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参数空间边界众数情形下后验期望的 Laplace 近似AI 解读

This article gives asymptotic expansions for posterior expectations when the mode is on the boundary of the parameter space. The idea, based on the divergence theorem, is to reduce the high-dimensional integrals over the parameters space to surface integrals over the boundary of the parameter space and then apply the usual interior-mode Laplace method to the latter integrals. It is shown that these approximations have second-order accuracy. The method is illustrated with…

错位且经像素平均的图像中的位移估计AI 解读

In problems where the recorded signal comprises two or more bands (i.e., wavelengths), it is often the case that the bands are not perfectly aligned in the focal plane. Such misregistration may be caused by atmospheric or oceanographic effects, which refract different bands to differing degrees, or it may result from features of the design of the recording equipment. This article develops two methods for estimating the lag, or the amount by which the bands are out of…

用于预测的神经网络模型AI 解读

In this article we introduce a neural net designed for nonlinear statistical prediction. The net is based on a stochastic model featuring a multilayer feedforward architecture with random connections between units and noisy response functions. A Bayesian inferential procedure for this model, based on the Kalman filter, is derived. The resulting learning algorithm generalizes the so-called onedimensional Newton method, an updating algorithm currently popular in the neural net…

异方差回归模型的拟合AI 解读

In heteroscedastic regression models assumptions about the error distribution determine the method of consistent estimation of parameters. For example, consider the case where the model specifies the regression and dispersion functions for the data but robustness is of concern and one wishes to use least absolute error regressions. Except in certain special circumstances, parameter estimates obtained in this way are inconsistent. In this article we expand the heteroscedastic…

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多元密度估计：理论、实践与可视化AI 解读

Representation and Geometry of Multivariate Data. Nonparametric Estimation Criteria. Histograms: Theory and Practice. Frequency Polygons. Averaged Shifted Histograms. Kernel Density Estimators. The Curse of Dimensionality and Dimension Reduction. Nonparametric Regression and Additive Models. Special Topics. Appendices. Indexes.

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Consider statistical inference about a scalar parameter and suppose that information about that parameter is to be summarized by a system of interval estimates. It is well known that methods of interval estimation that do not correspond to Bayesian inference with respect to some prior distribution have some logical difficulties. This article proposes a measure of how close a system of interval estimates is to being of Bayesian form. Using this measure, several non-Bayesian…

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逐步决策程序与置信集之间的关系AI 解读

This article considers the relationship between two standard methods of inference on a set of A: unknown parameters, namely stepwise decision procedures and the construction of simultaneous confidence intervals. Illustrative examples with k = 2 are discussed for one-sided step-down and step-up decision procedures and for a two-sided step-down decision procedure. For these examples with normal distributional assumptions, a set of confidence intervals associated with the…

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Marshall–Olkin二元指数分布的一种扩展AI 解读

This article extends Marshall and Olkin's bivariate exponential distribution such that it is absolutely continuous and need not be memoryless. The new marginal distribution has an increasing failure rate, and the joint distribution exhibits an aging pattern. It offers an advantage in separately identifying the shock arrival rates and their impacts. Regarding estimation of the model, both maximum likelihood and method-of-moments-type estimation are considered. The former is…

以相等概率抽取树的叶节点AI 解读

In the computer sciences, trees are among the most common data structures. Knuth proposed a method of sampling the leaves of a tree with known but unequal probabilities; he used the sample to estimate the behavior of backtrack algorithms. This article proposes two methods for sampling leaves with equal probabilities.

基于信息更丰富样本的单调经验贝叶斯估计AI 解读

An empirical Bayes estimator is constructed for the case of nonidentical components coming from an exponential family of distributions that is closed under convolution. Examples are the normal, Poisson, and binomial distributions. The construction is based on Robbins' approach to empirical Bayes estimation and generalizes results of O'Bryan and Stijnen and Van Houwelingen. The method is elaborated for the normal and Poisson case, and examples are given that show that this…

信息冲突下的后验何时渐近正态？AI 解读

When data conflicts with quantified prior beliefs, seemingly small changes in the functional form of the prior and/or likelihood can have a profound effect on posterior inferences. This article provides results on asymptotic forms of the posterior when two information sources conflict. In particular, let x be from the likelihood p 2(x − θ) with an unknown location parameter θ, with p 1(θ) the prior on θ. Sufficient conditions on p 1 and p 2 are provided to ensure that as x →…

涉及指数族的贝叶斯推断中后验累积量的关系AI 解读

For Bayesian inference in one-parameter contexts where either the likelihood or the prior has an exponential family form, relationships are derived for posterior moments and cumulants of (functions of) both the canonical and the expectation parameters. The identities exhibited generalize the simple relationships well known in the conjugate analysis case. Applications of these results are indicated in the areas of Bayesian robustness and approximation. In particular, results…

对线性回归模型生成的对象进行聚类AI 解读

This article describes a new clustering method designed for objects generated by a linear model with different states. The objective is to divide the objects into clusters, with each cluster containing only the objects taken when the system is in one particular state. The cluster centroids are matrices of predetermined rank and can be computed by the singular value decomposition (SVD) algorithm. The clustering problem is formulated as a combinatorial optimization problem.…

反卷积、频带限制与四阶谱AI 解读

In the largest application area of time series analysis—geophysical exploration—the underlying innovations sequence is of primary interest and must be estimated. This sequence is estimated by deconvolving the non-Gaussian, noninvertible time series. This involves estimation of a phase-shift correction from the time series, which can be carried out by maximizing the kurtosis of the series. Unfortunately, the method is hampered by the fact that the time series is typically…

L1回归估计量分布的解析与自助法近似AI 解读

Edgeworth and bootstrap approximations to estimator distributions in L1 regression are described. Analytic approximations based on Edgeworth expansions that mix lattice and nonlattice components and allow for an intercept term in the regression are developed under mild conditions, which do not even require a density for the error distribution. Under stronger assumptions on the error distribution, the Edgeworth expansion assumes a simpler form. Bootstrap approximations are…

基于功效准则的最优核权重AI 解读

We develop an approach to choosing optimal kernel weights for nonparametric estimation of the slope of the regression function which uses maximization of power, rather than minimization of integrated mean squared error (IMSE), as its optimality criterion. This power criterion leads to optimal kernel weights whose derivation is simpler than under other criteria and which provides an intuitive understanding of the nature of the optimality.