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贝叶斯极小极大估计量的构造AI 解读

Bayes estimation of the mean of a multivariate normal distribution is considered under quadratic loss. We show that, when particular spherical priors are used, the superharmonicity of the square root of the marginal density provides a viable method for constructing (possibly proper) Bayes (and admissible) minimax estimators. Examples illustrate the theory; most notably it is shown that a multivariate Student-$t$ prior yields a proper Bayes minimax estimate.

选择模型的稳健贝叶斯分析AI 解读

Selection models arise when the data are selected to enter the sample only if they occur in a certain region of the sample space. When this selection occurs according to some probability distribution, the resulting model is often instead called a weighted distribution model. In either case the "original" density becomes multiplied by a "weight function" $w(x)$. Often there is considerable uncertainty concerning this weight function; for instance, it may be known only that $w$…

可能错误设定模型下贝叶斯估计的渐近行为AI 解读

We prove that the posterior distribution in a possibly incorrect parametric model a.s. concentrates in a strong sense on the set of pseudotrue parameters determined by the true distribution. As a consequence, we obtain in the case of a unique pseudotrue parameter the strong consistency of pseudo-Bayes estimators w.r.t. general loss functions. Further, we present a simple example based on normal distributions and having two different pseudotrue parameters, where pseudo-Bayes…

具有马尔可夫状态切换的随机波动模型AI 解读

This article presents a new way of modeling time-varying volatility. We generalize the usual stochastic volatility models to encompass regime-switching properties. The unobserved state variables are governed by a first-order Markov process. Bayesian estimators are constructed by Gibbs sampling. High-, medium- and low-volatility states are identified for the Standard and Poor's 500 weekly return data. Persistence in volatility is explained by the persistence in the low- and…

典型求职搜寻模型的贝叶斯分析AI 解读

Bayesian analysis for a simple but widely applied dynamic programming model is obtained. The setting is the prototypal job-search model. The general case of wage and duration data, with potential censoring, is studied. The optimality condition implied by the dynamic programming setup is fully imposed. The posterior distribution reveals a 'ridge' reflecting the characteristic nonstandard nature of the inference problem. Marginal distributions and moments are obtained in a…

可交换信念的调整AI 解读

We consider geometrically the practical, theoretical and computational treatment of second-order exchangeability within Bayes linear analysis. We establish Bayes linear sufficiency for sample means through the representation theorem for second-order exchangeable beliefs. Interrelationships between collections of Bayes linear belief adjustments are analysed through the resolution transforms induced by a second-order exchangeable sample. It is shown that the resolution…

SUMMARY We propose a general Bayesian method of comparing models. The approach is based on the Kullback-Leibler distance between two families of models, one nested within the other. For each parameter value of a full model, we compute the projection of the model to the restricted parameter space and the corresponding minimum distance. From the posterior distribution of the minimum distance, we can judge whether or not a more parsimonious model is appropriate. We show how the…

This paper presents a new methodological approach for carrying out Bayesian inference about dynamic models for exponential family observations. The approach is simulationbased and involves the use of Markov chain Monte Carlo techniques. A Metropolis- Hastings algorithm is combined with the Gibbs sampler in repeated use of an adjusted version of normal dynamic linear models. Different alternative schemes based on sampling from the system disturbances and state parameters…

正态线性模型的 Schwarz 准则及相关方法AI 解读

In this paper we derive Schwarz's information criterion and two modifications for choosing fixed effects in normal linear mixed models. The first modification allows an arbitrary, possibly informative, prior for the parameter of interest. Replacing this prior with the normal, unit-information, prior of Kass & Wasserman (1995) and the generalised Cauchy prior of Jeffreys (1961) yields the usual Schwarz criterion and a second modification, respectively. Under the null…

约束参数问题贝叶斯分析的蒙特卡洛方法AI 解读

Constraints on the parameters in a Bayesian hierarchical model typically make Bayesian computation and analysis complicated. Posterior densities that contain analytically intractable integrals as normalising constants depending on the hyperparameters often make implementation of Gibbs sampling or the Metropolis algorithms difficult. By using reweighting mixtures (Geyer, 1995), we develop alternative simulation-based methods to determine properties of the desired Bayesian…

模型选择：最小后验预测损失方法AI 解读

Model choice is a fundamental and much discussed activity in the analysis of datasets. Nonnested hierarchical models introducing random effects may not be handled by classical methods. Bayesian approaches using predictive distributions can be used though the formal solution, which includes Bayes factors as a special case, can be criticised. We propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the…

用于小区域估计的广义线性模型AI 解读

Bayesian methods have been used quite extensively in recent years for solving small-area estimation problems. Particularly effective in this regard has been the hierarchical or empirical Bayes approach, which is especially suitable for a systematic connection of local areas through models. However, the development to date has mainly concentrated on continuous-valued variates. Often the survey data are discrete or categorical, so that hierarchical or empirical Bayes…

基于贝叶斯规则与贝叶斯因子的非线性小波收缩AI 解读

Wavelet shrinkage, the method proposed by the seminal work of Donoho and Johnstone is a disarmingly simple and efficient way of denoising data. Shrinking wavelet coefficients was proposed from several optimality criteria. In this article a wavelet shrinkage by coherent Bayesian inference in the wavelet domain is proposed. The methods are tested on standard Donoho-Johnstone test functions.

