相关论文: An attempt at reading Keynes' Treatise on Probabil…

In the present paper we demonstrate the results of a statistical analysis of some characteristics of precipitation events and propose a kind of a theoretical explanation of the proposed models in terms of mixed Poisson and mixed exponential…

As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occurrence statistics and use them in conjunction with the…

This paper presents a brief, semi-technical comparison of the essential features of the frequentist and Bayesian approaches to statistical inference, with several illustrative examples implemented in Python. The differences between…

This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…

Approximate Bayesian Computation (ABC for short) is a family of computational techniques which offer an almost automated solution in situations where evaluation of the posterior likelihood is computationally prohibitive, or whenever…

One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…

This paper presents an offering of some of the myriad connections between Combinatorics and Probability, directed in particular toward combinatorialists. The choice of material was dictated by the author's own interests, tastes and…

The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace…

These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…

A remarkable book on weather forecasting was published just one hundred years ago. Written by the brilliant and prescient applied mathematician, Lewis Fry Richardson, Weather Prediction by Numerical Process was published by Cambridge…

The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…

In previous work ("Knowledge from Probability", TARK 2021) we develop a question-relative, probabilistic account of belief. On this account, what someone believes relative to a given question is (i) closed under entailment, (ii)…

The concept of Probability of Causation (PC) is critically important in legal contexts and can help in many other domains. While it has been around since 1986, current operationalizations can obtain only the minimum and maximum values of…

A common problem faced in statistical inference is drawing conclusions from paired comparisons, in which two objects compete and one is declared the victor. A probabilistic approach to such a problem is the Bradley-Terry model, first…

I first met Leo Breiman in 1979 at the beginning of his third career, Professor of Statistics at Berkeley. He obtained his PhD with Lo\'eve at Berkeley in 1957. His first career was as a probabilist in the Mathematics Department at UCLA.…

Employing a generalized definition of Pratt (1964) and Arrow's (1965, 1971) probability premium, we introduce a new concept of attitude towards probability. We illustrate in a problem of risk sharing that whether attitude towards…

This paper modifies Jaynes's axioms of plausible reasoning and derives the minimum relative entropy principle, Bayes's rule, as well as maximum likelihood from first principles. The new axioms, which I call the Optimum Information…

There is available an ever-increasing variety of procedures for managing uncertainty. These methods are discussed in the literature of artificial intelligence, as well as in the literature of philosophy of science. Heretofore these methods…

This is an attempt to clarify certain concepts related to a debate on the interpretation of quantum mechanics, a debate between Andrei Khrennikov on the one side and Blake Stacey and R\"udiger Schack on the other side. Central to this…

Possibility and probability theories are alternative and complementary ways to deal with uncertainty, which has motivated over the last years an interest for the study of ways to transform probability distributions into possibility…