Say you want to fit a probability distribution to some data, but the distribution doesn't have a known PDF or CDF (e.g., stable distributions, for example). You can still do a non-parametric fit!

#probability #statistics

https://www.skewray.com/articles/fitting-characteristic-functions-to-sampled-data

My treatise on dice probability in TTRPGs is really coming along! Working out the probabilities for contested rolls was…way too difficult (thank you Interlock) but it’s mostly there. No idea how I’m going to fit in bonus dice with modifiers but that’s a problem for another day.

#statstab #389 Risk Ratio, odds ratio, risk difference… Which causal measure is easier to generalize?

Thoughts: Use this with #388 for better insight into the issue of risk, odds, probabilities, and more.

#odds #oddsratios #riskratios #probability

https://arxiv.org/html/2303.16008v3

How can #stats communication impact high-stakes judgments?

1. Intelligence analysts often failed to assign their agency's recommended words such as "likely" or "remote chance" to numeric #probability.

2. #Visualization of the probabilities didn't help?

https://doi.org/10.1080/02684527.2025.2468049

#statstab #388 The odds are it's wrong: Correcting a common mistake in statistics

Thoughts: Report probabilities instead, which in R (not SPSS) can be easily computed for your models.

#odds #oddsratios #riskratios #probability #r #logisticregression

https://onlinelibrary.wiley.com/doi/10.1111/test.12391

A quotation from Ambrose Bierce

REASON, v.i. To weight probabilities in the scales of desire.

Ambrose Bierce (1842-1914?) American writer and journalist
“Reason,” The Devil’s Dictionary (1911)

Sourcing, notes: wist.info/bierce-ambrose/77706…

My previous attempt to calculate how fast sums of the Pareto and Student's-t for parameter = 2 converge to a normal distribution failed due to both a bad fitting formula and accuracy issues. Now I am simulating the summation of up to 1e4930 random variables before something goes awry. Convergence is sloooooooow.

#probability #statistics #GCLT

https://www.skewray.com/articles/the-generalized-central-limit-theorem-for-a2-pareto-and-student-s-t

A quotation from Ambrose Bierce

REALLY, adv. Apparently.

Ambrose Bierce (1842-1914?) American writer and journalist
“Really,” The Devil’s Dictionary (1911)

Sourcing, notes: wist.info/bierce-ambrose/77534…

Happy birthday Edwin T. Jaynes, champion of sound physics & probability theory!

I find his text still the most illuminating about probability theory: <https://doi.org/10.1017/CBO9780511790423>

And also still a classic in statistical mechanics: <https://doi.org/10.1103/RevModPhys.34.143>

<https://bayes.wustl.edu/etj/etj.html>

Dear colleagues working with Markov-chain Monte Carlo: could you share any works that explore Markov-chain "convergence", and precision of mean estimates, with methods that use *quantiles* (or interquartile range, or median absolute deviation, or similar), rather than standard deviation and similar quantities?

Just to be clear, I don't mean estimation of quantiles, but estimation *by means of* quantiles.

Thank you!

If air molecules move randomly (albeit with some Brownian motion), there iis a probability that all of the air molecules will at some point move to the corner of the room you are in and you will sufficate.

Yes, I know the fallacy.

The Probability of a Hash Collision

https://kevingal.com/blog/collisions.html

Real coin flips are ~49-51 not 50-50 https://www.scientificamerican.com/article/scientists-destroy-illusion-that-coin-toss-flips-are-50-50/

But you can guarantee equal probability with a simple trick! Flip 2x in a row starting with the same side up.

HT->call it H
TH->call it T
HH,TT->try again

(due to von Neumann https://en.wikipedia.org/wiki/Randomness_extractor#Von_Neumann_extractor)

This leads to randomness extractors: from a given random process, what's the biggest uniform distribution you can get efficiently?

Randomness extractors give another interpretation of #entropy:

avg # bits needed to *describe* the outcome
=
# uniformly random bits you can *extract* from the outcome

oh f—

In grad school I noticed a printed message on the wall of our research lab. It was something like "distill information from the hint of implication" (bad memory).

I innocently said to an older grad student, "Yeah, that does sound like a way to commit Type-I errors" or something equivalent.

Well, that's not what the older grad student took from the sign and I got a very cold, slightly huffy response.

omg mein guter Freund zombiecalypse hat mal wieder abgeliefert: "Wieso gehen Pläne schief, erster Grund: Optimismus".

I spent two weeks trying to numerically demonstrate convergence of the generalized central limit theorem for the critical case where the variance just becomes infinite. I failed! I suspect my choice of norm was a poor one.

Modeling the sum of 10^30 random variables is challenging.

#probability #statistics

https://www.skewray.com/articles/the-generalized-central-limit-theorem-for-a2-pareto-and-student-s-t