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非识别模型中的信念更新AI 解读

A Bayesian analysis of a nonidentified model is always possible if a proper prior on all the parameters is specified. There is, however, no Bayesian free lunch. The “price” is that there exist quantities about which the data are uninformative, i.e., their marginal prior and posterior distributions are identical. In the case of improper priors the analysis is problematic—resulting posteriors can be improper. This study investigates both proper and improper cases through a…

两阶段层级模型中的三目标估计AI 解读

Summary The beauty of the Bayesian approach is its ability to structure complicated models, inferential goals and analyses. To take full advantage of it, methods should be linked to an inferential goal via a loss function. For example, in the two-stage, compound sampling model the posterior means are optimal under squared error loss. However, they can perform poorly in estimating the histogram of the parameters or in ranking them. ‘Triple-goal’ estimates are motivated by the…

小区域估计中贝叶斯与频率学派的误差度量AI 解读

Summary This paper compares analytically and empirically the frequentist and Bayesian measures of error in small area estimation. The model postulated is the nested error regression model which allows for random small area effects to represent the joint effect of small area characteristics that are not accounted for by the fixed regressor variables. When the variance components are known, then, under a uniform prior for the regression coefficients and normality of the error…

自相关误差下的加性非参数回归AI 解读

Summary A Bayesian approach is presented for nonparametric estimation of an additive regression model with autocorrelated errors. Each of the potentially non-linear components is modelled as a regression spline using many knots, while the errors are modelled by a high order stationary autoregressive process parameterized in terms of its autocorrelations. The distribution of significant knots and partial autocorrelations is accounted for using subset selection. Our approach…

In this paper, Markov chain Monte Carlo sampling methods are exploited to provide a unified, practical likelihood-based framework for the analysis of stochastic volatility models. A highly effective method is developed that samples all the unobserved volatilities at once using an approximating offset mixture model, followed by an importance reweighting procedure. This approach is compared with several alternative methods using real data. The paper also develops…

住宅成交数据的时空建模AI 解读

This article focuses on the location, time, and spatio-temporal components associated with suitably aggregated data to improve prediction of individual asset values. Such effects are introduced in the context of hierarchical models, which we find more natural than attempting to model covariance structure. Indeed, our cross-sectional database, a sample of 7,936 transactions for 49 subdivisions over a 10-year period in Baton Rouge, Louisiana, precludes covariance modeling. A…

随机波动模型的实证应用AI 解读

This paper studies the empirical performance of stochastic volatility models for twenty years of weekly exchange rate data for four major currencies. We concentrate on the effects of the distribution of the exchange rate innovations for both parameter estimates and for estimates of the latent volatility series. The density of the log of squared exchange rate innovations is modelled as a flexible mixture of normals. We use three different estimation techniques: quasi-maximum…

杂论：非线性问题中的序贯设计AI 解读

In this paper we study the consistency of parameter estimators in sequential nonlinear design. Our main tool is a recursion which holds for the sequence of posterior variances. Under mild conditions, we establish the strong consistency of Bayes estimators in stochastic regression models which cover a broad range of nonlinear problems. Four examples from nonlinear sequential design are discussed.

小波中的多重收缩与子集选择AI 解读

This paper discusses Bayesian methods for multiple shrinkage estimation in wavelets. Wavelets are used in applications for data denoising, via shrinkage of the coefficients towards zero, and for data compression, by shrinkage and setting small coefficients to zero. We approach wavelet shrinkage by using Bayesian hierarchical models, assigning a positive prior probability to the wavelet coefficients king zero. The resulting estimator for the wavelet coefficients is a multiple…

多变量 Probit 模型分析AI 解读

This paper provides a practical simulation-based Bayesian and non-Bayesian analysis of correlated binary data using the multivariate probit model. The posterior distribution is simulated by Markov chain Monte Carlo methods and maximum likelihood estimates are obtained by a Monte Carlo version of the EM algorithm. A practical approach for the computation of Bayes factors from the simulation output is also developed. The methods are applied to a dataset with a bivariate binary…

空间统计中的泊松／伽马随机场模型AI 解读

Doubly stochastic Bayesian hierarchical models are introduced to account for uncertainty and spatial variation in the underlying intensity measure for point process models. Inhomogeneous gamma process random fields and, more generally, Markov random fields with infinitely divisible distributions are used to construct positively autocorrelated intensity measures for spatial Poisson point processes; these in turn are used to model the number and location of individual events.…

SO(N) 上的反卷积密度估计AI 解读

This paper develops nonparametric deconvolution density estimation over $SO(N)$, the group of $N \times N$ orthogonal matrices of determinant 1. The methodology is to use the group and manifold structures to adapt the Euclidean deconvolution techniques to this Lie group environment. This is achieved by employing the theory of group representations explicit to $SO(N)$. General consistency results are obtained with specific rates of convergence achieved under sufficient…

