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汇率目标区模型：贝叶斯评估AI 解读

This paper develops a Bayesian approach to estimating exchange rate target zone models and rational expectations models in general. It also introduces a simultaneous-equation target zone model that incorporates stochastic realignment risk. Using FF/DM and IL/DM exchange rate data, we find that the signing of the 1987 Basle-Nyborg Agreement reduces both the magnitude and the likelihood of a central parity realignment, while the lagged exchange rate deviation from its central…

利用辅助变量对贝叶斯非共轭与层级模型进行 Gibbs 抽样AI 解读

Summary We demonstrate the use of auxiliary (or latent) variables for sampling non-standard densities which arise in the context of the Bayesian analysis of non-conjugate and hierarchical models by using a Gibbs sampler. Their strategic use can result in a Gibbs sampler having easily sampled full conditionals. We propose such a procedure to simplify or speed up the Markov chain Monte Carlo algorithm. The strength of this approach lies in its generality and its ease of…

利用平滑样条进行广义可加混合模型推断AI 解读

Summary Generalized additive mixed models are proposed for overdispersed and correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs. This class of models allows flexible functional dependence of an outcome variable on covariates by using nonparametric regression, while accounting for correlation between observations by using random effects. We estimate nonparametric functions by using smoothing splines and jointly estimate…

学习下随机过程的贝叶斯表示：重访 de Finetti 定理AI 解读

A probability distribution governing the evolution of a stochastic process has infinitely many Bayesian representations of the form mu = integral operator [subscript theta] mu[subscript theta] delta lambda (theta). Among these, a natural representation is one whose components (mu[subscript theta]'s) are 'learnable' (one can approximate mu[subscript theta] by conditioning mu on observation of the process) and 'sufficient for prediction' (mu[subscript theta]'s predictions are…

贝叶斯套利阈值分析AI 解读

A Bayesian estimation procedure is developed for estimating multiple-regime (multiple-threshold) error-correction models appropriate for deviations from financial arbitrage relationships. This approach has clear advantages over classical stepwise threshold autoregressive analysis. Unlike many other applications of threshold models, the knowledge of some costs involved in setting up arbitrage positions allows us to specify an informative prior. To illustrate the Bayesian…

美国失业率的动态非对称性AI 解读

The authors examine dynamic asymmetries in U.S. unemployment using nonlinear time series models and Bayesian methods. They find strong statistical evidence in favor of a two-regime threshold autoregressive model. Empirical results indicate that, once parameter and model uncertainty are both taken into account, there are economically interesting asymmetries in the unemployment rate. One finding of particular interest is that shocks that lower the unemployment rate tend to…

杂论：含加性噪声的时间序列AI 解读

We put forward a state space model where the unobservable state variable can be any Gaussian stochastic process. We discuss both maximum likelihood estimation and Bayesian inference for this generalised model. The methodology developed in this paper is particularly important for the class of long memory plus noise models. Armed with the simulation smoother introduced in this paper, we can estimate a class of non-Gaussian measurement time series models with long memory in the…

频率学派与贝叶斯推断尾概率的简便通用近似公式AI 解读

We describe a simple general formula for approximating the p-value for testing a scalar parameter in the presence of nuisance parameters. The formula covers both frequentist and Bayesian contexts and does not require explicit nuisance parameterisation. Implementation is discussed in terms of computer algebra packages. Examples are given and the relationship to Barndorff-Nielsen's approximation is discussed.

采用 CAR(1) 分布的层级模型后验分布AI 解读

We examine properties of the conditional autoregressive model, or CAR(1) model, which is commonly used to represent regional effects in Bayesian analyses of mortality rates. We consider a Bayesian hierarchical linear mixed model where the fixed effects have a vague prior such as a constant prior and the random effect follows a class of CAR(1) models including those whose joint prior distribution of the regional effects is improper. We give sufficient conditions for the…

贝叶斯形态学：快速无监督贝叶斯图像分析AI 解读

We consider the problems of image segmentation and classification, and image restoration when the true image is made up of a small number of (unordered) colors. Our emphasis is on both performance and speed; speed has become increasingly important for analyzing large images and multispectral images with many bands, processing large image databases, real-time or near realtime image analysis, and the online analysis of video. Bayesian image analysis provides an elegant…

非嵌套假设检验的默认贝叶斯因子AI 解读

Bayesian hypothesis testing for nonnested hypotheses is studied, using various “default” Bayes factors, such as the fractional Bayes factor, the median intrinsic Bayes factor, and the encompassing and expected intrinsic Bayes factors. The different default methods are first compared with each other and with the p value in normal one-sided testing, to illustrate the basic issues. General results for one-sided testing in location and scale models are then presented. The…

购买时点的动态模型及其直销应用AI 解读

Predicting changes in individual customer behavior is an important element for success in any direct marketing activity. In this article we develop a hierarchical Bayes model of customer interpurchase times based on the generalized gamma distribution. The model allows for both cross-sectional and temporal heterogeneity, with the latter introduced through the component mixture model dependent on lagged covariates. The model is applied to personal investment data to predict…

