Related papers: Lexicographic probability, conditional probability…
In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of…
After a brief introduction to Probability Bracket Notation (PBN), indicator operator and conditional density operator (CDO), we investigate probability spaces associated with various quantum systems: system with one observable (discrete or…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
Probabilities of causation play a crucial role in modern decision-making. Pearl defined three binary probabilities of causation, the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of…
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…
Many machine learning applications require the ability to learn from and reason about noisy multi-relational data. To address this, several effective representations have been developed that provide both a language for expressing the…
Probabilistic databases (PDBs) model uncertainty in data in a quantitative way. In the established formal framework, probabilistic (relational) databases are finite probability spaces over relational database instances. This finiteness can…
We introduce a formal logical language, called conditional probability logic (CPL), which extends first-order logic and which can express probabilities, conditional probabilities and which can compare conditional probabilities. Intuitively…
We address the problem of structural disambiguation in syntactic parsing. In psycholinguistics, a number of principles of disambiguation have been proposed, notably the Lexical Preference Rule (LPR), the Right Association Principle (RAP),…
We investigate the connection between steering and contextuality in general probabilistic theories. We show that for a class of bipartite states the steerability of the state by given set of measurements is equivalent to non-existence of…
Nonprobability (convenience) samples are increasingly sought to stabilize estimations for one or more population variables of interest that are performed using a randomized survey (reference) sample by increasing the effective sample size.…
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…
The propositional logic is generalized on the real numbers field. the logical function with all properties of the classical probability function is obtained. The logical analog of the Bernoulli independent tests scheme is constructed. The…
One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these…
The probabilistic type spaces in the sense of Harsanyi [Management Sci. 14 (1967/68) 159--182, 320--334, 486--502] are the prevalent models used to describe interactive uncertainty. In this paper we examine the existence of a universal type…
Probabilistic models require the notion of event space for defining a probability measure. An event space has a probability measure which ensues the Kolmogorov axioms. However, the probabilities observed from distinct sources, such as that…
Currently, there is a gap between the tools used by probability theorists and those used in formal reasoning about probabilistic programs. On the one hand, a probability theorist decomposes probabilistic state along the simple and natural…
We consider \textit{additive spaces}, consisting of two intervals of unit length or two general probability measures on ${\mathbb R}^1$, positioned on the axes in ${\mathbb R}^2$, with a natural additive measure $\rho$. We study the…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…