贝叶斯统计的发展及其争鸣

概述了贝叶斯统计的基本思想,通过实例分析了确定先验信息方法的思维合理性。探讨了贝叶斯统计未来理论发展及其应用空间。     

一类对数凸密度下的Bayes动态模型及其处理

提出了一种新的模型一对数凸密度下的Bayes动态模型，它是对正态密度下的Bayes动态模型的推广．我们证明了该模型的先验密度和后验密度满足“共轭性”。并可实现模型的修正递推和Bayes预测。     

NTM方法在非线性贝叶斯动态模型中的应用

将NTM方法应用于非线性贝叶斯动态模型，给出了它的递推公式以及随机变量的数字特征的计算，与蒙特卡洛方法相比提高了效率和精度.     

一类单参数指数族的共轭先验分布

共轭先验分布的选取是由似然函数L（θ）=p（x｜θ）中所含θ的因式决定的。本文通过单参数指数族的似然函数L（θ）的因式．找出了与L（θ）具有相同棱的分布作为先验分布．并验证了此先验分布是单参数指数族中参数θ的共轭先验分布。最后给出了一些常用的单参数指数分布的共轭先验分布．     

基于贝叶斯分析的新药研发评估模型研究

本文将贝叶斯方法应用于牡荆素对小鼠溃疡性结肠炎的药效作用评估中,在总体信息和先验概率的统计推断下,计算得到后验概率。首先利用一组试验数据在离散的贝叶斯公式下计算得到结果,该药的有效置信度从原来的0.3上升为0.3234;之后对连续情况进行计算,小鼠的体重变化均值提升到了95.773%。可见,应用贝叶斯方法对新药评估有着较好的效果,值得推广。     

带右删失数据的非线性随机效应模型参数估计

本文讨论了带右删失数据的非线性随机效应模型的参数估计,给出Gauss-Newton迭代法和改进后的Gauss-Newton迭代法,根据参数估计和算法给出数值模拟,验证了参数估计和算法的可行性.     

关于非线性动态系统神经网络辨识模型的分析

由线性动态网络和非线性静态网络组成的特殊结构，分析这种辨识模型的特点及在实际操作中的应用，并通过仿真手段证明神经网络的有效性。     

具有非线性捕获的杂食性随机Lotka-Volterra模型周期解的存在性

研究了具有非线性捕获的杂食性随机Lotka-Volterrav模型,在较弱的条件下证明了解的存在唯一性,通过构造适当的Lyapuno函数,得到了随机模型周期解存在的充分条件,通过数值模拟验证了本文所得到的结论。结果表明,具有非线性捕获的杂食性随机Lotka-Volterra模型存在周期解。     

基于HEVC的监控视频动态背景模型

高效视讯编码（HEVC）是新一代编码标准,在编码效率上有明显优势。监控视频结构特点是背景几乎不变,HEVC并没有考虑这种情况。使用动态背景模型（DBM）生成动态背景帧,作为HEVC帧间预测的参考帧,可以提高视频压缩效率。然而,运动缓慢的前景区域有时会被认为是背景区域,为此提出多层差值（MDM）算法,根据多层像素块差值更新背景,提高背景帧的质量。实验结果表明,与高效视讯编码测试模型HM14.0相比,在几乎不增加计算复杂度的情况下,采用该算法压缩效率平均提高了2%,最高提高了5.2%。     

正态总体方差的贝叶斯区间估计

区间估计是数理统计的一个重要内容,分析了贝叶斯可信区间估计与经典置信区间估计的区别,推出了正态总体方差的贝叶斯可信区间,数值分析表明可信区间比置信区间更精确。     

On the Estimation of Nonlinear Mixed-Effects Models and Latent Curve Models for Longitudinal Data

Nonlinear models are effective tools for the analysis of longitudinal data. These models provide a flexible means for describing data that follow complex forms of change. Exponential and logistic functions that include a parameter to represent an asymptote, for instance, are useful for describing responses that tend to level off with time. There are forms of nonlinear latent curve models and nonlinear mixed-effects model that are equivalent, and so given the same set of data, growth function, distributional assumptions, and method of estimation, the 2 models yield equivalent results. There are also forms that are strikingly different and can yield different interpretations for a given set of data. This article discusses cases in which nonlinear mixed-effects models and nonlinear latent curve models are equivalent and those in which they are different and clarifies the estimation needs of the different models. Examples based on empirical data help to illustrate these points.     

Bayesian Quantile Structural Equation Models

Structural equation modeling is a common multivariate technique for the assessment of the interrelationships among latent variables. Structural equation models have been extensively applied to behavioral, medical, and social sciences. Basic structural equation models consist of a measurement equation for characterizing latent variables through multiple observed variables and a mean regression-type structural equation for investigating how explanatory latent variables influence outcomes of interest. However, the conventional structural equation does not provide a comprehensive analysis of the relationship between latent variables. In this article, we introduce the quantile regression method into structural equation models to assess the conditional quantile of the outcome latent variable given the explanatory latent variables and covariates. The estimation is conducted in a Bayesian framework with Markov Chain Monte Carlo algorithm. The posterior inference is performed with the help of asymmetric Laplace distribution. A simulation shows that the proposed method performs satisfactorily. An application to a study of chronic kidney disease is presented.     