重尾实用指南：统计技术与应用AI 解读

Part 1 Applications: heavy tailed probability distributions in the World Wide Web, M.E. Crovella et al self-similarity and heavy tails - structural modelling of network traffic, W. Willinger et al heavy tails in high-frequency financial data, U.A. Muller et al stable paretian modelling in finance - some empirical and theoretical aspects, S. Mittnik et al risk management and quantile estimation, F. Bassi et al. Part 2 Time series: analyzing stable time series, R.J. Adler et…

贝叶斯形态学：快速无监督贝叶斯图像分析AI 解读

We consider the problems of image segmentation and classification, and image restoration when the true image is made up of a small number of (unordered) colors. Our emphasis is on both performance and speed; speed has become increasingly important for analyzing large images and multispectral images with many bands, processing large image databases, real-time or near realtime image analysis, and the online analysis of video. Bayesian image analysis provides an elegant…

估计置信度方法中的 Brown 悖论AI 解读

A widely held notion of classical conditional theory is that statistical inference in the presence of ancillary statistics should be independent of the distribution of those ancillary statistcs. In this paper, ancillary paradoxes which contradict this notion are presented for two scenarios involving confidence estimation. These results are related to Brown’s ancillary paradox in point estimation. Moreover, the confidence coefficient, the usual constant coverage probability…

通过扩展 Johnson 充分性公设刻画右中性先验AI 解读

In this paper we present a new characterization and perspective on a neutral to the right prior. This characterization is based on a sequence of predictive laws which provides explicitly the posterior parameters and Bayes estimators for such a prior.

计数过程的非参数贝叶斯估计量AI 解读

This paper is concerned with nonparametric Bayesian inference of the Aalen’s multiplicative counting process model. For a desired nonparametric prior distribution of the cumulative intensity function, a class of Lévy processes is considered, and it is shown that the class of Lévy processes is conjugate for the multiplicative counting process model, and formulas for obtaining a posterior process are derived. Finally, our results are applied to several practically important…

非参数问题中后验分布的一致性AI 解读

We give conditions that guarantee that the posterior probability of every Hellinger neighborhood of the true distribution tends to 1 almost surely. The conditions are (1) a requirement that the prior not put high mass near distributions with very rough densities and (2) a requirement that the prior put positive mass in Kullback-Leibler neighborhoods of the true distribution. The results are based on the idea of approximating the set of distributions with a finite-dimensional…

基于预测方差的回归模型最优设计准则AI 解读

In the context of nonlinear regression models, a new class of optimum design criteria is developed and illustrated. This new class, termed ΙL-optimality, is analogous to Kiefer's Φk-criterion but is based on predicted variance, whereas Kiefer's class is based on the eigenvalues of the information matrix; L-optimal designs are invariant with respect to different parameterisations of the model and contain G- and D- optimality as special cases. We provide a general equivalence…

利用单变量分布评估多变量非正态性AI 解读

This paper proposes diagnostics that can indicate regions where multivariate distributions are poorly behaved in the sense that they are far from normal. The measure of nonnormality developed by Slate (1994) for univariate distributions is extended to multivariate parametric models by application to univariate marginal and conditional distributions. The approach is illustrated for univariate conditional distributions using dynamic graphics in Xlisp-Stat (Tierney, 1990).…

缺失数据非参数分析的递归算法AI 解读

The mixture of Dirichlet processes posterior that arises in nonparametric Bayesian analysis has been analysed most effectively using Markov chain Monte Carlo. As a computationally simple alternative, we introduce a recursive approximation based on one-step posterior predictive distributions. Asymptotic calculations provide theoretical support for this approximation, and we investigate its actual behaviour in several numerical examples. From a non-Bayesian perspective, this…

Eaton马尔可夫链、其共轭伙伴与P可容许性AI 解读

Suppose that X is a random variable with density $f(x|\theta)$ and that $\pi(\theta|x)$ is a proper posterior corresponding to an improper prior $\nu(\theta)$. The prior is called $\mathscr{P}$-admissible if the generalized Bayes estimator of every bounded function of $\theta$ is almost-$\nu$-admissible under squared error loss. Eaton showed that recurrence of the Markov chain with transition density $R(\eta|\theta) = \int \pi(\eta|x)f(x|\theta) dx$ is a sufficient condition…

密度估计中 Dirichlet 混合的后验一致性AI 解读

A Dirichlet mixture of normal densities is a useful choice for a prior distribution on densities in the problem of Bayesian density estimation. In recent years, efficient Markov chain Monte Carlo method for the computation of the posterior distribution has been developed. The method has been applied to data arising from different fields of interest. The important issue of consistency was however left open. In this paper, we settle this issue in affirmative.

随机逼近版 EM 算法的收敛性AI 解读

The expectation-maximization (EM) algorithm is a powerful computational technique for locating maxima of functions. It is widely used in statistics for maximum likelihood or maximum a posteriori estimation in incomplete data models. In certain situations, however, this method is not applicable because the expectation step cannot be performed in closed form. To deal with these problems, a novel method is introduced, the stochastic approximation EM (SAEM), which replaces the…