6533b7d8fe1ef96bd126a534

RESEARCH PRODUCT

Backwards Martingales and Exchangeability

Achim Klenke

subject

Exchangeable random variablesDiscrete mathematicsIndependent and identically distributed random variablesDistribution (number theory)Conditional independenceJoint probability distributionProbability distributionConditional probability distributionRandom variableMathematics

description

With many data acquisitions, such as telephone surveys, the order in which the data come does not matter. Mathematically, we say that a family of random variables is exchangeable if the joint distribution does not change under finite permutations. De Finetti’s structural theorem says that an infinite family of E-valued exchangeable random variables can be described by a two-stage experiment. At the first stage, a probability distribution Ξ on E is drawn at random. At the second stage, independent and identically distributed random variables with distribution Ξ are implemented.

yearjournalcountryeditionlanguage
2020-01-01
https://doi.org/10.1007/978-3-030-56402-5_12