# 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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### correcting t-test for dependent but not paired data (in R)

My data $\{X_1,...X_N \}$ are assumed exchangeable with known correlation $\rho$. I want a "t-test" (or similar) of mean $E(\bar{X})=0$ in the R language. More generally, i seek an easy and ...
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### understanding exchangeability in GP regression

It is well known that exchangeability refers to the following property $p(X_1,\dots, X_n) = p(X_{\pi(1)}, \dots, X_{\pi(n)})$ for any finite $n$ and a permutation $\pi$ when we have an infinite ...
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### Exchangeability and joint distribution

The definition of an exchangeabilty for a finite sequence says that, if we have random variables $X_1,\ldots,X_n$, then for each permutation $\pi: \{1,\ldots,n\}\rightarrow\{1,\ldots,n\}$, the joint ...
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### Permutation tests and exchangeability [duplicate]

Permutation tests assume exchangeability of the response/observations under the null hypothesis. In what practical situations is this clearly violated? When is it unproblematic? Edit/additional ...
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### How does one actually determine if a sequence is exchangeable

Pardon me if the question is stupid, but I don't understand how you go about proving exchangeability of a random sequence. In the case of a distribution such as the normal distribution, I get that ...
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### Can We Use Permutation Test Everywhere to Check Difference When the Null Hypothesis Is "There Is No Difference Between Two Groups of Data?"

What I Am Trying to Do? Let's assume, I am working on a research problem where only one participant is present. I have a data set consisting that participant's respiration rate (The number of breaths ...
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### Is independence subjective?

I am trying to better understand exchangeability. Suppose that I would like to run an experiment. I will pick two people and give each a fair coin and tell them to toss N times in a row. The ...
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### Relationship between exchangeability and independence

If the random variables $X_1,...,X_n$ are I.I.d. when conditioned on an unknown parameter $\theta$, where $p(\theta)$ represents our prior beliefs about $\theta$, it follows from the commutativity of ...