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利用辅助变量对贝叶斯非共轭与层级模型进行 Gibbs 抽样AI 解读

Summary We demonstrate the use of auxiliary (or latent) variables for sampling non-standard densities which arise in the context of the Bayesian analysis of non-conjugate and hierarchical models by using a Gibbs sampler. Their strategic use can result in a Gibbs sampler having easily sampled full conditionals. We propose such a procedure to simplify or speed up the Markov chain Monte Carlo algorithm. The strength of this approach lies in its generality and its ease of…

通过EM算法直接计算信息矩阵AI 解读

Summary A simple explicit formula is provided for the matrix of second derivatives of the observed data log-likelihood in terms of derivatives of the criterion function (conditional expectation of the complete data log-likelihood given the observed data) invoked by the EM algorithm.

利用平滑样条进行广义可加混合模型推断AI 解读

Summary Generalized additive mixed models are proposed for overdispersed and correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs. This class of models allows flexible functional dependence of an outcome variable on covariates by using nonparametric regression, while accounting for correlation between observations by using random effects. We estimate nonparametric functions by using smoothing splines and jointly estimate…

自动化 Monte Carlo EM 算法最大化广义线性混合模型似然AI 解读

Summary Two new implementations of the EM algorithm are proposed for maximum likelihood fitting of generalized linear mixed models. Both methods use random (independent and identically distributed) sampling to construct Monte Carlo approximations at the E-step. One approach involves generating random samples from the exact conditional distribution of the random effects (given the data) by rejection sampling, using the marginal distribution as a candidate. The second method…

删失分布不等时现状数据的非参数检验AI 解读

Summary Nonparametric tests for the comparison of different treatments based on current status data are proposed. For this problem, most methods proposed in the literature require that observation times on all subjects follow the same distribution. In other words, censoring distributions are identical between the treatment groups. In this paper, we focus on the situation where the censoring distributions may be different for subjects in different treatment groups and the…

Logistic 回归模型的先验 elicitation、变量选择与贝叶斯计算AI 解读

Summary Bayesian selection of variables is often difficult to carry out because of the challenge in specifying prior distributions for the regression parameters for all possible models, specifying a prior distribution on the model space and computations. We address these three issues for the logistic regression model. For the first, we propose an informative prior distribution for variable selection. Several theoretical and computational properties of the prior are derived…

基于共轭潜在过程的指数族状态空间模型AI 解读

Summary This paper introduces non-linear and non-Gaussian state space models with analytic updating recursions for filtering and prediction. This new class of models involves some well-known results in the theory of exponential models and of exponential dispersion models and the latent process is defined in such a way that both the filtering and the prediction distributions turn out to be conjugate to the observation distribution at each step. The corresponding analytic and…

双盲反卷积：神经细胞突触后电流的分析AI 解读

Summary This paper is concerned with the analysis of observations made on a system that is being stimulated at fixed time intervals but where the precise nature and effect of any individual stimulus is unknown. The realized values are modelled as a stochastic process consisting of a random signal embedded in noise. The aim of the analysis is to use the data to unravel the unknown structure of the system and to ascertain the probabilistic behaviour of the stimuli. A method of…

缺失机制不可忽略时广义线性模型中的协变量缺失AI 解读

Summary We propose a method for estimating parameters in generalized linear models with missing covariates and a non-ignorable missing data mechanism. We use a multinomial model for the missing data indicators and propose a joint distribution for them which can be written as a sequence of one-dimensional conditional distributions, with each one-dimensional conditional distribution consisting of a logistic regression. We allow the covariates to be either categorical or…

通过检验反演构造自助法置信区间AI 解读

Summary In this paper we explore the theoretical and practical implications of using bootstrap test inversion to construct confidence intervals. In the presence of nuisance parameters, we show that the coverage error of such intervals is O(n −1/2) which may be reduced to O(n −1) if a Studentized statistic is used. We present three simulation studies and compare the performance of test inversion methods with established methods on the problem of estimating a confidence…

有意偏置的 Bootstrap 方法AI 解读

Summary A class of weighted bootstrap techniques, called biased bootstrap or b-bootstrap methods, is introduced. It is motivated by the need to adjust empirical methods, such as the ‘uniform’ bootstrap, in a surgical way to alter some of their features while leaving others unchanged. Depending on the nature of the adjustment, the b-bootstrap can be used to reduce bias, or to reduce variance or to render some characteristic equal to a predetermined quantity. Examples of the…

带索引随机模型的经验变换估计AI 解读

Summary We present a method for estimating the parameters in indexed stochastic models via a least squares approach based on empirical transforms. Asymptotic approximations are derived for the distribution of the resulting estimators. An explicit expression for the mean-squared error provides a natural way of selecting the transform variable, and a numerical example illustrates the performance of the resulting method. A common finding, which we term ‘diagonal optimization’,…

