Shannon entropy: a rigorous mathematical notion at the
... “Why dont you call it entropy”, von Neumann suggested. “In the first place, a mathematical development very much like yours already exists in Boltzmann’s statistical mechanics, and in the second place, no one understands entropy very well, so in any discussion you will be in a position of advantage” ...
... “Why dont you call it entropy”, von Neumann suggested. “In the first place, a mathematical development very much like yours already exists in Boltzmann’s statistical mechanics, and in the second place, no one understands entropy very well, so in any discussion you will be in a position of advantage” ...
here
... algorithms, Gen, Enc, Dec, and the generated key k were kept private; the idea was of course that the less information we give to the adversary, the harder it is to break the scheme. A design principle formulated by Kerchoff in 1884— known as Kerchoff’s principle—instead stipulates that the only thi ...
... algorithms, Gen, Enc, Dec, and the generated key k were kept private; the idea was of course that the less information we give to the adversary, the harder it is to break the scheme. A design principle formulated by Kerchoff in 1884— known as Kerchoff’s principle—instead stipulates that the only thi ...
Coherent conditional probabilities and proper scoring rules
... dominance, admissibility, Bregman divergence, gcoherence, total coherence, imprecise probability assessments. ...
... dominance, admissibility, Bregman divergence, gcoherence, total coherence, imprecise probability assessments. ...
Mathematical Structures in Computer Science Shannon entropy: a
... information’. ‘Why don’t you call it entropy’, von Neumann suggested. ‘In the first place, a mathematical development very much like yours already exists in Boltzmann’s statistical mechanics, and in the second place, no one understands entropy very well, so in any discussion you will be in a position ...
... information’. ‘Why don’t you call it entropy’, von Neumann suggested. ‘In the first place, a mathematical development very much like yours already exists in Boltzmann’s statistical mechanics, and in the second place, no one understands entropy very well, so in any discussion you will be in a position ...
THE INVARIANCE APPROACH TO THE PROBABILISTIC ENCODING OF INFORMATION by
... role, probability theory as a general means of reasoning about uncertainty is often distinguished by the adjective "Bayesian" from the more limited relative frequency or "classical" use of probability theory . The major difference between the personalistic and the "logical" approach is in the starti ...
... role, probability theory as a general means of reasoning about uncertainty is often distinguished by the adjective "Bayesian" from the more limited relative frequency or "classical" use of probability theory . The major difference between the personalistic and the "logical" approach is in the starti ...
Entropy (information theory)
... Main article: Diversity index to the entropy rate in the case of a stationary process.) Other quantities of information are also used to compare Entropy is one of several ways to measure diversity. or relate different sources of information. Specifically, Shannon entropy is the logarithm of 1 D, the I ...
... Main article: Diversity index to the entropy rate in the case of a stationary process.) Other quantities of information are also used to compare Entropy is one of several ways to measure diversity. or relate different sources of information. Specifically, Shannon entropy is the logarithm of 1 D, the I ...
Conditional Degree of Belief - Philsci
... we need no separate conceptual analysis of conditional degree of belief. Neither do we need a bridge between probability densities and conditional degrees of belief: the latter are reduced to unconditional degrees of belief. However, this approach fails to do justice to the cognitive role of conditi ...
... we need no separate conceptual analysis of conditional degree of belief. Neither do we need a bridge between probability densities and conditional degrees of belief: the latter are reduced to unconditional degrees of belief. However, this approach fails to do justice to the cognitive role of conditi ...
probability, logic, and probability logic
... However, by far the most systematic study of logical probability was by Carnap. He thought of probability theory as an elaboration of deductive logic, arrived at by adding extra rules. Specifically, he sought to explicate ‘the degree to which hypothesis h is confirmed by evidence e’, with the ‘corre ...
... However, by far the most systematic study of logical probability was by Carnap. He thought of probability theory as an elaboration of deductive logic, arrived at by adding extra rules. Specifically, he sought to explicate ‘the degree to which hypothesis h is confirmed by evidence e’, with the ‘corre ...
Algorithmic statistics - Information Theory, IEEE Transactions on
... a finite set of which the data is a “typical” member. Following Shen [17] (see also [21], [18], [20]), this can be generalized to computable probability mass functions for which the data is “typical.” Related aspects of “randomness deficiency” (formally defined later in (IV.1)) were formulated in [1 ...
... a finite set of which the data is a “typical” member. Following Shen [17] (see also [21], [18], [20]), this can be generalized to computable probability mass functions for which the data is “typical.” Related aspects of “randomness deficiency” (formally defined later in (IV.1)) were formulated in [1 ...
