Methoden vergleichen

	Bayesian Gaussian Process	Bayes'sche Lineare Regression	Bayesian Optimization
Fachgebiet	Maschinelles Lernen	Bayes-Statistik	Optimierung
Familie	Machine learning	Bayesian methods	Process / pipeline
Entstehungsjahr	1978–2006	2013 (modern reference); foundations 18th–19th century	1975 (foundational); 2012 (ML standard)
Urheber	O'Hagan, A.; Neal, R. M.; Rasmussen, C. E. & Williams, C. K. I.	Thomas Bayes / Pierre-Simon Laplace (foundations); modern workflow codified by Gelman et al.	Mockus (1975); popularised for ML by Snoek, Larochelle & Adams (2012)
Typ	Probabilistic kernel model	Bayesian linear model	Sequential model-based black-box optimization
Wegweisende Quelle	Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. MIT Press. ISBN: 978-0-262-18253-9	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.
Aliasnamen	GP regression, GPR, Gaussian process model, GP classifier	bayesian linear model, probabilistic linear regression, Bayesçi Doğrusal Regresyon	Bayesçi Optimizasyon (Hyperparameter Tuning), surrogate-based optimization, sequential model-based optimization, SMBO
Verwandt	3	4	2
Zusammenfassung	A Bayesian Gaussian Process (GP) places a probability distribution directly over functions, using a kernel to encode similarity between inputs. After observing data, Bayes' rule converts this prior into a posterior that yields not just point predictions but calibrated uncertainty estimates at every new input — making it one of the most principled probabilistic models in machine learning.	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.