方法对比
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| 马尔可夫链蒙特卡洛 (MCMC)× | 自助法模拟× | |
|---|---|---|
| 领域 | 仿真 | 仿真 |
| 方法族 | Process / pipeline | Process / pipeline |
| 起源年份≠ | 1953 (Metropolis-Hastings); 1984 (Gibbs) | 1979 |
| 提出者≠ | Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984) | Bradley Efron |
| 类型≠ | Simulation-based Bayesian inference / numerical integration | Simulation-based nonparametric inference |
| 开创性文献≠ | Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. & Rubin, D.B. (2013). Bayesian Data Analysis (3rd ed.). Chapman & Hall/CRC. DOI ↗ | Efron, B. & Tibshirani, R.J. (1993). An Introduction to the Bootstrap. Chapman & Hall/CRC. DOI ↗ |
| 别名 | MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs) | bootstrap resampling, empirical resampling, nonparametric bootstrap, Önyükleme Simülasyonu (Bootstrap Resampling) |
| 相关 | 5 | 5 |
| 摘要≠ | Markov Chain Monte Carlo (MCMC) is a family of simulation algorithms that constructs a Markov chain whose stationary distribution is the target posterior, enabling Bayesian inference and high-dimensional integral computation that would otherwise be analytically intractable. Pioneered by Metropolis and colleagues in 1953 and extended by Hastings in 1970, MCMC underpins modern Bayesian statistics. The two most widely used variants are Metropolis-Hastings, which proposes moves from a general proposal distribution, and Gibbs sampling, which draws each parameter in turn from its full conditional distribution. | Bootstrap simulation, introduced by Bradley Efron in 1979, is a simulation-based inference method that derives the sampling distribution of virtually any statistic by repeatedly resampling with replacement from the observed data. Because it requires no parametric distributional assumptions, it provides a robust, general-purpose alternative to analytical confidence intervals and parametric hypothesis tests across continuous, ordinal, binary, and count data. |
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