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一期临床试验中基于贝叶斯模型平均的持续再评估法AI 解读

The continual reassessment method (CRM) is a popular dose-finding design for phase I clinical trials. This method requires that practitioners prespecify the toxicity probability at each dose. Such prespecification can be arbitrary, and different specifications of toxicity probabilities may lead to very different design properties. To overcome the arbitrariness and further enhance the robustness of the design, we propose using multiple parallel CRM models, each with a…

大样本下基于 MCMC 的估计量的计算复杂度AI 解读

In this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metropolis random walks. Our analysis is motivated by the Laplace–Bernstein–Von Mises central limit theorem, which states that in large samples the posterior or quasi-posterior approaches a normal density. Using the conditions required for the central limit theorem to hold, we establish polynomial bounds…

后验风险率的渐近理论AI 解读

An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure. In this paper we provide a comprehensive analysis of the asymptotic behavior of such models. We investigate consistency of the posterior distribution and derive fixed sample size central limit theorems for both linear and…

高维正态均值向量估计的非参数经验贝叶斯与复合决策方法AI 解读

We consider the classical problem of estimating a vector μ=(μ1, …, μn) based on independent observations Yi∼N(μi, 1), i=1, …, n. Suppose μi, i=1, …, n are independent realizations from a completely unknown G. We suggest an easily computed estimator μ̂, such that the ratio of its risk E(μ̂−μ)2 with that of the Bayes procedure approaches 1. A related compound decision result is also obtained. Our asymptotics is of a triangular array; that is, we allow the distribution G to…

正态均值的一般最大似然经验贝叶斯估计AI 解读

We propose a general maximum likelihood empirical Bayes (GMLEB) method for the estimation of a mean vector based on observations with i.i.d. normal errors. We prove that under mild moment conditions on the unknown means, the average mean squared error (MSE) of the GMLEB is within an infinitesimal fraction of the minimum average MSE among all separable estimators which use a single deterministic estimating function on individual observations, provided that the risk is of…

已实现波动率预测：贝叶斯模型平均方法AI 解读

Abstract How to measure and model volatility is an important issue in finance. Recent research uses high‐frequency intraday data to construct ex post measures of daily volatility. This paper uses a Bayesian model‐averaging approach to forecast realized volatility. Candidate models include autoregressive and heterogeneous autoregressive specifications based on the logarithm of realized volatility, realized power variation, realized bipower variation, a jump and an asymmetric…

随机效应异方差 Probit 模型的贝叶斯估计AI 解读

Bayesian analysis is given of a random effects binary probit model that allows for heteroscedasticity. Real and simulated examples illustrate the approach and show that ignoring heteroscedasticity when it exists may lead to biased estimates and poor prediction. The computation is carried out by an efficient Markov chain Monte Carlo sampling scheme that generates the parameters in blocks. We use the Bayes factor, cross-validation of the predictive density, the deviance…

混合模型的鞍点近似AI 解读

Two-component mixture distributions with one component a point mass and the other a continuous density may be used as priors for Bayesian inference when sparse representation of an underlying signal is required. We show how saddlepoint approximation in such models can yield highly accurate quantiles for posterior distributions, and illustrate this numerically, using wavelet regression with point mass/Laplace and point mass/normal prior distributions.

随机效应的非参数贝叶斯局部分割模型AI 解读

This paper focuses on the problem of choosing a prior for an unknown random effects distribution within a Bayesian hierarchical model. The goal is to obtain a sparse representation by allowing a combination of global and local borrowing of information. A local partition process prior is proposed, which induces dependent local clustering. Subjects can be clustered together for a subset of their parameters, and one learns about similarities between subjects increasingly as…

非线性混合模型中小区域预测均方误差的刀切估计AI 解读

Empirical Bayes predictors of small area parameters of interest are often obtained under a linear mixed model for continuous response data or a generalized linear mixed model for binary responses or count data. However, estimation of the unconditional mean squared error of prediction is complicated, particularly for a nonlinear mixed model. Jiang et al. (2002) proposed a jackknife method for estimating the unconditional mean squared error and showed that the resulting…

参数数量发散时的收缩调节参数选择AI 解读

Summary Contemporary statistical research frequently deals with problems involving a diverging number of parameters. For those problems, various shrinkage methods (e.g. the lasso and smoothly clipped absolute deviation) are found to be particularly useful for variable selection. Nevertheless, the desirable performances of those shrinkage methods heavily hinge on an appropriate selection of the tuning parameters. With a fixed predictor dimension, Wang and co-worker have…

贝叶斯变量选择程序的一致性AI 解读

It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces a consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise models, and show that for a wide class of prior distributions, including intrinsic priors, the corresponding Bayesian procedure for variable selection in normal regression is consistent in the entire class of normal linear models. We find that…

信念在理性预期模型推断中的作用AI 解读

This paper discusses inference for rational expectations models estimated via minimum distance methods by characterizing the probability beliefs regarding the data generating process (DGP) that are compatible with given moment conditions. The null hypothesis is taken to be rational expectations and the alternative hypothesis to be distorted beliefs. This distorted beliefs alternative is analyzed from the perspective of a hypothetical semiparametric Bayesian who believes the…

