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Information content, the Glossary

In information theory, the information content, self-information, surprisal, or Shannon information is a basic quantity derived from the probability of a particular event occurring from a random variable.^[1]

74 relations: A Mathematical Theory of Communication, A priori and a posteriori, Additive map, Bernoulli trial, Categorical variable, Cauchy's functional equation, Claude Shannon, Coin flipping, Combination, Convolution, Degeneracy (mathematics), Degenerate distribution, Deterministic system, Dice, Differential entropy, Dirac measure, Discrete uniform distribution, E (mathematical constant), Entropy (information theory), Equiprobability, Event (probability theory), Expected value, Fair coin, Finite measure, George Carlin, Hartley (unit), Independence (probability theory), Independent and identically distributed random variables, Information theory, Integer, Isomorphism, Joint probability distribution, Kolmogorov complexity, Law of total probability, Likelihood function, Logarithm, Logit, Lottery, Lottery mathematics, Measure (mathematics), Measure space, Monotonic function, Multinomial distribution, Mutual information, Myron Tribus, Nat (unit), Natural logarithm, Normalization (statistics), Number, Obverse and reverse, ... Expand index (24 more) »
Entropy and information

A Mathematical Theory of Communication

"A Mathematical Theory of Communication" is an article by mathematician Claude E. Shannon published in Bell System Technical Journal in 1948. Information content and a Mathematical Theory of Communication are information theory.

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A priori and a posteriori

A priori ('from the earlier') and a posteriori ('from the later') are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on experience.

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Additive map

In algebra, an additive map, Z-linear map or additive function is a function f that preserves the addition operation: f(x + y).

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Bernoulli trial

In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted.

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Categorical variable

In statistics, a categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

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Cauchy's functional equation

Cauchy's functional equation is the functional equation: f(x+y).

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Claude Shannon

Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist and cryptographer known as the "father of information theory" and as the "father of the Information Age". Information content and Claude Shannon are information theory.

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Coin flipping

Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking which side is showing when it lands, in order to randomly choose between two alternatives, heads or tails, sometimes used to resolve a dispute between two parties.

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Combination

In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations).

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Convolution

In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (f and g) that produces a third function (f*g).

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Degeneracy (mathematics)

In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class; "degeneracy" is the condition of being a degenerate case.

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Degenerate distribution

In mathematics, a degenerate distribution (sometimes also Dirac distribution) is, according to some, a probability distribution in a space with support only on a manifold of lower dimension, and according to others a distribution with support only at a single point.

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Deterministic system

In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system.

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Dice

Dice (die or dice) are small, throwable objects with marked sides that can rest in multiple positions.

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Differential entropy

Differential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Claude Shannon to extend the idea of (Shannon) entropy (a measure of average surprisal) of a random variable, to continuous probability distributions. Information content and Differential entropy are entropy and information and information theory.

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Dirac measure

In mathematics, a Dirac measure assigns a size to a set based solely on whether it contains a fixed element x or not.

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Discrete uniform distribution

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n.

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E (mathematical constant)

The number is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways.

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Entropy (information theory)

In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Information content and entropy (information theory) are entropy and information and information theory.

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Equiprobability

Equiprobability is a property for a collection of events that each have the same probability of occurring.

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Event (probability theory)

In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

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Expected value

In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.

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Fair coin

In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin.

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Finite measure

In measure theory, a branch of mathematics, a finite measure or totally finite measure is a special measure that always takes on finite values.

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George Carlin

George Denis Patrick Carlin (May 12, 1937 – June 22, 2008) was an American stand-up comedian, social critic, actor, and author.

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Hartley (unit)

The hartley (symbol Hart), also called a ban, or a dit (short for "decimal digit"), is a logarithmic unit that measures information or entropy, based on base 10 logarithms and powers of 10.

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Independence (probability theory)

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

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Independent and identically distributed random variables

In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent.

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Information theory

Information theory is the mathematical study of the quantification, storage, and communication of information.

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Integer

An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.

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Isomorphism

In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping.

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Joint probability distribution

Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs.

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Kolmogorov complexity

In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. Information content and Kolmogorov complexity are information theory.

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Law of total probability

In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities.

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Likelihood function

A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability of seeing that data under different parameter values of the model.

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Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

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Logit

In statistics, the logit function is the quantile function associated with the standard logistic distribution.

