# Talk:Bayes' rule

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## The meaning of terms

In this article I can nowhere see that the meaning of O(A1:A2) is clearly defined. Unfortunately then nothing is really defined in this article, or? So to anyone who does not know the exact definition the article is just nonsense.

I see the same problem with a lot of statistical articles.

Nopedia (talk) 13:54, 25 October 2012 (UTC)

I agree. There should be a link to follow..

Tombadog (talk) 03:23, 25 January 2013 (UTC)

There was a link to the definition of odds but I think it should be in the article anyway since it is easy, and it makes the article self-contained. I have rewritten the lead and the first section of the article accordingly. Richard Gill (talk) 13:39, 19 April 2013 (UTC)
The O notation is horrible and I've never seen it in the literature (coming from graduate studies in stochastic analysis) — Preceding unsigned comment added by 129.240.223.135 (talk) 18:25, 15 May 2013 (UTC)

## Non-equivalence to the theorem

There has been an attempt to say that Bayes' rule is equivalent to Bayes' theorem. While this does hold for true pobaility distributions, it does not hold for improper distributions .... and the use of Bayes' rule for improper prior distributions is valid/useful while the "theorem" is not (or requires special interpretation). Melcombe (talk) 10:53, 20 April 2013 (UTC)

The attempt was made by me, but I admit it is "own research", I don't know sources which agree with me, but I also don't know of sources who disagree with me either!.
Bayes' theorem is a standard ingredient in an elementary probability course. In that context we are always talking about proper probability distributions. In that context the equivalence is true. The link is the law of total probability which is an even more elementary and standard fact. Improper priors have indeed been popular in Bayesian inference but I believe that their use is still controversial there. I understand from my Bayesian friends that they should be avoided. Richard Gill (talk) 10:44, 21 April 2013 (UTC)

## Merge Bayes' rule with Bayes' theorem?

Reading the literature, both modern and old, it is clear to me that the phrases Bayes' theorem, Bayes' law, and Bayes' rule are all used interchangeably for any and all of the following mathematical results:

$P(H|E)=\frac{P(H)P(E|H)}{P(E)}$
$P(H_i|E)=\frac{P(H_i)P(E|H_i)}{\sum_n P(E|H_n)P(H_n)}$
Posterior odds equals prior odds times likelihood ratio
Posterior is proportional to prior times likelihood

In my opinion they are all mathematically equivalent (if we take the law of total probability as given). I suggest the articles on Bayes' theorem and Bayes' rule are merged. Richard Gill (talk) 14:36, 22 April 2013 (UTC)

I agree 100% - in fact, Wikipedia seems to be the only place that the two are distinguished from each other. Any reference I've ever seen - and I've seen a lot - that mentions more than one of Bayes Theorem/Rule/Law/Formula states that they are alternative phrases for the same thing. And the only mentionings I noticed in a quick search for an "odds form" calls it the "odds form of Bayes Theorem" or "odds ratio." (Here, here, here, and here). I think this phantom name difference is just a way somebody imagined could (not did) distinguish various forms. JeffJor (talk) 15:48, 28 May 2013 (UTC)
This also seems like a merger to me, though I'm sure I'm not as expert in stats as some. I've never heard of a distinction between Bayes' Rule and Bayes' Theorem. Bryanrutherford0 (talk) 16:31, 29 October 2013 (UTC)