Talk:Probability

"There are two or three types of probability" SO EXPLAIN WHAT THEY ARE. Fucking morons. 04:36, 17 March 2011 (UTC)
 * I think that was referring to classical, frequentist, and Bayesian, but the paragraph was fairly confusing, so I deleted it. 04:44, 17 March 2011 (UTC)

Nice quote mine, the full thing was "There are two or three types of probability, depending on who you ask." with three footnotes leading to explanations of it. 11:36, 17 March 2011 (UTC)

Meta-probability
I have been having an interesting conversation with JimJast via email. He believes in an infinite universe. I would argue that: in an infinite universe, any event with non-zero probability will almost surely happen at least once, and any number of times even. No matter how small P(x), so long as P(x)>0, as the number of trials approaches infinity, the probability of x occurring in at least one of those trials must approach one. So, consider the following possible event: at some point, part of the universe arranges itself to be largely identical to this local spatiotemporal region, save that on 21 May 2011, green bunny rabbits invade the Earth from Alpha Centauri. What is its probability? No denying, it is exceedingly, exceedingly, exceedingly low. But is it zero or non-zero?

I suppose my intent, is I am trying to launch a kind of reductio ad absurdum against JimJast's suggestion that the universe is infinite. But the problem is, it only works if P(green bunny rabbit invasion)>0. It can be as small as one likes, but must be non-zero for my argument to succeed. But what actually is P(green bunny rabbit invasion)? It is hard to say exactly what it is with any confidence.

This follows on with some points I deposited on Tetronian's talk page: if we can speak of the probability of some proposition x (in a Bayesian sense), can't we also speak of the probability of the proposition that the given proposition has a certain probability. In other words, P(P(x)=c)=? Or P(a < P(x) < b) = ? In other words, meta-probability.

And here is a good example of where I think meta-probability is useful - to express our lack of confidence about our own probability assignments. I would say P(green bunny rabbits)>0. JimJast might say it is zero. But surely we must both admit, we have significant uncertainty about the correctness of our own assignments of probability. 0 < P(P(green bunny rabbits)=0) < 1. So this is a valid application of meta-probability.

Now, if meta-probability is valid, arguably Bayes rule is less than completely correct, because it only considers first order probabilities, and does not consider higher order probabilities. -- 07:50, 12 May 2011 (UTC)

Rewrite
I propose a rewrite of this article. I created a proposal which User:Nx moved to the following sandbox: User:Ungläubiger/Probability.

The main points I want to address with this rewrite are:

Some important things are currently missing.
 * The frequentist interpretation mentioned but not explained (share of results for a repeatable process).
 * Bayesian interpretation is mentioned but not explained (subjective certainty).
 * The dependency of probability calculation on model assumptions is not mentioned.
 * The common practice of creationists to apply probabilities to single events is problematic both under the Bayesian and frequentist interpretation, this is not mentioned.
 * Most (if not all) probabilities quoted by creationists use flawed assumptions and are in fact strawman arguments.

I would remove some parts because they have limited relevance for discussions with creationists.
 * Classical probability isn't really an interpretation which is used today, it may be of historical interest, but it is probably unhelpful for discussing creationists.
 * The section on zero probability is very mathematical and I wonder when it may be helpful outside a lecture.

Please feel free to change User:Ungläubiger/Probability. Ungläubiger (talk) 15:08, 12 June 2011 (UTC)

Where to put the link?
This needs a link to Improbable things happen, but I couldn't figure a way to work it in anywhere. (Outside of "see also".)--ZooGuard (talk) 12:55, 2 August 2013 (UTC)
 * Now it's a hatnote to the "Zero probability" section. Is OK? Sprocket J Cogswell (talk) 13:11, 2 August 2013 (UTC)

prosecutor's fallacy
Shouldn't there be a nice non-technical discussion of the wp:Prosecutor's fallacy? TomS TDotO (talk) 13:30, 24 August 2014 (UTC)

One of the main problems people have with probability
Can be summarised as distinguishing between the probability of 'meeting a specific person unexpectedly in a specific unexpected context' and 'meeting someone that you know in an unexpected context' (ie the cumulative figure of very many very low possibilities). Anna Livia (talk) 16:24, 1 July 2019 (UTC)

First footnote is belied by one of article's sections
The very first footnote claims that "Zero corresponds to false or cannot occur, and one corresponds to true or must occur", which is obviously a load of bollocks. "Zero probability" section neatly explains why the second part is false. Taking this reasoning one step further it's easy to see why "probability of this event is 1" does not mean necessarily that the event will occur. There's a reason "almost always" and "almost never" are actual terms in probability theory.&mdash; Unsigned, by: 2a01:11af:524:8400:1433:70f8:d738:3edb / talk