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通过幂后验估计边际似然AI 解读

Summary Model choice plays an increasingly important role in statistics. From a Bayesian perspective a crucial goal is to compute the marginal likelihood of the data for a given model. However, this is typically a difficult task since it amounts to integrating over all model parameters. The aim of the paper is to illustrate how this may be achieved by using ideas from thermodynamic integration or path sampling. We show how the marginal likelihood can be computed via Markov…

归一化常数难以计算时的高效马尔可夫链蒙特卡洛方法AI 解读

Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so…

一般可因子分解模型的高效递推AI 解读

Let n S‐valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum…

利用秩估计回归参数AI 解读

SUMMARY In this paper we consider the estimation of a regression parameter in a partially specified model where, after an unknown monotone increasing transformation, the response is normally distributed and related to an explanatory variable by a linear model. We consider a Monte Carlo resampling technique due to Doksum and various modifications of it. In addition a simple estimate based on a modification of Fisher and Yates' normal scores method and an estimate using the…

删失观测、重复测量与混合效应模型：正态误差下的 EM 方法AI 解读

Maximum likelihood estimation of a vector regression parameter and variance com ponents is considered for the mixed effects model when observations are right censored. A general scheme of estimation is given using the EM algorithm and detailed results found for the model with between and within block variation. This model is applied to the logarithms of survival times from a repeated measures design.

删失观测、重复测量与混合效应模型：正态误差下的 EM 方法AI 解读

Maximum likelihood estimation of a vector regression parameter and variance com ponents is considered for the mixed effects model when observations are right censored. A general scheme of estimation is given using the EM algorithm and detailed results found for the model with between and within block variation. This model is applied to the logarithms of survival times from a repeated measures design.

删失与分组数据的再加权最小二乘估计：EM 算法应用AI 解读

SUMMARY We consider the problem of adapting weighted least squares estimation so that estimates can be found with censored or grouped data. The EM algorithm is implemented for the linear model where the errors are assumed to be generated by a scale mixture of normal distributions. In particular, explicit results are given for the case where the marginal distribution of the error is Student-t with an even number of degrees of freedom. Expressions for the observed information…

并列值、分组连续数据与有序分类数据：两种模型的比较AI 解读

Likelihood ratio tests for no regression effect are considered when a linear model is used to explain the sample outcome where the observations are tied, grouped continuous or ordered categorical data. Two likelihoods are considered: one is an adaptation of a likelihood based on ranks modified for ties, and the second is a likelihood for grouped continuous data. The two likelihoods give asymptotically equivalent test statistics provided that the number of tied values or…

并列值、分组连续数据与有序分类数据：两种模型的比较AI 解读

Likelihood ratio tests for no regression effect are considered when a linear model is used to explain the sample outcome where the observations are tied, grouped continuous or ordered categorical data. Two likelihoods are considered: one is an adaptation of a likelihood based on ranks modified for ties, and the second is a likelihood for grouped continuous data. The two likelihoods give asymptotically equivalent test statistics provided that the number of tied values or…

摘要暂缺

利用符号秩对匹配对进行似然推断AI 解读

SUMMARY Exact and approximate inference based on the marginal likelihood which results from the signed ranks of the within pair differences of independent matched pairs is considered. Inference is made using Bayesian ideas. A quickly computed approximate analysis is introduced and this is shown to be extremely good when the within pair differences are assumed to have a normal distribution. Numerical comparisons are also made when the differences have a logistic distribution,…

评判者群组内外一致性的参数检验AI 解读

Series approximations to the logarithm of the probability of a permutation of the natural numbers, 1, …, K, using an extension of the Thurstone model, are investigated. The asymptotic bias of the quadratic and cubic approximations using the normal density is shown to be small. Approximate likelihood ratio tests are considered for testing for agreement between and within groups of judges and x2 approximations seem adequate for significance levels.

