Questions tagged [paradox]
A paradox is a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth.
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Applying Bayesian probability to a generalized Monty Hall problem
I posted this question about the Monty Hall problem and Monty's knowledge of the probability distribution several months ago. I got some good answers and this one in particular helped me gain some ...
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Odds Ratios paradox? Pooled OR inconsistent with subgroup ORs
I have two groups (A and B) that each produce ORs of 1.44 and 1.50. However, if I combine the frequencies for the two groups to create a pooled dataset, I get an OR of 1.40.
I get that it's not going ...
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A seeming paradox regarding estimation of the number of buttons
There is a computer with $N$ buttons in a secret room. We do not have access to the computer and we do not know $N$. But we know that $N\leq 100$ and we have a ever so slightly larger prior for ...
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Variation on St. Petersburg Paradox, with total loss at the end
I’m not too sure how to answer these variations I thought of and was hoping someone could enlighten me.
A casino offers a game of chance for a single player in which a fair coin is tossed at each ...
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In the Monty Hall problem, does it matter that the host knows which door the car is behind? If so, why?
If I'm thinking about this correctly, regardless of how the host chooses which door to open, there's a 1/3 chance the player initially picks the door with the car behind it, in which case they shouldn'...
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Propensity score paradox and propensity score matching
Propensity score paradox and propensity score matching
I went over the papers by King and Nielsen (2017) and Ripollone et al (2018) to figure out what is propensity score paradox in propensity score ...
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How to resolve the ambiguity in the Boy or Girl paradox?
Specifically, I was reading this article, which discusses this wording of the question:
Consider a family with two children. Given that one of the children is a boy, what is the probability that both ...
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Paradoxical Questions about confidence intervals
Let there be a repeatable real world experiment with two outcomes denoted by $0,1$ for convenience (Tossing a coin for example). Let $X_i$ be the random variable that models the ith repetition of the ...
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Is the sleeping beauty paradox really one? [duplicate]
See en.wikipedia.org/wiki/Sleeping_Beauty_problem for the statement of this problem.
This seems to me to be a simple weighted average problem. Because the total number of days awake varies between 1 (...
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How do we draw parallels between the BBG drug example and the businessman (affected by the election) anecdote in "The book of why"?
In "The book of why", Dr Pearl concludes that a BBG drug cannot exist after phrasing the sure-thing principle in 'a more correct way' (pg 214). He does this by first "insisting" ...
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Causal Inference - when Conditioning on a Collider is correct
I have been reading Judea Pearl's Book of Why and in it, he tackles the famous Monty Hall problem through a causal lens. Although it may still grind away at our initial instincts, hopefully nobody ...
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Power paradox: overestimated effect size in low-powered study, but the estimator is unbiased
If we have an underpowered study but manage to reject the null hypothesis, anyway, it makes sense to wonder if we have overestimated the effect size.
However, such a concern seems unwarranted if we ...
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simulating the St. Petersburg Paradox [duplicate]
from the following simulation it seems the fee I am willing to pay should be smaller than 10, instead of $\infty$, differs from the paradox, what is happening here?
Edit:
For those that aren't ...
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Resolve Lord's Paradox with principal components analysis (orthogonal distance regression)?
I've been reading Judea Pearl's description of Lord's Paradox in his 2018 book The Book of Why: The New Science of Cause and Effect, in which he presents the following plot:
In this special case ...
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What is actually Galton's paradox?
From One Thousand Exercises in Probability I found the exercise:
Galton's paradox. You flip three fair coins. At least two are alike, and it is an even chance that the third is a head or a tail. ...
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