On the sequence of Bayesian estimates of normal random walk process

Let (μ_t)^∞_t=0 be a k-variate (k?1) normal random walk process with successive increments being independently distributed as normal N(δ, R), and μ₀ being distributed as normal N(0, V₀). Let X_t have normal distribution N(μ_t, Σ) when μ_t is given, t = 1, 2,….Then the conditional distribution of μ_t given X₁, X₂,…, X_t is shown to be normal N(U_t, V_t) where U_t's and V_t's satisfy some recursive relations. It is found that there exists a positive definite matrix V and a constant θ, 0 < θ < 1, such that, for all t?1,

$\text{|R}\text{1}\text{2}\text{(V}{}^{\mathrm{?1}}{}_{\mathrm{t}}\text{?V}{}^{\mathrm{?1}}\text{R}\text{1}\text{2}\text{|<θ}{}^{\mathrm{t}}\text{|R}\text{1}\text{2}\text{(V}{}^{\mathrm{?1}}{}_0\text{?V}{}^{\mathrm{?1}}\text{)R}\text{1}\text{2}\text{|}$

where the norm |·| means that |A| is the largest eigenvalue of a positive definite matrix A. Thus, V_t approaches to V as t approaches to infinity. Under the quadratic loss, the Bayesian estimate of μ_t is U_t and the process {U_t}^∞_t=₀, U₀=0, is proved to have independent successive increments with normal N(θ, V_t?V_t+1+R) distribution. In particular, when V₀ =V then V_t = V for all t and {U_t}^∞_t=0 is the same as {μ_t}^∞_t=0 except that U₀ = 0 and μ₀ is random.     

Separation of spin synchronized signals

In the measurements of VLF electric fields with the Pioneer Venus spacecraft in sunlight, spin synchronized signals often dominate over the naturally generated emissions. We present a method to separate natural emissions from the several possible sources of noise. Our major objective by this method is not to remove all spin modulation, but to effectively subtract the background noise caused by the identifiable noise sources. Examination of the data shows that the background spin synchronized noise is quite sensitive to (n), the angle between the sense axis and the solar direction. We model the observed data asy(n)=w(n)t(n)f((n))+x(n), wheref() represents the phase response of the background noise andx(n) is the estimated natural emissions.t(n) andw(n) are the long-term trend component and time- and phase-independent component of the intensity of the background noise, respectively. The method to decomposey(n) is based on the Bayesian approach which has been recently applied to various inversion problems such as nonstationary time series modeling and image reconstruction. In this procedure, the estimated parametersw(n),t(n),f(), andx(n) can be determined automatically. We will describe the Bayesian scheme and its application to the Pioneer Venus VLF electric field data.     

Bipartite molecular approach for species delimitation and resolving cryptic speciation of Exobasidium vexans within the Exobasidium genus

Exobasidium vexans, a basidiomycete pathogen, is the causal organism of blister blight disease in tea. The molecular identification of the pathogen remains a challenge due to the limited availability of genomic data in sequence repositories and cryptic speciation within its genus Exobasidium. In this study, the nuclear internal transcribed spacer rDNA region (ITS) based DNA barcode was developed for E. vexans, to address the problem of molecular identification within the background of cryptic speciation. The isolation of E. vexans strain was confirmed through morphological studies followed by molecular identification utilizing the developed ITS barcode. Phylogenetic analysis based on Maximum Parsimony (MP), Maximum Likelihood (ML) and Bayesian Inference (BI) confirmed the molecular identification of the pathogen as E. vexans strain. Further, BI analysis using BEAST mediated the estimation of the divergence time and evolutionary relationship of E. vexans within genus Exobasidium. The speciation process followed the Yule diversification model wherein the genus Exobasidium is approximated to have diverged in the Paleozoic era. The study thus sheds light on the molecular barcode-based species delimitation and evolutionary relationship of E. vexans within its genus Exobasidium.     

An image-processing toolset for diffusion tensor tractography

Diffusion tensor imaging (DTI)-based fiber tractography holds great promise in delineating neuronal fiber tracts and, hence, providing connectivity maps of the neural networks in the human brain. An array of image-processing techniques has to be developed to turn DTI tractography into a practically useful tool. To this end, we have developed a suite of image-processing tools for fiber tractography with improved reliability. This article summarizes the main technical developments we have made to date, which include anisotropic smoothing, anisotropic interpolation, Bayesian fiber tracking and automatic fiber bundling. A primary focus of these techniques is the robustness to noise and partial volume averaging, the two major hurdles to reliable fiber tractography. Performance of these techniques has been comprehensively examined with simulated and in vivo DTI data, demonstrating improvements in the robustness and reliability of DTI tractography.     

