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用混合分布近似后验分布AI 解读

SUMMARY Kernel density estimation techniques are used to smooth simulated samples from importance sampling function approximations to posterior distributions, resulting in revised approximations that are mixtures of standard parametric forms, usually multivariate normal or T-distributions. Adaptive refinement of such mixture approximations involves repeating this process to home-in successively on the posterior. In fairly low dimensional problems, this provides a general and…

两阶段整群抽样下有限总体比例的贝叶斯预测推断AI 解读

SUMMARY Given binary data from a two-stage cluster sample, we present a method to carry out Bayesian predictive inference for a finite population proportion. Our probabilistic specification should be useful for many surveys of this type and yields simple analytical expressions for the prior and posterior mean and variance. Within cluster k, we assume that the Yki are a random sample from the Bernoulli distribution with probability θk. Conditional on β and τ, θ1,..., θN are a…

二元配对二值数据的逻辑回归参数估计AI 解读

SUMMARY Consider bivariate binary data, with possibly different covariates for each marginal binary observation. Suppose that the correlation between paired observations is a nuisance, and the interest lies in estimating logistic regression parameters associated with the covariates. We consider the estimator obtained by using the independence estimating equation, with corrected variance. This estimator can be very efficient and robust compared with maximum likelihood or the…

存在干扰参数时频率表现良好的贝叶斯区间AI 解读

SUMMARY Given a random sample from a distribution with density function that depends on an unknown parameter θ = (θ1 . . ., θp), we are concerned with the problem of setting confidence intervals for a particular component of it, say θ1, treating the remaining components as a nuisance parameter. Adopting an objective Bayesian approach, we show that the Bayes intervals with a certain conditional prior density on the parameter of interest, θ1, are confidence intervals as well,…

中心化最小二乘预测交叉验证中的 Moore–Penrose 广义逆降更新AI 解读

SUMMARY Given a p × p symmetric matrix B and a p-vector c outside the range of B, a simple expression is formulated for the action of the Moore-Penrose generalized inverse B + on a vector b in the range of B, in terms of b, c and (B + cc‱)+. A special case of this formula gives a ‘downdating’ formula for the vector of least squares regression coefficients based on the Moore-Penrose inverse of the centred sum of squares and products matrix. The formula is analogous to that…

采用张量积薄板样条的半参数方差分析AI 解读

SUMMARY We consider fitting multivariate models to response data based on analysis-of-variance (ANOVA)-like decompositions of functions of several variables, f(t 1,..., td) = C + σα f α(ta + σα < β f αβ(t α, t β) + · · · · A theory for fitting (some components of) these models with polynomial smoothing splines exists when each tα is in a subset of the real line. In this case the various estimated components turn out to be certain tensor sums and products of polynomial…

因果推断所依赖的假设AI 解读

SUMMARY Statisticians commonly make causal inferences from the results of randomized experiments, but usually question causal inferences from observational studies on the grounds that untestable assumptions are required. This paper explains the basis for this situation and examines, within quite a general framework, various assumptions that appear in the literature. It is demonstrated how the role of each assumption is intimately related to the sort of causal inference being…

似然、拟似然与伪似然的若干比较AI 解读

SUMMARY There is considerable interest in the fitting of models jointly to the mean and dispersion of a response. For the mean parameter, the Wedderburn estimating equations are widely accepted. However, there is some controversy about estimating the dispersion parameters. Finite sampling properties of several dispersion estimators are investigated for three models by simulation. We compare the maximum extended quasi-likelihood estimator, the maximum pseudolikelihood…

通过条件独立性刻画指数分布AI 解读

SUMMARY Let Y 1, Y 2, . . ., Yn be mutually independent non-negative random variables having an absolutely continuous distribution function Fi(y) over its support [0, ∞) and the corresponding density function f i(y) > 0 for y > 0. Let A denote the event that Yi – Y i+1 > 0 for all i = 1, 2, . . ., n – 1. Then we show that, conditional on the event A, Yi – Y i+1 and Y i+1 are independent for all i = 1, 2,. . ., k if and only if Yi (i = 1, 2, . . ., k) are exponentially…

似不相关回归模型的预测AI 解读

SUMMARY The seemingly unrelated regressions model is described and analysed from a Bayesian perspective. The predictive density for this model cannot, in general, be evaluated analytically. Two approximations are proposed and investigated. These are Gibbs sampling and a first-order approximation based on a Bayes estimate of the precision matrix. These approximations are then compared on simulated data and both appear to give good results. Extensions to allow for missing data…

多项分布协方差矩阵的精确 Cholesky 分解、广义逆及应用AI 解读

SUMMARY A symbolic formula is given for the square-root-free Cholesky decomposition of the variance–covariance matrix of the multinomial distribution. The evaluation of the symbolic Cholesky factors requires much fewer arithmetic operations than does the general Cholesky algorithm. Since the symbolic formula is not affected by an ill-conditioned matrix, it is particularly useful when the elements of a probability vector are of quite different orders of magnitude. A simpler…

基于最小消息长度估计的单因子分析AI 解读

SUMMARY The minimum message length (MML) technique is applied to the problem of estimating the parameters of a multivariate Gaussian model in which the correlation structure is modelled by a single common factor. Implicit estimator equations are derived and compared with those obtained from a maximum likelihood (ML) analysis. Unlike ML, the MML estimators remain consistent when used to estimate both the factor loadings and the factor scores. Tests on simulated data show the…

