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经验贝叶斯方法与贝叶斯敏感性分析的计算途径AI 解读

We consider situations in Bayesian analysis where we have a family of priors νh on the parameter θ, where h varies continuously over a space $\mathcal{H}$, and we deal with two related problems. The first involves sensitivity analysis and is stated as follows. Suppose we fix a function f of θ. How do we efficiently estimate the posterior expectation of f(θ) simultaneously for all h in $\mathcal{H}$? The second problem is how do we identify subsets of $\mathcal{H}$ which give…

采用高斯先验的贝叶斯逆问题AI 解读

The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the minimax rate. The frequentist coverage of credible sets is shown to depend on the combination of prior and true parameter, with smoother priors leading to zero coverage and rougher priors to conservative coverage.…

采用广义g先验的完全贝叶斯因子AI 解读

For the normal linear model variable selection problem, we propose selection criteria based on a fully Bayes formulation with a generalization of Zellner’s g-prior which allows for p > n. A special case of the prior formulation is seen to yield tractable closed forms for marginal densities and Bayes factors which reveal new model evaluation characteristics of potential interest.

回归变量数增长时高斯回归的 Bernstein–von Mises 定理AI 解读

This paper brings a contribution to the Bayesian theory of nonparametric and semiparametric estimation. We are interested in the asymptotic normality of the posterior distribution in Gaussian linear regression models when the number of regressors increases with the sample size. Two kinds of Bernstein–von Mises theorems are obtained in this framework: nonparametric theorems for the parameter itself, and semiparametric theorems for functionals of the parameter. We apply them…

多重结构变化下多元模型的模型选择准则AI 解读

This paper considers the issue of selecting the number of regressors and the number of structural breaks in multivariate regression models in the possible presence of multiple structural changes. We develop a modified Akaike information criterion (AIC), a modified Mallows' Cp criterion and a modified Bayesian information criterion (BIC). The penalty terms in these criteria are shown to be different from the usual terms. We prove that the modified BIC consistently selects the…

时间变换无限活动衍生品定价模型的序贯贝叶斯分析AI 解读

This article investigates time-changed infinite activity derivatives pricing models from the sequential Bayesian perspective. It proposes a sequential Monte Carlo method with the proposal density generated by the unscented Kalman filter. This approach overcomes to a large extent the particle impoverishment problem inherent to the conventional particle filter. Simulation study and real applications indicate that (1) using the underlying alone cannot capture the dynamics of…

用于金融市场风险价值预测的贝叶斯时变分位数模型AI 解读

Recently, advances in time-varying quantile modeling have proven effective in financial Value-at-Risk forecasting. Some well-known dynamic conditional autoregressive quantile models are generalized to a fully nonlinear family. The Bayesian solution to the general quantile regression problem, via the Skewed-Laplace distribution, is adapted and designed for parameter estimation in this model family via an adaptive Markov chain Monte Carlo sampling scheme. A simulation study…

仅基于模拟似然的贝叶斯推断：动态经济模型的粒子滤波分析AI 解读

We note that likelihood inference can be based on an unbiased simulation-based estimator of the likelihood when it is used inside a Metropolis–Hastings algorithm. This result has recently been introduced in statistics literature by Andrieu, Doucet, and Holenstein (2010, Journal of the Royal Statistical Society, Series B , 72, 269–342) and is perhaps surprising given the results on maximum simulated likelihood estimation. Bayesian inference based on simulated likelihood can…

贝叶斯保序密度回归AI 解读

Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not clear whether such priors have full support so that any true data-generating model…

基于预测递归边际似然的混合模型半参数推断AI 解读

Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in the additional unknown structural parameter. As an alternative to existing profile likelihood methods, we treat predictive recursion as a filter approximation by fitting a fully Bayes model, whereby an approximate marginal likelihood of…

光子稀少图像的贝叶斯平滑及其天文学应用AI 解读

Summary We consider a multiscale model for intensities in photon-limited images using a Bayesian framework. A typical Dirichlet prior on relative intensities is not efficient in picking up structures owing to the continuity of intensities. We propose a novel prior using the so-called ‘Chinese restaurant process’ to create structures in the form of equal intensities of some neighbouring pixels. Simulations are conducted using several photon-limited images, which are common in…

最优预测组合AI 解读

We consider the properties of weighted linear combinations of prediction models, or linear pools, evaluated using the log predictive scoring rule. Although exactly one model has limiting posterior probability, an optimal linear combination typically includes several models with positive weights. We derive several interesting results: for example, a model with positive weight in a pool may have zero weight if some other models are deleted from that pool. The results are…

