# 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 ...
14k views

### 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 ...
918 views

### 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 ...
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....
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 ...
110 views

### 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 ...
1k views

### 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?
2k views

### 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, <...
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 ...
151 views

### 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 ...
127 views

### 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 ...