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利用高分辨率贝叶斯隐马尔可夫正态混合模型进行 MRI 组织分类AI 解读

Magnetic resonance imaging (MRI) is used to identify the major tissues within a subject's brain. Classification is usually based on a single image providing one measurement for each volume element, or voxel, in a discretization of the brain. A simple model views each voxel as homogeneous, belonging entirely to one of the three major tissue types: gray matter, white matter, or cerebrospinal fluid. The measurements are normally distributed, with means and variances depending…

含无关数据与核验偏差样本的非参数极大似然估计AI 解读

Suppose that some measurements come from a distribution F that is of interest and others come from another, irrelevant distribution G. Some measurements from F are verified and known to be from F. The other, unverified measurements may be from F or from G. Not all measurements from F are equally likely to be verified, and no measurement from G is ever verified. This model applies to measurements of low concentrations obtained using gas chromatography/mass spectroscopy, for…

含无关数据与核验偏差样本的非参数最大似然估计AI 解读

Suppose that some measurements come from a distribution F that is of interest and others come from another, irrelevant distribution G. Some measurements from F are verified and known to be from F. The other, unverified measurements may be from F or from G. Not all measurements from F are equally likely to be verified, and no measurement from G is ever verified. This model applies to measurements of low concentrations obtained using gas chromatography/mass spectroscopy, for…

探索后验分布的马尔可夫链方法AI 解读

Several Markov chain methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm. In addition, several strategies are available for constructing hybrid algorithms. This paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues. On the theoretical side, results from the theory of general state space Markov chains can be used to obtain…

非正函数期望与方差的完全指数型拉普拉斯近似AI 解读

Tierney and Kadane (1986) presented a simple second-order approximation for posterior expectations of positive functions. They used Laplace's method for asymptotic evaluation of integrals, in which the integrand is written as f(θ)exp(-nh(θ)) and the function h is approximated by a quadratic. The form in which they applied Laplace's method, however, was fully exponential: The integrand was written instead as exp[− nh(θ) + log f(θ)]; this allowed first-order approximations to…

贝叶斯分析中影响与敏感性评估的近似方法AI 解读

We use asymptotic approximations to posterior expectations in deriving diagnostics for case influence and prior sensitivity. We obtain an easily-interpreted expression for the change in posterior expectation following perturbation of the problem, which also produces a useful interpretation of the likelihood displacement discussed by Cook & Weisberg (1982). In addition, we propose two simple diagnostics of posterior nonnor mality. The leukaemia data analysed by Feigl & Zelen…

非线性函数的边际密度近似AI 解读

This paper presents an asymptotic approximation for the marginal density of a nonlinear function g(θ) that is applicable when the joint density of θ is dominated by a single mode and the Jacobian of g is of full rank near that mode. The approximation is based on Laplace's method and its asymptotic properties are similar to those of the saddlepoint approximation. The approximation is applied to the computation of a marginal posterior density, a marginal sampling density and a…

Hájek 表示定理的一种替代正则条件AI 解读

Hajek's representation theorem states that under certain regularity conditions the limiting distribution of an estimator can be written as the convolution of a certain normal distribution with some other distribution. This result, originally developed for finite dimensional problems, has been extended to a number of infinite dimensional settings where it has been used, for example, to establish the asymptotic efficiency of the Kaplan-Meier estimator. The purpose of this note…

后验矩与边际密度的精确近似方法AI 解读

This article describes approximations to the posterior means and variances of positive functions of a real or vector-valued parameter, and to the marginal posterior densities of arbitrary (i.e., not necessarily positive) parameters. These approximations can also be used to compute approximate predictive densities. To apply the proposed method, one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima.…

混合泊松模型中极大似然估计的渐近性质AI 解读

This paper considers the asymptotic behavior of the maximum likelihood estimators (mle's) of the probabilities of a mixed Poisson distribution with a nonparametric mixing distribution. The vector of estimated probabilities is shown to converge in probability to the vector of mixed probabilities at rate $n^{1/2-\varepsilon}$ for any $\varepsilon > 0$ under a generalized $\chi^2$ distance function. It is then shown that any finite set of the mle's has the same joint limiting…

混合分布泛函估计量的渐近效率AI 解读

Suppose $F$ is a mixture of a known parametric family of distributions with an unknown nonparametric mixing distribution. Consider the problem of estimating the value $T(dF)$ of a smooth functional $T$ at the mixed distribution $F$. One nonparametric estimator of $T(dF)$ is $T(dF_n)$ where $F_n$ denotes the empirical distribution. Under a differentiability condition on $T$ given in this note, $T(dF_n)$ is shown to be fully efficient asymptotically in the sense that the…