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贝叶斯:贝叶斯建模、后验推断与 MCMC。
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Components of Bull and Bear Markets: Bull Corrections and Bear Rallies

牛熊市的内部组成:牛市回调与熊市反弹

Existing methods of partitioning the market index into bull and bear regimes do not identify market corrections or bear market rallies. In contrast, our probabilistic model of the return distribution allows for rich and heterogeneous intraregime dynamics. We focus on the characteristics and dynamics of bear market rallies and bull market corrections, including, for example, the probability of transition from a bear market rally into a bull market versus back to the primary…

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Time Varying Dimension Models

时变维度模型

Time varying parameter (TVP) models have enjoyed an increasing popularity in empirical macroeconomics. However, TVP models are parameter-rich and risk over-fitting unless the dimension of the model is small. Motivated by this worry, this article proposes several Time Varying Dimension (TVD) models where the dimension of the model can change over time, allowing for the model to automatically choose a more parsimonious TVP representation, or to switch between different…

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The Trace Restriction: An Alternative Identification Strategy for the Bayesian Multinomial Probit Model

迹约束:贝叶斯多项 Probit 模型的替代识别策略

Previous authors have made Bayesian multinomial probit models identifiable by fixing a parameter on the main diagonal of the covariance matrix. The choice of which element one fixes can influence posterior predictions. Thus, we propose restricting the trace of the covariance matrix, which we achieve without computational penalty. This permits a prior that is symmetric to permutations of the nonbase outcome categories. We find in real and simulated consumer choice datasets…

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Catching up Faster by Switching Sooner: A Predictive Approach to Adaptive Estimation with an Application to the AIC–BIC Dilemma

通过更早切换加快追赶:自适应估计与 AIC–BIC 困境

Summary Prediction and estimation based on Bayesian model selection and model averaging, and derived methods such as the Bayesian information criterion BIC, do not always converge at the fastest possible rate. We identify the catch-up phenomenon as a novel explanation for the slow convergence of Bayesian methods, which inspires a modification of the Bayesian predictive distribution, called the switch distribution. When used as an adaptive estimator, the switch distribution…

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Adjusted Bayesian Inference for Selected Parameters

对数据选择后参数的调整贝叶斯推断

Summary We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that providing Bayesian inference for selected parameters is a truncated data problem. We show that if the prior for the parameter is non-informative, or if the parameter is a ‘fixed’ unknown constant, then it is necessary to adjust the…

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Criteria for Bayesian model choice with application to variable selection

In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first formalize the most general and compelling of the various criteria that have been suggested, together with a new criterion. We then illustrate the potential of these criteria in determining objective model selection priors by considering their…

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Bernstein–von Mises theorem for linear functionals of the density

密度线性泛函的 Bernstein–von Mises 定理

In this paper, we study the asymptotic posterior distribution of linear functionals of the density by deriving general conditions to obtain a semi-parametric version of the Bernstein–von Mises theorem. The special case of the cumulative distributive function, evaluated at a specific point, is widely considered. In particular, we show that for infinite-dimensional exponential families, under quite general assumptions, the asymptotic posterior distribution of the functional…

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Bayesian modeling of joint and conditional distributions

联合分布与条件分布的贝叶斯建模

In this paper, we study a Bayesian approach to flexible modeling of conditional distributions. The approach uses a flexible model for the joint distribution of the dependent and independent variables and then extracts the conditional distributions of interest from the estimated joint distribution. We use a finite mixture of multivariate normals (FMMN) to estimate the joint distribution. The conditional distributions can then be assessed analytically or through simulations.…

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The HESSIAN method: Highly efficient simulation smoothing, in a nutshell

HESSIAN方法:高效模拟平滑的简明框架

I introduce the HESSIAN (highly efficient simulation smoothing in a nutshell) method for numerically efficient simulation smoothing in state space models with univariate states. Given a vector θ of parameters, the vector of states α=(α1,…,αn) is Gaussian and the observed vector y=(y1⊤,…,yn⊤)⊤ need not be. I describe a procedure to construct a close approximation q(α|θ,y) to the target density p(α|θ,y). It requires code to compute five derivatives of logp(yt|θ,αt) with…

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DD -Classifier: Nonparametric Classification Procedure Based on DD -Plot

DD 分类器:基于深度对深度图的非参数分类方法

Using the DD-plot (depth vs. depth plot), we introduce a new nonparametric classification algorithm and call it DD-classifier. The algorithm is completely nonparametric, and it requires no prior knowledge of the underlying distributions or the form of the separating curve. Thus, it can be applied to a wide range of classification problems. The algorithm is completely data driven and its classification outcome can be easily visualized in a two-dimensional plot regardless of…

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Nonparametric Bayesian Multiple Imputation for Missing Data Due to Mid-Study Switching of Measurement Methods

研究中途更换测量方法所致缺失数据的非参数贝叶斯多重插补

Investigators often change how variables are measured during the middle of data-collection, for example, in hopes of obtaining greater accuracy or reducing costs. The resulting data comprise sets of observations measured on two (or more) different scales, which complicates interpretation and can create bias in analyses that rely directly on the differentially measured variables. We develop approaches based on multiple imputation for handling mid-study changes in measurement…

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Bayesian Model Selection in High-Dimensional Settings

高维环境下的贝叶斯模型选择

Standard assumptions incorporated into Bayesian model selection procedures result in procedures that are not competitive with commonly used penalized likelihood methods. We propose modifications of these methods by imposing nonlocal prior densities on model parameters. We show that the resulting model selection procedures are consistent in linear model settings when the number of possible covariates p is bounded by the number of observations n, a property that has not been…

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The impact of data revisions on the robustness of growth determinants—a note on ‘determinants of economic growth: Will data tell?’

