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- Kirkwood_approximation abstract "The Kirkwood superposition approximation was introduced in 1935 by John G. Kirkwood as a means of representing a discrete probability distribution. The Kirkwood approximation for a discrete probability density function is given by where is the product of probabilities over all subsets of variables of size i in variable set . This kind of formula has been considered by Watanabe (1960) and, according to Watanabe, also by Robert Fano. For the three-variable case, it reduces to simply The Kirkwood approximation does not generally produce a valid probability distribution (the normalization condition is violated). Watanabe claims that for this reason informational expressions of this type are not meaningful, and indeed there has been very little written about the properties of this measure. The Kirkwood approximation is the probabilistic counterpart of the interaction information.Judea Pearl (1988 §3.2.4) indicates that an expression of this type can be exact in the case of a decomposable model, that is, a probability distribution that admits a graph structure whose cliques form a tree. In such cases, the numerator contains the product of the intra-clique joint distributions and the denominator contains the product of the clique intersection distributions.".
- Kirkwood_approximation wikiPageID "6968975".
- Kirkwood_approximation wikiPageRevisionID "589736057".
- Kirkwood_approximation hasPhotoCollection Kirkwood_approximation.
- Kirkwood_approximation subject Category:Discrete_distributions.
- Kirkwood_approximation subject Category:Probability_theory.
- Kirkwood_approximation subject Category:Statistical_approximations.
- Kirkwood_approximation type Abstraction100002137.
- Kirkwood_approximation type Arrangement105726596.
- Kirkwood_approximation type Calculation105802185.
- Kirkwood_approximation type Cognition100023271.
- Kirkwood_approximation type DiscreteDistributions.
- Kirkwood_approximation type Distribution105729036.
- Kirkwood_approximation type Estimate105803379.
- Kirkwood_approximation type HigherCognitiveProcess105770664.
- Kirkwood_approximation type ProblemSolving105796750.
- Kirkwood_approximation type Process105701363.
- Kirkwood_approximation type PsychologicalFeature100023100.
- Kirkwood_approximation type StatisticalApproximations.
- Kirkwood_approximation type Structure105726345.
- Kirkwood_approximation type Thinking105770926.
- Kirkwood_approximation comment "The Kirkwood superposition approximation was introduced in 1935 by John G. Kirkwood as a means of representing a discrete probability distribution. The Kirkwood approximation for a discrete probability density function is given by where is the product of probabilities over all subsets of variables of size i in variable set . This kind of formula has been considered by Watanabe (1960) and, according to Watanabe, also by Robert Fano.".
- Kirkwood_approximation label "Kirkwood approximation".
- Kirkwood_approximation sameAs m.0gz8cs.
- Kirkwood_approximation sameAs Q6415903.
- Kirkwood_approximation sameAs Q6415903.
- Kirkwood_approximation sameAs Kirkwood_approximation.
- Kirkwood_approximation wasDerivedFrom Kirkwood_approximation?oldid=589736057.
- Kirkwood_approximation isPrimaryTopicOf Kirkwood_approximation.