Talk:Bayesian probability

Bayesian Methodology
One point says: "For the frequentist a hypothesis is a proposition (which must be either true or false), so that the frequentist probability of a hypothesis is either one or zero. In Bayesian statistics, a probability can be assigned to a hypothesis that can differ from 0 or 1 if the truth value is uncertain." However, also the Bayesian approach is inherently aristotelian, i.e. an hypothesis is necessarily true or false, but we have a distribution over these truth values. This point probably mixes up Bayesianism with fuzzy concepts. Furthermore, in frequentist statistics we have a p-value, which is an error-probability of the hypothesis under test, so it generally does not assign 0/1-probabilities to hypotheses. User:193.170.104.110


 * "in frequentist statistics we have a p-value, which is an error-probability of the hypothesis under test, so it generally does not assign 0/1-probabilities to hypotheses." - please note that the p-value is not the probability of the hypothesis that is being tested, nor it is the probability that the hypothesis does not hold.
 * "However, also the Bayesian approach is inherently aristotelian, i.e. an hypothesis is necessarily true or false, but we have a distribution over these truth values." - yes, but that does not contradict the claim in the article. Ladislav Mecir (talk) 11:51, 13 April 2015 (UTC)


 * Then this point should not say that "frequentist probability of a hypothesis is either one or zero". Rather a frequentist does not assign a probability at all to hypotheses.
 * Maybe it's not wrong, but the phrasing of the point suggest that this would be a difference between Frequentism and Bayesianism.
 * Furthermore, I don't see why this point should specify an ingredience of "Bayesian Methodology". It is actually redundant to point one, "use of random variables for unknown quantities", e.g. truth values of hypotheses. User:193.170.104.110


 * "the phrasing of the point suggest that this would be a difference between Frequentism and Bayesianism" - yes, the phrasing reflects what independent reliable sources state. In fact, e.g. E. T. Jaynes, or other Bayesians are against the use of the term "random variable", which they see as a frequentist notion. They call them "unknown values" without thinking they are "variables". Please consult the Bayesian literature if you want to know more. Ladislav Mecir (talk) 11:51, 13 April 2015 (UTC)


 * In your first post you agreed with me that both Freuentism and Bayesianism are inherently Aristotelian; in your latter post you state that this view is a difference between these two approaches. I don't see what the discussion about random variables has to do with this discussion, since random variables are a preciseley defined notion in measure-theoretic based probability theory, which is the formal basis of both Frequentism and Bayesianism and free of any interpretation. Furthermore, telling people to read some literature in a discussion is snotty. I hold a PhD in proabilistic modeling, so I think my arguments can be taken seriously. — Preceding unsigned comment added by 193.170.104.110 (talk • contribs)


 * As mentioned in the article and in the cited sources, Bayesians assign probabilities in the 0 to 1 range to hypotheses, while frequentists don't. That is a difference between the approaches. Your note that both approaches are "inherently Aristotelian" does not contradict this. Ladislav Mecir (talk) 16:55, 9 February 2017 (UTC)
 * Quick note on something that caught my eye: you speak of measure-theoretic based probability theory, which is the formal basis of both Frequentism and Bayesianism. Measure theory is not the formal basis of Bayesianism. A weaker version of Kolmogorov's axioms is derived from the basic assumptions; that's it. The two approaches are very distinct. Dixit Jaynes (Appendix A of Proba Theory, the Logic of Science): [The] Kolmogorov approach to probability theory [...] could hardly be more different from ours in general viewpoint and motivation; yet the final results are identical in several respects.. — Gamall Wednesday Ida (t · c) 17:54, 9 February 2017 (UTC)
 * Wait. Ladislav Mecir, did you realise that the unsigned comment you reacted to today was from April 2015?  — Gamall Wednesday Ida (t · c) 19:39, 9 February 2017 (UTC)
 * You are right,, I did not realize that. Nevermind, I do not think it is an error to respond. Ladislav Mecir (talk) 21:56, 9 February 2017 (UTC)
 * Nor do I, I was just a bit taken aback when I noticed, after dropping the IP a welcome package in the hope they would learn to sign their messages properly. Anyway, cheers — Gamall Wednesday Ida (t · c) 22:50, 9 February 2017 (UTC)

“assigned [a probability]”
Please forgive, on one hand, and weigh, on the other, my limited but perhaps more formal (than that of those now encountering Bayes’s approach for the first time) instruction on this relatively subjective reasoning tool. Full disclosure: my imperfect-but-hardly-gonzo relevant background was as a BA physics graduate at one of the premier midwestern lib-arts undergrad institutions. Technically I was a just a physics major, but the math I did take was substantial, and (IIRC correctly) I chose to take even more of it than ‘’either’’ physics or maybe even math majors had to. The course (perhaps just Introduction to ...) “Probability and Statistics” probably was a physics-major requirement, was taught by a math prof, and included a intro to Bayes’s work. Our article may, or not, cover it as well as what my recollection of my course does, but I came away with a crucial recollection perhaps worth repeat ’’’shar‘’’ing, now that Bayesian statistics is ’’’at least‘’’ a candidate for epidemiology: formal math is something you can reduce to cold logic, including even formal statistics. But I was taught that Bayesian statistics uses rigorous math, and applies it to gaining ‘’mathematically’’ rigorous results, whose validity, usefulness, and value is based on its likely usefulness ’’’in‘’’ making important decisions that are outside the realms where mathematical logic can *prove* anything of the kind that we usually hope for, in using ‘’’when we use’’’ it. My perhaps gonzo picture is that Bayesian methods are a more powerful tool than flipping a coin, when you’ve admitted you most likely have to make up your mind what to do, and your educated ’’best guesses’’ about the “known unknowns” seem at least mildly likely to be worth being “weighed in’’’to that decision’’’”. We were offered only a passing ‘’’description’’’, but that educated introduction to the subject, in that half-ancient ‘’’but educated’’’ introduction may be valid in supporting ‘’’my’’’ confidence that the experts are doing ‘’what is’’, in the face of the inacessibility of detailed knowledge, the next best thing to our unachievable wish. —JerzyA (talk) 21:09 ‘’’& :50’’’, 21 February 2020 (UTC)
 * I'm not sure this comment is suggesting a change to this article? The article epidemiology does mention that probability is used in the field. -- Beland (talk) 15:08, 1 May 2020 (UTC)

Metaprobability
Metaprobability redirects here, but isn't explained in the article. -- Beland (talk) 14:56, 1 May 2020 (UTC)

"Degree of belief" listed at Redirects for discussion
The redirect [//en.wikipedia.org/w/index.php?title=Degree_of_belief&redirect=no Degree of belief] has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached. Hildeoc (talk) 00:44, 4 June 2023 (UTC)

Dutch book
I have difficulty understanding the section "Dutch book approach". A good first step may be to explain why it is sometimes used in support of bayesianism, before explaining that some non-bayesian approaches avoid Dutch Book as well. The given quote from Ian Hocking is also a bit hard to understand, since it introduces new terms such as "dynamic assumption" and "personalist". Alenoach (talk) 10:52, 14 November 2023 (UTC)

Objective criteria for priors
The statement, ‘Unfortunately, it is not clear how to assess the relative "objectivity" of the priors proposed under these methods’ is both unsupported by any references and hyperbolic. It is certainly possible to assess whether a prior respects a symmetry such as a transformation group (e.g., translation invariance), one of the methods specifically listed. Whether this is “unfortunate” or not, it is at least clear. I have weakened the hyperbole slightly. Jmacwiki (talk) 03:32, 25 March 2024 (UTC)