Bayesian finite mixtures with an unknown number of components: The allocation sampler

A new Markov chain Monte Carlo method for the Bayesian analysis of finite mixture distributions with an unknown number of components is presented. The sampler is characterized by a state space consisting only of the number of components and the latent allocation variables. Its main advantage is that it can be used, with minimal changes, for mixtures of components from any parametric family, under the assumption that the component parameters can be integrated out of the model analytically. Artificial and real data sets are used to illustrate the method and mixtures of univariate and of multivariate normals are explicitly considered. The problem of label switching, when parameter inference is of interest, is addressed in a post-processing stage.     

Assessing Poisson variation of intestinal tumour multiplicity in mice carrying a Robertsonian translocation

Summary.  Tumour multiplicity is a frequently measured phenotype in animal studies of cancer biology. Poisson variation of this measurement represents a biological and statistical reference point that is usually violated, even in highly controlled experiments, owing to sources of variation in the stochastic process of tumour formation. A recent experiment on murine intestinal tumours presented conditions which seem to generate Poisson-distributed tumour counts. If valid, this would support a claim about mechanisms by which the adenomatous polyposis coli gene is inactivated during tumour initiation. In considering hypothesis testing strategies, model choice and Bayesian approaches, we quantify the positive evidence favouring Poisson variation in this experiment. Statistical techniques used include likelihood ratio testing, the Bayes and Akaike information criteria, negative binomial modelling, reversible jump Markov chain Monte Carlo methods and posterior predictive checking. The posterior approximation that is based on the Bayes information criterion is found to be quite accurate in this small n case-study.     

Image segmentation using voronoi polygons and MCMC, with application to muscle fibre images

We investigate a Bayesian method for the segmentation of muscle fibre images. The images are reasonably well approximated by a Dirichlet tessellation, and so we use a deformable template model based on Voronoi polygons to represent the segmented image. We consider various prior distributions for the parameters and suggest an appropriate likelihood. Following the Bayesian paradigm, the mathematical form for the posterior distribution is obtained (up to an integrating constant). We introduce a Metropolis-Hastings algorithm and a reversible jump Markov chain Monte Carlo algorithm (RJMCMC) for simulation from the posterior when the number of polygons is fixed or unknown. The particular moves in the RJMCMC algorithm are birth, death and position/colour changes of the point process which determines the location of the polygons. Segmentation of the true image was carried out using the estimated posterior mode and posterior mean. A simulation study is presented which is helpful for tuning the hyperparameters and to assess the accuracy. The algorithms work well on a real image of a muscle fibre cross-section image, and an additional parameter, which models the boundaries of the muscle fibres, is included in the final model.     

ON LIKELIHOOD ESTIMATION FOR DISCRETELY OBSERVED MARKOV JUMP PROCESSES

The parameter estimation problem for a Markov jump process sampled at equidistant time points is considered here. Unlike the diffusion case where a closed form of the likelihood function is usually unavailable, here an explicit expansion of the likelihood function of the sampled chain is provided. Under suitable ergodicity conditions on the jump process, the consistency and the asymptotic normality of the likelihood estimator are established as the observation period tends to infinity. Simulation experiments are conducted to demonstrate the computational facility of the method.     

Detecting instants of jumps and estimating their intensity in the context of p derivatives with continuous or discrete data

In this article, we consider the ARD^(p)(1) process where D[0, 1] is the space of cadlag function and the pth derivative has a possible jump. One envisages to detect the position and intensity of jump in the context of p derivatives with continuous or discrete data. We also envisage jump for the (p + 1)th derivative. The main result allows to detect jump and to detect intensity of jump simultaneously. Asymptotic results are derived.     

基于状态空间的贝叶斯跳跃厚尾金融随机波动模型研究

针对金融市场中跳跃特征的刻画问题,提出了贝叶斯跳跃厚尾随机波动模型。通过随机波动模型的结构分析和状态空间转换,设计了模型参数估计的MCMC算法,利用Kalman滤波和高斯模拟平滑方法估计模型的潜在波动,运用贝叶斯因子对随机波动类模型进行比较分析,并利用中国和美国的股市收益数据进行实证分析。研究结果表明:在刻画中、美两国股票市场的波动特征方面,跳跃厚尾随机波动模型要明显优于厚尾随机波动模型和标准随机波动模型,并且金融危机背景下的中国和美国股票市场都具有明显的波动持续性以及跳跃特征。     

基于逆跳MCMC的贝叶斯分位自回归模型研究

考虑到传统信息理论方法确定模型存在不足,在贝叶斯理论框架下提出了基于逆跳马尔可夫链蒙特卡罗法确定分位自回归模型阶次的方法。在时间序列服从非对称Laplace分布的条件下,设计了马尔可夫链蒙特卡罗数值计算程序,得到了不同分位数下模型参数的贝叶斯估计值。实证研究表明：基于逆跳马尔可夫链蒙特卡罗法的贝叶斯分位自回归模型能有效地揭示滞后变量对响应变量的位置、尺度和形状的影响。     

基于半鞅过程的中国股市随机波动、跳跃和微观结构噪声统计特征研究

本文基于半鞅过程和非参数统计推断方法,利用已实现幂变差的渐进统计特性,构造检验统计量,在统一的分析框架下,对金融资产价格中随机波动、跳跃和微观结构噪声等问题进行全面系统的研究。并根据上海证券交易所不同行业的股票,上证50 股票指数及其成分股的高频数据进行实证研究。结果表明,我国A 股市场中,噪音交易显著;约43%的风险来源于资产收益过程的随机波动风险,可用股票期权交易对冲;不同来源风险的重要性程度依次为:随机波动的风险、系统性跳跃风险以及异质性跳跃风险;流动性越好的股票越显示出跳跃、尤其是无限小跳的证据。     

考虑跳跃和隔夜波动的中国股票市场波动率建模与预测

本文用已实现波动率（Realized Volatility, RV）度量上证综指和深证成指在交易时间内的波动率,并将其分解为连续路径变差部分和由跳跃引起的非连续部分。这两部分与隔夜波动率共同构成日波动率。本文对日波动率的三个组成部分建立HAR-CJN模型,探究了波动率不同成分之间的相互影响以及在预测中的作用。结果表明连续变差对日波动率的各组成部分均有显著的正向影响,在预测中的贡献最大;而跳变差的影响一般比连续变差的要弱,且随着滞后期的长短而有所不同。样本外预测结果显示HAR-CJN模型的预测表现要远远优于GARCH族模型,并在向前一天和一月的预测中优于普通的HAR-RV模型。     

考虑共同跳跃的波动建模:基于高频数据视角

针对共同跳跃研究的不足,文章沿袭已有理论框架,采用常用的日内跳跃检验方法,构建了共同跳跃(协)方差和连续样本路径(协)方差,并扩展HAR-RV-CJ模型,将(协)方差、共同跳跃置于统一波动模型框架内。通过对上证综指和深圳成指高频数据的实证分析,结果显示两指数共同跳跃占其各自的跳跃比例较大,且基本上都是同方向的跳跃;共同跳跃(协)方差和连续样本路径(协)方差对已实现(协)方差的影响都是显著的,考虑共同跳跃影响有助于提高(协)方差建模的准确性。此研究有助于投资者优化投资策略和为监管部门提供监管基础。