Talk:Bayesian inference

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Examples: contrast with frequentist approach

For the 'Examples', I think it would be useful to contrast this approach with a frequentist approach. This would be especially interesting if the frequentist approach used a different formula, yielded a different result, or was not calculable. Conversely, for the current 'Probability of a hypothesis' example I am thinking there is negligible difference to a frequentist approach.
—DIV (120.17.126.118 (talk) 04:19, 23 January 2017 (UTC))[reply]

Introduction to Bayes' rule

The statement of Bayes's rule bothers me. Bayes's Rule is a mathematical description of the relation between joint probability and conditional probability. Every statistician, whether "frequentist" or bayesian, uses Bayes. It's an indispensable mathematical fact of elementary probability and statistics. Yet the way it's formulated here, one would think it is fundamentally connected to the notion of priors, likelihoods and posteriors, and that it involves "evidence," data and hypotheses. These are terms used by the modern bayesian and are much later ideas. I wish Bayes's Rule were not introduced as if it were bound up with the more modern notions of evidence, priors and posteriors, and as if, to employ it, you had to think the way modern bayesians think. If someone reading this has a feeling of ownership on this section, I urge you to introduce the rule as it is (a relation between joint and conditional probabilities) without the modern bayesian terminological overhead. Bayesians and non-bayesians alike use Bayes Rule. Chafe66 (talk) 22:47, 25 April 2019 (UTC)[reply]

The term 'likelihood' has a long tradition in both frequentist and Bayesian statistics, and there are technical reasons why it is not called a probability. The application of Bayes' rule becomes trickier when you add statistical parameters into the mix, which is why the statistical terminology diverges from elementary probability. The section could do with providing more motivation for the definitions. — Charles Stewart (talk) 01:35, 26 April 2019 (UTC)[reply]

Is that meant to address my point? Not sure who you're responding to, but I see no relation between my point and your response. I did not mention the likelihood at all. I'm quite familiar with what a likelihood is and why it's called what it's called. Chafe66 (talk) 17:48, 30 April 2019 (UTC)[reply]

Function of H/E

"The likelihood function is a function of the evidence, E {\displaystyle \textstyle E} \textstyle E, while the posterior probability is a function of the hypothesis, H {\displaystyle \textstyle H} \textstyle H." I think technically both are functions of both H and E. --Davyker (talk) 18:08, 18 July 2019 (UTC)[reply]

Technically, a conditional probability is a function of the conditional random variable and the article is incorrect, see Conditional_probability#Conditioning_on_a_random_variable. I think the author is confusing probabilities with density functions.

P(A|B)

is a function of the random variable

B

but

f(y|x)

short for

f_{Y|X=x}(y)

is a function of

y

. I don't think the current wording provides much clarity and it should probably be revised. 2602:41:80E4:C500:D94A:F14:3766:2B34 (talk) 02:25, 4 November 2019 (UTC)[reply]

Making a prediction section

This section uses archaeology as an example in a way that bears no relation to how archaeology would deal with the hypothetical scenario and isn't clear. Martinlc (talk) 11:00, 7 May 2021 (UTC)[reply]

'Updating' not explained?

To me as a non-statistician, the section on 'alternatives to Bayesian updating' seems to come out of the blue, as there is no previous explanation of what Bayesian updating is. I guess that it involves modifying the prior probability in the light of the new evidence, but whether this is done simply by substituting the 'posterior' probability, or something more complicated, is not clear. 2A00:23C8:7907:4B01:38EA:2480:36E4:F344 (talk) 20:42, 26 December 2021 (UTC)[reply]

"Alternatives to Bayesian updating" needs work

I can get nothing out of the subsection "Alternatives to Bayesian updating" as currently written. I am a working mathematician, though not in probability or statistics, and I do not believe the problem is mine. The subsection is extremely vague and does not for instance include any alternative formula for performing updates. The quote by Hacking which is a large fraction of the subsection's text is more philosophical than mathematical and in any case uses many terms in a technical way without defining them or linking to any standard definitions. It seems to me the section needs to either be cut or expanded. I was initially interested in the subsection because as a non-expert I was wondering if anybody actually uses alternative rules in practice. Perhaps the answer is "no" and such things are relegated to philosophy journals? 172.250.24.180 (talk) 23:59, 20 September 2022 (UTC)[reply]