A Bayesian method for classification and discrimination

We discuss Bayesian analyses of traditional normal-mixture models for classification and discrimination. The development involves application of an iterative resampling approach to Monte Carlo inference, commonly called Gibbs sampling, and demonstrates routine application. We stress the benefits of exact analyses over traditional classification and discrimination techniques, including the ease with which such analyses may be performed in a quite general setting, with possibly several normal-mixture components having different covariance matrices, the computation of exact posterior classification probabilities for observed data and for future cases to be classified, and posterior distributions for these probabilities that allow for assessment of second-level uncertainties in classification.     

关于R—积分的区问可列可加性

本文将数学分析中R—积分(即黎曼积分)的区间可加性加以推广,给出了R—积分区间可列可加性.     

Finite mixture models with concomitant information: assessing diagnostic criteria for diabetes

The World Health Organization (WHO) diagnostic criteria for diabetes mellitus were determined in part by evidence that in some populations the plasma glucose level 2 h after an oral glucose load is a mixture of two distinct distributions. We present a finite mixture model that allows the two component densities to be generalized linear models and the mixture probability to be a logistic regression model. The model allows us to estimate the prevalence of diabetes and sensitivity and specificity of the diagnostic criteria as a function of covariates and to estimate them in the absence of an external standard. Sensitivity is the probability that a test indicates disease conditionally on disease being present. Specificity is the probability that a test indicates no disease conditionally on no disease being present. We obtained maximum likelihood estimates via the EM algorithm and derived the standard errors from the information matrix and by the bootstrap. In the application to data from the diabetes in Egypt project a two-component mixture model fits well and the two components are interpreted as normal and diabetes. The means and variances are similar to results found in other populations. The minimum misclassification cutpoints decrease with age, are lower in urban areas and are higher in rural areas than the 200 mg dl^-1 cutpoint recommended by the WHO. These differences are modest and our results generally support the WHO criterion. Our methods allow the direct inclusion of concomitant data whereas past analyses were based on partitioning the data.     

Bootstrapping Periodic State-Space Models

This article is concerned with how the bootstrap can be applied to study conditional forecast error distributions and construct prediction regions for future observations in periodic time-varying state-space models. We derive, first, an algorithm for assessing the precision of quasi-maximum likelihood estimates of the parameters. As a result, the derived algorithm is exploited for numerically evaluating the conditional forecast accuracy of a periodic time series model expressed in state space form. We propose a method which requires the backward, or reverse-time, representation of the model for assessing conditional forecast errors. Finally, the small sample properties of the proposed procedures will be investigated by some simulation studies. Furthermore, we illustrate the results by applying the proposed method to a real time series.     

Non parametric mixture of strictly monotone regression models

In this article, we propose the non parametric mixture of strictly monotone regression models. For implementation, a two-step procedure is derived. We further establish the asymptotic normality of the resultant estimator and demonstrate its good performance through numerical examples.     

双电机驱动自同步振动磨动力响应研究

以双电机驱动自同步振动磨为研究对象,对其进行简化处理,建立力学模型。通过对其施加X,y方向的简谐激 振力,建立无阻尼系统强迫振动和有阻尼系统强迫振动的数学模型,在此基础上,确定Rayleigh阻尼的常数α和β,利用 有限元ANSYS软件进行瞬态动力学分析,研究其在动载荷作用下的变形情况。研究结果表明：在工况频率16 Hz下,节 点运动轨迹更接近圆形,距理想粉碎效果的圆形轨迹较近,粉碎效果较好,进入稳定期的时间较快;在共振频率42 Hz 下,节点轨迹振幅更大,进入稳定期较慢,阻尼对振动的衰减作用较强;不同阻尼比对振动的衰减作用成正比关系。因 此,可以通过控制阻尼比等参数获得更有利的研磨效果,提高研磨效率。     

Finite mixture of regression models for a stratified sample

Despite the popularity and importance, there is limited work on modelling data which come from complex survey design using finite mixture models. In this work, we explored the use of finite mixture regression models when the samples were drawn using a complex survey design. In particular, we considered modelling data collected based on stratified sampling design. We developed a new design-based inference where we integrated sampling weights in the complete-data log-likelihood function. The expectation–maximisation algorithm was developed accordingly. A simulation study was conducted to compare the new methodology with the usual finite mixture of a regression model. The comparison was done using bias-variance components of mean square error. Additionally, a simulation study was conducted to assess the ability of the Bayesian information criterion to select the optimal number of components under the proposed modelling approach. The methodology was implemented on real data with good results.     

On approximations via convolution-defined mixture models

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture distribution is sufficiently complex. This fact is often not made concrete. We investigate and review theorems that provide approximation bounds for mixing distributions. Connections between the approximation bounds of mixing distributions and estimation bounds for the maximum likelihood estimator of finite mixtures of location-scale distributions are reviewed.     

Bayesian density regression for discrete outcomes

We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining conditional densities from the multivariate ones. The approach to multivariate mixed scale outcome density estimation that we describe represents discrete variables, either responses or covariates, as discretised versions of continuous latent variables. We present and compare several models for obtaining these thresholds in the challenging context of count data analysis where the response may be over‐ and/or under‐dispersed in some of the regions of the covariate space. We utilise a nonparametric mixture of multivariate Gaussians to model the directly observed and the latent continuous variables. The paper presents a Markov chain Monte Carlo algorithm for posterior sampling, sufficient conditions for weak consistency, and illustrations on density, mean and quantile regression utilising simulated and real datasets.     

Finite normal mixture copulas for multivariate discrete data modeling

A new family of copulas is introduced that provides flexible dependence structure while being tractable and simple to use for multivariate discrete data modeling. The construction exploits finite mixtures of uncorrelated normal distributions. Accordingly, the cumulative distribution function is simply the product of univariate normal distributions. At the same time, however, the mixing operation introduces association. The properties of the new family of copulas are examined and a concrete application is used to show its applicability.