Generalized Nonlinear Irreducible Auto-Correlation and Its Applications in Nonlinear Prediction Models Identification

There is still an obstacle to prevent neural network from wider and more effective applications, i.e. , the lack of effective theories of models identification. Based on information theory and its generalization, this paper introduces a universal method to achieve nonlinear models identification. Two key quantities, which are called nonlinear irreducible auto-correlation (NIAC) and generalized nonlinear irreducible auto-correlation (GNIAC), are defined and discussed. NIAC and GNIAC correspond with intrinstic irreducible auto-dependency (IAD) and generalized irreducible autodependency (GLAD) of time series respectively. By investigating the evolving trend of NIAL; and GNIAC, the optimal auto-regressive order of nonlinear auto-regressive models could be determined naturally, Subsequently, an efficient algorithm computing NIAC and GNIAC is discussed. Experiments on simulating data sets and typical nonlinear prediction models indicate remarkable correlation between optimal auto-regressive order and the highest order that NIAC-GNIAC have a remarkable non-zero value, therefore demonstrate the validity of the proposal in this paper.     

Two-Level Dynamic Structural Equation Models with Small Samples

Advances in data collection have made intensive longitudinal data easier to collect, unlocking potential for methodological innovations to model such data. Dynamic structural equation modeling (DSEM) is one such methodology but recent studies have suggested that its small N performance is poor. This is problematic because small N data are omnipresent in empirical applications due to logistical and financial concerns associated with gathering many measurements on many people. In this paper, we discuss how previous studies considering small samples have focused on Bayesian methods with diffuse priors. The small sample literature has shown that diffuse priors may cause problems because they become unintentionally informative. Instead, we outline how researchers can create weakly informative admissible-range-restricted priors, even in the absence of previous studies. A simulation study shows that metrics like relative bias and non-null detection rates with these admissible-range-restricted priors improve small N properties of DSEM compared to diffuse priors.     

Fitting Nonlinear Latent Growth Curve Models With Individually Varying Time Points

Individual growth trajectories of psychological phenomena are often theorized to be nonlinear. Additionally, individuals’ measurement schedules might be unique. In a structural equation framework, latent growth curve model (LGM) applications typically have either (a) modeled nonlinearity assuming some degree of balance in measurement schedules, or (b) accommodated truly individually varying time points, assuming linear growth. This article describes how to fit 4 popular nonlinear LGMs (polynomial, shape-factor, piecewise, and structured latent curve) with truly individually varying time points, via a definition variable approach. The extension is straightforward for certain nonlinear LGMs (e.g., polynomial and structured latent curve) but in the case of shape-factor LGMs requires a reexpression of the model, and in the case of piecewise LGMs requires introduction of a general framework for imparting piecewise structure, along with tools for its automation. All 4 nonlinear LGMs with individually varying time scores are demonstrated using an empirical example on infant weight, and software syntax is provided. The discussion highlights some advantages of modeling nonlinear growth within structural equation versus multilevel frameworks, when time scores individually vary.     

仿射非线性系统的动态反馈线性化与系统线性近似的能控性

用微分几何方法讨论了m=n-1仿射非线性系统的动态反馈线性化与系统的线性近似能控性的关系，出了系统可动态反馈线性化的条件。     

一类非正态总体未知参数的Bayes假设检验

利用贝叶斯统计思想总结了两种常见的假设检验方法,在此基础上针对H0∶θ=0θ,θ≠θ0这样的假设检验问题,提出了构造参数θ的否定域,即求出参数θ的置信概率为1-α的最大后验区间,区域Θ-D为参数θ的否定域,检验θ是否在否定域内,若在就否定H0,运用这样的思想对其进行检验.并且讨论了γ-分布与β-分布,β-分布与F-分布,γ-分布与χ2-分布之间的相互关系,借助以上的性质,研究三类非正态总体指数分布、二项分布和泊松分布的未知参数的贝叶斯假设检验,给出了相应的否定域.     

一类非线性时滞系统的自适应动态面控制

针对一类严格反馈非线性时滞系统,提出了一种自适应神经网络动态面控制方案。通过引入一阶滤波器,避免了传统反演设计中的＂计算膨胀＂问题。通过构造恰当的Lyapunov-Krasovskii函数,对未知时滞项进行了补偿。此外,基于Lyapunov稳定性理论,证明了闭环系统所有信号半全局一致最终有界。最后,仿真实例表明了所提控制方案的有效性。