. We reformulate this problem as the Bayesian filtering and smoothing of a non standard state space model. Towards this goal, we build a hybrid algorithm that relies on particle filtering and Markov chain Monte Carlo ideas. The approach is illustrated by a GARCH change point model.     

Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices

We propose a Bayesian approach for inference in the multivariate probit model, taking into account the association structure between binary observations. We model the association through the correlation matrix of the latent Gaussian variables. Conditional independence is imposed by setting some off-diagonal elements of the inverse correlation matrix to zero and this sparsity structure is modeled using a decomposable graphical model. We propose an efficient Markov chain Monte Carlo algorithm relying on a parameter expansion scheme to sample from the resulting posterior distribution. This algorithm updates the correlation matrix within a simple Gibbs sampling framework and allows us to infer the correlation structure from the data, generalizing methods used for inference in decomposable Gaussian graphical models to multivariate binary observations. We demonstrate the performance of this model and of the Markov chain Monte Carlo algorithm on simulated and real datasets. This article has online supplementary materials.