论文检索

对称正定矩阵流形上收缩估计的经验贝叶斯方法AI 解读

The James–Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a variety of problems. Nonetheless, research on shrinkage estimation for manifold-valued data is scarce. In this article, we propose shrinkage estimators for the parameters of the Log-Normal distribution defined on the manifold of N × N…

基于经验过程的MCMC经验贝叶斯推断与贝叶斯敏感性分析AI 解读

Consider a Bayesian situation in which we observe $Y\sim p_{\theta}$, where $\theta\in\Theta$, and we have a family $\{\nu_{h},h\in\mathcal{H}\}$ of potential prior distributions on $\Theta$. Let $g$ be a real-valued function of $\theta$, and let $I_{g}(h)$ be the posterior expectation of $g(\theta)$ when the prior is $\nu_{h}$. We are interested in two problems: (i) selecting a particular value of $h$, and (ii) estimating the family of posterior expectations $\{I_{g}(h),h\in\mathcal{H}\}$…

利用再生法估计多条马尔可夫链的归一化常数比及标准误AI 解读

Summary In the classical biased sampling problem, we have k densities π1(·), …,πk(·), each known up to a normalizing constant, i.e., for l = 1, …,k, πl(·)=νl(·)/ml, where νl(·) is a known function and ml is an unknown constant. For each l, we have an independent and identically distributed sample from πl, and the problem is to estimate the ratios ml/ms for all l and all s. This problem arises frequently in several situations in both frequentist and Bayesian inference. An…

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…

随机效应元分析的贝叶斯半参数模型AI 解读

In meta-analysis, there is an increasing trend to explicitly acknowledge the presence of study variability through random-effects models. That is, one assumes that for each study there is a study-specific effect and one is observing an estimate of this latent variable. In a random-effects model, one assumes that these study-specific effects come from some distribution, and one can estimate the parameters of this distribution, as well as the study-specific effects themselves.…

使用马尔可夫链蒙特卡洛构建系统发育树AI 解读

We describe a Bayesian method based on Markov chain simulation to study the phylogenetic relationship in a group of DNA sequences. Under simple models of mutational events, our method produces a Markov chain whose stationary distribution is the conditional distribution of the phylogeny given the observed sequences. Our algorithm strikes a reasonable balance between the desire to move globally through the space of phylogenies and the need to make computationally feasible…

利用 Gibbs 抽样对含冗余设计的相干系统进行贝叶斯非参数估计AI 解读

We consider a coherent system S consisting of m independent components for which we do not know the distributions of the components' lifelengths. If we know the structure function of the system, then we can estimate the distribution of the system lifelength by estimating the distributions of the lifelengths of the individual components. Suppose that we can collect data under the "autopsy model," wherein a system is run until a failure occurs and then the status (functioning…

马尔可夫链模拟方法的收敛性AI 解读

The Markov chain simulation method has been successfully used in many problems, including some that arise in Bayesian statistics. We give a self-contained proof of the convergence of this method in general state spaces under conditions that are easy to verify.

利用局部线性拟合对生命史数据进行非参数回归AI 解读

Most hazard regression models in survival analysis specify a given functional form to describe the influence of the covariates on the hazard rate. For instance, Cox's model assumes that the covariates act multiplicatively on the hazard rate, and Aalen's additive risk model stipulates that the covariates have a linear additive effect on the hazard rate. In this paper we study a fully nonparametric model which makes no assumption on the association between the hazard rate and…

通过逐次替代抽样进行不完整数据的贝叶斯非参数估计AI 解读

In the problem of estimating an unknown distribution function $F$ in the presence of censoring, one can use a nonparametric estimator such as the Kaplan-Meier estimator, or one can consider parametric modeling. There are many situations where physical reasons indicate that a certain parametric model holds approximately. In these cases a nonparametric estimator may be very inefficient relative to a parametric estimator. On the other hand, if the parametric model is only a…

