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条件高斯状态空间模型中的马尔可夫链蒙特卡洛AI 解读

A Bayesian analysis is given for a state space model with errors that are finite mixtures of normals and with coefficients that can assume a finite number of different values. A sequence of indicator variables determines which components the errors belong to and the values of the coefficients. The computation is carried out using Markov chain Monte Carlo, with the indicator variables generated without conditioning on the states. Previous approaches use the Gibbs sampler to…

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…

地震时间演化的贝叶斯分析AI 解读

We adopt a Bayesian approach to analyze the occurrence times of seismic events and their magnitudes. We choose an epidemic model for the process of occurrence times conditional on the observed magnitude values. The locations of, and dependencies between, the model parameters are determined on the basis of historical and physical information. The overall prior variability is deliberately made diffuse. We generate samples from the joint posterior distribution of the model…

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…

群体药代动力学模型中协变量的贝叶斯建模AI 解读

Pharmacokinetic (PK) models describe how the concentrations of a drug and its metabolite vary with time. Population PK models identify and quantify sources of between-individual variability in observed concentrations. Crucial to this aim is the identification of those covariates (i.e., individual-specific characteristics) responsible for explaining the variability. In this article we discuss how covariate modeling can be carried out for population PK models. We argue that…

通过正交化模型混合进行预测AI 解读

We introduce an approach and algorithms for model mixing in large prediction problems with correlated predictors. We focus on the choice of predictors in linear models, and mix over possible subsets of candidate predictors. Our approach is based on expressing the space of models in terms of an orthogonalization of the design matrix. Advantages are both statistical and computational. Statistically, orthogonalization often leads to a reduction in the number of competing models…

随机序约束下生存概率的贝叶斯推断AI 解读

In the statistical analysis of survival data arising from two populations, it often happens that the analyst knows, a priori, that the life lengths in one population are stochastically shorter than those in the other. Nevertheless, survival probability estimates, if determined separately from the corresponding samples, may not be consistent with this prior assumption, because of inherent statistical variability in the observations. This problem has been considered in a…

基于方向邻域的含噪图像上下文分类AI 解读

The directional neighborhoods approach (DNA) to classifying pixels and reconstructing images from remotely sensed noisy data is a newly proposed computer-intensive procedure that is partly Bayesian and partly data analytic. It uses the observational data to select an optimal, generally asymmetric, but relatively homogeneous neighborhood for contextually classifying pixels. A criterion for “homogeneity of neighborhood” is developed. DNA involves two stages: a zero-neighbor…

统计决策理论导论AI 解读

The Bayesian revolution in statistics -- where statistics is integrated with decision making in areas such as management, public policy, engineering, and clinical medicine -- is here to stay. Introduction to Statistical Decision Theory states the case and in a self-contained, comprehensive way shows how the approach is operational and relevant for real-world decision making under uncertainty. Starting with an extensive account of the foundations of decision theory, the…

通过正交化模型混合进行预测AI 解读

We introduce an approach and algorithms for model mixing in large prediction problems with correlated predictors. We focus on the choice of predictors in linear models, and mix over possible subsets of candidate predictors. Our approach is based on expressing the space of models in terms of an orthogonalization of the design matrix. Advantages are both statistical and computational. Statistically, orthogonalization often leads to a reduction in the number of competing models…

噪声图像上下文分类的方向邻域方法AI 解读

The directional neighborhoods approach (DNA) to classifying pixels and reconstructing images from remotely sensed noisy data is a newly proposed computer-intensive procedure that is partly Bayesian and partly data analytic. It uses the observational data to select an optimal, generally asymmetric, but relatively homogeneous neighborhood for contextually classifying pixels. A criterion for “homogeneity of neighborhood” is developed. DNA involves two stages: a zero-neighbor…

地震时间演化的贝叶斯分析AI 解读

We adopt a Bayesian approach to analyze the occurrence times of seismic events and their magnitudes. We choose an epidemic model for the process of occurrence times conditional on the observed magnitude values. The locations of, and dependencies between, the model parameters are determined on the basis of historical and physical information. The overall prior variability is deliberately made diffuse. We generate samples from the joint posterior distribution of the model…

随机序约束下生存概率的贝叶斯推断AI 解读

In the statistical analysis of survival data arising from two populations, it often happens that the analyst knows, a priori, that the life lengths in one population are stochastically shorter than those in the other. Nevertheless, survival probability estimates, if determined separately from the corresponding samples, may not be consistent with this prior assumption, because of inherent statistical variability in the observations. This problem has been considered in a…

Ritov 贝叶斯方法与 CUSUM 极小极大性质的连续时间札记AI 解读

We consider, in a Bayesian framework, the model $W_t = B_t + \theta (t - \nu)^+$, where B is a standard Brownian motion, $\theta$ is arbitrary but known and $\nu$ is the unknown change-point. We transfer the construction of Ritov to this continuous time setup and show that the corresponding Bayes problems can be reduced to generalized parking problems.