条件似然比检验与通常似然比检验的比较AI 解读

SUMMARY This paper compares, under contiguous alternatives, the conditional likelihood ratio test of Cox and Reid with the usual likelihood ratio test on the basis of second-order power. It is seen that although the power of the former is identical, up to the second order, with that of the likelihood ratio test with known nuisance parameter, it does not hold with the latter. This provides a justification for the use of the conditional likelihood ratio test, rather than the…

SUMMARY An extension of the threshold method for extreme values is developed, to consider the joint distribution of extremes of two variables. The methodology is based on the point process representation of bivariate extremes. Both parametric and nonparametric models are considered. The simplest case to handle is that in which both marginal distributions are known. For the more realistic case in which the marginal distributions are unknown, a mixed parametric-nonparametric…

筛选问题的核方法AI 解读

SUMMARY Screening methods are developed which raise the proportion of individuals possessing an attribute in the retained population to a predetermined level. A specification region for the screening variable is derived by using a kernel smoothing approach. The sensitivity of the procedure is assessed within a range of parametric models. Comparisons are also made with empirical and estimative solutions. The kernel method is illustrated by an example of screening within a…

跟踪软件可靠性增长的非齐次自回归过程及贝叶斯分析AI 解读

SUMMARY We motivate a non-homogeneous autoregressive process as a model for reliability growth and consider two formulations, both Bayesian, which alleviate a limitation that least squares estimators for such processes of order greater than 1 exist only when repeated measurements of the time series are available. In one formulation, the prior assumption involves exchangeability of coefficients, whereas in the other an autoregressive structure is imposed on them. Both…

Bootstrap 后的 Jackknife：标准误与影响函数AI 解读

SUMMARY This paper shows how to derive more information from a bootstrap analysis, information about the accuracy of the usual bootstrap estimates. Suppose that we observe data x = (x 1 x 2, . . ., xn), compute a statistic of interest s(x) and further compute B bootstrap replications of s, say s(x*1) s(x*2), . . ., s(x*B), where B is some large number like 1000. Various accuracy measures for s(x) can be obtained from the bootstrap values, e.g. the bootstrap estimates of…

分类数据的多元回归分析AI 解读

SUMMARY It is common to observe a vector of discrete and/or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes. The response vector can comprise repeated observations on one variable, as in longitudinal studies or genetic studies of families, or can include observations for different variables. This paper discusses a class of models…

近似贝叶斯因子与正交参数：两个二项比例相等性检验AI 解读

SUMMARY We use asymptotic expansions to approximate Bayes factors, improving on a method used by Jeffreys. Suppose that the hypothesis H 0: ψ = ψ0 is to be tested against H A: ψ ≠ ψ0 in the presence of a nuisance parameter β, and initially priors π0(β) under H 0 and π(β, ψ) under H A are used. We consider the problem of assessing sensitivity of the Bayes factor to small changes in π0 and π. We show that for local alternatives (which, for moderate sample sizes, are consistent…

SUMMARY Maximum entropy (ME) inversion is a non-linear inversion technique for inverse problems where the object to be recovered is known to be positive. It has been applied in areas ranging from radio astronomy to various forms of spectroscopy, sometimes with dramatic success. In some cases, ME has attained an order of magnitude finer resolution and/or an order of magnitude smaller noise level than that obtainable by standard linear methods. The dramatic successes all seem…

一种二阶渐近独立性AI 解读

SUMMARY Suppose that a random vector x is partitioned into two subvectors and that generic coordinates of these subvectors are indicated by xa, xb, … and xr, xs, … respectively. If the joint cumulant (matrix) (ka,r) equals 0 then xa and xr are asymptotically independent to order O(n -1/2) under ordinary repeated sampling. When the third-order joint cumulant (array) (ka,b,r) is also 0 this independence statement may be sharpened to asymptotic independence to order O(n -1) of…

非线性回归中的嵌入模型AI 解读

SUMMARY A problem that is often encountered in non-linear regression is instability in the computation of parameter estimates. Such instability may arise from models with too many parameters, resulting in estimating equations that are ill conditioned and consequent problems of identification. This paper shows that in some cases these difficulties can be explained by the presence of an embedded model, a special case of the original model involving fewer parameters but one…

似然比与条件似然比检验的贝叶斯及频率学派 Bartlett 修正AI 解读

SUMMARY This paper characterizes priors under which the Bayesian and frequentist Bartlett corrections for the likelihood ratio and the conditional likelihood ratio (CLR) statistics differ by o(1). It is seen that, except for sample points with negligible probability, the CLR statistic has a posterior distribution for which a posterior Bartlett correction exists. This observation leads to an alternative proof of the existence of a frequentist Bartlett correction for the CLR…

定期观测三状态马尔可夫过程的非参数估计及艾滋病应用AI 解读

SUMMARY Estimation in a three-state Markov process with irreversible transitions in the presence of interval-censored data is considered. A nonparametric maximum likelihood procedure for the estimation of the cumulative transition intensities is presented. A self-consistent estimator of the parameters is defined and it is shown that the maximum likelihood estimator is a self-consistent estimator. This extends the idea of self-consistency introduced by Efron to the estimation…