The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform
Claudio Macci - One of the best experts on this subject based on the ideXlab platform.
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On the Lebesgue Decomposition of the posterior distribution with respect to the prior in regular Bayesian experiments
Statistics & Probability Letters, 1996Co-Authors: Claudio MacciAbstract:Given a regular Bayesian experiment we can consider the Lebesgue Decomposition of the posterior distributions w.r.t. the prior. Then, by using the Lebesgue Decomposition of each sampling distribution w.r.t. the predictive distribution, we show that the absolutely continuous parts of the posteriors are only determined by the absolutely continuous parts of the sampling distributions, while the singular parts of the posteriors are only determined by the singular parts.
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Relationship between the posterior distributions of two regular Bayesian experiments related to a fixed family of sampling distributions
Annali Dell'universita' Di Ferrara, 1994Co-Authors: Claudio MacciAbstract:Let us consider twoRegular Bayesian Experiments (see [1]) related to a fixed family of sampling distributions in which the parameter space and the sample space are assumed to be Polish Spaces. In this paper we shall study the relationship between the posterior distributions of these two Bayesian Experiments considering all the different cases concerning the Lebesgue Decomposition of the second prior distribution w.r.t. the first one.
Tamás Titkos - One of the best experts on this subject based on the ideXlab platform.
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The Singular Part as Fixed Point
The American Mathematical Monthly, 2017Co-Authors: Tamás TitkosAbstract:The aim of this note is to investigate the Lebesgue Decomposition theorem of nonnegative finite measures from a new point of view. Using a standard iteration scheme, we identify the singular part a...
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On the order structure of representable functionals
arXiv: Functional Analysis, 2016Co-Authors: Zsigmond Tarcsay, Tamás TitkosAbstract:The main purpose of this paper is to investigate some natural problems regarding the order structure of representable functionals on $^*$-algebras. We describe the extreme points of order intervals, and give a nontrivial sufficient condition to decide whether or not the infimum of two representable functionals exists. To this aim we offer a suitable approach to the Lebesgue Decomposition theory, which is in complete analogy with the one developed by Ando in the context of positive operators. This tight analogy allows to invoke Ando's results to characterize uniqueness of the Decomposition, and solve the infimum problem over certain operator algebras.
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On the uniqueness of the Lebesgue Decomposition of normal states on $B(H)$
arXiv: Operator Algebras, 2015Co-Authors: Zoltán Sebestyén, Zsigmond Tarcsay, Tamás TitkosAbstract:The non-commutative theory of the Lebesgue-type Decomposition of positive functionals is originated with S. P. Gudder. Although H. Kosaki's counterexample shows that the Decomposition is not unique in general, the complete characterization of uniqueness is still not known. Using the famous operator-Decomposition of T. Ando, we give a necessary and sufficient condition for uniqueness in the particular case when the underlying algebra is $B(H)$, the $C^*$-algebra of all continuous linear operators on a Hilbert space $H$. Namely, given a normal state $f$, the $f$-Lebesgue Decomposition of any other normal state is unique if and only if the representing trace class operator of $f$ has finite rank. Some recent results tell that the Decomposition is unique over a large class of commutative algebras. Our characterization demonstrates that the lack of commutativity is not the real cause of non-uniqueness.
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on the uniqueness of the Lebesgue Decomposition of normal states on b h
arXiv: Operator Algebras, 2015Co-Authors: Zoltán Sebestyén, Zsigmond Tarcsay, Tamás TitkosAbstract:The non-commutative theory of the Lebesgue-type Decomposition of positive functionals is originated with S. P. Gudder. Although H. Kosaki's counterexample shows that the Decomposition is not unique in general, the complete characterization of uniqueness is still not known. Using the famous operator-Decomposition of T. Ando, we give a necessary and sufficient condition for uniqueness in the particular case when the underlying algebra is $B(H)$, the $C^*$-algebra of all continuous linear operators on a Hilbert space $H$. Namely, given a normal state $f$, the $f$-Lebesgue Decomposition of any other normal state is unique if and only if the representing trace class operator of $f$ has finite rank. Some recent results tell that the Decomposition is unique over a large class of commutative algebras. Our characterization demonstrates that the lack of commutativity is not the real cause of non-uniqueness.
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A Simple Proof of the Lebesgue Decomposition Theorem
The American Mathematical Monthly, 2015Co-Authors: Tamás TitkosAbstract:Motivated by the notion of operator, a short and simple proof of Lebesgue's Decomposition theorem is presented in this note.
Genki Yagawa - One of the best experts on this subject based on the ideXlab platform.
