Andrec M, Prestegard J H
Department of Chemistry, Yale University, New Haven, Connecticut, 06511, USA.
J Magn Reson. 1998 Feb;130(2):217-32. doi: 10.1006/jmre.1997.1304.
The Bayesian perspective on statistics asserts that it makes sense to speak of a probability of an unknown parameter having a particular value. Given a model for an observed, noise-corrupted signal, we may use Bayesian methods to estimate not only the most probable value for each parameter but also their distributions. We present an implementation of the Bayesian parameter estimation formalism developed by G. L. Bretthorst (1990, J. Magn. Reson. 88, 533) using the Metropolis Monte Carlo sampling algorithm to perform the parameter and error estimation. This allows us to make very few assumptions about the shape of the posterior distribution, and allows the easy introduction of prior knowledge about constraints among the model parameters. We present evidence that the error estimates obtained in this manner are realistic, and that the Monte Carlo approach can be used to accurately estimate coupling constants from antiphase doublets in synthetic and experimental data.
统计学中的贝叶斯观点认为，谈论未知参数具有特定值的概率是有意义的。给定一个用于观测到的、受噪声干扰信号的模型，我们不仅可以使用贝叶斯方法来估计每个参数的最可能值，还可以估计它们的分布。我们展示了由G. L. Bretthorst（1990年，《磁共振杂志》88卷，533页）开发的贝叶斯参数估计形式的一种实现方式，使用 metropolis 蒙特卡罗采样算法来进行参数和误差估计。这使我们能够对后验分布的形状做出极少的假设，并允许轻松引入关于模型参数之间约束的先验知识。我们提供的证据表明，以这种方式获得的误差估计是现实的，并且蒙特卡罗方法可用于从合成数据和实验数据中的反相双峰准确估计耦合常数。
