# Questions tagged [conditional-independence]

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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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### Is my current understanding of the conditional independence assumption in bayesian inference correct?

Standard bayesian inference asssumptions: model $M=\{p(\cdot | \theta) | \theta \in \mathcal{T} \}$ as a prior, choose a distribution $\pi$ on $\mathcal{T}$ then assume observations are generated as ...
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### Conditional Independence between two Independent Variables

I have the following question: if $x$ and $y$ are independent random variables/events, $z$ depends on $x$ and $z$ depends on $y$. Are $x$ and $y$ conditional independent on $z$. My first intuition is ...
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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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### How to calculate by hand dependent variables sampled from a Frank Copula?

Let's consider this code: ...
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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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### Is it always possible to find a joint distribution $p(x_1,x_2,x_3,x_4)$ consistent with these local conditional distributions?

I am currently studying Bayesian Reasoning and Machine Learning by David Barber, the 4th chapter exercise 4.1 (p 79). The exercise is the following: Exercise 4.1 Consider the pairwise Markov network, ...
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### Bootstrap method for chi squared test of independence

I really need some advice about using the chi-squared test of independence. I want to use the bootstrap-chi-squared method for conditional independence testing. The problem is that the DOF is really ...
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### Conditional indepencies in Bayesian network. Redundant edges in structure learning?

I am confused about whether I can have connected 'triangles' in BN assuming that all variables are observed (no missing values). I see that 'bnlearn' software and other softwares too give me a network ...
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1 vote
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### If $X \in \{1, 2, 3\}$, $Y, Z \in \mathbb{R}$ are random variables, what is meant by $X \not\!\perp\!\!\!\perp Y|Z$?
Let $X \in \{1, 2, 3\}$, and $Y \in \mathbb{R}$ and $Z \in \mathbb{R}$ denote random variables. Suppose that: $$X \not\!\perp\!\!\!\perp Y|Z.$$ In words, $X$ is not conditionally independent of $Y$ ...