多元随机波动率模型中的动态相关结构AI 解读

This paper proposes two types of stochastic correlation structures for Multivariate Stochastic Volatility (MSV) models, namely the constant correlation (CC) MSV and dynamic correlation (DC) MSV models, from which the stochastic covariance structures can easily be obtained. Both structures can be used for purposes of determining optimal portfolio and risk management strategies through the use of correlation matrices, and for calculating Value-at-Risk (VaR) forecasts and…

基于最高后验密度的贝叶斯混合模型标签确定AI 解读

A fundamental problem for Bayesian mixture model analysis is label switching, which occurs as a result of the nonidentifiability of the mixture components under symmetric priors. We propose two labeling methods to solve this problem. The first method, denoted by PM(ALG), is based on the posterior modes and an ascending algorithm generically denoted ALG. We use each Markov chain Monte Carlo sample as the starting point in an ascending algorithm, and label the sample based on…

存在并列与近似并列时总体排名的置信区间AI 解读

Frequentist confidence intervals for population ranks and their statistical justifications are not well established, even though there is a great need for such procedures in practice. How do we assign confidence bounds for the ranks of health care facilities, schools, and financial institutions based on data that do not clearly separate the performance of different entities apart? The commonly used bootstrap-based frequentist confidence intervals and Bayesian intervals for…

存在干扰参数时基于伪似然的先验分布AI 解读

Consider a model parameterized by θ == (ψ, λ), where ψ is the parameter of interest. The problem of eliminating the nuisance parameter λ can be tackled by resorting to a pseudo-likelihood function L**(ψ) for ψ—namely, a function of ψ only and the data y with properties similar to those of a likelihood function. If one treats L**(ψ) as a true likelihood, the posterior distribution π**(ψ | y) ∝ π(ψ)L**(ψ) for ψ can be considered, where π(ψ) is a prior distribution on ψ. The…

干预与因果关系：利用动态贝叶斯网络预测交通流AI 解读

Real-time traffic flow data across entire networks can be used in a traffic management system to monitor current traffic flows so that traffic can be directed and managed efficiently. Reliable short-term forecasting models of traffic flows are crucial for the success of any traffic management system. The model proposed in this article for forecasting traffic flows is a multivariate Bayesian dynamic model called the multiregression dynamic model (MDM). This model is an…

有序贝叶斯社会科学模型的非参数先验：设定与估计AI 解读

A generalized linear mixed model, ordered probit, is used to estimate levels of stress in presidential political appointees as a means of understanding their surprisingly short tenures. A Bayesian approach is developed, where the random effects are modeled with a Dirichlet process mixture prior, allowing for useful incorporation of prior information, but retaining some vagueness in the form of the prior. Applications of Bayesian models in the social sciences are typically…

利用参数与半参数贝叶斯折点回归分析 SEER 癌症发生率AI 解读

Cancer is the second leading cause of death in the United States. Cancer incidence and mortality rates measure the progress against cancer; these rates are obtained from the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute (NCI). Lung cancer has the highest mortality rate among all cancers, whereas prostate cancer has the highest number of new cases among males. In this article, we analyze the incidence rates of these two cancers,…

内禀自回归时空模型及其在汇总出生结局中的应用AI 解读

A class of hierarchical Bayesian models is proposed for adverse birth outcomes such as preterm birth, which are assumed to follow a conditional binomial distribution. The log-odds of an adverse outcome in a particular county, logit(pi), follow a linear model that includes observed covariates and normally-distributed random effects. Spatial dependence between neighboring regions is allowed for by including an intrinsically autoregressive (IAR) prior or an IAR convolution…

古代森林制图：利用化石花粉记录推断森林组成的时空趋势AI 解读

Ecologists use the relative abundance of fossil pollen in sediments to estimate how tree species abundances change over space and time. To predict historical forest composition and quantify the available information, we build a Bayesian hierarchical model of forest composition in central New England, USA, based on pollen in a network of ponds. The critical relationships between abundances of taxa in the pollen record and abundances as actual vegetation are estimated for the…

用于基因关联分析的对数线性模型AI 解读

We describe a class of log-linear models for the detection of interactions in high-dimensional genomic data. This class of models leads to a Bayesian model selection algorithm that can be applied to data that have been reduced to contingency tables using ranks of observations within subjects, and discretization of these ranks within gene/network components. Many normalization issues associated with the analysis of genomic data are thereby avoided. A prior density based on…

利用二元 von Mises 分布与贝叶斯非参数方法估计蛋白质构象角密度AI 解读

Interest in predicting protein backbone conformational angles has prompted the development of modeling and inference procedures for bivariate angular distributions. We present a Bayesian approach to density estimation for bivariate angular data that uses a Dirichlet process mixture model and a bivariate von Mises distribution. We derive the necessary full conditional distributions to fit the model, as well as the details for sampling from the posterior predictive…