Questions tagged [exchangeability]

A set of random variables is exchangeable when their joint distribution is invariant under any permutation of the random variables.

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If random variables are drawn from an identical distribution, why doesn't this guarantee they are independent?

Having read a little about exchangeability, I went back to thinking about the iid condition required for the central limit theorem. It struck me that if two random variables are drawn from an ...
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Can someone explain the concept of 'exchangeability'?

I see the concept of 'exchangeability' being used in different contexts (e.g., bayesian models) but I have never understood the term very well. What does this concept mean? Under what circumstances ...
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Exchangeability and IID random variables

Every IID sequence of random variables is considered to be exchangeable, i understand why its necessary for the random variables to be identically distributed to assume exchangeability, but why the ...
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592 views

Partial exchangeability - Theory and results

De Finetti has defined in 1938 the concept of partial exchangeability as a weaker form of exchangeability in order to deal with situations in which the symmetry among all observations is not desirable....
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397 views

Why are words in a document for bag-of-words model exchangeable but not independent?

I've been watching a talk (section between 07:20-08:00) given by Michael Jordan and I'm getting confused between independence and exchangeability. He says that "If we have a document and you ...
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Exchangeability of group effects

Regarding this basic model with an individual-level covariate $x_{ij}$, group effects $U_{0j}$, and individual effects $R_{ij}$: $Y_{ij}=\gamma_{00}+\gamma_{10}x_{ij}+U_{0j}+R_{ij}$ the multilevel ...
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Why the exchangeability of random variables is essential in hierarchical bayesian models?

Why the exchangeability of random variables is essential for the hierarchical Bayesian modeling?
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What is the intuition behind exchangeable samples under the null hypothesis?

Permutation tests (also called a randomization test, re-randomization test, or an exact test) are very useful and come in handy when the assumption of normal distribution required by for instance, <...
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394 views

What are some statistical tests for exchangeability of a data set?

The representation theorem of de Finetti is seen by some as motivation for the use of Bayesian and/or hierarchical modeling. In some settings, it may be plausible to assume measurements are ...
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Wilcoxon signed rank test independence assumption

Let us say we perform Wilcoxon signed-rank test on paired samples $x_{1,i}$ and $x_{2,i}$. I am trying to understand the independence assumption of the test. My questions are: Which quantities must ...
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Permutation test comparing nested non-linear models with an exchangeable dummy variable

This question is closely related to an earlier question, but I realized my case was actually a lot more specific than the way I formulated it there, in ways that I think merit a separate answer. I ...
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When are observations not weakly exchangeable?

In the book "Common errors in statistics" https://www.amazon.com/Common-Errors-Statistics-Avoid-Them/dp/1118294394, I read the following statement Permutation tests only yield exact significance ...
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Fixed Regressor Conspiracy and Connection to Exchangeability

In simple regression model regressors are treated as fixed rather than stochastic. Whoever picks the experimental values for the regressors, decides in which frequency to include each value. This can ...