Talk:Bayesian linear regression

message: I've got some questions about this article.
What this method gives you is a weighted combination of some prior slope, and a new slope estimate from new data.
Q1) the weights are determined by the A. In this one-dimensional case I presume this is just a variance. There are no details as to how this A would be calculated or estimated. Does anyone know?
Q2) I could set this problem up using classical statistics, I think. I'd say "let's make a prediction based on a weighted combination of the prior slope and the new slope". Then I'd do some algebra to derive an expression for the weight. Does anyone have any idea whether the final answer would be much, if any, different?
thanks
82.44.214.29 20:09, 14 October 2007 (UTC)
thread_title:  Some questions 

message: Maybe a section on computation would be helpful.  When the amount of data is large, direct computation can be difficult.
— Preceding unsigned comment added by 173.166.26.241 (talk • contribs) 14:00, 7 August 2011‎
:I would suggest that the computations be kept separate from the analytic results using the conjugate prior. I'm doing research, and I come to this page, and all I want is the posterior. It is there, but it is buried in computations. I don't care about the computations; I already know how to do them. I'm not saying get rid of the computations, but not having the posterior, posterior mean, etc, all available quickly makes this article less useful. --68.101.66.185 (talk) 19:08, 9 September 2012 (UTC)
thread_title:  Computations 

message: I've added a suggested merge tag, suggesting the page be merged into ridge regression, since this is essentially a Bayesian interpretation of ridge regression, which has exactly the same mathematics.  Jheald (talk) 17:39, 11 November 2012 (UTC)
thread_title:  Suggested merge 

message: Single-variable linear regression is just a special case of multivariable. I see no reason to have two articles; if anything, it's confusing. InverseHypercube (talk) 07:11, 27 March 2016 (UTC)
replies: text: Oppose merge; while it is true that the single-variable case is a special case of the multivariable one, it is helpful to keep them separate because those without a mathematical specialism may more easily understand the single-variable case. Klbrain (talk) 21:09, 8 January 2018 (UTC)
replies: text: Closing, given lack of support. Klbrain (talk) 09:37, 15 February 2018 (UTC)
thread_title:  Proposed merge with [[Bayesian multivariate linear regression]] 

message: Substituted at 19:49, 1 May 2016 (UTC)
thread_title: Assessment comment

message: In linear regression, one of the most important results is a confidence interval on the parameter estimates. The bayesian analog is, I believe, the credibility interval. To most practitioners (of merit), a parameter estimate without an accompanying confidence interval is more or less useless. So why no section on inference/credibility intervals in this article? That is a big part of looking at results of models but there is no mention at all here, so I think the article is missing a crucial component. Chafe66 (talk) 20:45, 19 April 2018 (UTC)
thread_title: What about Inference?

message: The solutions given for the posterior appear to be somewhat wrong to me. The equations for the posterior mean should contain a dependence on the estimated noise variance, but it does not. The weight for the likelihood based inference should be \frac{1}{\sigma^2} X^TX not just X^TX I guess. I cannot pinpoint immediately, where this dependence is lost, but the same mean independent of \sigma is certainly wrong. Xenonoxid (talk) 14:13, 19 March 2024 (UTC)
thread_title:  Dependence on noise variance dropped?