相关论文: On the proper treatment of improper distributions

In 1933 Kolmogorov constructed a general theory that defines the modern concept of conditional probability. In 1955 Renyi fomulated a new axiomatic theory for probability motivated by the need to include unbounded measures. We introduce a…

In 1933 Kolmogorov constructed a general theory that defines the modern concept of conditional expectation. In 1955 Renyi fomulated a new axiomatic theory for probability motivated by the need to include unbounded measures. We introduce a…

The purpose of this paper is to present a mathematical theory that can be used as a foundation for statistics that include improper priors. This theory includes improper laws in the initial axioms and has in particular Bayes theorem as a…

Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…

Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables,…

Kolmogorov's first axiom of probability is probability takes values between 0 and 1; however, in Cox's derivation of probability having a maximum value of unity is arbitrary since he derives probability as a tool to rank degrees of…

This is a chapter for the forthcoming New Handbook of Mathematical Psychology, to be published by Cambridge University Press. A systematic theory of random variables and joint distributions under varying conditions is presented. This is a…

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…

Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of…

In 1933 Kolmogorov constructed a general theory that defines the modern concept of conditional probability. In 1955 Renyi fomulated a new axiomatic theory for probability motivated by the need to include unbounded measures. This note…

In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob's inequality for submartingale and Kolmogrov's inequality. By Kolmogrov's inequality, we obtain a special version of Kolmogrov's law of…

By formulating the axioms of quantum mechanics, von Neumann also laid the foundations of a "quantum probability theory". As such, it is regarded a generalization of the "classical probability theory" due to Kolmogorov. Outside of quantum…

Unexpectedness is a central concept in Simplicity Theory, a theory of cognition relating various inferential processes to the computation of Kolmogorov complexities, rather than probabilities. Its predictive power has been confirmed by…

Universality of local eigenvalue statistics is one of the most striking phenomena of Random Matrix Theory, that also accounts for a lot of the attention that the field has attracted over the past 15 years. In this paper we focus on the…

Using the ideas of abstract algebra, we introduce the basic concepts of abstract probability theory that generalize the Kolmogorov's probability theory, possibility theory and other theories that deal with uncertainty. Based on abstract…

Kolmogorov's axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional…

This work advances and substantiates the thesis that the resolution of this crisis lies in the domain of possibility theory, specifically in the axiomatic approach developed in Bychkovs article. Unlike numerous attempts to fix Dempster…

Bayesian inference paradigms are regarded as powerful tools for solution of inverse problems. However, when applied to inverse problems in physical sciences, Bayesian formulations suffer from a number of inconsistencies that are often…

The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.

This paper contains an answer to the question of existence of regularities of the so called \textit{random in a broad sense} mass phenomena, asked by A. N. Kolmogorov in \cite{Kolmogorov}. It turns out that some family of finitely-additive…