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>> "Probability" does not mean "maybe yes, maybe not, let me assign some gut feeling value measuring how much I believe something to be the case." That's exact
by YeGoblynQueenne 9mo ago
>> "Probability" does not mean "maybe yes, maybe not, let me assign some gut feeling value measuring how much I believe something to be the case."
That's exactly what Baeysian probabilities are: gut feelings. Speaking of values attached to random variables, a good Bayesian basically pulls their probabilities out their ass. Probabilities, in that context, are nothing but arbitrary degrees of belief based on other probabilities. That's the difference with the frequentist paradigm which attempts to set the values of probabilities by observing the frequency of events. Frequentists ... believe that observing frequencies is somehow more accurate than pulling degrees of belief out one's ass, but that's just a belief itself.
You can put a theoretical sheen on things by speaking of sets or probability spaces etc, but all that follows from the basic fact that either you choose to believe, or you choose to believe because data. In either case, reasoning under uncertainty is all about accepting the fact that there is always uncertainty and there is never complete certainty under any probabilistic paradigm.
- teiferer 9mo agoBaffling to see such a take on HN. If I give you a die and ask about the probabiliy for a 6, then it's exactly 1/6. Being able to quantify this exactly is the great success story of probability theory. You can have a different "gut feeling", and indeed many people do (lotteries are popular), but you would be wrong. If you run this experiment a large number of times, then about 1/6 of the outcomes will be a 6, proving the 1/6 right and the deviating "gut feeling" wrong. That number is not "pulled out of somebody's ass" or some frequentist approach. It's what probability means.
- YeGoblynQueenne 9mo agoYes, that's the frequentist approach. Surely, even on HN, there is an understanding that there are two interpretations of probability?
- CyberDildonics 9mo agoYou don't think that the probability of each side of a die is 1/6 ?
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- YeGoblynQueenne 9mo agoI see, you don't know what I'm talking about. My apologies, I assumed a common background. Here's some introductory materials on Bayesian vs frequentist interpretations of probability: Bayesian and frequentist reasoning in plain English https://stats.stackexchange.com/questions/22/bayesian-and-frequentist-reasoning-in-plain-english https://stats.stackexchange.com/questions/22/bayesian-and-fr... Comparison of frequentist and Bayesian inference https://ocw.mit.edu/courses/18-05-introduction-to-probability-and-statistics-spring-2022/mit18_05_s22_class20-prep.pdf https://ocw.mit.edu/courses/18-05-introduction-to-probabilit... To Be a Frequentist or Bayesian? Five Positions in a Spectrum https://hdsr.mitpress.mit.edu/pub/axvcupj4/release/1 https://hdsr.mitpress.mit.edu/pub/axvcupj4/release/1 Beyond Bayesians and Frequentists - Computer Science https://cs.stanford.edu/~jsteinhardt/stats-essay.pdf https://cs.stanford.edu/~jsteinhardt/stats-essay.pdf You'll find that it's a big subject with a long history and many strongly-held opinions that have nevertheless evolved over the years. Happy reading!
- CyberDildonics 9mo agoWhich one of these answers the question I asked?
- YeGoblynQueenne 9mo agoOh it's you. I didn't notice the username change.