增长曲线模型（一般协方差结构）的Bayes影响分析

本文讨论具有一般协方差结构的增长曲线模型中未知参数矩阵的Ｂａｙｅｓ影响分析问题．在无信息先验分布假设下,Ｋ－Ｌ距离被用来评估指定响应阵对参数矩阵的后验分布的影响程度．     

信息复杂性准则的深入探讨

介绍联系拟合优度与模型复杂性测度的一种模型选择准则一信息复杂性(ICOMP)准则的基本原理.由Bozdogan提出的信息复杂性(ICOMP)准则可以视为两个Kullback-Leibler距离之和的一种近似.首先研究了所考虑模型中有真实模型的情况下,ICOMP准则类的渐近相容性;然后又介绍并完成了所考虑模型中没有真实模型的情况下,ICOMP准则类的渐近相容性.在有限样本容量的情况下,用ICOMP准则选择的估计模型,比用其他通用的准则选择的估计模型,更接近于真实模型.     

A Fenchel Duality Aspect of Iterative I-Projection Procedures

In this paper we interpret Dykstra's iterative procedure for finding anI-projection onto the intersection of closed, convex sets in terms of itsFenchel dual. Seen in terms of its dual formulation, Dykstra's algorithm isintuitive and can be shown to converge monotonically to the correctsolution. Moreover, we show that it is possible to sharply bound thelocation of the constrained optimal solution.     

Combining marginal probability distributions via minimization of weighted sum of Kullback-Leibler divergences

This paper deals with the problem of combining marginal probability distributions as a means for aggregating pieces of expert information. A novel approach, which takes the combining problem as an analogy of statistical estimation, is proposed and discussed. The combined distribution is then searched as a minimizer of a weighted sum of Kullback-Leibler divergences of the given marginal distributions and corresponding marginals of the searched one. Necessary and sufficient conditions for a distribution to be a minimizer are stated. For discrete random variables an iterative algorithm for approximate solution of the minimization problem is proposed and its convergence is proved.     

Scaled Bregman divergences in a Tsallis scenario

There exist two different versions of the Kullback-Leibler divergence (K-Ld) in Tsallis statistics, namely the usual generalized K-Ld and the generalized Bregman K-Ld. Problems have been encountered in trying to reconcile them. A condition for consistency between these two generalized K-Ld forms is derived by recourse to the additive duality of Tsallis statistics. It is also shown that the usual generalized K-Ld subjected to this additive duality, known as the dual generalized K-Ld, is a scaled Bregman divergence. This leads to an interesting conclusion: the dual generalized mutual information is a scaled Bregman information. The utility and implications of these results are discussed.     

Approximating conditional density functions using dimension reduction

We propose to approximate the conditional density function of a random variable Y given a dependent random d-vector X by that of Y given θ^τX, where the unit vector θ is selected such that the average Kullback-Leibler discrepancy distance between the two conditional density functions obtains the minimum. Our approach is nonparametric as far as the estimation of the conditional density functions is concerned. We have shown that this nonparametric estimator is asymptotically adaptive to the unknown index θ in the sense that the first order asymptotic mean squared error of the estimator is the same as that when θ was known. The proposed method is illustrated using both simulated and real-data examples.     

Entropic Kullback-Leibler type distance measures for quantum distributions

Entropic distance measures for quantum mechanical probability distributions, which are characterized by nodal structure and symmetry holes, are considered. We illustrate how the Kullback-Leibler (KL) distance is not well defined in some instances and propose instead the use of the cumulative residual Kullback-Leibler (CRKL) distance. The KL and CRKL measures are compared and contrasted for some representative quantum mechanical systems: The particle in an infinite well, the harmonic oscillator, and hydrogenic systems. We present cases where CRKL can be used to obtain distances whereas KL cannot be used, and also highlight examples where the KL and CRKL measures yield different behaviors and interpretations. An extension of the CRKL definition is obtained for application to harmonic oscillator systems defined over [−∞, ∞]. Distance measures for two-variable (particle) distributions are also considered to address generalizations of the mutual information correlation measure. The use of CRKL in measuring distances between orbitals is also discussed.     

Constructing elementary procedures for inference of the gamma distribution

The aim of the present paper is to construct a series of estimators and tests in the one and the two sample problems in the gamma distribution through the Kullback-Leibler loss. Some of them are newly introduced here. When the approach is applied to the case of the normal distribution, the well known estimators and tests are derived. It is found that the conditional maximum likelihood estimator of the dispersion parameter plays a key role.     

Heat and entropy in nonextensive thermodynamics

The concepts of the quantity of heat and work are deduced in the context of non-extensive statistical mechanics, following steps parallel to those employed in extensive statistical mechanics.Received: 31 January 2003, Accepted: 6 May 2003, Published online: 21 November 2003PACS: 05.70.-a, 05.30.-d, 05.90. + m     

Equity Market Description under High and Low Volatility Regimes Using Maximum Entropy Pairwise Distribution

The financial market is a complex system in which the assets influence each other, causing, among other factors, price interactions and co-movement of returns. Using the Maximum Entropy Principle approach, we analyze the interactions between a selected set of stock assets and equity indices under different high and low return volatility episodes at the 2008 Subprime Crisis and the 2020 COVID-19 outbreak. We carry out an inference process to identify the interactions, in which we implement the a pairwise Ising distribution model describing the first and second moments of the distribution of the discretized returns of each asset. Our results indicate that second-order interactions explain more than 80% of the entropy in the system during the Subprime Crisis and slightly higher than 50% during the COVID-19 outbreak independently of the period of high or low volatility analyzed. The evidence shows that during these periods, slight changes in the second-order interactions are enough to induce large changes in assets correlations but the proportion of positive and negative interactions remains virtually unchanged. Although some interactions change signs, the proportion of these changes are the same period to period, which keeps the system in a ferromagnetic state. These results are similar even when analyzing triadic structures in the signed network of couplings.