A mixed theory of information—X: Information functions and information measures

In the probabilistic theory of information, measures of information depend only upon the probabilities of the events, whereas in the nonprobabilistic theory these measures depend only upon the events. In a new, mixed theory of information the measures of information are assumed to depend on both the probabilities and the events. In this paper we consider measures depending upon a n-tuple of events and upon a finite number of n-ary complete, discrete probability distributions and characterize these measures of information only by two properties: by a recursivity condition, which states how the information changes by splitting one event of a system (one outcome of an experiment, market situation etc.) into two events, and by a weak symmetry condition (no regularity condition is assumed). Our result generalizes all recent results on this topic and especially we get from this one theorem a lot of characterization theorems for some well-known (purely probabilistic) information measures like the Shannon entropy, the entropy of degree α, the inaccuracy, the directed divergence, and the information improvement.     

A Note on the characterization of Shannon-Wiener’s measure of information

Summary In [1] the author treated a characterization problem of the ShannonWiener measure of information for continuous probability distributions defined over an abstract measure space (R, S, m), wherem is a σ-finite measure over a σ-field S of subsets ofR, whose rangeM(S) is such thatM(S)=[0, ∞]. This condition on the range of the basic measure, however, can slightly be altered such thatM(S)=[0,1], and this modification is useful for characterization of the Kullback-Leibler mean information. In the present paper, it is shown that the characterization procedure of [1] can be applicable to continuous probability distributions defined on a finite measure space.     

Linear information for approximation of the Itô integrals

We study optimal approximation of stochastic integrals in the Itô sense when linear information, consisting of certain integrals of trajectories of Brownian motion, is available. Upper bounds on the nth minimal error, where n is the fixed cardinality of information, are obtained by the Wagner–Platen algorithm and are O(n ^???3/2) or O(n ^???2), depending on considered class of integrands. We also show that Ω(n ^???2) is a lower bound which holds even for very smooth integrands.     

Subscription information

ISSN Print edition:1006一9283 ISSN 616CtroniC edition:1862一2763 Volume 49(12 issues)WIll aPPearin2006 SubscriPtion rates For information on subseriPtion rates Please eontaet: CUStomer ServiCe China:sales@seiehina力rg North and SOUth AmeriCa: lournals一ny@sPringer·sbm.eom OUtside NOrth and SOUth AmeriCa: SDC一Journals@sPringer一sbm.eom Orders and inquiries: China SCienCe in China PreSS 16DonghuangehenggenNorthstreet，Beiiing100717，Chins Te}: 86 1 0 64034559 Of 86 1 0 …     

Subscription information

ISSN Print edition:1006一9283 ISSN electronic edition:Pending Vo!ume 49(12 issues)will aPPear in 2006 SubscriPtion rates For information on subseriPtion rates Please eontaet: Customer ServiCe China:sales@seiehina.org North and SOUth Amerioa: iournals一ny@sPringer一sbm.eom OUtside NOrth and SOUth AmeriCa: SDC一iournals@sPringer一sbm，eom Orders and inquiries: China SCienCe in China PreSS 华ponghUangChenggen North Street，Beijing 100717 切n}na Tel: 86 1 0 64034559 or 86 1 0 …     

Subscription information

ISSN Print edition:1006一9283 ISSN G16Ctronio edition:1862·2763 Volume 49(12 issues)will aPPearin2006 SUbSCriotion rates For information on subseriPtion CUStomer SerVICe rates Please eontaet: China:sales@seiehina.org NOrth and SOUth AmeriC日: iournals一ny@sPringer-sbm.eom Outsid6 North and SOUth AmeriCa: SDCjournals@sPringer一sbm.eom Orders and inquiries: China SeienCe in China PreSS华一onghuangchenggen North St『eet，Beijing 100717，七产日Ina Tel: 86 1 0 64034559 or 86…     

Subscription information

ISSN Print edition:1006一9283 ISSN el6CtroniC 6dition:1862一2763 Volume 50(12 issues)w川aPPearjn2007 SubscriPtion rates For information on subseriPtion rates Please eontaet: CUStomer SeFVICe China:sales@seiehina.org NOrth and SOUth AmeriCa: lournals一ny@s…     

Quasi-likelihood estimation of average treatment effects based on model information

In this paper, the estimation of average treatment effects is considered when we have the model information of the conditional mean and conditional variance for the responses given the covariates. The quasi-likelihood method adapted to treatment effects data is developed to estimate the parameters in the conditional mean and conditional variance models. Based on the model information, we define three estimators by imputation, regression and inverse probability weighted methods. All the estimators are shown asymptotically normal. Our simulation results show that by using the model information, the substantial efficiency gains are obtained which are comparable with the existing estimators.     

Adaptive spline–wavelet decompositions of two-dimensional numerical information flows

We consider triangulations of a domain that admit a local enlargement such that the obtained triangulation remains topologically correct. We discuss embedded Courant spaces for embedded triangulations and adaptive spline-wavelet decompositions of these spaces. The decomposition and reconstruction formulas for two-dimensional numerical flows are deduced. Bibliography: 5 titles.     

“Value” of additional information in multicriterion analysis under uncertainty

The expected value of information in classical (monocriterion) decision analysis has been well covered in the literature. One cannot say the same thing about the multicriterion analysis, particularly when one is in the presence of multicriterion aggregation procedures based on outranking relations for a ranking problematic. The objective of this paper is to try to extend the Bayesian approach to a multicriterion analysis in the context of uncertainty. After illustrating the a posteriori analysis, we shall mention some difficulties associated with the pre a posteriori analysis and the concepts of the “expected value” of perfect or imperfect information.     

Necessary conditions for the convergence of kullback-leibler’s mean information

Summary Two types of necessary conditions are given for the convergence of Kullback-Leibler’s mean information, one of which is connected with an asymptotic equivalence of two sequences of probability measures, and in special cases, with convergence of a sequence of probability distributions. The other is given in terms of the generalized probability density functions.