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周期成分动态线性模型中的贝叶斯推断AI 解读

Dynamic linear models (DLM's) with time-varying cyclical components are developed for the analysis of time series with persistent though time-varying cyclical behavior. The development covers inference on wavelengths of possibly several persistent cycles in nonstationary time series, permitting explicit time variation in amplitudes and phases of component waveforms, decomposition of stochastic inputs into purely observational noise and innovations that impact on the waveform…

利用混合模型进行贝叶斯密度估计与推断AI 解读

We describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes. These models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions. Efficient simulation methods are used to approximate various prior, posterior, and predictive distributions. This allows for direct inference on a variety of practical issues, including…

用混合分布近似后验分布AI 解读

SUMMARY Kernel density estimation techniques are used to smooth simulated samples from importance sampling function approximations to posterior distributions, resulting in revised approximations that are mixtures of standard parametric forms, usually multivariate normal or T-distributions. Adaptive refinement of such mixture approximations involves repeating this process to home-in successively on the posterior. In fairly low dimensional problems, this provides a general and…

数据库错误检测与预测AI 解读

We develop and analyze models for a class of problems involving inferences about uncertain numbers of errors in data bases. In particular, we study two error detection methods. In the duplicate performance method, all items in a data base are processed by two individuals (or machines), and the resulting records are compared to find disagreements, which are then resolved. In the known errors method, a data base is first extended to include additional items known to be in…

数据库错误检测与预测AI 解读

We develop and analyze models for a class of problems involving inferences about uncertain numbers of errors in data bases. In particular, we study two error detection methods. In the duplicate performance method, all items in a data base are processed by two individuals (or machines), and the resulting records are compared to find disagreements, which are then resolved. In the known errors method, a data base is first extended to include additional items known to be in…

动态线性模型的诊断方法AI 解读

In time series analysis using dynamic linear models, retrospective analysis involves the calculation of filtered, or smoothed, distributions for state parameters in the past. We develop and illustrate novel results that are useful in retrospective assessment of the influence of individual observations on such distributions. In particular, new and computationally simple filtering equations are derived for past state parameters based on leaving out one observation at a time,…

核密度估计与边缘化一致性AI 解读

Kernel density estimates, as commonly applied, generally have no exact model-based interpretation since they violate conditions that define coherent joint distributions. The issue of marginalization consistency is considered here. It is shown that most commonly used kernel functions violate this condition. It is also shown that marginalization consistency holds only for classes of kernel estimates based on Laplacian, or double-exponential kernels whose window width…

动态线性模型诊断AI 解读

In time series analysis using dynamic linear models, retrospective analysis involves the calculation of filtered, or smoothed, distributions for state parameters in the past. We develop and illustrate novel results that are useful in retrospective assessment of the influence of individual observations on such distributions. In particular, new and computationally simple filtering equations are derived for past state parameters based on leaving out one observation at a time,…

核密度估计与边缘化一致性AI 解读

Kernel density estimates, as commonly applied, generally have no exact model-based interpretation since they violate conditions that define coherent joint distributions. The issue of marginalization consistency is considered here. It is shown that most commonly used kernel functions violate this condition. It is also shown that marginalization consistency holds only for classes of kernel estimates based on Laplacian, or double-exponential kernels whose window width…

贝叶斯模型监测AI 解读

SUMMARY A simple method of monitoring the predictive performance of a class of Bayesian models is introduced. The models involve sequential analyses of sequences of observations and are appropriate for a variety of monitoring and forecasting applications. For any given model, the monitoring technique is based on a comparison of the predictive ability of the model, measured by the observed values of predictive densities, with that of a single alternative. The alternative is…

贝叶斯预测模型的监控与适应AI 解读

Practical aspects of a new technique for monitoring and controlling the predictive performance of Bayesian forecasting models are discussed. The basic features of the approach to model monitoring introduced in a general setting in West (1986) are described and extended to a wide class of dynamic, nonnormal, and nonlinear Bayesian forecasting models. An associated method of automatically detecting and rejecting outliers and adapting models to abrupt structural changes in the…

贝叶斯线性回归中的异常值模型与先验分布AI 解读

SUMMARY Bayesian inference in regression models is considered using heavy-tailed error distributions to accommodate outliers. The particular class of distributions that can be constructed as scale mixtures of normal distributions are examined and use is made of them as both error models and prior distributions in Bayesian linear modelling, including simple regression and more complex hierarchical models with structured priors depending on unknown hyperprior parameters.