方法对比
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| 贝叶斯描述性统计× | 贝叶斯卡方检验× | |
|---|---|---|
| 领域 | 统计学 | 统计学 |
| 方法族 | Hypothesis test | Hypothesis test |
| 起源年份≠ | 1763/1812 | 1967 |
| 提出者≠ | Thomas Bayes / Pierre-Simon Laplace | I. J. Good; extended by Gunel, Dickey, and Wagenmakers et al. |
| 类型≠ | Bayesian parameter estimation | Bayesian nonparametric association test |
| 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.). CRC Press. ISBN: 978-1439840955 | Good, I. J. (1967). A Bayesian significance test for multinomial distributions. Journal of the Royal Statistical Society: Series B (Methodological), 29(3), 399–418. DOI ↗ |
| 别名 | Bayesian summaries, posterior descriptives, Bayesian parameter estimation, credible-interval summaries | Bayesian contingency table test, Bayes factor chi-square, Bayesian goodness-of-fit test, Bayesian association test |
| 相关≠ | 5 | 3 |
| 摘要≠ | Bayesian descriptive statistics summarizes data by combining observed information with prior knowledge through Bayes' theorem, yielding posterior distributions over parameters such as the mean and variance. Instead of point estimates and p-values, results are expressed as posterior means, medians, and credible intervals that carry a direct probability interpretation. | The Bayesian chi-square test evaluates independence or goodness-of-fit in frequency tables using Bayes factors rather than classical p-values. It quantifies evidence for or against an association between categorical variables, updating prior beliefs with observed counts and delivering an odds-like ratio that distinguishes 'no evidence' from 'evidence of no effect'. |
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