数据修订如何影响增长决定因素的稳健性:一则回应

SUMMARY Ciccone and Jarociński ( American Economic Journal: Macroeconomics 2010; 2 : 222–246) show that inference in Bayesian model averaging (BMA) can be highly sensitive to small data perturbations. In particular, they demonstrate that the importance attributed to potential growth determinants varies tremendously over different revisions of international income data. They conclude that ‘agnostic’ priors appear too sensitive for this strand of growth empirics. In response,…

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Bayesian estimation approaches to first-price auctions

第一价格拍卖的贝叶斯估计方法

This paper considers Bayesian estimation strategies for first-price auctions within the independent private value paradigm. We develop an ‘optimization’ error approach that allows for estimation of values assuming that observed bids differ from optimal bids. We further augment this approach by allowing systematic over or underbidding by bidders using ideas from the stochastic frontier literature. We perform a simulation study to showcase the appeal of the method and apply…

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Information acquisition and/or bid preparation: A structural analysis of entry and bidding in timber sale auctions

信息获取与投标准备:木材拍卖进入和竞价的结构分析

Recently, several auction models with entry have been proposed: in one model (Levin and Smith, 1994; Li and Zheng, 2009), bidders are assumed to draw their private values after they decide to enter. In another model (Samuelson, 1985; Li and Zheng, 2009), bidders are assumed to learn their values before their entry decisions are made. The entry cost in the latter model can be interpreted as bid preparation cost, while the entry cost in the former model consists of both costs…

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Determinants of Economic Growth: A Bayesian Panel Data Approach

经济增长的决定因素:贝叶斯面板数据方法

Model uncertainty hampers consensus on the key determinants of economic growth. Some recent cross-country cross-sectional analyses have employed Bayesian model averaging to tackle the issue of model uncertainty. This paper extends that approach to panel data models with country-specific fixed effects in order to simultaneously address model uncertainty and endogeneity issues. The empirical findings suggest that in a panel setting, the most robust growth determinants are the…

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Bayesian empirical likelihood for quantile regression

分位数回归的贝叶斯经验似然

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful investigation. This paper considers the Bayesian empirical likelihood approach to quantile regression. Taking the empirical likelihood into a Bayesian framework, we show that the resultant posterior from any fixed prior is asymptotically normal;…

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Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process

长记忆或中间记忆高斯过程谱密度的贝叶斯非参数估计

A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is continuous and positive. We propose a novel Bayesian nonparametric approach for the estimation of the spectral density of such processes. We prove posterior consistency for both $d$ and $g$, under appropriate conditions on the prior…

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Bayes factors and the geometry of discrete hierarchical loglinear models

贝叶斯因子与离散层次对数线性模型的几何

A standard tool for model selection in a Bayesian framework is the Bayes factor which compares the marginal likelihood of the data under two given different models. In this paper, we consider the class of hierarchical loglinear models for discrete data given under the form of a contingency table with multinomial sampling. We assume that the prior distribution on the loglinear parameters is the Diaconis–Ylvisaker conjugate prior, and the uniform is the prior distribution on…

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Bayesian averaging, prediction and nonnested model selection

贝叶斯平均、预测与非嵌套模型选择

This paper studies the asymptotic relationship between Bayesian model averaging and post-selection frequentist predictors in both nested and nonnested models. We derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples. This result depends crucially on the relation between posterior odds and frequentist model selection criteria. Weak conditions are given under which consistent…

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A semiparametric stochastic volatility model

一种半参数随机波动率模型

In this paper the correlation structure in the classical leverage stochastic volatility (SV) model is generalized based on a linear spline. In the new model the correlation between the return and volatility innovations is time varying and depends nonparametrically on the type of news arrived to the market. Theoretical properties of the proposed model are examined. The model estimation and comparison are conducted by Bayesian methods. The performance of the estimates are…

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Revealing the preferences of the US Federal Reserve

揭示美联储的政策偏好

Abstract We use Bayesian methods to estimate changes in US post‐war monetary policy in the Smets and Wouters model. We perform the estimations by allowing for a break in monetary policy at the time of Volcker's appointment as chairman. This enables us to capture changes in the monetary policy regime introduced by Volcker during the Volcker–Greenspan period. We find support for the assumption that monetary policy in the Volcker–Greenspan period performed optimally under…

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Modelling dependence using skew t copulas: Bayesian inference and applications

偏斜 t Copula 的依赖建模:贝叶斯推断与应用

Abstract We construct a copula from the skew t distribution of Sahu et al. ( 2003 ). This copula can capture asymmetric and extreme dependence between variables, and is one of the few copulas that can do so and still be used in high dimensions effectively. However, it is difficult to estimate the copula model by maximum likelihood when the multivariate dimension is high, or when some or all of the marginal distributions are discrete‐valued, or when the parameters in the…

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A direct approach to sparse discriminant analysis in ultra-high dimensions

超高维稀疏判别分析的直接方法

Sparse discriminant methods based on independence rules, such as the nearest shrunken centroids classifier (Tibshirani et al., 2002) and features annealed independence rules (Fan & Fan, 2008), have been proposed as computationally attractive tools for feature selection and classification with high-dimensional data. A fundamental drawback of these rules is that they ignore correlations among features and thus could produce misleading feature selection and inferior…

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