日期精度：到日 2009 篇 · 到月 2034 篇 · 到年 253 篇 · 未提供 1 篇
参数约束不确定性下的贝叶斯估计
When estimating a normal location parameter, an inequality constraint is sometimes indicated by theoretical considerations. If, however, this constraint is assumed a priori definitely to hold, then the data will never be permitted to formally contradict the theory. We propose a family of skew prior distributions which reflect uncertainty about the constraint.
多参数估计的若干替代方法
Bayesian and classical alternatives are considered, interpreted, and compared with simultaneous estimation methods in the literature. The main topics explored are the estimation of several normal means, and of several binomial or Poisson parameters. An empirical comparison and three real examples are included.
回归问题的贝叶斯分析
A general Bayesian formulation of the regression problem is considered, which derives from a direct specification of a prior distribution for the unknown joint probability distribution of the random variables. The resulting estimators are related to the least squares and ridge estimators of the regression coefficients.
贝叶斯序贯检验的频率学派性质
Let X1 , X2 , … denote independent random variables which are normally distributed with unknown mean θ and unit variance. We consider sequential tests of the hypothesis H0 : θ < –δ versus H1 : θ > δ. The tests which we consider were shown by Schwarz (1962) to approximate the optimal Bayesian tests with respect to a general loss structure and any prior density which is everywhere positive. Their continuation regions are bounded subsets of the ( n , S n ) plane, where S n is…
Empirical Bayes estimators, asymptotically optimal with rates, are proposed. In the component problem there is a pair $(X, \omega)$ of real valued random variables. The Lebesgue density of $X$, conditional on $\omega$, is of the form $u(x)C(\omega)e^{\omega x}$. Based on a realization of $X$, the problem is squared error loss estimation of $\omega$. Let $G$ be a prior distribution on $\omega$, and $R(G)$ be the Bayes optimal risk wrt $G$. Using $(X_1, \cdots, X_n)$, the…
将随机效应估计纳入 Gauss–Markov 定理的扩展
The general mixed linear model can be written $y = X\alpha + Zb$, where $\alpha$ is a vector of fixed effects and $b$ is a vector of random variables. Assume that $E(b) = 0$ and that $\operatorname{Var} (b) = \sigma^2D$ with $D$ known. Consider the estimation of $\lambda_1'\alpha + \lambda_2'\beta$, where $\lambda_1'\alpha$ is estimable and $\beta$ is the realized, though unobservable, value of $b$. Among linear estimators $c + r'y$ having $E(c + r'y) \equiv E(\lambda_1'\alpha + \lambda_2'b)$…
位置向量坐标的广义贝叶斯估计可容许性
Let $X$ be an $n$-dimensional random vector with density $f(x - \theta)$. It is desired to estimate $\theta_1$, under a strictly convex loss $L(\delta - \theta_1)$. If $F$ is a generalized Bayes prior density, the admissibility of the corresponding generalized Bayes estimator, $\delta_F$, is considered. An asymptotic approximation to $\delta_F$ is found. Using this approximation, it is shown that if (i) $f$ has enough moments, (ii) $L$ and $F$ are smooth enough, and (iii) $F(\theta) \leqq K(|\theta_1| + \sum^n_{i=2} \theta_i^2)^{(3-n)/2}$…
位置向量坐标的广义贝叶斯估计量不可容许性结果
Let $X = (X_1, \cdots, X_n)$ be an $n$-dimensional random vector with density $f(x - \theta)$. Assume the loss incurred in estimating $\theta$ by $d$ is $L(d - \theta)$ and is convex. Let $F$ be a generalized prior density. The question of inadmissibility of generalized Bayes estimators of $\theta$ is considered. As in Brown (1974c), the crucial role played by the "moment structure" in determining inadmissibility results is indicated (moments defined as the quantities $m_{i,j(1), \cdots, j(l)} = \int \prod^l_{k=1} x_{j(k)} \cdot \lbrack(\partial/\partial x_i)L(x)\rbrack f(x) dx)$…
均匀先验导致的强不一致性
Behavior of this type will be called strong inconsistency. Box and Tiao [2, p. 310] might, apparently, tolerate such behavior by the simple device of ignoring (1.3), which, based on a sampling distribution, is regarded as irrelevant to the Bayesian inference. In support orf this, Box and Tiao [2, p. 304] could employ once again a form of argument used to defend a particular improper prior in their analysis of the random effects model; namely, that (a) for any particular x,…
评论：非可积先验在贝叶斯推断中的作用
This illuminating paper by Stone is the latest in a series of papers drawing attention to possible disadvantages of using nonintegrable prior densities. In these comments, I shall attempt to clarify the role of nonintegrable prior densities in Bayesian inference, thereby providing also a delayed answer to James and Stein [5], Dempster [1], Stone [9], Klotz, et al. [6], and Portnoy [7]. More extensive discussion of the ideas introduced will be given in a subsequent paper.
