Live briefing
Everything about Bayesian linear regression
Method of statistical analysis
Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables, with the goal of obtaining the posterior probability of the regression coefficients and ultimately allowing the out-of-sample prediction of the regressand conditional on observed values of the regressors. The simplest and most widely used version of this model is the normal linear model, in which given is distributed Gaussian. In this model, and under a particular choice of prior probabilities for the parameters—so-called conjugate priors—the posterior can be found analytically. With more arbitrarily chosen priors, the posteriors generally have to be approximated. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Bayesian linear regressionA 5-minute orientation
- Skim a recent paper: Positional error compensation for aviation drilling robot based on Bayesian linear regressionInfluential work since 2022
- Pick up a classic book: Regression and Other StoriesThe most-reprinted book on the subject
- Read the landmark paper: Bayesian Model Averaging for Linear Regression ModelsCited 1,654 times
- Go sideways: Bayesian multivariate linear regressionA closely related topic
- Go sideways: Chen distributionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Bayesian Model Averaging for Linear Regression Models
Bayesian Variable Selection in Linear Regression
Non-linear regression models for Approximate Bayesian Computation
Bayesian linear regression with sparse priors
A Bayesian Look at Inverse Linear Regression
Bayesian linear regression for surface roughness prediction
Bayesian Robust Multivariate Linear Regression with Incomplete Data
A Bayesian approach to linear regression in astronomy
🆕 Influential since 2022
Positional error compensation for aviation drilling robot based on Bayesian linear regression
Contrasting random and learned features in deep Bayesian linear regression
Physics-based Bayesian linear regression model for predicting length of mixed oil
Linear and non-linear bayesian regression methods for software fault prediction
Bayesian scale mixtures of normals linear regression and Bayesian quantile regression with big data and variable selection
📚 Books worth reading
Regression and Other StoriesAndrew Gelman, Jennifer Hill · 2020
Bayesian estimation and experimental design in linear regression modelsJürgen Pilz · 1983
Handbook of Financial Econometrics, Mathematics, Statistics, and Machine LearningCheng Few Lee, John C. Lee · 2020
A Beginner's Guide to Generalized Additive Mixed Models with RAlain F. Zuur, Anatoly A. Saveliev · 2014- 📕Bayesian assessment of assumptions of regression analysisIrwin Guttman · 1988
- 📕Estimating the number of aberrant laboratoriesIrwin Guttman · 1993
- 📕Bayesian assessment of assumptions of regression analysisParthasarathy Bagchi · 1989
Mathematical Statistics Theory and ApplicationsYu. A. Prokhorov, V. V. Sazonov · 2020
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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