Maximum likelihood drift estimation for multiscale diffusions
Maximum likelihood drift estimation for multiscale diffusions
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DOI：
10.1016/j.spa.2009.05.003
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发表时间：
2009-10-01
影响因子：
1.4
通讯作者：
Stuart, A. M.
中科院分区：
文献类型：
--
作者：
Papavasiliou, A.;Pavliotis, G. A.;Stuart, A. M.
研究了随机微分方程快/慢系统参数估计的极大似然问题。我们的目标是阐明小尺度下模型/数据不匹配的问题。我们考虑两类快速/缓慢问题，对于这两类问题，慢变量的闭粗粒度方程可以严格推导出来，我们称之为平均和均匀化问题。我们的问题是，给定快/慢系统中慢变量的数据，我们是否可以使用最大似然法正确估计慢变量粗粒度方程漂移中的参数。我们证明，对于平均问题，极大似然估计量是渐近无偏的，而对于均匀化问题，除非我们以适当的速率对数据进行次采样，否则极大似然估计量是失败的。给出了对数似然函数渐近误差的显式表达式。我们的理论应用于分子动力学中的两个简单例子。(C) 2009 Elsevier B.V.版权所有
We Study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of fast/slow problems for which a closed coarse-grained equation for the slow variables can be rigorously derived, which we refer to as averaging and homogenization problems. We ask whether, given data from the slow variable in the fast/slow system, we can correctly estimate parameters in the drift of the coarse-grained equation For the slow variable, using maximum likelihood. We show that, whereas the maximum likelihood estimator is asymptotically unbiased for the averaging problem, for the homogenization problem maximum likelihood fails unless we subsample the data at an appropriate rate. An explicit formula For the asymptotic error in the log-likelihood function is presented. Our theory is applied to two simple examples from molecular dynamics. (C) 2009 Elsevier B.V. All rights reserved.