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| Байесов регресионен модел× | Гаусов процес× | Марковски Монте Карло вериги (MCMC)× | |
|---|---|---|---|
| Област≠ | Бейсови методи | Машинно обучение | Бейсови методи |
| Семейство≠ | Bayesian methods | Machine learning | Bayesian methods |
| Година на възникване≠ | — | 2006 (book); roots in Kriging, 1951) | — |
| Създател≠ | — | Rasmussen, C. E. & Williams, C. K. I. | — |
| Тип≠ | Bayesian linear model | Probabilistic non-parametric model | Posterior sampling algorithm |
| Основополагащ източник≠ | 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 | 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 |
| Други названия≠ | bayesian linear regression, probabilistic regression, bayesian regresyon | GP, Gaussian Process Regression, GPR, Kriging | markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo) |
| Свързани≠ | 2 | 3 | 3 |
| Резюме≠ | Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a full posterior probability distribution for each parameter, from which credible intervals and predictions are read off. | 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. | Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model. |
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