Re: probability vs. statistics (was Re: Model of induction)

Posted by Eric Charles-2 on Dec 13, 2016; 1:00pm
URL: http://friam.383.s1.nabble.com/Model-of-induction-tp7588431p7588447.html

I don't have an answer per se, but I have some relevant information:

Back in the early days of statistics, one could become a pariah in the eyes of the field if it became suspected one had surreptitiously used Bayes' Theorem in a proof. This was because the early statisticians believed future events were probable. They really, deeply believed it. They were defining a new world view, to be contrasted with the deterministic world view. If you smoked, there was a probability that in the future you might get cancer; it was not certain, nothing was predetermined. In such a context, any talk of backwards-probability is nonsensical. After you have lung cancer, there is not "a probability" that you smoked. Either you did or you did not; it already happened! Thus, at least for the early statisticians, people like Fisher, time was inherent to claims about probability.

Now, it is worth noting that one can wager on past events of any kind, given someone willing to take the bet. And in such a context, Bayes' Theorem can be mighty useful. The Theorem is thus quite popular these days, but that is a different matter. Whatever the results of such equations are --- between 1 and 0, having certain properties, etc. --- so long as the results refer to past events, Fisher and many others would have insisted that the result is not "a probability" that said event occurred.  

Also, from what I can tell, as mathematicians became more prevalent in statistics, as opposed to the grand tradition of scientist-philosophers who happened to be highly proficient in mathematics, such ontological/metaphysical points seem to have become much less important.

On Mon, Dec 12, 2016 at 6:47 PM, glen ☣ <[hidden email]> wrote:

I have a large stash of nonsense I could write that might be on topic.  But the topic coincides with an argument I had about 2 weeks ago.  My opponent said something generalizing about the use of statistics and I made a comment (I thought was funny, but apparently not) that I don't really know what statistics _is_.  I also made the mistake of claiming that I _do_ know what probability theory is. [sigh]  Fast forward through lots of nonsense to the gist:

My opponent claims that time (the experience of, the passage of, etc.) is required by probability theory.  He seemed to hinge his entire argument on the vernacular concept of an "event".  My argument was that, akin to the idea that we discover (rather than invent) math theorems, probability theory was all about counting -- or measurement.  So, it's all already there, including things like power sets.  There's no need for time to pass in order to measure the size of any given subset of the possibility space.

In any case, I'm a bit of a jerk, obviously.  So, I just assumed I was right and didn't look anything up.  But after this conversation here, I decided to spend lunch doing so.  And ran across the idea that probability is the forward map (given the generator, what phenomena will emerge?) and statistics is the inverse map (given the phenomena you see, what's the generator?).  And although neither of these really require time, per se, there is a definite role for [ir]reversibility or at least asymmetry.

So, does anyone here have an opinion on the ontological status of one or both probability and/or statistics?  Am I demonstrating my ignorance by suggesting the "events" we study in probability are not (identical to) the events we experience in space & time?


On 12/11/2016 11:31 PM, Nick Thompson wrote:
> Would the following work?
>
> */Imagine you enter a casino that has a thousand roulette tables.  The rumor circulates around the casino that one of the wheels is loaded.  So, you call up a thousand of your friends and you all work together to find the loaded wheel.  Why, because if you use your knowledge to play that wheel you will make a LOT of money.  Now the problem you all face, of course, is that a run of successes is not an infallible sign of a loaded wheel.  In fact, given randomness, it is assured that with a thousand players playing a thousand wheels as fast as they can, there will be random long runs of successes.  But the longer a run of success continues, the greater is the probability that the wheel that produces those successes is biased.  So, your team of players would be paid, on this account, for beginning to focus its play on those wheels with the longest runs. /*
>
>
>
> FWIW, this, I think, is Peirce’s model of scientific induction.

--
☣ glen

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