- Wiley Online Library
... bias mutational responses: some bias them with respect to time of occurrence (e.g. stress-induced mechanisms), others with respect to genomic site of occurrence (e.g. mechanisms targeting specific DNA sequences) and others with respect to intensity (e.g. mechanisms that increase mutation rate). The ...
... bias mutational responses: some bias them with respect to time of occurrence (e.g. stress-induced mechanisms), others with respect to genomic site of occurrence (e.g. mechanisms targeting specific DNA sequences) and others with respect to intensity (e.g. mechanisms that increase mutation rate). The ...
Estimating the probability of negative events
... 1951; Morlock & Hertz, 1964) gave some grounds for believing that people’s estimates of an event’s probability are influenced, to some extent, by the event’s utility. However, these initial studies typically used choice paradigms, and thus assessed probability judgments only indirectly. Given that ch ...
... 1951; Morlock & Hertz, 1964) gave some grounds for believing that people’s estimates of an event’s probability are influenced, to some extent, by the event’s utility. However, these initial studies typically used choice paradigms, and thus assessed probability judgments only indirectly. Given that ch ...
Black-Box Composition Does Not Imply Adaptive Security
... In this paper we show that there is no non-relativizing proof that composition of functions provides security against adaptive adversaries. Thus, this work falls into a general research program that demonstrates the limitations of black-box constructions in cryptography. Examples of such research i ...
... In this paper we show that there is no non-relativizing proof that composition of functions provides security against adaptive adversaries. Thus, this work falls into a general research program that demonstrates the limitations of black-box constructions in cryptography. Examples of such research i ...
A version of this paper appeared in Statistical Science (vol
... practical tasks. Physicians rely on computer programs that use probabilistic methods to interpret the results of some medical tests. The worker at the readymix company used a chart based on probability theory when he mixed the concrete for the foundation of my house, and the tax assessor used a stat ...
... practical tasks. Physicians rely on computer programs that use probabilistic methods to interpret the results of some medical tests. The worker at the readymix company used a chart based on probability theory when he mixed the concrete for the foundation of my house, and the tax assessor used a stat ...
MATH/STAT 341: PROBABILITY: FALL 2016 COMMENTS ON HW
... whether or not there is a set of size strictly between N and P(N). Work of Kurt Gödel and Paul Cohen proved the continuum hypothesis is independent of the other standard axioms of set theory. See http://en.wikipedia.org/wiki/ Continuum_hypothesis. It’s interesting to think about whether or not it sh ...
... whether or not there is a set of size strictly between N and P(N). Work of Kurt Gödel and Paul Cohen proved the continuum hypothesis is independent of the other standard axioms of set theory. See http://en.wikipedia.org/wiki/ Continuum_hypothesis. It’s interesting to think about whether or not it sh ...
Membership Functions and Probability Measures of Fuzzy Sets
... its framework. Thus probabilities of fuzzy events can be logically induced. The philosophical underpinnings that make this happen are a subjectivistic interpretation of probability, an introduction of Laplace’s famous genie, and the mathematics of encoding expert testimony. The benefit of making pro ...
... its framework. Thus probabilities of fuzzy events can be logically induced. The philosophical underpinnings that make this happen are a subjectivistic interpretation of probability, an introduction of Laplace’s famous genie, and the mathematics of encoding expert testimony. The benefit of making pro ...
Combinatorial Probability
... You should consider this the next time you think about spending $1 for a chance to win $10 million. On the other hand when the probabilities of success are small it is not sensible to think in terms of how much you’ll win on the average. World Series continued. Using (2.3) we can easily compute the ...
... You should consider this the next time you think about spending $1 for a chance to win $10 million. On the other hand when the probabilities of success are small it is not sensible to think in terms of how much you’ll win on the average. World Series continued. Using (2.3) we can easily compute the ...
Stochastic Processes
... notes with 33 illustrations gordan itkovi department of mathematics the university of texas at austin, stochastic processes stanford university - preface these are the lecture notes for a one quarter graduate course in stochastic pro cessesthat i taught at stanford university in 2002and 2003, stocha ...
... notes with 33 illustrations gordan itkovi department of mathematics the university of texas at austin, stochastic processes stanford university - preface these are the lecture notes for a one quarter graduate course in stochastic pro cessesthat i taught at stanford university in 2002and 2003, stocha ...
Twenty-One Arguments Against Propensity Analyses of Probability
... that plays a role in some larger conceptual economy. (To give an example: a nonHumean analysis of causation in terms of necessary connections between events might well satisfy all of Carnap’s criteria, and yet be rejected for the “occultness” of its posited forces.) The overall aim will be to propos ...
