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SUMMARY A simple method for approximate conditional inference is described. The methodology is applied to natural exponential family models where it is shown to provide accurate approximations to fully conditional estimates. The approximation technique can be applied much more generally than in this particular class of models. The technique depends only on the construction of certain 'projected scores' derived from higher order likelihood derivatives and their covariances…

通过改进实验设计减少毒理研究与测试中的动物使用AI 解读

SUMMARY More than 50 million animals are used in biomedical research in the world each year. It is highly desirable that this number is reduced both for ethical and for economic reasons. Better experimental design could lead to the use of fewer animals and improve the repeatability of animal experiments so that alternative methods would be easier to validate. Screening experiments aimed at identifying rodent carcinogens would be more powerful if more than one strain of mice…

SUMMARY This paper discusses design issues in 'ecological studies' —epidemiological studies in which the relationship between disease and behavioural and environmental determinants is studied at the population rather than the individual level. The number of study populations has little relevance beyond a certain point, the power and precision being limited by the total number of disease events and by the size of the sample surveys used to estimate the distributions of…

大型系统的实验设计与观测AI 解读

SUMMARY Large systems require new methods of experimental designs suitable for the highly adaptive models which are employed to cope with complex non-linear responses and high dimensionality of input spaces. The area of computer experiments has started to provide such designs especially Latin hypercube and lattice designs. System decomposition, prevalent in several branches of engineering, can be employed to decrease complexity. A combination of system decomposition using a…

多项数据的推断：从一袋弹珠中学习AI 解读

SUMMARY A new method is proposed for making inferences from multinomial data in cases where there is no prior information. A paradigm is the problem of predicting the colour of the next marble to be drawn from a bag whose contents are (initially) completely unknown. In such problems we may be unable to formulate a sample space because we do not know what outcomes are possible. This suggests an invariance principle: inferences based on observations should not depend on the…

通过 Lasso 实现回归收缩与变量选择AI 解读

SUMMARY We propose a new method for estimation in linear models. The ‘lasso’ minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It…

具有近似频率学有效性的扰动椭球与最高后验密度区域AI 解读

SUMMARY This paper considers, in the multiparameter case, perturbed ellipsoidal and highest posterior density regions with both Bayesian and frequentist validity up to o(n −1).

SUMMARY It is shown that the usual Laplace approximation is not a valid asymptotic approximation when the dimension of the integral is comparable with the limiting parameter n. The formal Laplace expansion for multidimensional integrals is given and used to construct asymptotic approximations for high dimensional integrals. One example is considered in which the dimension of the integral is O(n 1/2) and the relative error of the unmodified Laplace approximation is O(1).…

异质处理效应下半参数两样本模型的经验过程方法AI 解读

SUMMARY Two types of semiparametric model are proposed for comparing two samples with possibly heterogeneous treatment effects. One model is a two-sample location-scale model which assumes that the Q-Q-plot of the two distributions involved is linear; the other is the class of two-sample transformation models which assume parametric forms for a probability plot—the receiver operating characteristic curve. The empirical process approach is used to construct strong…

最优探索的一类贝叶斯模型AI 解读

SUMMARY Each of several locations contains an unknown number of objects of value. A single search of a location will discover some of these objects which are then removed. Discoveries yield rewards. A ‘distribution of effort’ problem is posed concerning how to explore the locations optimally—i.e. to maximize the expected return from discoveries made. This is formulated as a Bayes sequential decision problem for which index policies are optimal. A natural simple case is one…

存在信息性退出的纵向二元响应回归模型AI 解读

SUMMARY This paper reviews both likelihood-based and non-likelihood (generalized estimating equations) regression models for longitudinal binary responses when there are drop-outs. Throughout, it is assumed that the regression parameters for the marginal expectations of the binary responses are of primary scientific interest. The association or time dependence between the responses is largely regarded as a nuisance characteristic of the data. The performance of the methods…

在函数型主成分分析中纳入参数效应AI 解读

SUMMARY The ideas of functional principal component analysis are extended to deal with data that are hybrids of ‘functional’ and ‘parametric’ effects. The parametric effects may be more general than just the addition of a multiple of a given function. A detailed development is given in the case of shifts of the time axis for functions observed on a periodic interval, and some remarks are made for the extension to a far more general case. Given data, a Procrustes fitting…

