方法对比
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| 贝叶斯泊松回归× | 负二项回归× | |
|---|---|---|
| 领域≠ | 统计学 | 计量经济学 |
| 方法族 | Regression model | Regression model |
| 起源年份≠ | 1989 (GLM foundation); Bayesian treatment formalized in 1990s–2000s | 2011 |
| 提出者≠ | Gelman et al. (BDA); classical Poisson GLM from McCullagh & Nelder (1989) | Hilbe (textbook treatment); generalized linear model framework |
| 类型≠ | Bayesian generalized linear model for count data | Generalized linear model for count data |
| 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 | Hilbe, J. M. (2011). Negative Binomial Regression (2nd ed.). Cambridge University Press. DOI ↗ |
| 别名≠ | Bayesian log-linear count model, Bayesian GLM Poisson, Poisson regression with priors, Bayesian count regression | NB regression, NB2 regression, negatif binom regresyonu |
| 相关≠ | 6 | 4 |
| 摘要≠ | Bayesian Poisson regression models non-negative integer count outcomes using a Poisson likelihood with a log link, placing prior distributions on the regression coefficients. Posterior inference — combining prior beliefs with the data likelihood — produces full probability distributions over the coefficients rather than single-point estimates, enabling coherent uncertainty quantification and incorporation of domain knowledge. | Negative Binomial Regression is a generalized linear model for count outcomes that extends Poisson regression to handle overdispersion, where the variance of the counts exceeds their mean. Developed in the GLM tradition and treated in depth by Hilbe (2011), it adds a dispersion parameter so that inference stays valid when Poisson would understate the spread of the data. |
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