Estimating Bayes factors via thermodynamic integration and population MCMC
Estimating Bayes factors via thermodynamic integration and population MCMC
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DOI：
10.1016/j.csda.2009.07.025
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发表时间：
2009-10-01
影响因子：
1.8
通讯作者：
Girolami, Mark
中科院分区：
文献类型：
--
作者：
Calderhead, Ben;Girolami, Mark
考虑了基于积分似然或边际似然的贝叶斯模型比较方法，并将其应用于线性回归模型和非线性常微分方程（ODE）模型，以阐明和进一步发展现有的统计方法。重点讨论了边际似然估计的两种方法。首先，强调了广泛使用的后验调和均值估计的统计失效。研究表明，存在一种能够显著扭曲贝叶斯因子估计的系统偏差，这在以前的文献中没有得到强调。其次，对最近提出的热力学积分估计器进行了详细的研究，该估计器具有与离散形式相关的误差特征。一项使用易分析线性回归模型的实验研究强调了与最近发表的关于最佳离散化的结果的实质性差异。最后，随着所获得的见解，展示了如何将种群MCMC和热力学集成方法优雅地结合起来，以足够准确地估计贝叶斯因子，以区分基于ode系统的非线性模型，这在描述各种研究领域（如系统生物学，计算生态学和化学工程）中出现的复杂过程的行为方面具有重要应用。(C) 2009 Elsevier B.V.版权所有
A Bayesian approach to model comparison based on the integrated or marginal likelihood is considered, and applications to linear regression models and nonlinear ordinary differential equation (ODE) models are used as the setting in which to elucidate and further develop existing statistical methodology. The focus is on two methods of marginal likelihood estimation. First, a statistical failure of the widely employed Posterior Harmonic Mean estimator is highlighted. It is demonstrated that there is a systematic bias capable of significantly skewing Bayes factor estimates, which has not previously been highlighted in the literature. Second, a detailed study of the recently proposed Thermodynamic Integral estimator is presented, which characterises the error associated with its discrete form. An experimental study using analytically tractable linear regression models highlights substantial differences with recently published results regarding optimal discretisation. Finally, with the insights gained, it is demonstrated how Population MCMC and thermodynamic integration methods may be elegantly combined to estimate Bayes factors accurately enough to discriminate between nonlinear models based on systems of ODEs, which has important application in describing the behaviour of complex processes arising in a wide variety of research areas, such as Systems Biology, Computational Ecology and Chemical Engineering. (C) 2009 Elsevier B.V. All rights reserved.