厚尾与偏态的贝叶斯建模AI 解读

We consider a Bayesian analysis of linear regression models that can account for skewed error distributions with fat tails. The latter two features are often observed characteristics of empirical datasets, and we formally incorporate them in the inferential process. A general procedure for introducing skewness into symmetric distributions is first proposed. Even though this allows for a great deal of flexibility in distributional shape, tail behavior is not affected.…

通过模型聚类识别含杂波的空间点过程特征AI 解读

We consider the problem of detecting features, such as minefields or seismic faults, in spatial point processes when there is substantial clutter. We use model-based clustering based on a mixture model for the process, in which features are assumed to generate points according to highly linear multivariate normal densities, and the clutter arises according to a spatial Poisson process. Nonlinear features are represented by several densities, giving a piecewise linear…

广义线性混合模型中的预测标准误AI 解读

The unconditional mean squared error of prediction (UMSEP) is widely used as a measure of prediction variance for inferences concerning linear combinations of fixed and random effects in the classical normal theory mixed model. But the UMSEP is inappropriate for generalized linear mixed models where the conditional variance of the random effects depends on the data. When the random effects describe variation between independent small domains and domain-specific prediction is…

用于诊断马尔可夫链蒙特卡洛收敛的耦合再生方案AI 解读

Here I propose a convergence diagnostic for Markov chain Monte Carlo (MCMC) algorithms based on couplings of a Markov chain with an auxiliary chain that is periodically restarted from a fixed parameter value. The diagnostic provides a mechanism for estimating the specific constants governing the rate of convergence of geometrically and uniformly ergodic chains, and provides a lower bound on the effective sample size of a MCMC run. It also provides a simple procedure for…

稳健二元非参数回归的贝叶斯方法AI 解读

This article presents a Bayesian approach to binary nonparametric regression that assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions. The article makes the following contributions. First, a comprehensive approach is presented in which the function estimates are smoothing splines with the smoothing parameters integrated out and the estimates are made robust to outliers. Second, the approach can…

美国职业橄榄球联赛比分的状态空间模型AI 解读

This article develops a predictive model for National Football League (NFL) game scores using data from the period 1988–1993. The parameters of primary interest—measures of team strength—are expected to vary over time. Our model accounts for this source of variability by modeling football outcomes using a state-space model that assumes team strength parameters follow a first-order autoregressive process. Two sources of variation in team strengths are addressed in our model;…

Generalized Linear Models.- Linear Models, Vector Spaces, and Residual Likelihood.- An Assessment of Approximate Maximum Likelihood Estimators in Generalized Linear Models.- Scaled Link Functions for Heterogeneous Ordinal Response Data.- Longitudinal Data Analysis.- Software Design for Longitudinal Data Analysis.- Asymptotic Properties of Nonlinear Mized-Effects Models.- Structured Antedependence Models for Longitudinal Data.- Effect of Confounding and Other Misspecification…

厚尾与偏度的贝叶斯建模AI 解读

We consider a Bayesian analysis of linear regression models that can account for skewed error distributions with fat tails.The latter two features are often observed characteristics of empirical data sets, and we will formally incorporate them in the inferential process.A general procedure for introducing skewness into symmetric distributions is rst proposed.Even though this allows for a great deal of exibility in distributional shape, tail behaviour is not aected.In…

稳健二元非参数回归的贝叶斯方法AI 解读

This article presents a Bayesian approach to binary nonparametric regression that assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions. The article makes the following contributions. First, a comprehensive approach is presented in which the function estimates are smoothing splines with the smoothing parameters integrated out and the estimates are made robust to outliers. Second, the approach can…

摘要暂缺

非平稳时间序列模型中后验密度的大样本性质、贝叶斯信息准则与似然原则AI 解读

Asymptotic normality of posterior is a well understood result for dynamic as well as non-dynamic models based on sets of abstract conditions that are hard to verify especially for the case of nonstationarity. In this paper the authors provide a set of conditions by which they can relatively easily prove the asymptotic posterior normality under quite general situations of possible nonstationarity. This result reinforces and generalizes the validity of inference based on the…