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自适应模型选择AI 解读

Most model selection procedures use a fixed penalty penalizing an increase in the size of a model. These nonadaptive selection procedures perform well only in one type of situation. For instance, Bayesian information criterion (BIC) with a large penalty performs well for “small” models and poorly for “large” models, and Akaike's information criterion (AIC) does just the opposite. This article proposes an adaptive model selection procedure that uses a data-adaptive complexity…

测量误差问题中的贝叶斯平滑样条与回归样条AI 解读

In the presence of covariate measurement error, estimating a regression function nonparametrically is extremely difficult, the problem being related to deconvolution. Various frequentist approaches exist for this problem, but to date there has been no Bayesian treatment. In this article we describe Bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error. The regression function is modeled with smoothing splines and…

跨多个受试者整合图像信息AI 解读

This article introduces a Bayesian hierarchical model for combining information across multiple images. Our work was motivated by an invasive functional brain mapping technique called direct cortical electrical interference that gives a sparse set of binary observations of an underlying “true” region at multiple sites on the brain surface. To model region shapes that may vary widely across individuals, we use mixtures of simple templates, for example, circles. These…

随机时空场的贝叶斯空间预测及 PM2.5 暴露制图应用AI 解读

This article presents a multivariate spatial prediction methodology in a Bayesian framework. The method is especially suited for use in environmetrics, where vector-valued responses are observed at a small set of ambient monitoring stations “(gauged sites)” at successive time points. However, the stations may have varying start-up times so that the data have a “staircase” pattern (“monotone” pattern in the terminology of Rubin and Shaffer). The lowest step corresponds to the…

DNA 微阵列基因表达数据的贝叶斯模型AI 解读

Two of the critical issues that arise when examining DNA microarray data are (1) determination of which genes best discriminate among the different types of tissue, and (2) characterization of expression patterns in tumor tissues. For (1), there are many genes that characterize DNA expression, and it is of critical importance to try and identify a small set of genes that best discriminate between normal and tumor tissues. For (2), it is critical to be able to characterize…

基于疗效与死亡结果选择多疗程临床试验治疗策略AI 解读

Therapy of rapidly fatal diseases often requires multiple courses of treatment. In each course, the treatment may achieve the desired clinical goal (“response”), the patient may survive without response (“failure”), or the patient may die. When treatment fails in a given course, it is common medical practice to switch to a different treatment for the next course. Most statistical approaches to such settings simply ignore the multicourse structure. They characterize patient…

排序数据的贝叶斯分析：灵长类智力实验应用AI 解读

A model for analyzing rank data obtained from multiple evaluators, possibly using different ranking criteria, is proposed. The model is specified hierarchically within the Bayesian paradigm and includes parameters that represent the probabilities that two items are assigned equal rankings. Also included are parameters that account for the relative precision of rankings obtained from distinct evaluation schemes. The model is illustrated through a meta-analysis of rank data…

基于地震数据与钻井观测的储层变量预测AI 解读

Offshore petroleum reservoirs are usually explored by acquisition of vast amounts of seismic reflection data and observations along a small number of wells drilled through the reservoirs. The seismic data are indirect measurements of reservoir characteristics and have good spatial coverage but low precision. The well observations are sparse but precise. Information from these sources of data are integrated to characterize the reservoir variables of interest—reservoir…

摘要暂缺

含随机系数的随机前沿模型AI 解读

Abstract The paper proposes a stochastic frontier model with random coefficients to separate technical inefficiency from technological differences across firms, and free the frontier model from the restrictive assumption that all firms must share exactly the same technological possibilities. Inference procedures for the new model are developed based on Bayesian techniques, and computations are performed using Gibbs sampling with data augmentation to allow finite‐sample…

购买力平价偏离半衰期的不确定性量化AI 解读

Abstract We propose a Bayesian framework in which the uncertainty about the half‐life of deviations from purchasing power parity can be quantified. Based on the responses to a survey study, we propose a prior probability distribution for the half‐life under the recent float intended to capture widely held views among economists. We derive the posterior probability distribution of the half‐life under this consensus prior and confirm the presence of substantial uncertainty…

二项比例置信区间及其渐近展开AI 解读

We address the classic problem of interval estimation of a binomial proportion. The Wald interval $\hat{p}\pm z_{\alpha/2} n^{-1/2} (\hat{p} (1 - \hat{p}))^{1/2}$ is currently in near universal use. We first show that the coverage properties of the Wald interval are persistently poor and defy virtually all conventional wisdom. We then proceed to a theoretical comparison of the standard interval and four additional alternative intervals by asymptotic expansions of their…

