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从自动建模视角估计过参数化模型AI 解读

From a model-building perspective, we propose a paradigm shift for fitting over-parameterized models. Philosophically, the mindset is to fit models to future observations rather than to the observed sample. Technically, given an imputation method to generate future observations, we fit over-parameterized models to these future observations by optimizing an approximation of the desired expected loss function based on its sample counterpart and an adaptive duality function.…

边际推断模型：针对目标参数的无先验概率推断AI 解读

The inferential models (IM) framework provides prior-free, frequency-calibrated, and posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown parameters. When nuisance parameters are present, a marginalization step can reduce the dimension of the auxiliary variable which, in turn, leads to more efficient inference. For regular problems, exact marginalization can be achieved,…

条件推断模型：汇集信息以进行无先验概率推断AI 解读

Summary The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher dimension than the parameter. Here we show that features of the auxiliary variable are often fully observed and, in such cases, a simultaneous dimension reduction and information aggregation can be achieved by conditioning. This…

推断模型：无需先验的后验概率推断框架AI 解读

Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher’s fiducial inference, Dempster–Shafer theory of belief functions, and Bayesian inference with default priors are attempts to achieve this goal but, to date, none has given a completely satisfactory picture. This article presents a new framework for probabilistic inference, based on inferential models (IMs), which not only provides data-dependent probabilistic measures…

蒙特卡洛计算中的随机逼近AI 解读

The Wang–Landau (WL) algorithm is an adaptive Markov chain Monte Carlo algorithm used to calculate the spectral density for a physical system. A remarkable feature of the WL algorithm is that it is not trapped by local energy minima, which is very important for systems with rugged energy landscapes. This feature has led to many successful applications of the algorithm in statistical physics and biophysics; however, there does not exist rigorous theory to support its…

通过交替子空间张成重采样加速马尔可夫链蒙特卡洛模拟AI 解读

This article provides a simple method to accelerate Markov chain Monte Carlo sampling algorithms, such as the data augmentation algorithm and the Gibbs sampler, via alternating subspace-spanning resampling (ASSR). The ASSR algorithm often shares the simplicity of its parent sampler but has dramatically improved efficiency. The methodology is illustrated with Bayesian estimation for analysis of censored data from fractionated experiments. The relationships between ASSR and…

一类单纯形约束下的离散分布估计AI 解读

Simplex constraints, such as monotonicity and convexity or concavity on the probabilities of a set of discrete distributions, are useful for modeling and analyzing discrete data. This article considers both maximum likelihood estimation and Bayesian estimation of discrete distribution with a class of simplex constraints using the Expectation-Maximization (EM) algorithm and the data augmentation (DA) algorithm. The formulation and implementation of EM and DA for binomial,…

具有一类单纯形约束的离散分布估计AI 解读

Simplex constraints, such as monotonicity and convexity or concavity on the probabilities of a set of discrete distributions, are useful for modeling and analyzing discrete data. This article considers both maximum likelihood estimation and Bayesian estimation of discrete distribution with a class of simplex constraints using the Expectation-Maximization (EM) algorithm and the data augmentation (DA) algorithm. The formulation and implementation of EM and DA for binomial,…

未提问与未回答：多项调查的多重插补AI 解读

We present a method of analyzing a series of independent cross-sectional surveys in which some questions are not answered in some surveys and some respondents do not answer some of the questions posed. The method is also applicable to a single survey in which different questions are asked or different sampling methods are used in different strata or clusters. Our method involves multiply imputing the missing items and questions by adding to existing methods of imputation…

未问与未答：多项调查的多重插补AI 解读

We present a method of analyzing a series of independent cross-sectional surveys in which some questions are not answered in some surveys and some respondents do not answer some of the questions posed. The method is also applicable to a single survey in which different questions are asked or different sampling methods are used in different strata or clusters. Our method involves multiply imputing the missing items and questions by adding to existing methods of imputation…

摘要暂缺

不完整数据下稳健多元线性回归的贝叶斯分析AI 解读

The multivariate t distribution and other normal/independent multivariate distributions, such as the multivariate slash distribution and the multivariate contaminated distribution, are used for robust regression with complete or incomplete data. Most previous work focused on the method of maximum likelihood estimation for linear regression using normal/independent distributions. This article considers Bayesian estimation of multivariate linear regression models using…

ECME 算法：具有更快单调收敛的 EM 与 ECM 扩展AI 解读

A generalisation of the ecm algorithm (Meng & Rubin, 1993), which is itself an extension of the em algorithm (Dempster, Laird & Rubin, 1977), can be obtained by replacing some CM-steps of ECM, which maximise the constrained expected complete-data loglikelihood function, with steps that maximise the correspondingly constrained actual likelihood function. This algorithm, which we call ecme algorithm, for Expectation/Conditional Maximisation Either, shares with both em and ecm…