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非加性经验风险下 Gibbs 后验的一般不等式AI 解读

The Gibbs posterior is a useful tool for risk minimization, which adopts a Bayesian framework and can incorporate convenient computational algorithms such as Markov chain Monte Carlo. We derive risk bounds for the Gibbs posterior using some general nonasymptotic inequalities, which can be used to derive nearly optimal convergence rates and select models to optimally balance the approximation errors and the stochastic errors. These inequalities are formulated in a very…

带变量选择的时间序列二元选择风险最小化AI 解读

This paper considers the problem of predicting binary choices by selecting from a possibly large set of candidate explanatory variables, which can include both exogenous variables and lagged dependent variables. We consider risk minimization with the risk function being the predictive classification error. We study the convergence rates of empirical risk minimization in both the frequentist and Bayesian approaches. The Bayesian treatment uses a Gibbs posterior constructed…

高维分类与数据挖掘中的 Gibbs 后验变量选择AI 解读

In the popular approach of “Bayesian variable selection” (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a Gibbs posterior originating in statistical mechanics. The Gibbs posterior is constructed from a risk function of practical interest (such as the classification error) and aims at minimizing a risk function without modeling the data…

指数族回归的层次专家混合模型：逼近与最大似然估计AI 解读

We consider hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form $\psi(\alpha + \mathbf{x}^T \mathbf{\beta})$ are mixed. Here $\psi(\cdot)$ is the inverse link function. Suppose the true response $y$ follows an exponential family regression model with mean function belonging to a class of smooth functions of the form $\psi(h(\mathbf{x}))$ where $h(\cdot)\in W_{2; K_0}^{\infty}$ (a Sobolev…

统计推断工具：后验分布与似然函数的探索方法AI 解读

A unified introduction to a variety of computational algorithms for likelihood and Bayesian inference. This third edition expands the discussion of many of the techniques presented, and includes additional examples as well as exercise sets at the end of each chapter.

专家混合与层级专家混合模型的贝叶斯推断：语音识别应用AI 解读

Machine classification of acoustic waveforms as speech events is often difficult due to context dependencies. Here a vowel recognition task with multiple speakers is studied via the use of a class of modular and hierarchical systems referred to as mixtures-of-experts and hierarchical mixtures-of-experts models. The statistical model underlying the systems is a mixture model in which both the mixture coefficients and the mixture components are generalized linear models. A…

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利用 Gibbs 抽样进行指数族近似条件推断AI 解读

This article presents the Gibbs-Skovgaard algorithm for approximate frequentist inference. The method makes use of the double saddlepoint approximation of Skovgaard to the conditional cumulative distribution function of a sufficient statistic given the remaining sufficient statistics. This approximation is then used in the Gibbs sampler to generate a Markov chain. The equilibrium distribution of this chain approximates the joint distribution of the sufficient statistics…

分组生存数据边际似然的最大化AI 解读

Grouped failure time data occur in studies where subjects are monitored periodically to determine whether failure has occurred in the intervening interval. Here the model under consideration is Cox's (1972, 1975) proportional hazards model, but the commonly used method of partial likelihood needs modification with grouped data due to a potentially large number of ties. This paper demonstrates how the Monte Carlo em algorithm (Wei & Tanner, 1990) can be used on grouped data…

统计推断工具：观测数据与数据增广方法AI 解读

Observed data techniques - normal approximation observed data techniques the EM algorithm data augmentation the Gibbs sampler.

改进 Gibbs 抽样：Gibbs Stopper 与 Griddy-Gibbs 方法AI 解读

The article briefly reviews the history, literature, and form of the Gibbs sampler. An importance sampling device is proposed for converting the output of the Gibbs sampler to a sample from the exact posterior. This Gibbs stopper technique is also useful for assessing convergence of the Gibbs sampler for moderate sized problems. Also presented is an approach for implementing the Gibbs sampler in nonconjugate situations. The basic idea is to approximate the true cdf of each…

删失回归数据的后验计算AI 解读

This article describes the computation of and sampling from the posterior density for censored regression problems with normal and generalized log-gamma errors. The data augmentation algorithm (Tanner and Wong 1987) is facilitated in the normal error case because of the form of the augmented posterior. In the generalized log-gamma context, this simplicity is absent. The work of Sweeting (1981) is used as a motivation to develop an importance sampling scheme to sample from an…

EM 算法的蒙特卡洛实现与简易数据增广算法AI 解读

The first part of this article presents the Monte Carlo implementation of the E step of the EM algorithm. Given the current guess to the maximizer of the posterior distribution, latent data patterns are generated from the conditional predictive distribution. The expected value of the augmented log-posterior is then updated as a mixture of augmented log-posteriors, mixed over the generated latent data patterns (multiple imputations). In the M step of the algorithm, this…

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通过数据增广计算最高后验密度区域的概率含量与边界AI 解读

This note considers the computation of the content and the boundary of the highest posterior density region in the context of data augmentation. The notion of the highest posterior density region and the data augmentation algorithm are reviewed. The sampling-based approach for calculating the content and the boundary of the highest posterior density region is then presented. The method is illustrated in the context of right-censored regression data.

通过数据增广计算后验分布AI 解读

The idea of data augmentation arises naturally in missing value problems, as exemplified by the standard ways of filling in missing cells in balanced two-way tables. Thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze. This device is used to great advantage by the EM algorithm (Dempster, Laird, and Rubin 1977) in solving maximum likelihood problems. In situations when the likelihood cannot be approximated closely by…

随机删失数据风险函数变核估计的一则注记AI 解读

In a recent paper (Tanner and Wong, 1983b), a family of data-based nonparametric hazard estimators was introduced. Several of these estimators were studied in an extensive simulation experiment. The estimator which allows for variable bandwidth was found to have a superior performance. In this note, sufficient conditions for the variable kernel estimator to be strongly consistent are presented.

随机删失数据的风险函数核估计AI 解读

By convolution smoothing of the empirical hazards, a kernel estimate of the hazard function from censored data is obtained. Small and large sample expressions for the mean and the variance of the estimator are given. Conditions for asymptotic normality are investigated using the Hajek projection method.