# 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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### What does 'Exchangeability' mean in multiple testing?

In A practical guide to methods controlling false discoveries in computational biology, the author mentioned 'Exchangeability': According to Wiki, the definition of 'Exchangeability' is : ...
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### How useful is exchangeability for non-extendible sequences?

Question How to model the predictive distribution $\mathrm{P}(X'\mid X_1=x_1, \dotsc, X_n=x_n)$ if I know that the sequence $X_1, \dotsc, X_n, X'$ is exchangeable, but I cannot assume it to be $N$-...
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### exchangeability in LDA

Can someone help me understand how exchangeability works for Latent Dirichlet Allocation (LDA) and how it enables us to treat words in the test set that are not present in the training set? I know ...
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### procrustes alternative

Im comparing two multidimensional MDS solutions, the solutions have the same number of dimensions. I don't think I can use the permutation version of procrustes analysis (commonly, PROTEST in R::vegan)...
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### Is this a valid statement according to the de Finetti theorem?

Some background on my problem - Let us consider a discrete memoryless channel (DMC) $W_{Y|X}$ from Alice to Bob. A DMC is a conditional probability distribution over the random variable $Y$ given ...
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### Is the converse of de Finetti's theorem true?

As I understand it from Wikipedia, de Finetti's theorem says: "Exchangeability implies that variables are conditionally independent given some latent variable". Is the converse true as well?
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### Show that the variance of the longitudinal estimate is $\dfrac{2 \sigma^2(1-\rho)} { n}$ rather than $\dfrac{\sigma^2(\rho)}{n}$

patients are randomızed to elther treatment, their pressures are measured at baseline, treatment is administered for two weeks and $\mathrm{BP}$ is then measured a second time. The treatment effect is ...
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### Are there examples of ML or stats approaches that are valid for IID data, but not exchangeable data?

Lots of supervised learning theory is motivated using the IID assumption. Do most of these methods apply equally well if data is only exchangeable, and not IID? Can you provide an example where this ...
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### How to derive g-computation for a longitudinal experiment from sequential conditional exchangeability?

We have a longitudinal experiment, with interventions $\bar{A}=\{A_1,A_2,\ldots,A_K\}$ and outcomes $\bar{Y}=\{Y_1,Y_2,\ldots,Y_K\}$. Using some sequential conditional exchangeability assumptions, it ...
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### Switching interventions after randomization

Suppose in a randomized control study, we assigned each individual to one of two interventions (A or B) with equal probability. And suppose for the sake of argument, there is complete balance in ...
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### How do you calculate the expected value of a discrete distribution without replacement?

Say I have a set of 10 values I want to draw 3 values from, uniformly, without replacement. For instance: $$S = \{0,0,0,0,22.95,0,0,0,19.125,25.5\}$$ With replacement, this seems simple, you just add ...
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### Exchangeability, causal inference, and partial pooling

In Statistical Rethinking, Richard McElreath writes the following concerning the use of partial pooling (i.e. varying/random effects) in Bayesian hierarchical models: Could we also use partial ...
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### Proof for a seemingly simple property for fully-connected coloured random graphs?

I have a probability distribution defined over a set of fully-connected simple graphs depending on their coloring. Let us have a fully connected graph with $N$ nodes, a node may have a color $i$ ...
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