使用秩似然进行线性模型推断AI 解读

Summary An approximation to the marginal likelihood of the ranks of a set of observations is used to analyse data. The observations, after some arbitrary monotone transformation, are assumed to be independently normally distributed with means related by a linear model. An approximate posterior distribution for the parameters of the linear model is given and used to find predictive distributions for the ordering of future observations. A numerical example is given. Appendices…

评判者组内与组间一致性的参数检验AI 解读

Series approximations to the logarithm of the probability of a permutation of the natural numbers, 1, …, K, using an extension of the Thurstone model, are investigated. The asymptotic bias of the quadratic and cubic approximations using the normal density is shown to be small. Approximate likelihood ratio tests are considered for testing for agreement between and within groups of judges and x2 approximations seem adequate for significance levels.

利用秩计算变点的后验概率AI 解读

Simple approximate methods of analysis are given for change-point models using ranked observations. The models can be applied to continuous observations, providing a robust analysis in this case. For ranked observations, the models provide analyses for association. Numerical examples, involving continuous and ranked observations, are given.

利用秩计算变点的后验概率AI 解读

Simple approximate methods of analysis are given for change-point models using ranked observations. The models can be applied to continuous observations, providing a robust analysis in this case. For ranked observations, the models provide analyses for association. Numerical examples, involving continuous and ranked observations, are given.

零一观测变点问题的简单累积和型统计量AI 解读

A simple cumulative sum type statistic for the change-point with zero-one observations is introduced. A conditional test of no change against change is introduced and compared with a likelihood ratio test. The estimation of the change-point is also considered, using the simple statistic, and the method is shown to be asymptotically equivalent to the maximum likelihood estimator in certain circumstances and almost equivalent in others. To investigate the small sample…

两样本 Cramér–von Mises 型秩统计量AI 解读

Summary In this paper weighted Cramér-von Mises type two-sample rank statistics are considered. It is shown that the statistics can be written as sums of squares of linear rank statistics. The asymptotic equivalence of the statistics to an easily computed version is shown and the asymptotic distribution of the statistics investigated. Finally, some specific examples are considered relating the Cramér-von Mises statistics to the Wilcoxon, Mood, Normal Scores and Savage rank…

与皮尔逊矩比统计量相关的 Cramér–von Mises 型拟合优度统计量AI 解读

Summary We investigate a statistic introduced by de Wet and Venter to test for normality and a Cramér–von Mises statistic asymptotically equivalent to this statistic. It is shown that the Cramér–von Mises statistic can be written as a sum of components which are polynomial functions of the original standardized observations, the most important of which are Pearson's moment ratio statistics, √b 1 and b 2. Approximate small sample percentage points are given for the de Wet and…

删失数据下基于 Cramér–von Mises 统计量的指数分布检验AI 解读

SUMMARY This paper considers modifications of Cramer-von Mfises type statistics so that the statistics can be used to test the goodness of fit of censored data to the exponential distribution. Asymptotic percentage points are given for the statistics. In this paper we give the asymptotic distributions of two Cramer-von Mises type statistics used to test for the exponential distribution with censored data when the scale parameter must be estimated. The distributions given are…

删失样本正态性检验的 Cramér–von Mises 统计量AI 解读

Asymptotic theory is developed for the distribution of Cramér-von Mises statistics for testing the goodness of fit of censored samples. Asymptotic percentage points are given and also small-sample Monte Carlo percentage points for testing for normality.

删失数据的修正 Cramér–von Mises 统计量AI 解读

Cramér-von Mises type statistics are modified so that they can be used to test the goodness of fit of a censored sample, when the distribution function is known completely. Asymptotic percentage points are given, small-sample applications are discussed and asymptotic power considered.

双样本Anderson–Darling秩统计量AI 解读

A two-sample Anderson-Darling statistic is introduced and small-sample percentage points are given. An approximation to the distribution is also given. The statistic is related to Wilcoxon's and Mood's rank statistics. Asymptotic power comparisons are made with other two-sample rank statistics for shifts in location and scale.