受限因变量过程的模拟似然推断AI 解读

This paper looks at the problem of performing likelihood inference for limited dependent processes. Throughout we use simulation to carry out either classical inference through a simulated score method (simulated EM algorithm) or Bayesian analysis. A common theme is to develop computationally robust methods which are likely to perform well for any time series problem. The central tools we use to deal with the time series dimension of the models are the scan sampler and the…

通过间接推断估计随机波动率模型AI 解读

We propose as a tool for the estimation of stochastic volatility models two indirect inference estimators based on the choice of an autoregressive auxiliary model and an ARMA auxiliary model, respectively. These choices make the auxiliary parameter easy to estimate and at the same time allow the derivation of optimal indirect inference estimators. The results of some Monte Carlo experiments provide evidence that the indirect inference estimators perform well in finite…

使用吉布斯抽样进行 GARCH 模型的贝叶斯推断AI 解读

This paper explains how the Gibbs sampler can be used to perform Bayesian inference on GARCH models. Although the Gibbs sampler is usually based on the analyti-cal knowledge of the full conditional posterior densities, such knowledge is not available in regression models with GARCH errors. We show that the Gibbs sampler can be combined with a unidimensional deterministic integration rule applied to each coordinate of the poste-rior density. The full conditional densities are…

纵向数据的半参数随机混合模型AI 解读

We consider inference for a semiparametric stochastic mixed model for longitudinal data. This model uses parametric fixed effects to represent the covariate effects and an arbitrary smooth function to model the time effect and accounts for the within-subject correlation using random effects and a stationary or nonstationary stochastic process. We derive maximum penalized likelihood estimators of the regression coefficients and the nonparametric function. The resulting…

死刑陪审员的公正性：不同层级与缺失机制下的贝叶斯模型比较AI 解读

Jurors who are opposed to the death penalty are excluded from serving on trials in which the defendant may be sentenced to death. The exclusion of such jurors from death-penalty trials raises some concern about the fairness of these juries in deciding the guilt or innocence of a defendant. This article uses data from a survey of behaviors and beliefs of jurors conducted at the conclusion of non–capital offense trials to study this issue. A Bayesian hierarchical model is…

含间歇观测时变二元协变量的删失生存数据分析AI 解读

In survival analyses that include a time-dependent covariate, the standard partial likelihood approach is often complicated by the fact that the necessary observations of the time-dependent covariate are not always available for the subjects in each risk set. In this article, we consider the situation of a binary time-dependent covariate. We specify a longitudinal model for the binary covariate with missing observations and a proportional hazards model for survival time…

识别多元时间序列模型的统一方法AI 解读

This article proposes a Bayesian procedure for simultaneous identification of the Kronecker indices and model parameters of a multivariate linear system. The model parameters include the starting values and innovations of the system so that the series considered may be co-integrated or non-invertible. The procedure uses some recent developments in stochastic search variable selection in linear regression analysis and Markov chain Monte Carlo methods in statistical computing.…

马尔可夫链蒙特卡洛的辅助变量方法及应用AI 解读

Suppose that one wishes to sample from the density π(x) using Markov chain Monte Carlo (MCMC). An auxiliary variable u and its conditional distribution π(u|x) can be defined, giving the joint distribution π(x, u) = π(x)π(u|x). A MCMC scheme that samples over this joint distribution can lead to substantial gains in efficiency compared to standard approaches. The revolutionary algorithm of Swendsen and Wang is one such example. Besides reviewing the Swendsen-Wang algorithm and…

利用链路计数数据进行网络流量的贝叶斯推断AI 解读

We study Bayesian models and methods for analysing network traffic counts in problems of inference about the traffic intensity between directed pairs of origins and destinations in networks. This is a class of problems very recently discussed by Vardi in a 1996 JASA article and is of interest in both communication and transportation network studies. The current article develops the theoretical framework of variants of the origin-destination flow problem and introduces…

图像处理中的边缘保持平滑器AI 解读

Classical smoothers have limited usefulness in image processing, because sharp “edges” tend to be blurred. There is a literature on edge-preserving smoothers, but these all require moderately large “smooth stretches.” Here we discuss an approach to this problem called “sigma filtering” and propose an improvement based on running M estimation. Both computational and theoretical aspects are developed. For image processing, the methods have a niche between standard filtering…

多元时间序列模型识别的统一方法AI 解读

This article proposes a Bayesian procedure for simultaneous identification of the Kronecker indices and model parameters of a multivariate linear system. The model parameters include the starting values and innovations of the system so that the series considered may be co-integrated or non-invertible. The procedure uses some recent developments in stochastic search variable selection in linear regression analysis and Markov chain Monte Carlo methods in statistical computing.…

死刑陪审员的公正性：不同层级与缺失机制的贝叶斯模型比较AI 解读

Jurors who are opposed to the death penalty are excluded from serving on trials in which the defendant may be sentenced to death. The exclusion of such jurors from death-penalty trials raises some concern about the fairness of these juries in deciding the guilt or innocence of a defendant. This article uses data from a survey of behaviors and beliefs of jurors conducted at the conclusion of non–capital offense trials to study this issue. A Bayesian hierarchical model is…