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Lottery

A lottery (or lotto) is a form of gambling that involves the drawing of numbers at random for a prize.

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Lottery mathematics

Lottery mathematics is used to calculate probabilities of winning or losing a lottery game.

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Measure (mathematics)

In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events.

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Measure space

A measure space is a basic object of measure theory, a branch of mathematics that studies generalized notions of volumes.

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Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

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Multinomial distribution

In probability theory, the multinomial distribution is a generalization of the binomial distribution.

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Mutual information

In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. Information content and mutual information are entropy and information and information theory.

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Myron Tribus

Myron Tribus (October 30, 1921 – August 31, 2016) was an American organizational theorist, who was the director of the Center for Advanced Engineering Study at MIT from 1974 to 1986.

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Nat (unit)

The natural unit of information (symbol: nat), sometimes also nit or nepit, is a unit of information or information entropy, based on natural logarithms and powers of ''e'', rather than the powers of 2 and base 2 logarithms, which define the shannon.

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Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to.

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Normalization (statistics)

In statistics and applications of statistics, normalization can have a range of meanings.

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Number

A number is a mathematical object used to count, measure, and label.

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Obverse and reverse

The obverse and reverse are the two flat faces of coins and some other two-sided objects, including paper money, flags, seals, medals, drawings, old master prints and other works of art, and printed fabrics.

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Odds

In probability theory, odds provide a measure of the probability of a particular outcome.

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One half

One half is the irreducible fraction resulting from dividing one (1) by two (2), or the fraction resulting from dividing any number by its double.

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Outcome (probability)

In probability theory, an outcome is a possible result of an experiment or trial.

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Polar regions of Earth

The polar regions, also called the frigid zones or polar zones, of Earth are Earth's polar ice caps, the regions of the planet that surround its geographical poles (the North and South Poles), lying within the polar circles.

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Probability

Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur.

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Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment.

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Probability mass function

In probability and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the probability that a discrete random variable is exactly equal to some value.

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Probability measure

In mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies measure properties such as countable additivity.

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Probability space

In probability theory, a probability space or a probability triple (\Omega, \mathcal, P) is a mathematical construct that provides a formal model of a random process or "experiment".

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Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability.

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Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.

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Random variate

In probability and statistics, a random variate or simply variate is a particular outcome or ''realization'' of a random variable; the random variates which are other outcomes of the same random variable might have different values (random numbers).

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Relationships among probability distributions

In probability theory and statistics, there are several relationships among probability distributions.

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Sampling (signal processing)

In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal.

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Scoring rule

In decision theory, a scoring rule provides evaluation metrics for probabilistic predictions or forecasts.

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Shannon (unit)

The shannon (symbol: Sh) is a unit of information named after Claude Shannon, the founder of information theory.

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Shannon's source coding theorem

In information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the statistical limits to possible data compression for data whose source is an independent identically-distributed random variable, and the operational meaning of the Shannon entropy. Information content and Shannon's source coding theorem are information theory.

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Sigma-additive set function

In mathematics, an additive set function is a function \mu mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely, \mu(A \cup B).

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Support (mathematics)

In mathematics, the support of a real-valued function f is the subset of the function domain containing the elements which are not mapped to zero.

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Surprisal analysis

Surprisal analysis is an information-theoretical analysis technique that integrates and applies principles of thermodynamics and maximal entropy. Information content and Surprisal analysis are information theory.

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Surprise (emotion)

Surprise is a rapid, fleeting, mental and physiological state.

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Units of information

In digital computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. Information content and units of information are information theory.

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Variance

In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable.

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Without loss of generality

Without loss of generality (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is a frequently used expression in mathematics.

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References

[1] https://en.wikipedia.org/wiki/Information_content

Also known as Self inform, Self information, Self informed, Self informing, Self informs, Self-entropy, Self-inform, Self-information, Self-informed, Self-informing, Self-informs, Shannon information, Shannon information content, Surprisal, Surprisals.

, Odds, One half, Outcome (probability), Polar regions of Earth, Probability, Probability distribution, Probability mass function, Probability measure, Probability space, Probability theory, Random variable, Random variate, Relationships among probability distributions, Sampling (signal processing), Scoring rule, Shannon (unit), Shannon's source coding theorem, Sigma-additive set function, Support (mathematics), Surprisal analysis, Surprise (emotion), Units of information, Variance, Without loss of generality.

Information content, the Glossary

Table of Contents

See also

Entropy and information

References