函数混合模型框架下的稳健自适应函数回归AI 解读

Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be…

线性与二元回归中贝叶斯变量选择和模型平均的 Rao–Blackwell 化AI 解读

Choosing the subset of covariates to use in regression or generalized linear models is a ubiquitous problem. The Bayesian paradigm addresses the problem of model uncertainty by considering models corresponding to all possible subsets of the covariates, where the posterior distribution over models is used to select models or combine them via Bayesian model averaging (BMA). Although conceptually straightforward, BMA is often difficult to implement in practice, since either the…

依赖条件下错误发现比例的预测AI 解读

We present a flexible framework for predicting error measures in multiple testing situations under dependence. Our approach is based on modeling the distribution of the probit transform of the p-values by mixtures of multivariate skew-normal distributions. The model can incorporate dependence among p-values and it allows for shape restrictions on the p-value density. A nonparametric Bayesian scheme for estimating the components of the mixture model is outlined and Markov…

具有随机序约束的非参数贝叶斯潜在类别模型AI 解读

Latent class models (LCMs) are used increasingly for addressing a broad variety of problems, including sparse modeling of multivariate and longitudinal data, model-based clustering, and flexible inferences on predictor effects. Typical frequentist LCMs require estimation of a single finite number of classes, which does not increase with the sample size, and have a well-known sensitivity to parametric assumptions on the distributions within a class. Bayesian nonparametric…

预测变量缺失下参数与非参数回归的变分贝叶斯推断AI 解读

Bayesian hierarchical models are attractive structures for conducting regression analyses when the data are subject to missingness. However, the requisite probability calculus is challenging and Monte Carlo methods typically are employed. We develop an alternative approach based on deterministic variational Bayes approximations. Both parametric and nonparametric regression are considered. Attention is restricted to the more challenging case of missing predictor data. We…

多重检验与高通量检测中的发现后验概率和预期发现率AI 解读

Technologies of measuring millions of quantities at once have been rapidly developed and used in biological and biomedical research and other fields in the past decade. Yet a key issue remains unsettled, namely, how to control spurious findings for the ensuing massive number of hypothesis tests. An emerging consensus is to control false discovery rate (FDR), with FDR defined as the expected proportion of true nulls among discoveries, and a discovery the rejection of a null…

空间随机效应模型的贝叶斯推断AI 解读

Spatial statistical analysis of massive amounts of spatial data can be challenging because computation of optimal procedures can break down. The Spatial Random Effects (SRE) model uses a fixed number of known but not necessarily orthogonal (multiresolutional) spatial basis functions, which gives a flexible family of nonstationary covariance functions, results in dimension reduction, and yields optimal spatial predictors whose computations are scalable. By modeling spatial…

分类测试误差的自适应置信区间AI 解读

The estimated test error of a learned classifier is the most commonly reported measure of classifier performance. However, constructing a high quality point estimator of the test error has proved to be very difficult. Furthermore, common interval estimators (e.g. confidence intervals) are based on the point estimator of the test error and thus inherit all the difficulties associated with the point estimation problem. As a result, these confidence intervals do not reliably…

BMA中如何使用交互项：对相关评论的回应AI 解读

Jesus Crespo Cuaresma (How different is Africa? A comment on Masanjala and Papageorgiou. Journal of Applied Econometrics, 2011) shows that the results in Masanjala and Papageorgiou (Rough and lonely road to prosperity: a reexamination of the sources of growth in Africa using Bayesian model averaging. Journal of Applied Econometrics 2008; 23(5): 671–682) are sensitive to an alternative prior model structure in considering interaction terms. As a side issue, the algorithm for…

非洲有多不同？对 Masanjala 与 Papageorgiou 的评论AI 解读

Masanjala and Papageorgiou (Rough and lonely road to prosperity: a reexamination of the sources of growth in Africa using Bayesian model averaging, Journal of Applied Econometrics 2008; 23(5): 671–682) use Bayesian model averaging to evaluate the existence of parameter heterogeneity between African and non-African countries in the framework of cross-country growth regressions. We show that their results are not robust to the use of a prior over the model space that respects…

参数还是非参数？模型选择的参数性指数AI 解读

In model selection literature, two classes of criteria perform well asymptotically in different situations: Bayesian information criterion (BIC) (as a representative) is consistent in selection when the true model is finite dimensional (parametric scenario); Akaike’s information criterion (AIC) performs well in an asymptotic efficiency when the true model is infinite dimensional (nonparametric scenario). But there is little work that addresses if it is possible and how to…

连续字典下的随机展开：Lévy 自适应回归核AI 解读

This article describes a new class of prior distributions for nonparametric function estimation. The unknown function is modeled as a limit of weighted sums of kernels or generator functions indexed by continuous parameters that control local and global features such as their translation, dilation, modulation and shape. Lévy random fields and their stochastic integrals are employed to induce prior distributions for the unknown functions or, equivalently, for the number of…