# Questions tagged [conditional-independence]

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### Why does dimensionality affect significance and effect size in a Full Conditional Independence (FullCI) test?

The 2018 Runge et al paper titled "Detecting causal associations in large non linear time series datasets" describes the PCMCI method. It compares the new PCMCI method with another method ...
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1 vote
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### Hierarchical models and conditional independence

Suppose that we have a hierarchical model given by (this is Example 4.4.5 of Berger and Casella(2002)) \begin{align*} X\mid Y&\sim\text{binomial}(Y,p),\\ Y\mid\Lambda&\sim\text{Poisson}(\...
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### Conditional independence in BUGs/JAGs?

I am trying to create a hierarchical model in BUGs. I am actually attempting to implement this is Nimble, but I suspect that a JAGs implementation will be informative. To attempt to reduce my problem ...
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### Dependence through an unknown parameter?

Consider an urn from which we sample with replacement. Let $\pi$ represent the proportion of the urn's balls that are black, with the remainder being white. From a frequentist perspective, each ...
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### Bayesian network extracting further conditional independence statements then just from d-separation theorem

Given a Bayesian network $(p,\mathcal{G})$, where $p$ is our joint distribution, and $\mathcal{G}$ is a DAG. Then by the d-separation theorem we can deduce conditional independence statements, in ...
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### Conditional likelihood, conditional independence and joint independence

Consider a sequence of data samples generated from $n$ independent random vectors $(X_1, Y_1), (X_2,Y_2), (X_3,Y_3) ...$ $$D = (x_1,y_1), (x_2,y_2), (x_3,y_3) ...$$ Where $(X_i, Y_i)$ - is a random ...
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1 vote
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### Conditional expectation function and causal inference

!For the question itself skip to the last paragraph! It is my understanding that iff we have a model of the form $$Y = m(X) + e$$ and $E[e|X] = 0$ we know that $m(X)$ is the conditional expectation ...
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### A question of "elementary imsets" in an ADMG

In [The m-connecting imset and factorization for ADMG models] (https://doi.org/10.48550/arXiv.2207.08963), it was mentioned the notation of an "elementary imset". The definition of ...
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### How do I control for pscore?

I see that people usually implement pscore matching or control for pscore fixed effects. Why do I need to do pscore matching? Why can't I just include pscore as a continuous variable in my regression ...
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### Dropping condition from conditional probability

Consider 3 random variables $X$, $Y$ and $Z$. Under which conditions would we have $P(X\mid Y,Z) = P(X\mid Z)$?
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