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Comment by enaaem | Hacker News Reader

The difference between Bayesian and Frequentist is in the interpretation of randomness. In Bayesian statistics 'randomness' is not a property of nature but a description of our knowledge.

What's randomness in a coin toss? If we had all the information we could perfectly predict the result of a toss. But if we know nothing then at most we can say is that both outcomes are equally probable.

Another example, if you had no idea who the next presidential winner will be between two candidates, than saying it's 50-50 is an accurate description of your knowledge.

If anyone is more interested I would refer to you to [1]. Here, probability theory is interpreted as an extension of logic. Very interesting stuff.

[1] http://www.med.mcgill.ca/epidemiology/hanley/bios601/Gaussia...

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> Another example, if you had no idea who the next presidential winner will be between two candidates, than saying it's 50-50 is an accurate description of your knowledge.

How do you capture the difference between having no idea and having the absolute best possible idea that anyone has or can has and that idea being the probability is 50-50?

    50-50 = no idea, zero certainty
    50-50 = expert analysis with as high degree of certainty as possible of a very, very close race

These two things are expressed as being equal? Feels like something important has been lost.

>>> What's randomness in a coin toss? If we had all the information we could perfectly predict the result of a toss. But if we know nothing then at most we can say is that both outcomes are equally probable.

That's because you know it's a coin toss. If it was something else like whether a seed will germinate or not, I wouldn't assume equal probability.

Admittedly, this is something that's always puzzled me about Bayesian statistics, though I'm not sure it's fundamental.

>> What's randomness in a coin toss? If we had all the information we could perfectly predict the result of a toss. But if we know nothing then at most we can say is that both outcomes are equally probable.

Perhaps I'm being dense or overall don't understand, but how is this possible? What is "all the information"? Isn't it at most likely they the outcome is 50/50?

Each coin-toss is a deterministic physical process governed by laws of motion. If we had perfect information about the motion of all components in the system (hand, coin, air, floor, etc.), then we could, in principle, perfectly predict the outcome of every toss. Each individual toss would have a 100% probability of its predicted outcome.

Since we typically lack any of that information, we are stuck with the 50 / 50 prior distribution.

This is very debatable if you throw QM into the mix. From all what we know, we cannot predict everything with 100% success rate -- QM cannot be explained by a hidden variables model.

Argh - yes it can. Bell explicitly have a pretty trivial one in one of his early papers. QM cannot be explained by a non-contextual hidden variables model. (The simplest physical version of contextuality is locality - so as Bell showed you cannot explain quantum theory with a local hidden variables model).

Let's not break causality by observing non-local hidden variables.

Presumably talking to the wind here as this thread is old, but nonlocal hidden variables do not break causality! This can be seen explicitly in Bell's trivial model, where the state of a system is just the regular quantum state plus a uniform random number between 0 and 1 (hidden). Or put it this way, if this model "breaks causality" then so does regular non-relativistic quantum theory.

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