粒子滤波及其在导航系统中的应用综述

传统的扩展卡尔曼滤波方法要求对非线性系统近似线性化,有可能会引入较大的模型误差.应用粒子滤波解决了这一问题.该算法可以直接应用于原系统的非线性模型当中,并且不需考虑系统噪声和量测噪声是否为高斯白噪声,都能得到很好的滤波效果.文中介绍了粒子滤波的理论基础-贝叶斯估计及具体的实现方式-蒙特卡罗方法;指出粒子滤波存在的退化问题,并从减小退化现象入手将重要性采样和再采样方法引入到算法之中;最后阐述了粒子滤波在导航系统中的一些应用.     

厚尾随机波动率模型的贝叶斯参数估计及实证研究

针对现有时间序列模型难以刻画参数渐变性的问题,对厚尾随机波动(SV)模型的参数估计方法进行了推广,采用基于贝叶斯的MCMC方法,选取2013年5月~2016年6月这一经历多轮震荡的上证指数作为实证分析对象,构造了基于Gibbs抽样的MCMC过程进行仿真分析.结果显示,以卡方分布作为厚尾参数的先验分布能够有效地描述数据波动的厚尾特征,并且能得到较高精度的参数估计结果.结果表明,厚尾SV模型能有效反映出我国股市尖峰厚尾和波动长期记忆性的特征.     

Optimal Estimation and Cramér-Rao Bounds for Partial Non-Gaussian State Space Models

Partial non-Gaussian state-space models include many models of interest while keeping a convenient analytical structure. In this paper, two problems related to partial non-Gaussian models are addressed. First, we present an efficient sequential Monte Carlo method to perform Bayesian inference. Second, we derive simple recursions to compute posterior Cramér-Rao bounds (PCRB). An application to jump Markov linear systems (JMLS) is given.     

Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data

We present a unified semiparametric Bayesian approach based on Markov random field priors for analyzing the dependence of multicategorical response variables on time, space and further covariates. The general model extends dynamic, or state space, models for categorical time series and longitudinal data by including spatial effects as well as nonlinear effects of metrical covariates in flexible semiparametric form. Trend and seasonal components, different types of covariates and spatial effects are all treated within the same general framework by assigning appropriate priors with different forms and degrees of smoothness. Inference is fully Bayesian and uses MCMC techniques for posterior analysis. The approach in this paper is based on latent semiparametric utility models and is particularly useful for probit models. The methods are illustrated by applications to unemployment data and a forest damage survey.     

Approximate Bayesian Approach to Non-Gaussian Estimation in a Linear Model with Dependent State and Noise Vectors

This paper extends the results of Masreliez [8] on the design of non-Gaussian estimators for a more general class of the parameter estimation problem when the system state and the observation noise may be dependent and non-Gaussian simultaneously. It is shown that the proposed non-Gaussian algorithms can approximate with high precision the minimum mean square estimator. Application of the approach to the design of different optimal (and stable) estimation algorithms is illustrated. The efficiency of the proposed algorithms is tested in some simulation experiments. Accepted 5 September 2000. Online publication 26 February 2001.     

基于贝叶斯神经网络的近红外光谱实木地板表面缺陷检测

实木地板的表面缺陷直接影响其力学性能和产品等级,表面缺陷的快速检测对实木地板的在线分选具有重要的现实意义。针对视觉方法检测实木地板表面缺陷识别率低的问题,提出了一种基于近红外光谱分析技术的检测方法。首先,分别采集规格为200 mm×100 mm×20 mm的表面带有活节、死节以及无缺陷的实木地板的光谱数据各60份,其中30份作为训练样本,30份作为测试样本;其次,使用高斯滤波(GSF)、分段多元散射校正(PMSC)和去趋势法(DT)等方法对采集到的光谱数据进行预处理,降低光谱噪声、消除光谱的散射影响;然后,利用改进遗传算法从处理后的光谱中提取特征波长用于构建缺陷识别与分类模型;最后,使用基于贝叶斯理论改进的神经网络构建实木地板缺陷识别和分类模型。实验使用含有活节、死节以及无缺陷的实木地板样本对模型进行训练和测试,结果表明：通过贝叶斯神经网络构建的缺陷识别与分类模型能够准确识别活节、死节和无缺陷三类实木地板,识别率分别为92.20%, 94.47%和95.57%。证明了实木地板表面缺陷类型与其近红外吸收光谱密切相关,并为下一步实现实木地板表面缺陷的准确定位提供快速检测方法。