具有相关扰动的线性模型之间的判别
PROBLEMS OF COMPARING or choosing among models of a stochastic process are frequently encountered in empirical research. In many such situations, conventional statistical procedures offer little guidance since they assume that the model is given. If the alternative models can be nested in a more general model, standard estimation and testing procedures can be employed. Often, however, such general models are not readily available and other considerations may dictate against…
多元经验贝叶斯与协方差矩阵估计
The problem of estimating several normal mean vectors in an empirical Bayes situation is considered. In this case, it reduces to the problem of estimating the inverse of a covariance matrix in the standard multivariate normal situation using a particular loss function. Estimators which dominate any constant multiple of the inverse sample covariance matrix are presented. These estimators work by shrinking the sample eigenvalues toward a central value, in much the same way as…
预测分析的渐近方法
An asymptotic approach to inference problems in prediction analysis is discussed. An approximation for the Bayesian predictive distribution is derived and a correspondence with a classical method noted. A comparative example is given for the exponential model.
推断与缺失数据
When making sampling distribution inferences about the parameter of the data, θ, it is appropriate to ignore the process that causes missing data if the missing data are ‘missing at random’ and the observed data are ‘observed at random’, but these inferences are generally conditional on the observed pattern of missing data. When making direct-likelihood or Bayesian inferences about θ, it is appropriate to ignore the process that causes missing data if the missing data are…
后验联合众数与边际众数
Posterior joint modes have often been used as point estimators in Bayesian applications to avoid laborious numerical integration of complicated posterior densities. We present methods facilitating the straightforward computation of posterior marginal modes in a wide variety of models, and discuss whether marginal modes provide better approximations than joint modes to the posterior means.
多参数估计的若干替代方法
Bayesian and classical alternatives are considered, interpreted, and compared with simultaneous estimation methods in the literature. The main topics explored are the estimation of several normal means, and of several binomial or Poisson parameters. An empirical comparison and three real examples are included.
回归问题的贝叶斯分析
A general Bayesian formulation of the regression problem is considered, which derives from a direct specification of a prior distribution for the unknown joint probability distribution of the random variables. The resulting estimators are related to the least squares and ridge estimators of the regression coefficients.
关于“随机变量序列变点推断的贝叶斯方法”的文献提示
The author's attention has been drawn to a similar approach: BROEMELING, L. D. (1974). Bayesian inferences about a changing sequence of random variables. Comm. Statist. 3, 243–55.
von Mises–Fisher 分布的贝叶斯推断
The main aim of this note is to give a theoretical discussion of Bayesian inference for the von Mises-Fisher distribution. The choice of particular priors is considered and the admissibility of certain Bayesian estimators studied. For the multisample case estimators are given. Some problems of testing hypotheses are summarized in the form of posterior odds against the null hypothesis.
参数约束存在不确定性时的贝叶斯估计
When estimating a normal location parameter, an inequality constraint is sometimes indicated by theoretical considerations. If, however, this constraint is assumed a priori definitely to hold, then the data will never be permitted to formally contradict the theory. We propose a family of skew prior distributions which reflect uncertainty about the constraint.
基于自回归先验的批次验收方案
In many batch sampling situations it is reasonable to assume that a correlation exists between the true mean qualities of successively produced batches. A model considered by Campling (1968) is here reanalyzed using the Bayesian linear model framework of Lindley & Smith (1972), and a wider class of serial sampling acceptance schemes derived and compared.
贝叶斯序贯检验的频率学性质
Let X1 , X2 , … denote independent random variables which are normally distributed with unknown mean θ and unit variance. We consider sequential tests of the hypothesis H0 : θ < –δ versus H1 : θ > δ. The tests which we consider were shown by Schwarz (1962) to approximate the optimal Bayesian tests with respect to a general loss structure and any prior density which is everywhere positive. Their continuation regions are bounded subsets of the ( n , S n ) plane, where S n is…