方法对比

	贝叶斯推断	贝叶斯线性回归	最大似然估计
领域	统计学	贝叶斯	统计学
方法族	Bayesian methods	Bayesian methods	Regression model
起源年份	1763	2013 (modern reference); foundations 18th–19th century	1922
提出者	Thomas Bayes; Pierre-Simon Laplace	Thomas Bayes / Pierre-Simon Laplace (foundations); modern workflow codified by Gelman et al.	R. A. Fisher
类型	Probabilistic inference paradigm	Bayesian linear model	Parametric point estimator
开创性文献	Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370–418.	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London, Series A, 222, 309–368.
别名	Bayes inference, Bayesian statistics, Bayesian updating, posterior inference	bayesian linear model, probabilistic linear regression, Bayesçi Doğrusal Regresyon	MLE, maximum-likelihood estimator, ML estimation, Fisher's method of maximum likelihood
相关	3	4	4
摘要	Bayesian inference is a statistical paradigm in which probability represents degrees of belief rather than long-run frequencies. It encodes prior knowledge about parameters in a prior distribution, combines that prior with the likelihood of observed data via Bayes' theorem, and produces a posterior distribution that quantifies updated uncertainty. The foundational theorem was published posthumously by Thomas Bayes in 1763 and subsequently systematized by Pierre-Simon Laplace in his 1812 Théorie analytique des probabilités.	Bayesian linear regression is a probabilistic extension of the ordinary linear model, introduced through Bayes' rule and formalised in its modern computational workflow by Gelman et al. (2013). Rather than returning a single point estimate for each coefficient, it combines a user-specified prior distribution with the likelihood of the observed data to produce a full posterior distribution over all parameters, from which credible intervals and posterior predictive distributions are derived.	Maximum Likelihood Estimation (MLE) is a general-purpose parametric method for estimating the unknown parameters of a statistical model by finding the parameter values that make the observed data most probable. Formalized by R. A. Fisher in his landmark 1922 paper in the Philosophical Transactions of the Royal Society, MLE has become the dominant parameter-estimation paradigm in modern statistics and is the foundational engine behind logistic regression, generalized linear models, structural equation modeling, and virtually all parametric inference procedures.