Correlation Structure in Exchangeable Sequences

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  • Presentation type: Poster (EBEB)
  • Track: EBEB
  • Keywords: Exchangeability; De Finetti's theorem; Conditional independence; Stochastic dependence; Prior distribution;
  • 1 University of Campinas

Correlation Structure in Exchangeable Sequences

Vinícius Litvinoff Justus

University of Campinas

Abstract

In this work we rescue notions that generalize the property of independence between random variables, looking for a constrain on the value of the Pearson's correlation coefficient between the variables, two by two. We introduce the concept of infinitely exchangeable sequence, and within the framework of this notion, is stated a version of De Finetti's representation theorem. The result guarantees the existence of an entity, theta, that has an associated distribution (prior distribution). We investigate how De Finetti's theorem leads to restricting the values of the Pearson's coefficient between pairs of variables that constitute the infinitely exchangeable sequence, that coefficient is expressed in function of theta. The rest of the work shows examples, that illustrate the notions and the results collected here.

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Vinícius Litvinoff Justus

The fourth reference (“Exchangeability, correlation, and Bayes’ effect”) has a very interesting interpretation for this result in the Bayesian inference: if all variables have the same marginal distribution and depends on the same unknow pararmeter (with associated prior distribution), so we will use the previous observations to update the distribution of the new variables, because we use the observations to update the prior distribution. The name of this fact in the cited reference is "Bayes' effect".

 

 

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