手法を比較

	ベイズ線形回帰	ベイズ最適化	ガウス過程
分野	ベイズ	最適化	機械学習
系統	Bayesian methods	Process / pipeline	Machine learning
提唱年	2013 (modern reference); foundations 18th–19th century	1975 (foundational); 2012 (ML standard)	2006 (book); roots in Kriging, 1951)
提唱者	Thomas Bayes / Pierre-Simon Laplace (foundations); modern workflow codified by Gelman et al.	Mockus (1975); popularised for ML by Snoek, Larochelle & Adams (2012)	Rasmussen, C. E. & Williams, C. K. I.
種類	Bayesian linear model	Sequential model-based black-box optimization	Probabilistic non-parametric model
原典	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	Snoek, J., Larochelle, H., & Adams, R.P. (2012). Practical Bayesian Optimization of Machine Learning Algorithms. Advances in Neural Information Processing Systems (NeurIPS), 25.	Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. MIT Press. ISBN: 978-0-262-18253-9
別名	bayesian linear model, probabilistic linear regression, Bayesçi Doğrusal Regresyon	Bayesçi Optimizasyon (Hyperparameter Tuning), surrogate-based optimization, sequential model-based optimization, SMBO	GP, Gaussian Process Regression, GPR, Kriging
関連	4	2	3
概要	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.	Bayesian Optimization is a sequential, model-based strategy for finding the optimum of expensive black-box functions with as few evaluations as possible. Rooted in the work of Mockus (1975) and brought to mainstream machine-learning practice by Snoek, Larochelle, and Adams (2012), it fits a probabilistic surrogate model — typically a Gaussian Process — to past observations and uses an acquisition function to decide where to probe next, balancing exploration of unknown regions with exploitation of promising ones.	A Gaussian Process (GP) is a non-parametric, fully probabilistic machine learning model that places a prior distribution directly over functions. Rather than predicting a single value, it returns a predictive mean and a calibrated uncertainty estimate at every test point, making it especially valuable for regression on small to medium datasets and for Bayesian optimization tasks.