方法对比
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| 贝叶斯非参数方法× | 马尔可夫链蒙特卡洛 (MCMC)× | |
|---|---|---|
| 领域 | 贝叶斯 | 贝叶斯 |
| 方法族 | Bayesian methods | Bayesian methods |
| 起源年份≠ | 1973 (DP); 2006 (GP canonical text) | — |
| 提出者≠ | Ferguson (Dirichlet Process, 1973); Rasmussen & Williams (GP, 2006) | — |
| 类型≠ | Bayesian nonparametric model | Posterior sampling algorithm |
| 开创性文献≠ | Rasmussen, C.E. & Williams, C.K.I. (2006). Gaussian Processes for Machine Learning. MIT Press. ISBN: 978-0262182539 | 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 |
| 别名≠ | BNP, Dirichlet process mixture, DPM, Gaussian process regression | markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo) |
| 相关 | 3 | 3 |
| 摘要≠ | Bayesian nonparametric methods are a family of flexible Bayesian models in which model complexity is not fixed in advance but grows automatically with the data. The two most widely used members are the Dirichlet Process Mixture (DPM), which clusters observations without pre-specifying the number of clusters, and Gaussian Process (GP) regression, which places a prior directly over functions and performs regression or classification without committing to a parametric form. Both frameworks were formalised in the Bayesian nonparametric literature, with the canonical GP treatment given by Rasmussen and Williams (2006). | 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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