... that plays a role in some larger conceptual economy. (To give an example: a nonHumean analysis of causation in terms of necessary connections between events might well satisfy all of Carnap’s criteria, and yet be rejected for the “occultness” of its posited forces.) The overall aim will be to propos ...
APPLICATIONS OF PROBABILITY THEORY TO GRAPHS Contents
... p. Let us denote this model of the random graph as Gp on the vertex set V = {1, 2, ..., n}. Note that Gp is actually a probability distribution of graphs on n vertices. To be more precise, we will use the Bollobás and Erdös random graph: Definition 4.1. A random graph G ∈ G (N, p) is a collection ...
... p. Let us denote this model of the random graph as Gp on the vertex set V = {1, 2, ..., n}. Note that Gp is actually a probability distribution of graphs on n vertices. To be more precise, we will use the Bollobás and Erdös random graph: Definition 4.1. A random graph G ∈ G (N, p) is a collection ...
Intransitive Dice
... Both surprise and puzzlement are the universal reactions to learning about intransitive dice, and, indeed, that was the case for all of us, but once we had seen some examples, we began to wonder just how special they are. For example, suppose we pick three dice randomly and find that A beats B and B ...
... Both surprise and puzzlement are the universal reactions to learning about intransitive dice, and, indeed, that was the case for all of us, but once we had seen some examples, we began to wonder just how special they are. For example, suppose we pick three dice randomly and find that A beats B and B ...
The Topology of Change: Foundations of Probability with Black Swans
... tive to a combination of countably additive and purely finitely additive measures. We also identify a new family of purely finitely additive measures that is continuous with respect to the ”topology of change”. Somewhat surprisingly, we show that the change in topology - from probability distributio ...
... tive to a combination of countably additive and purely finitely additive measures. We also identify a new family of purely finitely additive measures that is continuous with respect to the ”topology of change”. Somewhat surprisingly, we show that the change in topology - from probability distributio ...
Section 3 - Electronic Colloquium on Computational Complexity
... of these structurally much simpler core testers can distinguish whether they are given conditional access to (a) a pair of random identical distributions (D1 , D1 ), or (b) two distributions (D1 , D2 ) drawn according to a similar process, but which are far apart. At a high level, our lower bound wo ...
... of these structurally much simpler core testers can distinguish whether they are given conditional access to (a) a pair of random identical distributions (D1 , D1 ), or (b) two distributions (D1 , D2 ) drawn according to a similar process, but which are far apart. At a high level, our lower bound wo ...
Reality and Probability: Introducing a New Type
... all know that we can have a very simple piece of wood in a state such that it ‘has’ both properties at once. Most pieces of wood indeed do have both properties at once most of the time. How do we arrive at this belief in our daily conception of reality? Let us analyze this matter. What we do is the ...
... all know that we can have a very simple piece of wood in a state such that it ‘has’ both properties at once. Most pieces of wood indeed do have both properties at once most of the time. How do we arrive at this belief in our daily conception of reality? Let us analyze this matter. What we do is the ...
Topic 4
... for the subjunctive conditional statement about what would happen if the coin were flipped an infinite number of times. Propensities and Objective Probabilities A very different conception of probabilities, but one that is also an empirically based one, is that of propensities. Consider, for example ...
... for the subjunctive conditional statement about what would happen if the coin were flipped an infinite number of times. Propensities and Objective Probabilities A very different conception of probabilities, but one that is also an empirically based one, is that of propensities. Consider, for example ...
Interpretations of Probability.pdf
... of various concepts of probability’, and ‘interpreting probability’ is the task of providing such analyses. Or perhaps better still, if our goal is to transform inexact concepts of probability familiar to ordinary folk into exact ones suitable for philosophical and scientific theorizing, then the ta ...
... of various concepts of probability’, and ‘interpreting probability’ is the task of providing such analyses. Or perhaps better still, if our goal is to transform inexact concepts of probability familiar to ordinary folk into exact ones suitable for philosophical and scientific theorizing, then the ta ...
History of randomness
In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. At the same time, most ancient cultures used various methods of divination to attempt to circumvent randomness and fate.The Chinese were perhaps the earliest people to formalize odds and chance 3,000 years ago. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the sixteenth century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of modern calculus had a positive impact on the formal study of randomness. In the 19th century the concept of entropy was introduced in physics.The early part of the twentieth century saw a rapid growth in the formal analysis of randomness, and mathematical foundations for probability were introduced, leading to its axiomatization in 1933. At the same time, the advent of quantum mechanics changed the scientific perspective on determinacy. In the mid to late 20th-century, ideas of algorithmic information theory introduced new dimensions to the field via the concept of algorithmic randomness.Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the twentieth century computer scientists began to realize that the deliberate introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases, such randomized algorithms are able to outperform the best deterministic methods.