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0 votes
0 answers
47 views

Why implied Conditional Independencies of mediator and confounder are the same?

I am trying to understand why the impliedConditionalIndependencies function of the rethinking package returns the same value for ...
Quinten's user avatar
  • 389
1 vote
0 answers
63 views

Directed graphical models and independence (exercise)

Context: this is Ex. 1 in these notes http://www.stat.cmu.edu/~larry/=sml/DAGs.pdf . The exercise asks to prove that, given a directed graphical model associated to a DAG (directed acyclic graph) $G$: ...
Thomas's user avatar
  • 910
2 votes
3 answers
325 views

Bishop PRML Question 8.10: d-separation [closed]

I have trouble with solving the second part of question 8.10 from Bishop's PRML (attached as image). I tried several things. Here's my latest attempt: \begin{align} p(a, b, d) &= \int p(a)p(b)p(...
David's user avatar
  • 122
2 votes
1 answer
311 views

Conditional independence problem for poisson random variables

I have this problem: Let $X = V + W$ and $Y = V + Z$ where $V, W, Z$ are independent Pois($\lambda$) random variables. I found that $Cov(X, Y) = Var(V) = \lambda$ It now asks to find whether $X$ ...
Wyuw's user avatar
  • 125
0 votes
1 answer
60 views

Is the example distribution conditionally independent?

I am studying for my machine learning exam and i have problems with basic conditional probability. I have to solve the following exercise: The formular for conditionally independence is $P(Y|x) = \...
Jens's user avatar
  • 127