摘要暂缺

摘要暂缺

Cox模型中随协变量变化的中位生存时间置信带AI 解读

Let ξp (x) be the pth quantile of the distribution of the life length of an individual with covariate vector x in the Cox model. We introduce an estimator ξp (x) of ξp (x) and develop several families of confidence bands for ξ(x) as a function of x. To construct one type of band, we proceed as follows. We show that as n → ∞, where n is the number of individuals in the study, ) converges weakly to a Gaussian process W(x) with a complicated covariance structure. We then…

广义 Pearson–Fisher 卡方拟合优度检验及生命历程数据应用AI 解读

Suppose that $X_1,\ldots,X_n$ are i.i.d. $\sim F$, and we wish to test the null hypothesis that $F$ is a member of the parametric family $\mathscr{F} = \{F_\theta(x); \theta \in \Theta\}$ where $\Theta \subset \mathbb{R}^q$. The classical Pearson-Fisher chi-square test involves partitioning the real axis into $k$ cells $I_1,\ldots, I_k$ and forming the chi-square statistic $X^2 = \sum^k_{i = 1}(O_i - nF_{\hat{\theta}}(I_i))^2/nF_{\hat{\theta}}(I_i)$, where $O_i$ is the…

分位数过程弱收敛的初等方法及其在删失生存数据中的应用AI 解读

Let ξ be a continuously differentiable function with positive derivative, and let ξ n be a sequence of right-continuous increasing processes. We show that if n 1/2(ξ n − ξ) W, where W is continuous, then n 1/2(ξ−1 n − ξ−1) − W(ξ−1)/ξ′(ξ−1). This result is applied to classical processes such as the empirical distribution function, the Kaplan-Meier estimator, and some other situations. We also prove an analogous result for the bootstrapped version of n 1/2(ξ n − ξ) and show…

利用相互删失方法联合估计系统与部件可靠性AI 解读

Let $F$ denote the life distribution of a coherent structure of independent components. Suppose that we have a sample of independent systems, all having the same structure. Each system is continuously observed until it fails. For every component in each system, either a failure time or a censoring time is recorded. A failure time is recorded if the component fails before or at the time of system failure; otherwise a censoring time is recorded. We introduce a method for…

两个点过程之间依赖关系的估计AI 解读

To assess the dependence structure in a stationary bivariate point process the second-order distribution can be very useful. We prove that the natural estimates of this distribution, based on a realization $A_1 < A_2 < \cdots < A_{n_A}, B_1 < B_2 < \cdots < B_{n_B}$ are asymptotically normal and we present a method for constructing approximate confidence intervals for this distribution.

不存在无偏估计时降低偏差的代价AI 解读

Let $\phi$ be a parameter for which there is no unbiased estimator. This note shows that for an arbitrary sequence of estimators $T^{(k)}$, if the biases of $T^{(k)}$ tend to 0 then their variances must tend to $\infty$.

中位数的贝叶斯非参数估计：第二部分，估计量的渐近性质AI 解读

For data $\theta + \varepsilon_i, i = 1, \ldots, n$ where $\varepsilon_i$ are i.i.d. $\sim F$ with the median of $F$ equal to $0$ but $F$ otherwise unknown, it is desired to estimate $\theta$. In Doss (1985) priors are put on the pair $(F, \theta)$, the marginal posterior distribution of $\theta$ is computed, and the mean of the posterior is taken as the estimate of $\theta$. In the present paper a frequentist point of view is adopted. The consistency properties of the Bayes…

中位数的贝叶斯非参数估计：第一部分，估计值计算AI 解读

Let $X_i, i = 1, \ldots, n$ be i.i.d. $\sim F_\theta$, where $F_\theta(x) = F(x - \theta)$ for some $F$ that has median equal to 0. $F$ is assumed unknown or only partially known, and the problem is to estimate $\theta$. Priors are put on the pair $(F, \theta)$. The priors on $F$ concentrate all their mass on c.d.f.s with median equal to 0. These priors include "Dirichlet-type" priors. The marginal posterior distribution of $\theta$ given $X_1, \ldots, X_n$ is computed. The…