Kullback–Leibler divergence and Prior probability

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Difference between Kullback–Leibler divergence and Prior probability

Kullback–Leibler divergence vs. Prior probability

In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy) is a measure of how one probability distribution diverges from a second, expected probability distribution. In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into account.

Bayes' theorem

In probability theory and statistics, Bayes’ theorem (alternatively Bayes’ law or Bayes' rule, also written as Bayes’s theorem) describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

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Coding theory

Coding theory is the study of the properties of codes and their respective fitness for specific applications.

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Cross entropy

In information theory, the cross entropy between two probability distributions p and q over the same underlying set of events measures the average number of bits needed to identify an event drawn from the set, if a coding scheme is used that is optimized for an "unnatural" probability distribution q, rather than the "true" distribution p. The cross entropy for the distributions p and q over a given set is defined as follows: where H(p) is the entropy of p, and D_(p \| q) is the Kullback–Leibler divergence of q from p (also known as the relative entropy of p with respect to q — note the reversal of emphasis).

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Edwin Thompson Jaynes

Edwin Thompson Jaynes (July 5, 1922 – April 30, 1998) was the Wayman Crow Distinguished Professor of Physics at Washington University in St. Louis.

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Entropy (information theory)

Information entropy is the average rate at which information is produced by a stochastic source of data.

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Expected value

In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.

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Marginal distribution

In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset.

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Posterior probability

In Bayesian statistics, the posterior probability of a random event or an uncertain proposition is the conditional probability that is assigned after the relevant evidence or background is taken into account.

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Principle of indifference

The principle of indifference (also called principle of insufficient reason) is a rule for assigning epistemic probabilities.

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Principle of maximum entropy

The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge is the one with largest entropy, in the context of precisely stated prior data (such as a proposition that expresses testable information).

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Prior probability

In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into account.

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Probability distribution

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

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