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通过单峰化输运处理多峰分布：Warp-U采样与随机桥采样估计AI 解读

Monte Carlo integration is a powerful tool for scientific and statistical computation, but faces significant challenges when the integrand is a multi-modal distribution, even when the mode locations are known. This work introduces novel Monte Carlo sampling and integration estimation strategies for the multi-modal context by leveraging a generalized version of the stochastic Warp-U transformation (Wang et al., 2022). We propose two flexible classes of Warp-U transformations,…

依赖关系中的BELIEF：以二元数据的线性性质重思广义线性模型AI 解读

Two linearly uncorrelated binary variables must be also independent because nonlinear dependence cannot manifest with only two possible states. This inherent linearity is the atom of dependency constituting any complex form of relationship. Inspired by this observation, we develop a framework called binary expansion linear effect (BELIEF) for understanding arbitrary relationships with a binary outcome. Models from the BELIEF framework are easily interpretable because they…

Warp 桥采样的新一代方法AI 解读

Bridge sampling is an effective Monte Carlo (MC) method for estimating the ratio of normalizing constants of two probability densities, a routine computational problem in statistics, physics, chemistry, and other fields. The MC error of the bridge sampling estimator is determined by the amount of overlap between the two densities. In the case of unimodal densities, Warp-I, II, and III transformations are effective for increasing the initial overlap, but they are less so for…

用扩展先验样本量评估先验影响及先验—似然不协调AI 解读

Abstract This paper outlines a framework for quantifying the prior’s contribution to posterior inference in the presence of prior-likelihood discordance, a broader concept than the usual notion of prior-likelihood conflict. We achieve this dual purpose by extending the classic notion of prior sample size, M, in three directions: (I) estimating M beyond conjugate families; (II) formulating M as a relative notion that is as a function of the likelihood sample size k, M(k),…

无限维、零直接样本情形的多分辨率近似理论：过渡推断与个体化预测AI 解读

Transitional inference is an empiricism concept, rooted and practiced in clinical medicine since ancient Greece. Knowledge and experiences gained from treating one entity (e.g., a disease or a group of patients) are applied to treat a related but distinctively different one (e.g., a similar disease or a new patient). This notion of “transition to the similar” renders individualized treatments an operational meaning, yet its theoretical foundation defies the familiar…

通过乘法收缩实现天文仪器校准一致性AI 解读

Calibration data are often obtained by observing several well-understood objects simultaneously with multiple instruments, such as satellites for measuring astronomical sources. Analyzing such data and obtaining proper concordance among the instruments is challenging when the physical source models are not well understood, when there are uncertainties in “known” physical quantities, or when data quality varies in ways that cannot be fully quantified. Furthermore, the number…

多中心生存研究的多分辨率风险模型AI 解读

In multicenter studies, one often needs to make inference about a population survival curve based on multiple, possibly heterogeneous survival data from individual centers. We investigate a flexible Bayesian method for estimating a population survival curve based on a semiparametric multiresolution hazard model that can incorporate covariates and account for center heterogeneity. The method yields a smooth estimate of the survival curve for "multiple resolutions" or time…

Antithetic coupling is a general stratification strategy for reducing Monte Carlo variance without increasing the simulation size. The use of the antithetic principle in the Monte Carlo literature typically employs two strata via antithetic quantile coupling. We demonstrate here that further stratification, obtained by using k>2 (e.g., k=3–10) antithetically coupled variates, can offer substantial additional gain in Monte Carlo efficiency, in terms of both variance and bias.…

对 Brooks、Giudici 与 Roberts 论文的讨论AI 解读

This paper aims to develop general strategies for improving jumps between models in reversible jump Markov chain Monte Carlo (MCMC) algorithms, which is quite an important and timely goal. Indeed, in practical implementations of the method, we usually find that the choice of proposals is paramount: in many cases, the ‘natural choice’ leads to a zero acceptance probability and the construction of well-tuned moves is often quite costly. Given that the reversible jump MCMC…

单观测无偏先验AI 解读

This paper studies a class of default priors, which we call single observation unbiased priors (SOUP). A prior for a parameter is a SOUP if the corresponding posterior mean of the parameter based on a single observation is an unbiased estimator of the parameter. We prove that, under mild regularity conditions, a default prior for a convolution parameter is "noninformative" in the sense of yielding a posterior inference invariant under amalgamation only if it is a SOUP.…

缺失数据：拨 M 找寻什么？AI 解读

The question mark is common notation for the missing data that occur in most applied statistical analyses. Over the past century, statisticians and other scientists not only have invented numerous methods for handling missing/incomplete data, but also have invented many forms of missing data, including data augmentation, hidden states, latent variables, potential outcome, and auxiliary variables. Purposely constructing unobserved/unobservable variables offers an…

