Related papers: "Negative probabilities" as relative probabilistic…

Because the stochastic calculus yields rarely random variables with laws defined by explicit closed formulas, probabilistic numerical computations are done most often by simulation. The simulation by the shift, whose field of application is…

In this paper we provide a simple random-variable example of inconsistent information, and analyze it using three different approaches: Bayesian, quantum-like, and negative probabilities. We then show that, at least for this particular…

Positivity, the assumption that every unique combination of confounding variables that occurs in a population has a non-zero probability of an action, can be further delineated as deterministic positivity and stochastic positivity. Here, we…

Negative probabilities emerged at intermediate steps in various attempts to predict the distributions of quantum interference. There is no consensus on their meaning yet. It has been suggested (Khrennikov, 1998) that negative probabilities…

We consider reusing established non-probabilistic output analyses (either forward or backwards) that yield over-approximations of a program's pre-image or image relation, e.g., interval analyses. We assume a probability measure over the…

There is much interest in providing probabilistic semantics for defaults but most approaches seem to suffer from one of two problems: either they require numbers, a problem defaults were intended to avoid, or they generate peculiar side…

Negative probability values have been widely employed as an indicator of the nonclassicality of quantum systems. Known as a quasiprobability distribution, they are regarded as a useful tool that provides significant insight into the…

We consider probabilistic circuits working over the real numbers, and using arbitrary semialgebraic functions of bounded description complexity as gates. In particular, such circuits can use all arithmetic operations +, -, x, /,…

We present experimental results on the effects of using quantum or 'truly' random numbers, as opposed to pseudorandom numbers, in a system that exhibits computational creativity (given its ability to compose original chess problems). The…

Probabilistic program analysis aims to quantify the probability that a given program satisfies a required property. It has many potential applications, from program understanding and debugging to computing program reliability, compiler…

Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…

In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…

Optimization problems frequently appear in any scientific domain. Most of the times, the corresponding decision problem turns out to be NP-hard, and in these cases genetic algorithms are often used to obtain approximated solutions. However,…

Negative and complex numbers are so familiar in modern mathematics, physics, and engineering that it is easy to forget how uncertain their status once was. They did not become established through a single route. This article follows four…

In the classical probability in continuous random variables there is no distinguishing between the probability involving strict inequality and non strict inequality. Moreover a probability involves equality collapse to zero without…

To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables…

In this paper we discuss quantum-like decision-making experiments using negative probabilities. We do so by showing how the two-slit experiment, in the simplified version of the Mach-Zehnder interferometer, can be described by this…

A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…

A signed probability distribution may extend a given traditional probability from observable events to all events. We formalize and illustrate this approach. We also illustrate its limitation. We argue that the right question is not what…

Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…