多工具变量情形下的最优推断AI 解读

In this paper, I derive the efficiency bound of the structural parameter in a linear simultaneous equations model with many instruments. The bound is derived by applying a convolution theorem to Bekker's (1994, Econometrica 62, 657–681) asymptotic approximation, where the number of instruments grows to infinity at the same rate as the sample size. Usual instrumental variables estimators with a small number of instruments are heuristically argued to be efficient estimators in…

样条非参数回归中的模型选择AI 解读

Summary A Bayesian approach is presented for model selection in nonparametric regression with Gaussian errors and in binary nonparametric regression. A smoothness prior is assumed for each component of the model and the posterior probabilities of the candidate models are approximated using the Bayesian information criterion. We study the model selection method by simulation and show that it has excellent frequentist properties and gives improved estimates of the regression…

伯恩斯坦多项式后验的一致性AI 解读

Summary A Bernstein prior is a probability measure on the space of all the distribution functions on [0, 1]. Under very general assumptions, it selects absolutely continuous distribution functions, whose densities are mixtures of known beta densities. The Bernstein prior is of interest in Bayesian nonparametric inference with continuous data. We study the consistency of the posterior from a Bernstein prior. We first show that, under mild assumptions, the posterior is weakly…

随机波动率模型的贝叶斯分析AI 解读

New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain coverage in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance…

基于自由结点样条的贝叶斯曲线拟合AI 解读

We describe a Bayesian method, for fitting curves to data drawn from an exponential family, that uses splines for which the number and locations of knots are free parameters. The method uses reversible‐jump Markov chain Monte Carlo to change the knot configurations and a locality heuristic to speed up mixing. For nonnormal models, we approximate the integrated likelihood ratios needed to compute acceptance probabilities by using the Bayesian information criterion, BIC, under…

长程相依的贝叶斯半参数推断AI 解读

We develop a Bayesian semiparametric procedure for the analysis of stationary long‐range dependent time series. We use frequency domain methods to partition the infinite‐dimensional parameter space into regions where genuine prior information on the form of the spectral density is available, and others where vague prior beliefs are adopted; the solution to the partition problem, which is equivalent to bandwidth choice from a frequentist point of view, is obtained via Bayes…

含分类协变量的病例对照研究贝叶斯分析AI 解读

In a case‐control study the appropriate likelihood is the ‘retrospective’ likelihood, i.e. the likelihood of exposure given disease. For the classical frequentist analysis, the ‘prospective’ likelihood, i.e. the likelihood of disease given exposure, and the retrospective likelihood produce the same odds‐ratio estimators for exposure, and so logistic regression may be used for both. The Bayesian analysis is not so simple, but the Bayesian framework for case‐control studies…

求职搜寻模型中的最优性检验AI 解读

Models of search in labor markets are potentially of great use for policy analy-sis since their parameters are structural. However, a common feature of these models is that an assumption of optimal behavior on the part of agents is necessary to achieve identifica-tion. From a classical econometric perspective, this means the assumption of optimality is untestable and, if optimality is not imposed, it is impossible to learn about the unidentified parameters. This paper argues…

贝叶斯半参数中位数回归建模AI 解读

Median regression models become an attractive alternative to mean regression models when employing flexible families of distributions for the errors. Classical approaches are typically algorithmic with desirable properties emerging asymptotically. However, nonparametric error models may be most attractive in the case of smaller sample sizes where parametric specifications are difficult to justify. Hence, a Bayesian approach, enabling exact inference given the observed data,…

选择模型的半参数贝叶斯分析AI 解读

Selection models are appropriate when a datum x enters the sample only with probability or weight w(x). It is typically assumed that the weight function w is monotone, but the precise functional form of the weight function is often unknown. In this article, the Dirichlet process prior, centered on a parametric form, is used as a prior distribution on the weight function. This allows for incorporation of knowledge about the weight function, without restricting it to be of…

空间相关数据的客观贝叶斯分析AI 解读

Spatially varying phenomena are often modeled using Gaussian random fields, specified by their mean function and covariance function. The spatial correlation structure of these models is commonly specified to be of a certain form (e.g., spherical, power exponential, rational quadratic, or Matérn) with a small number of unknown parameters. We consider objective Bayesian analysis of such spatial models, when the mean function of the Gaussian random field is specified as in a…

通过边际密度分解进行有限混合模型的贝叶斯选择AI 解读

We consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture model, in which d is bounded by some fixed finite number N. Our approach relies on the use of a prior over the space of mixing distributions with at most N components. By decomposing the resulting marginal density under this prior, we discover a weighted Bayes factor method for consistently estimating d that can be implemented by an iid generalized…