混合效应模型的快速EM类算法实现AI 解读

Summary The mixed effects model, in its various forms, is a common model in applied statistics. A useful strategy for fitting this model implements EM-type algorithms by treating the random effects as missing data. Such implementations, however, can be painfully slow when the variances of the random effects are small relative to the residual variance. In this paper, we apply the ‘working parameter’ approach to derive alternative EM-type implementations for fitting mixed…

全信息项目因子模型的拟合与桥接抽样的实证考察AI 解读

Based on item response theory, Bock and Aitken introduced a method of item factor analysis, termed full-information item factor (FIIF) analysis by Bartholomew because it uses all distinct item response vectors as data. But a limitation of their fitting algorithm is its reliance on fixed-point Gauss—Hermite quadrature, which can produce appreciable numerical errors, especially in high-dimension problems. The first purpose of this article is to offer more reliable methods by…

后验预测 p 值AI 解读

Extending work of Rubin, this paper explores a Bayesian counterpart of the classical $p$-value, namely, a tail-area probability of a "test statistic" under a null hypothesis. The Bayesian formulation, using posterior predictive replications of the data, allows a "test statistic" to depend on both data and unknown (nuisance) parameters and thus permits a direct measure of the discrepancy between sample and population quantities. The tail-area probability for a "test…

相关曲线：回归局部解释方差的度量AI 解读

We call (a model for) an experiment heterocorrelatious if the strength of the relationship between a response variable Y and a covariate X is different in different regions of the covariate space. For such experiments we introduce a correlation curve that measures heter-ocorrelaticity in terms of the variance explained by regression locally at each covariate value. More precisely, the squared correlation curve is obtained by first expressing the usual linear model “variance…

作为回归局部方差解释度量的相关曲线AI 解读

We call (a model for) an experiment heterocorrelatious if the strength of the relationship between a response variable Y and a covariate X is different in different regions of the covariate space. For such experiments we introduce a correlation curve that measures heter-ocorrelaticity in terms of the variance explained by regression locally at each covariate value. More precisely, the squared correlation curve is obtained by first expressing the usual linear model “variance…

ECM 算法的收敛速率AI 解读

The fundamental result on the rate of convergence of the EM algorithm has proven to be theoretically valuable and practically useful. Here, this result is generalized to the ECM algorithm, a more flexible and applicable iterative algorithm proposed recently by Meng and Rubin. Results on the rate of convergence of variations of ECM are also presented. An example is given to show that intuitions accurate for complete-data iterative algorithms may not be trustworthy in the…

通过 ECM 算法进行最大似然估计：一般框架AI 解读

Two major reasons for the popularity of the EM algorithm are that its maximum step involves only complete-data maximum likelihood estimation, which is often computationally simple, and that its convergence is stable, with each iteration increasing the likelihood. When the associated complete-data maximum likelihood estimation itself is complicated, EM is less attractive because the M-step is computationally unattractive. In many cases, however, complete-data maximum…

多重插补数据集的似然比检验AI 解读

Existing procedures for obtaining significance levels from multiply-imputed data either (i) require access to the completed-data point estimates and variance-covariance matrices, which may not be available in practice when the dimensionality of the estimand is high, or (ii) directly combine p-values with less satisfactory results. Taking advantage of the well-known relationship between the Wald and log likelihood ratio test statistics, we propose a complete-data log…

右删失两样本处理效应一般估计量的大样本性质AI 解读

The estimation of the treatment effect in the two-sample problem with right censoring is of interest in survival analysis. In this article we consider both the location shift model and the scale change model. We establish the large-sample properties of a generalized Hodges-Lehmann type estimator. The strong consistency is established under the minimal possible conditions. The asymptotic normality is also obtained without imposing any conditions on the censoring mechanisms.…

利用 EM 获得渐近方差协方差矩阵：SEM 算法AI 解读

The expectation maximization (EM) algorithm is a popular, and often remarkably simple, method for maximum likelihood estimation in incomplete-data problems. One criticism of EM in practice is that asymptotic variance–covariance matrices for parameters (e.g., standard errors) are not automatic byproducts, as they are when using some other methods, such as Newton–Raphson. In this article we define and illustrate a procedure that obtains numerically stable asymptotic…

严重删失数据下处理效应的一般估计量AI 解读

A generalized Hodges-Lehmann type estimator for the treatment effect in the two-sample problem with right censoring, is proposed based on an inverse-quantile-type idea using truncated versions of the Kaplan-Meier estimators over the subspace where they are consistent. Its strong consistency and asymptotic normality can be obtained, under no conditions on the uninformative censorings, and the resulting variance is easily estimable from the data. In simulation studies the…

重度删失数据下处理效应的一般估计量AI 解读

A generalized Hodges-Lehmann type estimator for the treatment effect in the two-sample problem with right censoring, is proposed based on an inverse-quantile-type idea using truncated versions of the Kaplan-Meier estimators over the subspace where they are consistent. Its strong consistency and asymptotic normality can be obtained, under no conditions on the uninformative censorings, and the resulting variance is easily estimable from the data. In simulation studies the…