离子通道信号的贝叶斯恢复AI 解读

Summary We present a Bayesian method of ion channel analysis and apply it to a simulated data set. An alternating renewal process prior is assigned to the signal, and an autoregressive process is fitted to the noise. After choosing model hyperconstants to yield ‘uninformative’ priors on the parameters, the joint posterior distribution is computed by using the reversible jump Markov chain Monte Carlo method. A novel form of simulated tempering is used to improve the mixing of…

利用小波方法估计右删失数据的密度与风险率AI 解读

Summary This paper describes a wavelet method for the estimation of density and hazard rate functions from randomly right-censored data. We adopt a nonparametric approach in assuming that the density and hazard rate have no specific parametric form. The method is based on dividing the time axis into a dyadic number of intervals and then counting the number of events within each interval. The number of events and the survival function of the observations are then separately…

通过核回归理解指数平滑AI 解读

Summary Exponential smoothing is the most common model-free means of forecasting a future realization of a time series. It requires the specification of a smoothing factor which is usually chosen from the data to minimize the average squared residual of previous one-step-ahead forecasts. In this paper we show that exponential smoothing can be put into a nonparametric regression framework and gain some interesting insights into its performance through this interpretation. We…

非参数回归中的偏差校正置信带AI 解读

Summary Bias-corrected confidence bands for general nonparametric regression models are considered. We use local polynomial fitting to construct the confidence bands and combine the cross-validation method and the plug-in method to select the bandwidths. Related asymptotic results are obtained. Our simulations show that confidence bands constructed by local polynomial fitting have much better coverage than those constructed by using the Nadaraya–Watson estimator. The results…

机器生成 AR(1) 模型的统计推断AI 解读

Summary We have obtained the asymptotic bias and the limiting distribution for the Yule–Walker estimator of the autoregressive parameter under a considerably weaker assumption than that of independence in the noise sequence. Among other things, these suggest robustness of the classical results and throw some light on the use of simulations based on pseudorandom numbers in verifying these results.

论有效的点预测系统AI 解读

Summary Assume that a forecaster observes a sequence of random variables and issues predictions according to a point prediction systems, i.e. a rule which, at every time t, issues a point prediction for the next observation at time t+1. We introduce the concept of efficiency of a point prediction system, for the case that the joint distribution of the sequence of observations is known to belong to a parametric family, and performance is assessed by the long run sum of…

非参数回归中的方差估计：怎样选择才合理？AI 解读

Summary The exact mean-squared error (MSE) of estimators of the variance in nonparametric regression based on quadratic forms is investigated. In particular, two classes of estimators are compared: Hall, Kay and Titterington's optimal difference-based estimators and a class of ordinary difference-based estimators which generalize methods proposed by Rice and Gasser, Sroka and Jennen-Steinmetz. For small sample sizes the MSE of the first estimator is essentially increased by…

一类局部似然方法与近参数渐近理论AI 解读

Summary The local maximum likelihood estimate θ^ t of a parameter in a statistical model f(x, θ) is defined by maximizing a weighted version of the likelihood function which gives more weight to observations in the neighbourhood of t. The paper studies the sense in which f(t, θ^t) is closer to the true distribution g(t) than the usual estimate f(t, θ^) is. Asymptotic results are presented for the case in which the model misspecification becomes vanishingly small as the…

非参数回归中的异方差检验AI 解读

Summary The importance of being able to detect heteroscedasticity in regression is widely recognized because efficient inference for the regression function requires that heteroscedasticity is taken into account. In this paper a simple consistent test for heteroscedasticity is proposed in a nonparametric regression set-up. The test is based on an estimator for the best L 2-approximation of the variance function by a constant. Under mild assumptions asymptotic normality of…

随机曲线分布众数的非参数估计AI 解读

Summary Motivated by the need to develop meaningful empirical approximations to a ‘typical’ data value, we introduce methods for density and mode estimation when data are in the form of random curves. Our approach is based on finite dimensional approximations via generalized Fourier expansions on an empirically chosen basis. The mode estimation problem is reduced to a problem of kernel-type multivariate estimation from vector data and is solved using a new recursive…

多类型流行病模型中的估计AI 解读

Summary A multitype epidemic model is analysed assuming proportionate mixing between types. Estimation procedures for the susceptibilities and infectivities are derived for three sets of data: complete data, meaning that the whole epidemic process is observed continuously; the removal processes are observed continuously; only the final state is observed. Under the assumption of a major outbreak in a population of size n it is shown that, for all three data sets, the…

基于马尔可夫链蒙特卡洛与彩色连续三角剖分模型的贝叶斯图像分析AI 解读

Summary It is now possible to carry out Bayesian image segmentation from a continuum parametric model with an unknown number of regions. However, few suitable parametric models exist. We set out to model processes which have realizations that are naturally described by coloured planar triangulations. Triangulations are already used, to represent image structure in machine vision, and in finite element analysis, for domain decomposition. However, no normalizable parametric…