可逆短记忆与长记忆 ARIMA 模型差分参数的最大似然估计AI 解读

SUMMARY In practical applications of Box-Jenkins autoregressive integrated moving average (ARIMA) models, the number of times that the observed time series must be differenced to achieve approximate stationarity is usually determined by careful, but mostly informal, analysis of the differenced series. For many time series, some differencing seems appropriate, but taking the first or the second difference may be too strong. As an alternative, Hosking, and Granger and Joyeux…

质量控制与动力系统中的序贯变点检测AI 解读

SUMMARY After a brief survey of a large variety of sequential detection procedures that are widely scattered in statistical references on quality control and engineering references on fault detection and signal processing, we study some open problems concerning these procedures and introduce a unified theory of sequential changepoint detection. This theory leads to a class of sequential detection rules which are not too demanding in computational and memory requirements for…

摘要暂缺

若干二维中位数的影响函数AI 解读

SUMMARY The asymptotic efficiency, influence function and breakdown properties of the multivariate median proposed by Oja are investigated and comparisons are made with two other generalizations of the median: the spatial median and the vector of marginal medians. It is shown that, for distributions with finite expectations, the Oja median has a bounded influence function although this median has 0% breakdown. For circular distributions, the influence functions of the Oja…

无限可分分布的近似随机数生成及其贝叶斯推断应用AI 解读

SUMMARY Stochastic processes with independent increments play a central role in Bayesian nonparametric inference. The distributions of the increments of these processes, aside from fixed points of discontinuity, are infinitely divisible and their Laplace and/or Fourier transforms in the Lévy representation are usually known. Conventional Bayesian inference in this context has been limited largely to providing point estimates of the random quantities of interest, although…

回归模型两侧的非参数变换AI 解读

SUMMARY One way to model heteroscedasticity and skewness of the error distribution in regression is to transform both sides of the regression equation. If it is possible to transform the regression equation to result in normally distributed errors, then we can obtain more efficient parameter estimates and valid prediction intervals. One problem with this approach is that the choice of transformation is usually restricted to the power or shifted power family. Often there is…

多元判别分析与最大惩罚似然密度估计AI 解读

SUMMARY A new theoretical point of view is discussed in the framework of density estimation. The multivariate true density, viewed as a prior or penalizing factor in a Bayesian framework, is modelled by a Gibbs potential. Estimating the density consists in maximizing the posterior. For efficiency of time, we are interested in an approximate estimator f̂ = Bπ of the true density f, where B is a stochastic operator and π is the raw histogram. Then, we investigate the…

通过马尔可夫链蒙特卡洛方法进行贝叶斯模型选择AI 解读

SUMMARY Markov chain Monte Carlo (MCMC) integration methods enable the fitting of models of virtually unlimited complexity, and as such have revolutionized the practice of Bayesian data analysis. However, comparison across models may not proceed in a completely analogous fashion, owing to violations of the conditions sufficient to ensure convergence of the Markov chain. In this paper we present a framework for Bayesian model choice, along with an MCMC algorithm that does not…

摘要暂缺

SUMMARY It is known that iterative weighted least squares (IWLS) does not merely yield a convenient way of fitting the general class of regression models considered by Green but is also a useful means of unifying techniques of model checking. However, an extension of these results to models containing nuisance or incidental parameters has made little progress beyond some special cases. Unfortunately, regression models with nuisance parameters that are not dispersion…

混沌 Logistic 映射的不变分布与 Lyapunov 指数性质AI 解读

SUMMARY Statistical scientists have recently focused sharp attention on properties of iterated chaotic maps, with a view to employing such processes to model naturally occurring phenomena. In the present paper we treat the logistic map, which has earlier been studied in the context of modelling biological systems. We derive theory describing properties of ‘invariant’ or ‘stationary’ distributions under logistic maps and apply those results in conjunction with numerical work…

含随机效应广义线性模型的渐近无偏估计AI 解读

SUMMARY Obtaining estimates that are nearly unbiased has proven to be difficult when random effects are incorporated into a generalized linear model. In this paper, we propose a general method of adjusting any conveniently defined initial estimates to result in estimates which are asymptotically unbiased and consistent. The method is motivated by iterative bias correction and can be applied in principle to any parametric model. A simulation-based approach of implementing the…