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随机场谱密度函数的非参数贝叶斯推断AI 解读

A powerful technique for inference concerning spatial dependence in a random field is to use spectral methods based on frequency domain analysis. Here we develop a nonparametric Bayesian approach to statistical inference for the spectral density of a random field. We construct a multi-dimensional Bernstein polynomial prior for the spectral density and devise a Markov chain Monte Carlo algorithm to simulate from the posterior of the spectral density. The posterior sampling…

非参数贝叶斯分析中的最小信息先验分布AI 解读

Summary We address the problem of how to conduct a minimally informative, non-parametric Bayesian analysis. The central question is how to devise a model so that the posterior distribution satisfies a few basic properties. The concept of ‘local mass’ provides the key to the development of the limiting Dirichlet process model. This model is then used to provide an engine for inference in the compound decision problem and for multiple-comparisons inference in a one-way…

非局部先验密度在贝叶斯假设检验中的应用AI 解读

Summary We examine philosophical problems and sampling deficiencies that are associated with current Bayesian hypothesis testing methodology, paying particular attention to objective Bayes methodology. Because the prior densities that are used to define alternative hypotheses in many Bayesian tests assign non-negligible probability to regions of the parameter space that are consistent with null hypotheses, resulting tests provide exponential accumulation of evidence in…

适配随机分块 MCMC 方法及其在 DSGE 模型中的应用AI 解读

In this paper we develop new Markov chain Monte Carlo schemes for the estimation of Bayesian models. One key feature of our method, which we call the tailored randomized block Metropolis-Hastings (TaRB-MH) method, is the random clustering of the parameters at every iteration into an arbitrary number of blocks. Then each block is sequentially updated through an M-H step. Another feature is that the proposal density for each block is tailored to the location and curvature of…

基于动态结构贝叶斯聚类的转折点定年与预测：奥地利应用AI 解读

Abstract The information contained in a large panel dataset is used to date historical turning points and to forecast future ones. We estimate groups of series with similar time series dynamics and link the groups with a dynamic structure. The dynamic structure identifies a group of leading and a group of coincident series. Robust results across data vintages are obtained when series‐specific information is incorporated in the design of the prior group probability…

贝叶斯分位数回归方法AI 解读

Abstract This paper is a study of the application of Bayesian exponentially tilted empirical likelihood to inference about quantile regressions. In the case of simple quantiles we show the exact form for the likelihood implied by this method and compare it with the Bayesian bootstrap and with Jeffreys' method. For regression quantiles we derive the asymptotic form of the posterior density. We also examine Markov chain Monte Carlo simulations with a proposal density formed…

矩不等式模型的贝叶斯分析AI 解读

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information likelihood. The posterior distribution converges to zero exponentially fast on any δ-contraction outside the identified region. Inside, it is bounded below by a positive constant if the identified region is assumed to have a nonempty interior.…

Beta 混合后验的收敛速度与自适应非参数密度估计AI 解读

In this paper, we investigate the asymptotic properties of nonparametric Bayesian mixtures of Betas for estimating a smooth density on [0, 1]. We consider a parametrization of Beta distributions in terms of mean and scale parameters and construct a mixture of these Betas in the mean parameter, while putting a prior on this scaling parameter. We prove that such Bayesian nonparametric models have good frequentist asymptotic properties. We determine the posterior rate of…

两种模型平均技术的比较及其在增长实证中的应用AI 解读

Parameter estimation under model uncertainty is a difficult and fundamental issue in econometrics. This paper compares the performance of various model averaging techniques. In particular, it contrasts Bayesian model averaging (BMA) -- currently one of the standard methods used in growth empirics -- with a new method called weighted-average least squares (WALS). The new method has two major advantages over BMA: its computational burden is trivial and it is based on a…

高斯与部分非高斯状态空间模型的随机设定搜索AI 解读

Model specification for state space models is a difficult task as one has to decide which components to include in the model and to specify whether these components are fixed or time-varying. To this aim a new model space MCMC method is developed in this paper. It is based on extending the Bayesian variable selection approach which is usually applied to variable selection in regression models to state space models. For non-Gaussian state space models stochastic model search…

贝叶斯结构VAR模型中的脉冲响应先验AI 解读

This article develops a comprehensive approach to formally introduce the prior for impulse responses into the Bayesian structural VAR (SVAR) models, with considerable attention paid to careful prior specification. Furthermore, we present an efficient algorithm to estimate the SVAR with a Gaussian prior for impulse responses using simulation methods. We also illustrate our methodology using an example in which we verifiy some facts concerning the impact of monetary policy…

基于偏斜t分布的非高斯面板数据模型聚类AI 解读

We propose a model-based method to cluster units within a panel. The underlying model is autoregressive and non-Gaussian, allowing for both skewness and fat tails, and the units are clustered according to their dynamic behavior, equilibrium level, and the effect of covariates. Inference is addressed from a Bayesian perspective, and model comparison is conducted using Bayes factors. Particular attention is paid to prior elicitation and posterior propriety. We suggest priors…

