Related papers: Random Worlds and Maximum Entropy

In this thesis we start by providing some detail regarding how we arrived at our present understanding of probabilities and how we manipulate them - the product and addition rules by Cox. We also discuss the modern view of entropy and how…

Analytic continuation of numerical data obtained in imaginary time or frequency has become an essential part of many branches of quantum computational physics. It is, however, an ill-conditioned procedure and thus a hard numerical problem.…

The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…

In recent years, researchers in decision analysis and artificial intelligence (Al) have used Bayesian belief networks to build models of expert opinion. Using standard methods drawn from the theory of computational complexity, workers in…

We develop the method of Maximum Entropy (ME) as a technique to generate approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…

The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…

The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…

We propose a novel approach framed in terms of information theory and entropy to tackle the issue of conspiracy theories propagation. We start with the report of an event (such as 9/11 terroristic attack) represented as a series of…

It has been shown that one can accommodate data (Bayes) and constraints (MaxEnt) in one method, the method of Maximum (relative) Entropy (ME) (Giffin 2007). In this paper we show a complex agent based example of inference with two different…

We consider a generic system composed of a fixed number of particles distributed over a finite number of energy levels. We make only general assumptions about system's properties and the entropy. System's constraints other than fixed number…

Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…

Computational pseudorandomness studies the extent to which a random variable $\bf{Z}$ looks like the uniform distribution according to a class of tests $\cal{F}$. Computational entropy generalizes computational pseudorandomness by studying…

We develop a quantum version of the probability estimation framework [arXiv:1709.06159] for randomness generation with quantum side information. We show that most of the properties of probability estimation hold for quantum probability…

We investigate estimating a human's world belief state using a robot's observations in a dynamic, 3D, and partially observable environment. The methods are grounded in mental model theory, which posits that human decision making, contextual…

We consider the first-order theory of random variables with the probabilistic independence relation, which concerns statements consisting of random variables, the probabilistic independence symbol, logical operators, and existential and…

Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…

We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…

Entropy serves as a central observable which indicates uncertainty in many chemical, thermodynamical, biological and ecological systems, and the principle of the maximum entropy (MaxEnt) is widely supported in natural science. Recently,…

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…

We demonstrate how information in the form of observable data and moment constraints are introduced into the method of Maximum relative Entropy (ME). A general example of updating with data and moments is shown. A specific econometric…