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Recursive distribution method for probabilistic structural integrity analysis
Computer Methods in Applied Mechanics and Engineering, 1999Co-Authors: Hiroshi Akiba, Genki YagawaAbstract:The Recursive Distribution (RD) method represents a time-evolution law of a joint distribution function of a random vector which follows a deterministic time-evolution law under the prescription of an initial random vector. The recursive formula for the distribution function can be decomposed into the absolutely continuous part and the singular part, which is the Lebesgue Decomposition of the distribution function. In this paper, a theory of the Lebesgue Decomposition of the recursive formula is discussed, and a numerical algorithm of the RD method is given. The present method is applied to a probabilistic fracture mechanics analysis for piping integrity problem. In order to calculate the probability of the unstable fracture of the pipe, it is needed to evaluate the singular part of the Lebesgue Decomposition. A numerical example and its comparison with the MC method are presented.
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Recursive distribution method for probabilistic fracture mechanics and its application to evaluation of LWR piping
1996Co-Authors: Hiroshi Akiba, Masabumi Suzuki, Shinobu Yoshimura, Genki YagawaAbstract:The present authors have previously developed a new method for Probabilistic Fracture Mechanics (PFM), which they call Recursive Distribution (RD) method. The method is based on the construction of the Lebesgue-Stieltjes measure through a deterministic mapping defining a crack growth process. In the present paper, its theoretical background is first discussed, and the Lebesgue Decomposition of the measure is given. Then a numerical example of a Light Water Reactor (LWR)`s piping problem is solved by the present method, and the results are compared with those of the Monte Carlo (MC) method. In addition to leakage probability, a variation in stress cycles of the marginal distribution of an aspect ratio of a semi-elliptical surface crack is calculated, which will be used in a study on LBB evaluation.
Hiroshi Akiba - One of the best experts on this subject based on the ideXlab platform.
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Recursive distribution method for probabilistic structural integrity analysis
Computer Methods in Applied Mechanics and Engineering, 1999Co-Authors: Hiroshi Akiba, Genki YagawaAbstract:The Recursive Distribution (RD) method represents a time-evolution law of a joint distribution function of a random vector which follows a deterministic time-evolution law under the prescription of an initial random vector. The recursive formula for the distribution function can be decomposed into the absolutely continuous part and the singular part, which is the Lebesgue Decomposition of the distribution function. In this paper, a theory of the Lebesgue Decomposition of the recursive formula is discussed, and a numerical algorithm of the RD method is given. The present method is applied to a probabilistic fracture mechanics analysis for piping integrity problem. In order to calculate the probability of the unstable fracture of the pipe, it is needed to evaluate the singular part of the Lebesgue Decomposition. A numerical example and its comparison with the MC method are presented.
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Recursive distribution method for probabilistic fracture mechanics and its application to evaluation of LWR piping
1996Co-Authors: Hiroshi Akiba, Masabumi Suzuki, Shinobu Yoshimura, Genki YagawaAbstract:The present authors have previously developed a new method for Probabilistic Fracture Mechanics (PFM), which they call Recursive Distribution (RD) method. The method is based on the construction of the Lebesgue-Stieltjes measure through a deterministic mapping defining a crack growth process. In the present paper, its theoretical background is first discussed, and the Lebesgue Decomposition of the measure is given. Then a numerical example of a Light Water Reactor (LWR)`s piping problem is solved by the present method, and the results are compared with those of the Monte Carlo (MC) method. In addition to leakage probability, a variation in stress cycles of the marginal distribution of an aspect ratio of a semi-elliptical surface crack is calculated, which will be used in a study on LBB evaluation.
Qiang Zhang - One of the best experts on this subject based on the ideXlab platform.
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Lebesgue Decomposition theorem for σ-finite signed fuzzy measures
Fuzzy Sets and Systems, 1999Co-Authors: Qiang ZhangAbstract:Further research on signed fuzzy measures is made. Lebesgue Decomposition theorems for σ-finite signed fuzzy measures and fuzzy measures are proved under the null-null additive condition. Thus, the relative result in classical measure theory is generalized.
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On the applied basis of /spl lambda/-additive fuzzy measures
1997 IEEE International Conference on Intelligent Processing Systems (Cat. No.97TH8335), 1Co-Authors: Qiang ZhangAbstract:The relationship between probability measures and /spl lambda/-additive fuzzy measures is used to give the definition of the product measures of /spl lambda/-additive fuzzy measures and Fubini's theorem is discussed. A Lebesgue Decomposition-like theorem, Kolmogorov's zero-one law and the important Borel-Cantelli lemma for /spl lambda/-additive fuzzy measures are established.