大型贝叶斯向量自回归AI 解读

Abstract This paper shows that vector auto regression (VAR) with Bayesian shrinkage is an appropriate tool for large dynamic models. We build on the results of De Mol and co‐workers (2008) and show that, when the degree of shrinkage is set in relation to the cross‐sectional dimension, the forecasting performance of small monetary VARs can be improved by adding additional macroeconomic variables and sectoral information. In addition, we show that large VARs with shrinkage…

避免维度诅咒的非线性动态模型求解、估计与选择AI 解读

We present a comprehensive framework for Bayesian estimation of structural nonlinear dynamic economic models on sparse grids to overcome the curse of dimensionality for approximations. We apply sparse grids to a global polynomial approximation of the model solution, to the quadrature of integrals arising as rational expectations, and to three new nonlinear state space filters which speed up the sequential importance resampling particle filter. The posterior of the structural…

无差异交易者回忆录：从预测市场估计预测分布AI 解读

Prediction markets for future events are increasingly common and they often trade several contracts for the same event. This paper considers the distribution of a normative risk-neutral trader who, given any portfolio of contracts traded on the event, would choose not to reallocate that portfolio of contracts even if transactions costs were zero. Because common parametric distributions can conflict with observed prediction market prices, the distribution is given a…

自适应近似贝叶斯计算AI 解读

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.’s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the…

矩阵正态图模型的贝叶斯分析AI 解读

We present Bayesian analyses of matrix-variate normal data with conditional independencies induced by graphical model structuring of the characterizing covariance matrix parameters. This framework of matrix normal graphical models includes prior specifications, posterior computation using Markov chain Monte Carlo methods, evaluation of graphical model uncertainty and model structure search. Extensions to matrix-variate time series embed matrix normal graphs in dynamic…

贝叶斯 lasso 回归AI 解读

The lasso estimate for linear regression corresponds to a posterior mode when independent, double-exponential prior distributions are placed on the regression coefficients. This paper introduces new aspects of the broader Bayesian treatment of lasso regression. A direct characterization of the regression coefficients’ posterior distribution is provided, and computation and inference under this characterization is shown to be straightforward. Emphasis is placed on point…

离散层级对数线性模型的共轭先验AI 解读

In Bayesian analysis of multi-way contingency tables, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameters is a major challenge. In this paper, we define a flexible family of conjugate priors for the wide class of discrete hierarchical log-linear models, which includes the class of graphical models. These priors are defined as the Diaconis–Ylvisaker conjugate priors on the log-linear parameters subject to “baseline…

使用平滑自适应高斯混合的回归密度估计AI 解读

We model a regression density flexibly so that at each value of the covariates the density is a mixture of normals with the means, variances and mixture probabilities of the components changing smoothly as a function of the covariates. The model extends the existing models in two important ways. First, the components are allowed to be heteroscedastic regressions as the standard model with homoscedastic regressions can give a poor fit to heteroscedastic data, especially when…

广义多层函数型回归AI 解读

We introduce Generalized Multilevel Functional Linear Models (GMFLMs), a novel statistical framework for regression models where exposure has a multilevel functional structure. We show that GMFLMs are, in fact, generalized multilevel mixed models (GLMMs). Thus, GMFLMs can be analyzed using the mixed effects inferential machinery and can be generalized within a well researched statistical framework. We propose and compare two methods for inference: 1) a two-stage frequentist…

向邻近链学习：并行链与区域自适应 MCMCAI 解读

Starting with the seminal paper of Haario, Saksman, and Tamminen (Haario, Saksman, and Tamminen 2001), a substantial amount of work has been done to validate adaptive Markov chain Monte Carlo algorithms. In this paper we focus on two practical aspects of adaptive Metropolis samplers. First, we draw attention to the deficient performance of standard adaptation when the target distribution is multimodal. We propose a parallel chain adaptation strategy that incorporates…

结合变量选择的非参数贝叶斯条件分布建模AI 解读

This article considers a methodology for flexibly characterizing the relationship between a response and multiple predictors. Goals are (1) to estimate the conditional response distribution addressing the distributional changes across the predictor space, and (2) to identify important predictors for the response distribution change both within local regions and globally. We first introduce the probit stick-breaking process (PSBP) as a prior for an uncountable collection of…

非识别模型后验分布的极限是什么，为何值得关注？AI 解读

In health research and other fields, the observational data available to researchers often fall short of the data that ideally would be available, due to the inherent limitations of study design and data acquisition. Were they available, these ideal data might be readily analyzed via straightforward statistical models with such desirable properties as parameter identifiability. Conversely, realistic models for the available data that incorporate uncertainty about the link…