Thank you so much for your amazing article! Apologies if this is a silly question, but what are the main obstacles keeping us from using "true randomness" (insofar as that can be said to exist) in statistical experiments? Stark and Ottoboni showed that PRNG were not particularly good at generating this "true randomness", but from my understanding, there are accessible RNG's based on quantum events or atmospheric noise that would fulfill the desired properties. What is stopping us from using these?
The one drawback of physical randomness is that it's often hard to get high bit rates. But in a pinch, you can take the samples from the NIST beacon and use it to set your random seeds in your PRNG.
Whoa, thank you professor; this seems really cool! Do you think RANLUX has similar bit rate issues? From my understanding, it can passes many of the standard PRNG checks, though RANLUX does not seem to be as commonly used as some others. What are the main factors that would be considered to decide between different PRNG's (eg. RANLUX and numpy's current PRNG)?
Pearson's second paragraph seems to be alluding to the fact that humans are often bad at evaluating randomness? E.g. song shuffling algorithms have been adapted from "traditional" random to perceptually random for better user experience (this one is old but I'm curious what people are using now https://engineering.atspotify.com/2014/02/how-to-shuffle-songs/).
So does evaluating randomness just come down to designing the right tests for your purposes? This seems hard, and subjective, but maybe this is what you're getting at.
Pearson was referring to statistical tests that produce p-values. This still seems to be how people go about testing pseudo-randomness for cryptography applications.
But I think you're right: what randomness you need is application specific. If you just want to generate white noise for a synthesizer, it just has to sound good.
But whether it's p-values or some other metric, he is still telling people to resist the urge to conclude that seeing improbable events => non-randomness, right? This feels like acknowledgement that our intuitions about probability are kind of wrong, at least in certain contexts.
"So much of what bothers me about statistics and the general flattening of experience into pat answers and chance comes from their work in eugenics." As a researcher in statistical genetics, "hear! hear!". Sure they made useful mathematical and statistical contributions, but they held repugnant beliefs about individuals who were not "of their stature" so to speak.
"I’ve run into many statisticians who think Stark and Ottoboni’s worries about pseudorandomness are pedantic. But I always ask them which part of statistics they think is not pedantic." -- love it!
Von Neumann 1949: "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin".
And yet we're all sinners in 2024.
Thank you so much for your amazing article! Apologies if this is a silly question, but what are the main obstacles keeping us from using "true randomness" (insofar as that can be said to exist) in statistical experiments? Stark and Ottoboni showed that PRNG were not particularly good at generating this "true randomness", but from my understanding, there are accessible RNG's based on quantum events or atmospheric noise that would fulfill the desired properties. What is stopping us from using these?
Thank you!
I don't think there's anything stopping us from using them! NIST even has "Randomness Beacons" you can get samples from.
https://csrc.nist.gov/projects/interoperable-randomness-beacons
The one drawback of physical randomness is that it's often hard to get high bit rates. But in a pinch, you can take the samples from the NIST beacon and use it to set your random seeds in your PRNG.
Whoa, thank you professor; this seems really cool! Do you think RANLUX has similar bit rate issues? From my understanding, it can passes many of the standard PRNG checks, though RANLUX does not seem to be as commonly used as some others. What are the main factors that would be considered to decide between different PRNG's (eg. RANLUX and numpy's current PRNG)?
Pearson's second paragraph seems to be alluding to the fact that humans are often bad at evaluating randomness? E.g. song shuffling algorithms have been adapted from "traditional" random to perceptually random for better user experience (this one is old but I'm curious what people are using now https://engineering.atspotify.com/2014/02/how-to-shuffle-songs/).
So does evaluating randomness just come down to designing the right tests for your purposes? This seems hard, and subjective, but maybe this is what you're getting at.
Pearson was referring to statistical tests that produce p-values. This still seems to be how people go about testing pseudo-randomness for cryptography applications.
But I think you're right: what randomness you need is application specific. If you just want to generate white noise for a synthesizer, it just has to sound good.
But whether it's p-values or some other metric, he is still telling people to resist the urge to conclude that seeing improbable events => non-randomness, right? This feels like acknowledgement that our intuitions about probability are kind of wrong, at least in certain contexts.
Totally agree. But it points to how too much faith in randomness can lead us down some foolish paths.
"So much of what bothers me about statistics and the general flattening of experience into pat answers and chance comes from their work in eugenics." As a researcher in statistical genetics, "hear! hear!". Sure they made useful mathematical and statistical contributions, but they held repugnant beliefs about individuals who were not "of their stature" so to speak.
Well put. Statistical thinking too often encourages us to abstract away humanity through conceptions of population.
"I’ve run into many statisticians who think Stark and Ottoboni’s worries about pseudorandomness are pedantic. But I always ask them which part of statistics they think is not pedantic." -- love it!