Related papers: The two envelopes probability paradox: Much ado ab…
Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain…
We suggest that one individual holds multiple degrees of belief about an outcome, given the evidence. We then investigate the implications of such noisy probabilities for a buyer and a seller of binary options and find the odds agreed upon…
Classical countably additive real-valued probabilities come at a philosophical cost: in many infinite situations, they assign the same probability value -- namely, zero -- to cases that are impossible as well as to cases that are possible.…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
We consider the problem of refuting equivalence of probabilistic programs, i.e., the problem of proving that two probabilistic programs induce different output distributions. We study this problem in the context of programs with…
We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…
Completeness and transitivity are standard rationality conditions in economics. However, under ambiguity, decision makers sometimes violate these requirements because of the difficulty of forming accurate predictions about ambiguous events.…
The 1961 Ellsberg paradox is typically seen as an empirical challenge to the subjective expected utility framework. Experiments based on Ellsberg's design have spawned a variety of new approaches, culminating in a new paradigm represented…
Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of…
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…
This article extends the hypotheses assessment method to the case with two competing simple hypotheses. In doing so we further clarify the benefits that hypotheses assessments can bring to classical statistical analyses. Given that…
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…
In this paper we study different concepts of independence for convex sets of probabilities. There will be two basic ideas for independence. The first is irrelevance. Two variables are independent when a change on the knowledge about one…
The violation of local uncertainty relations is a valuable tool for detecting entanglement, especially in multi-dimensional systems. The orbital angular momentum of light provides such a multi-dimensional system. We study quantum…
The Fermi Paradox is the apparent contradiction between the high probability extraterrestrial civilizations' existence and the lack of contact with such civilizations. In general, solutions to Fermi's paradox come down to either estimation…
The method of maximum entropy has been very successful but there are cases where it has either failed or led to paradoxes that have cast doubt on its general legitimacy. My more optimistic assessment is that such failures and paradoxes…
This study demonstrates that incorrect data are entered into a pairwise comparisons matrix for processing into weights for the data collected by a rating scale. Unprocessed rating scale data lead to a paradox. A solution to it, based on…
Some risks have extremely high stakes. For example, a worldwide pandemic or asteroid impact could potentially kill more than a billion people. Comfortingly, scientific calculations often put very low probabilities on the occurrence of such…
We discuss a rather surprising version of the twin paradox in which (contrary to the familiar classical version) the twin who accelerates is older on the reunion than his never accelerating brother.
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…