贝叶斯计量经济学：最初二十年AI 解读

This paper sketches the history of how Bayesian inference was adopted and utilized in econometrics during its first 20 years. It focuses on the causes of the Bayesian movement, the ways in which Bayesian inference was applied, the problems that the application was intended to solve, and the results achieved. It shows that Bayesian research has largely followed mainstream econometric development as far as the major econometric ideas and methods are concerned and that Bayesian…

计量经济学中的马尔可夫链蒙特卡洛模拟方法AI 解读

We present several Markov chain Monte Carlo simulation methods that have been widely used in recent years in econometrics and statistics. Among these is the Gibbs sampler, which has been of particular interest to econometricians. Although the paper summarizes some of the relevant theoretical literature, its emphasis is on the presentation and explanation of applications to important models that are studied in econometrics. We include a discussion of some implementation…

预测更新方法及其在贝叶斯分类中的应用AI 解读

SUMMARY We propose algorithms based on random draws from predictive distributions of unknown quantities (missing values, for instance). This procedure can either be iterative, which is a special variation of the Gibbs sampler, or be sequential, which is a variation of sequential imputation. In the latter case one can update the posterior distribution with new observations easily. The methods proposed have intuitive statistical implications and can be generalized to…

贝叶斯线性充分性与专家后验评估系统AI 解读

SUMMARY Data arising in the form of expert assessments are received by a decision maker. The decision maker is required to estimate a set of unknown quantities, and receives expert assessments at varying levels of accuracy, on samples of the quantities of interest. We present a Bayes linear analysis of this problem. In the absence of other assessments, the decision maker will accept as his or her current estimate of any single quantity the most accurate received assessment…

计量经济模型的确定AI 解读

This paper is concerned with model determination methods and their use in the prediction of economic time series. The methods are Bayesian but they can be justified by classical arguments as well. The paper continues some recent work on Bayesian asymptotic, develops embedding techniques for vector martingales, and implements the modeling ideas in a multivariate regression framework that includes Bayesian vector autoregression (BVAR's) and reduced rank regressions (RRR's). It…

预测分布的渐近性质AI 解读

Second-order asymptotic theory of predictive distributions is investigated. It is shown that estimative distributions with asymptotically efficient estimators can be improved to predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. Predictive distributions can be constructed by shifting estimative distributions in a direction orthogonal to the model. The average Kullback-Leibler divergence from the…

广义线性模型的近似贝叶斯因子与模型不确定性处理AI 解读

Ways of obtaining approximate Bayes factors for generalised linear models are described, based on the Laplace method for integrals. We propose a new approximation which uses only the output of standard computer programs for estimating generalised linear models, this appears to be quite accurate. A reference set of proper priors is suggested, both to represent the situation where there is not much prior information, and to assess the sensitivity of the results to the prior…

一组筛查程序最优排序的贝叶斯模型AI 解读

Bergman & Gittins (1985) propose a screen design problem in which a collection of screens for therapeutic activity and toxicity of pharmaceutical compounds is to be sequenced. They describe conditions under which a natural ordering heuristic based on failure probability per unit cost for each screen is optimal. We propose a Bayesian model in which measures of activity and toxicity are given a joint prior density. The above conditions for optimality are satisfied for this…

使多个参数函数的贝叶斯推断具有频率学有效性的先验AI 解读

We characterise priors which match, up to O(n−1), the posterior joint cumulative distribution function of multiple parametric functions with the corresponding frequentist cumulative distribution function. This work extends and unifies the work of Ghosh & Mukerjee (1993) and Datta & Ghosh (1995a) on the topic of probability-matching priors. A set of necessary and sufficient conditions is obtained for the above characterisation. Some of these conditions depend only on the…

随机区组设计的半参数贝叶斯模型AI 解读

A model is proposed for a Bayesian semiparametric analysis of randomised block experiments. The model is a hierarchical model in which a Dirichlet process is inserted at the middle stage for the distribution of the block effects. This model allows an arbitrary distribution of block effects, and it results in effective estimates of treatment contrasts, block effects and the distribution of block effects. An effective computational strategy is presented for describing the…