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多因子仿射收益率曲线模型分析AI 解读

In finance and economics much work has been done on the theoretical modeling and statistical estimation of the yield curve, defined as the relationship between (−1/τ) log pt(τ) and τ, where pt(τ) is the time t price of a zero-coupon bond with payoff 1 at maturity date t+τ. Of considerable current interest are models of the yield curve in which a collection of observed and latent factors determine the market price of factor risks, the stochastic discount factor, and the…

微观模拟模型的贝叶斯校准AI 解读

Microsimulation models that describe disease processes synthesize information from multiple sources and can be used to estimate the effects of screening and treatment on cancer incidence and mortality at a population level. These models are characterized by simulation of individual event histories for an idealized population of interest. Microsimulation models are complex and invariably include parameters that are not well informed by existing data. Therefore, a key…

双参数 Poisson–Dirichlet 过程先验下的物种多样性贝叶斯非参数推断AI 解读

Summary A Bayesian non-parametric methodology has been recently proposed to deal with the issue of prediction within species sampling problems. Such problems concern the evaluation, conditional on a sample of size n, of the species variety featured by an additional sample of size m. Genomic applications pose the additional challenge of having to deal with large values of both n and m. In such a case the computation of the Bayesian non-parametric estimators is cumbersome and…

一种贝叶斯发现程序AI 解读

Summary We discuss a Bayesian discovery procedure for multiple-comparison problems. We show that, under a coherent decision theoretic framework, a loss function combining true positive and false positive counts leads to a decision rule that is based on a threshold of the posterior probability of the alternative. Under a semiparametric model for the data, we show that the Bayes rule can be approximated by the optimal discovery procedure, which was recently introduced by…

多元核回归带宽选择的贝叶斯方法及其状态价格密度应用AI 解读

This paper presents a Bayesian approach to bandwidth selection for multivariate kernel regression. A Monte Carlo study shows that under the average squared error criterion, the Bayesian bandwidth selector is comparable to the cross-validation method and clearly outperforms the bootstrapping and rule-of-thumb bandwidth selectors. The Bayesian bandwidth selector is applied to a multivariate kernel regression model that is often used to estimate the state-price density of…

使用逆 Gamma 带宽高斯随机场的自适应贝叶斯估计AI 解读

We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an inverse Gamma bandwidth. The procedure is studied from a frequentist perspective in three statistical settings involving replicated observations (density estimation, regression and classification). We prove that the resulting posterior…

利用平滑方法改进 SAMC：理论与贝叶斯模型选择应用AI 解读

Stochastic approximation Monte Carlo (SAMC) has recently been proposed by Liang, Liu and Carroll [J. Amer. Statist. Assoc. 102 (2007) 305–320] as a general simulation and optimization algorithm. In this paper, we propose to improve its convergence using smoothing methods and discuss the application of the new algorithm to Bayesian model selection problems. The new algorithm is tested through a change-point identification example. The numerical results indicate that the new…

贝叶斯与频率学派的混合推断AI 解读

Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a set of multiple parameters, which can be divided into two disjoint subsets. On one set, a frequentist method may be favored and on the other, the Bayesian. This motivates a joint estimation procedure in which some of the parameters are…

经验似然与贝叶斯最大后验估计的渐近等价性AI 解读

In this paper we are interested in empirical likelihood (EL) as a method of estimation, and we address the following two problems: (1) selecting among various empirical discrepancies in an EL framework and (2) demonstrating that EL has a well-defined probabilistic interpretation that would justify its use in a Bayesian context. Using the large deviations approach, a Bayesian law of large numbers is developed that implies that EL and the Bayesian maximum a posteriori…

混合分布递归估计的一致性AI 解读

Mixture models have received considerable attention recently and Newton [Sankhyā Ser. A 64 (2002) 306–322] proposed a fast recursive algorithm for estimating a mixing distribution. We prove almost sure consistency of this recursive estimate in the weak topology under mild conditions on the family of densities being mixed. This recursive estimate depends on the data ordering and a permutation-invariant modification is proposed, which is an average of the original over…

二元选择模型的参数化链接函数：频率学派与贝叶斯的对话AI 解读

The familiar logit and probit models provide convenient settings for many binary response applications, but a larger class of link functions may be occasionally desirable. Two parametric families of link functions are investigated: the Gosset link based on the Student t latent variable model with the degrees of freedom parameter controlling the tail behavior, and the Pregibon link based on the (generalized) Tukey [lambda] family, with two shape parameters controlling…

分位数回归模型的有限样本推断AI 解读

Under minimal assumptions, finite sample confidence bands for quantile regression models can be constructed. These confidence bands are based on the "conditional pivotal property" of estimating equations that quantile regression methods solve and provide valid finite sample inference for linear and nonlinear quantile models with endogenous or exogenous covariates. The confidence regions can be computed using Markov Chain Monte Carlo (MCMC) methods. We illustrate the finite…

