Distances between probability measures and coefficients of

... Representation with sets of probabilities Coecients of ergodicity for imprecise Markov chains Coecients of ergodicity Coecients of ergodicity for imprecise Markov chains Generalisations of distance functions to imprecise probabilities Uniform coecient of ergodicity Weak coecient of ergodicity O ...

... Representation with sets of probabilities Coecients of ergodicity for imprecise Markov chains Coecients of ergodicity Coecients of ergodicity for imprecise Markov chains Generalisations of distance functions to imprecise probabilities Uniform coecient of ergodicity Weak coecient of ergodicity O ...

An Introduction to Statistical Signal Processing

... These simple proofs, however, often provide the groundwork for “handwaving” justifications of more general and complicated results that are semi-rigorous in that they can be made rigorous by the appropriate delta-epsilontics of real analysis or measure theory. A primary goal of this approach is thus ...

... These simple proofs, however, often provide the groundwork for “handwaving” justifications of more general and complicated results that are semi-rigorous in that they can be made rigorous by the appropriate delta-epsilontics of real analysis or measure theory. A primary goal of this approach is thus ...

Entropy Demystified : The Second Law Reduced to Plain Common

... While writing this book, I asked myself several times at exactly what point in time I decided that this book was worth writing. I think there were three such points. First, was the recognition of the crucial and the indispensable facts that matter is composed of a huge number of particles, and that ...

... While writing this book, I asked myself several times at exactly what point in time I decided that this book was worth writing. I think there were three such points. First, was the recognition of the crucial and the indispensable facts that matter is composed of a huge number of particles, and that ...

Nucleation and growth in two dimensions

... are infected (randomly) at a rate which depends on the number of their neighbours that are already infected. This model includes bootstrap percolation and first-passage percolation as its extreme points. We give a precise description of the evolution of this process on the graph Z2 , significantly s ...

... are infected (randomly) at a rate which depends on the number of their neighbours that are already infected. This model includes bootstrap percolation and first-passage percolation as its extreme points. We give a precise description of the evolution of this process on the graph Z2 , significantly s ...

1222grading1198 - Emerson Statistics

... observations near the middle and end of each line represent clustering of censoring events which are not easily discernable due to the high number of observations in this study. It is evident that at all times points those with high serum CRP have lower survival probabilities. The associated HR for ...

... observations near the middle and end of each line represent clustering of censoring events which are not easily discernable due to the high number of observations in this study. It is evident that at all times points those with high serum CRP have lower survival probabilities. The associated HR for ...

Bayesian Algorithmic Modeling in Cognitive Science

... 2012a,b) and to cognitive modeling, in a broad sense (Serkhane et al.; 2005, Colas et al.; 2007, Laurens and Droulez; 2007, Colas et al.; 2009, Möbus and Eilers; 2009, Möbus et al.; 2009, Colas et al.; 2010, Eilers and Möbus; 2010, Lenk and Möbus; 2010, Möbus and Eilers; 2010a,b, Eilers and Möbus; 2 ...

... 2012a,b) and to cognitive modeling, in a broad sense (Serkhane et al.; 2005, Colas et al.; 2007, Laurens and Droulez; 2007, Colas et al.; 2009, Möbus and Eilers; 2009, Möbus et al.; 2009, Colas et al.; 2010, Eilers and Möbus; 2010, Lenk and Möbus; 2010, Möbus and Eilers; 2010a,b, Eilers and Möbus; 2 ...

What Can the Duration of Discovered Cartels Tell Us About the

... measurement issue is a concern. For example, suppose a customer complained and firms learned about it which then caused the cartel to collapse. Thus, at the time a formal investigation is opened up, the cartel would be inactive and one might be inclined to conclude that the cartel collapsed and was ...

... measurement issue is a concern. For example, suppose a customer complained and firms learned about it which then caused the cartel to collapse. Thus, at the time a formal investigation is opened up, the cartel would be inactive and one might be inclined to conclude that the cartel collapsed and was ...

Logical Foundations of Induction

... the human species; John, Peter and Smith eat; therefore every man eats. It may here be said that the conclusion asserts a causal relation between humanity and eating, (ii) Aristotle may not insist on regarding the conclusion as asserting a causal relation, but show the fact that men eat, by complete ...

... the human species; John, Peter and Smith eat; therefore every man eats. It may here be said that the conclusion asserts a causal relation between humanity and eating, (ii) Aristotle may not insist on regarding the conclusion as asserting a causal relation, but show the fact that men eat, by complete ...

Bayesian Perceptual Psychology

... Bayesian decision theory is a mathematical framework that models reasoning and decision-making under uncertainty. Around 1990, perceptual psychologists began constructing detailed Bayesian models of perception.1 This research program has proved enormously fruitful. As two leading perceptual psycholo ...

... Bayesian decision theory is a mathematical framework that models reasoning and decision-making under uncertainty. Around 1990, perceptual psychologists began constructing detailed Bayesian models of perception.1 This research program has proved enormously fruitful. As two leading perceptual psycholo ...

Link (PDF, 5.57 MB) (PDF, 5441 KB)

... 3.9.7 WS: Wait and see approach . . . . . . . . . . . . . . . . . 3.9.8 EEV: Expected result of the EV solution . . . . . . . . . . 3.9.9 Expected value of perfect information and expected result 3.9.10 RFS: Reliability of the first–stage solution . . . . . . . . . 3.9.11 Current solver availability ...

... 3.9.7 WS: Wait and see approach . . . . . . . . . . . . . . . . . 3.9.8 EEV: Expected result of the EV solution . . . . . . . . . . 3.9.9 Expected value of perfect information and expected result 3.9.10 RFS: Reliability of the first–stage solution . . . . . . . . . 3.9.11 Current solver availability ...

doc - John L. Pollock

... the same empirical considerations that enable us to evaluate prob inductively also determine . It is convenient to be able to write proportions in the same logical form as probabilities, so where and are open formulas with free variable x, let x ( / ) ({x | & },{x | }) . Note tha ...

... the same empirical considerations that enable us to evaluate prob inductively also determine . It is convenient to be able to write proportions in the same logical form as probabilities, so where and are open formulas with free variable x, let x ( / ) ({x | & },{x | }) . Note tha ...

Symmetry Principles in Polyadic Inductive Logic

... Probability functions have a number of desirable properties5 . Note in particular that logically equivalent sentences are given the same value by a probability function, and that convex sums of probability functions are probability functions. Any probability function w satisfying just (P1) and (P2) ...

... Probability functions have a number of desirable properties5 . Note in particular that logically equivalent sentences are given the same value by a probability function, and that convex sums of probability functions are probability functions. Any probability function w satisfying just (P1) and (P2) ...

# Probability box

A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed. Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes.An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds may have almost any shapes, including step functions, so long as they are monotonically increasing and do not cross each other. A p-box is used to express simultaneously incertitude (epistemic uncertainty), which is represented by the breadth between the left and right edges of the p-box, and variability (aleatory uncertainty), which is represented by the overall slant of the p-box.