Questions tagged [conditional-independence]
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What does it mean for tests to be independent?
When reading about cumulation if type-1 Error, the sentence "for independent statistical tests" occures alot, now I was wondering what this is actually means.
Since tests are also random ...
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Intuition of conditional independence in DAGs
In the DAG above, we have $A$ conditionally independent of $E$ when $C$ and $B$ are observed (that is $A\perp E|B,C$), but not when only $C$ is observed (that is $A\not\perp E|C$). I don't have a ...
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Is A independent of B conditioned on B?
Does $A \perp\!\!\!\!\!\!\perp B | B$ always hold?
Part of me is like yes: if we know the value of $B$, then more information about $B$ can't tell us anything about $A$, and vice versa.
Consider this ...
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What's the relationship between statement "Z causes both X and Y" and "X and Y are independent given Z"?
Suppose I have two statements:
Statement 1: Random variable Z is the common cause for random variable X and Y (Z causes both X and Y)
Statement 2: Random variable X and Y are (conditionally) ...
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What does conditional independence mean semantically?
I've just spent the last 3 hours reading every post, question, Medium article, and textbook entry on conditional independence, and I still don't really understand it. Can somebody explain what it ...
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Implications of violating Bayesian network independence assumptions during inference
Consider the example Bayesian network below where $X \perp \!\!\! \perp Y $ (X is independent of Y).
Assuming that this is the true independence structure of the process that is generating the data, ...
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Informative Censoring vs. Random Censoring vs. Conditionally Independent Censoring
Let us consider the case of survival analysis with one event. Let $X$ represent a set of covariates about each unit. Let $T_E$ be the (latent) event time of the unit, let $T_C$ be the (latent) ...
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Does conditional independence imply the following identities?
I was reading this paper https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.143.8127&rep=rep1&type=pdf , and it heavily uses conditional independencies for deriving various identities, ...
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Clarify, with example, completeness conjecture by Pearl and Paz
I was going through Probabilistic Reasoning In Intelligent Systems by Judea Pearl. A completeness conjecture (for which no complete proof is there as yet, but has been found to be true generally, as ...
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If I engineer a new feature such that feature C = feature A/feature B, must I drop features A and B from a Gaussian Naive Bayes model?
As the question asks, is it bad data science not to drop the dividend and divisor features when creating a new feature that is their quotient when working with a Naive Bayes model? My understanding of ...
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Quick way to determine the different independence assumptions
This question is different than my previous question in that I'm asking sort of a "meta" question.
Here's two graphical models (a Belief Network and a Markov Network):
I would like to ...
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Determining unconditional independence in Markov Networks
I would like to know whether $E \perp\kern-5pt\perp A $ in the following Markov Network and would like to know if my reasoning is correct:
So, since this is a Pairwise Markov Network, it factorizes ...
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Checking for conditional independence in graphical models
I would like to know whether $B \perp\kern-5pt\perp C | D,A $ and $D \perp\kern-5pt\perp A | B,C $ in the following two graphical models and would like to know if my reasoning is correct:
For the ...
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Is $C \perp\kern-5pt\perp D | A $ for the two graphical models? [duplicate]
I would like to know whether $C \perp\kern-5pt\perp D | A $ in the following two graphical models and would like to know if my reasoning is correct:
For the left model (Belief Network), here's my ...
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Is $B \perp\kern-5pt\perp C | A $ for the two graphical models?
I would like to know whether $B \perp\kern-5pt\perp C | A $ in the following two graphical models and would like to know if my reasoning is correct:
For the left graphical model, which is a Belief ...
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