第一价格拍卖中的进入与竞争效应：采购拍卖的理论和证据AI 解读

Motivated by several interesting features of the highway mowing auction data from the Texas Department of Transportation (TDoT), we study three competing procurement auction models with endogenous entry. Our entry and bidding models provide several interesting implications. For the first time, we show that even within an independent private value paradigm, as the number of potential bidders increases, bidders' equilibrium bidding behaviour can become less aggressive, and the…

融入判断信息的预测AI 解读

This article shows how to account for nonsample information in the classical forecasting framework. We explicitly incorporate two elements: a default decision and a probability reflecting the confidence associated with it. Starting from the default decision, the new estimator increases the objective function only as long as its first derivatives are statistically different from zero. It includes as a special case the classical estimator and has clear analogies with Bayesian…

模型不确定性下利用英国货币总量进行实时预测AI 解读

A popular account for the demise of the U.K.’s monetary targeting regime in the 1980s blames the fluctuating predictive relationships between broad money and inflation and real output growth. Yet ex post policy analysis based on heavily revised data suggests no fluctuations in the predictive content of money. In this paper, we investigate the predictive relationships for inflation and output growth using both real-time and heavily revised data. We consider a large set of…

α-积和式的近似计算AI 解读

The standard matrix permanent is the solution to a number of combinatorial and graph-theoretic problems, and the α-weighted permanent is the density function for a class of Cox processes called boson processes. The exact computation of the ordinary permanent is known to be #P-complete, and the same appears to be the case for the α-permanent for most values of α. At present, the lack of a satisfactory algorithm for approximating the α-permanent is a formidable obstacle to the…

加性风险回归模型的经验贝叶斯估计AI 解读

We develop a novel empirical Bayesian framework for the semiparametric additive hazards regression model. The integrated likelihood, obtained by integration over the unknown prior of the nonparametric baseline cumulative hazard, can be maximized using standard statistical software. Unlike the corresponding full Bayes method, our empirical Bayes estimators of regression parameters, survival curves and their corresponding standard errors have easily computed closed-form…

高斯图模型中的客观贝叶斯模型选择AI 解读

This paper presents a default model-selection procedure for Gaussian graphical models that involves two new developments. First, we develop a default version of the hyper-inverse Wishart prior for restricted covariance matrices, called the hyper-inverse Wishart g-prior, and show how it corresponds to the implied fractional prior for selecting a graph using fractional Bayes factors. Second, we apply a class of priors that automatically handles the problem of multiple…

函数型数据的混合式 Dirichlet 混合模型AI 解读

Summary In functional data analysis, curves or surfaces are observed, up to measurement error, at a finite set of locations, for, say, a sample of n individuals. Often, the curves are homogeneous, except perhaps for individual-specific regions that provide heterogeneous behaviour (e.g. ‘damaged’ areas of irregular shape on an otherwise smooth surface). Motivated by applications with functional data of this nature, we propose a Bayesian mixture model, with the aim of…

含测量误差协变量平滑效应的 Cox 模型AI 解读

We propose, develop, and implement a fully Bayesian inferential approach for the Cox model when the log hazard function contains unknown smooth functions of the variables measured with error. Our approach is to model nonparametrically both the log-baseline hazard and the smooth components of the log-hazard functions using low-rank penalized splines. Careful implementation of the Bayesian inferential machinery is shown to produce remarkably better results than the naive…

大规模预测问题的经验贝叶斯估计AI 解读

Classical prediction methods such as Fisher's linear discriminant function were designed for small-scale problems, where the number of predictors N is much smaller than the number of observations n. Modern scientific devices often reverse this situation. A microarray analysis, for example, might include n = 100 subjects measured on N = 10,000 genes, each of which is a potential predictor. This paper proposes an empirical Bayes approach to large-scale prediction, where the…

二维列联表内禀独立性检验的稳健性评估AI 解读

For testing nested hypotheses from a Bayesian standpoint, a desirable condition is that the prior for the alternative model concentrates mass around the smaller, or null, model. For testing independence in contingency tables, the intrinsic priors satisfy this requirement. Furthermore, the degree of concentration of the priors is controlled by a discrete parameter, t, the training sample size, which plays an important role in the resulting answer. In this article we report on…

多元无序分类数据的非参数贝叶斯建模AI 解读

Modeling of multivariate unordered categorical (nominal) data is a challenging problem, particularly in high dimensions and cases in which one wishes to avoid strong assumptions about the dependence structure. Commonly used approaches rely on the incorporation of latent Gaussian random variables or parametric latent class models. The goal of this article is to develop a nonparametric Bayes approach, which defines a prior with full support on the space of distributions for…

多重集采样器AI 解读

We introduce the multiset sampler (MSS), a new Metropolis–Hastings algorithm for drawing samples from a posterior distribution. The MSS is designed to be effective when the posterior has the feature that the parameters can be divided into two sets, X, the parameters of interest and Y, the nuisance parameters. We contemplate a sampler that iterates between X moves and Y moves. We consider the case where either (a) Y is discrete and lives on a finite set or (b) Y is continuous…