Bayesian methods
拉普拉斯近似
拉普拉斯近似是一种经典的解析技术，它用一个以后验模式为中心的多元高斯分布来替代难以处理的后验分布，并利用该模式下对数后验的曲率来设定协方差。Tierney 和 Kadane (1986) 在他们发表于《美国统计学会杂志》的里程碑式论文中将其形式化为贝叶斯统计学的一部分，它提供了一种快速、确定性的替代马尔可夫链蒙特卡洛（MCMC）的方法，并构成了集成嵌套拉普拉斯近似（INLA）的数学核心。
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来源
- Tierney, L. & Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81(393), 82–86. DOI: 10.1080/01621459.1986.10478240 ↗
- MacKay, D. J. C. (2003). Information Theory, Inference, and Learning Algorithms. Cambridge University Press. ISBN: 978-0521642989
- Rue, H., Martino, S. & Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society: Series B, 71(2), 319–392. DOI: 10.1111/j.1467-9868.2008.00700.x ↗
如何引用本页
ScholarGate. (2026, June 3). Laplace Approximation to the Posterior. ScholarGate. https://scholargate.app/zh/bayesian/laplace-approximation
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