All Questions
Tagged with conditional-independence mathematical-statistics
11
questions
2
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Borel-Cantelli lemma on conditional probabilities
In a probability space $\big( \Omega, \mathcal{F}, P \big)$, suppose $\{E_n\}_{n\in \mathbb{N}} \subseteq \mathcal{F}$ is a sequence of mutually independent events. By Borel-Cantelli Lemma, the ...
1
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0
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66
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Conditional independence statements for probabilistic motivation for linear regression
So the motivation for using the squared loss in linear regression can be written as the following (I think):
Assume $\{(\mathbf{x}_i, y_i) \mid i = 1, \dots n\}$ are repeated independent samples from ...
- 359
1
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0
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88
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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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"Predictive dependence" between two variables
Given two random variables $X$ and $Y$, it is natural to use the conditional entropy $H[Y|X]$ to quantify the extent to which knowing $X$ decreases the uncertainty about $Y$. However, consider the ...
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1
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1
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148
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Conditional independence situation with three variables
Say we have three random variables, $X, Y$ and $Z$, where $X$ is independent of $Z$ (but not $Y$).
Does $E\bigg[ \dfrac{X}{f(Y,Z)} \bigg| Y \bigg] = E[X|Y] * E\bigg[ \dfrac{1}{f(Y,Z)} \bigg|Y \bigg]$?
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1
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Is there any work on, given a set of conditional independences, build the graphical model?
The graphical model Represents probabilistic independence.
Given a set of conditional independence assumptions, how to find the probabilistic graphical model that maximizes some metrics (e.g, minimum ...
1
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0
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31
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Shouldn’t we say independent given the distribution?
In statistics we often deal with iid random variables: independent identically distributed. But if we don’t know the distribution (say we still know the support is {0, 1}), and we get a sample x1, say ...
4
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1
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62
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How would I find $P(X \ne Y)$ given independent conditional probability mass functions?
Suppose that $W$ has a discrete uniform distribution on $\{1,\cdots,n\}$. Further, suppose that given $W=w$, the random variables $X$ and $Y$ are independently identically distributed geometric random ...
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3
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2
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conditional probability involving mixed variable types
I'm trying to answer the following question
A defective coin minting machine produces coins whose probability of heads is a random variable $T$ with PDF $f_{T}(p) = 1+\mathrm{sin}(2\pi p)$ if $p \in ...
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0
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1
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Is joint conditionally independent equivalent to marginally conditionally independent？
Heading ##I am wondering whether these two properties are equivalent:
$X$ is conditionally independent of $Y$ given $Z$
$X$ is conditionally independent of $Y$ given $a^T Z$, $\forall a \in R^p$
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4
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Conditional independence: conditioning on an empty set of random variables
Is $X \perp\!\!\!\perp Y$ a conditional independence, arguing that the independence is conditioned on an empty set of random variables? If so, does that mean that an unconditional independence is ...
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