Related papers: Negative probability in the framework of combined …
A new three parameter natural extension of the Conway-Maxwell-Poisson (COM-Poisson) distribution is proposed. This distribution includes the recently proposed COM-Poisson type negative binomial (COM-NB) distribution [Chakraborty, S. and…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
When researchers carry out a null hypothesis significance test, it is tempting to assume that a statistically significant result lowers Prob(H0), the probability of the null hypothesis being true. Technically, such a statement is…
In classical physics, probabilistic or statistical knowledge has been always related to ignorance or inaccurate subjective knowledge about an actual state of affairs. This idea has been extended to quantum mechanics through a completely…
Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by a probability assignment to each argument. There are various interpretations that can be ascribed…
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.…
When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…
The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability…
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…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
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…
This article starts out with a detailed example illustrating the utility of applying quantum probability to psychology. Then it describes several alternative mathematical methods for mapping fundamental quantum concepts (such as state…
The notion of random self-decomposability is generalized further. The notion is then extended to non-negative integer-valued distributions.
Generalized linear models are often assumed to fit propensity scores, which are used to compute inverse probability weighted (IPW) estimators. In order to derive the asymptotic properties of IPW estimators, the propensity score is supposed…
Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample…
In this paper we obtain some possibilistic variants of the probabilistic laws of large numbers, different from those obtained by other authors, but very natural extensions of the corresponding ones in probability theory. Our results are…
In this paper one generalizes the classical probability and imprecise probability to the notion of "neutrosophic probability" in order to be able to model Heisenberg's Uncertainty Principle of a particle's behavior, Schr"dinger's Cat…