方法对比
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| 贝叶斯方差分析 (Bayesian ANOVA)× | 贝叶斯因子检验× | 马尔可夫链蒙特卡洛 (MCMC)× | |
|---|---|---|---|
| 领域 | 贝叶斯 | 贝叶斯 | 贝叶斯 |
| 方法族 | Bayesian methods | Bayesian methods | Bayesian methods |
| 起源年份≠ | 2012 | 1961 | — |
| 提出者≠ | Rouder, Morey, Speckman & Province | Harold Jeffreys | — |
| 类型≠ | Bayesian hypothesis test / group comparison | Bayesian hypothesis comparison | Posterior sampling algorithm |
| 开创性文献≠ | Rouder, J. N., Morey, R. D., Speckman, P. L. & Province, J. M. (2012). Default Bayes Factors for ANOVA Designs. Journal of Mathematical Psychology, 56(5), 356–374. DOI ↗ | Jeffreys, H. (1961). Theory of Probability (3rd ed.). Clarendon Press / Oxford University Press. ISBN: 978-0198503682 | 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≠ | bayesian analysis of variance, bayes factor ANOVA, JZS ANOVA, Bayesçi ANOVA — Bayes Faktörü ile Grup Karşılaştırması | bayes factor, BF10, Bayesian hypothesis test, Bayes Faktörü — Hipotez Testi | markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo) |
| 相关≠ | 4 | 3 | 3 |
| 摘要≠ | Bayesian ANOVA, formalised by Rouder, Morey, Speckman and Province (2012), tests whether group means differ by quantifying the evidence for the alternative hypothesis relative to the null using the Bayes Factor (BF₁₀). Unlike classical ANOVA, it can also measure evidence in favour of the null hypothesis, making it equally informative when groups do not differ. | The Bayes factor test, formalised by Harold Jeffreys in 1961, is a Bayesian method for comparing two competing hypotheses. Rather than returning a binary reject/retain verdict, it produces a continuous ratio BF₁₀ that quantifies how much more (or less) probable the data are under the alternative hypothesis H₁ than under the null hypothesis H₀. | 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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