I have a number of related questions about the derivation of the front-door adjustment formula as given on page 236. Here is the derivation. I would have typed it up, but the diagrams at the far right would have been a pain to include. There is a typo in Line 4, caught in the errata. It should...

Background I am solving problems from "Elements of causal inference" by Peters, Janzing, Schölkopf (2017, MIT Press). The book is available in open access (link). I'm stumped by problem 6.57b. Since the full question statement and relevant definitions is available publicly, I'll try to give only...

Does $(A \perp B)|X$ implies $(A|X)\perp B$ ? I managed to derive it, but it feels wrong. Here is my derivation. Is it flawed? If $(A \perp B)|X$ then $(A|X) \perp (B|X)$ and therefore $p[A|(X, (B|X) ) ]=p[A|X]$ in addition: $p[A|(X, (B|X) ) ] = p[A|(X, B) ]$, because both $X$ and $B$ ...

Getting into the causality tools. Suppose I have a causal graph $X\to R\to T\leftarrow U.$ I can work out that $R$ and $U$ are independent; i.e., $P(r, u) = P(r)\,P(u).$ Also $X$ and $T$ are conditionally independent given $R;$ i.e., $P(x|t,r) = P(x|r).$ I think there must be a way to prove: ...

Does anybody know a source where the correct answers to study questions from the mentioned book are described? I would like to validate whether my way of thinking is correct. I have found only two questions on the forum while in the book there are many more. Any tip would be appreciated.

I am reading Pearl's Causal Inference book and attempted at solving study question 1.2.4. Here is the entire problem: In an attempt to estimate the effectiveness of a new drug, a randomized experiment is conducted. In all, 50% of the patients are assigned to receive the new drug and 50% to recei...

this is my first question here, a little background about me, im a biomedical engineer, im studying a PhD in Neuroscience, and a Micromaster in Statistics and Data Science. Here in my lab, very few people are interested at maths , models, etc. (incredible i know...) So i have so little referen...

In Judea Pearl's The Book of Why we find the following causal diagram: where $U_1$ and $U_2$ are unobserved variables. The diagram is accompanied by a comment that ensures that neither the back door criterion nor the front door criterion are sufficient to figure out the causal effect $P(Y | d...

If we have two non-zero correlated random variables then they are dependent. Why then do we have the saying "Correlation does not imply Causation". A change in one variable may not cause exactly the same change in another but there is at least some 'causal' link.

source : Judea Pearl, 2010, An Introduction to Causal Inference, The International Journal of Biostatistics, pp15-16 Problem. There is a causal Markovian model, By the definition of interventional probability, $$ P(y\mid \text{do}(x)) =\sum_{z_1,z_2,z_3}P(z_1)P(z_2)P(z_...

In the real world, it seems you can often take a set of things and create new things with them. Let's say you want to make bread, for example. Normally, you can create bread by putting together flour, milk, eggs, and a few other ingredients, and cooking. It would seem, that this could be written...

In the Book of Why by Judea Pearl (page 14) he says to work out the effect a drug (D) will have on a patients lifespan (L) taking into account other factors (Z) can be calculated as P(L | D, Z) x P(Z) What is the purpose of multiplying by P(Z) when trying to calculate the effect of D on L?

I have a number of related questions about the derivation of the front-door adjustment formula as given on page 236. Here is the derivation. I would have typed it up, but the diagrams at the far right would have been a pain to include. There is a typo in Line 4, caught in the errata. It should...

In Judea Pearl's The Book of Why we find the following causal diagram: where $U_1$ and $U_2$ are unobserved variables. The diagram is accompanied by a comment that ensures that neither the back door criterion nor the front door criterion are sufficient to figure out the causal effect $P(Y | d...