摘要翻译：
亚椭圆扩散过程可以用来模拟从分子动力学到音频信号分析等应用中的各种现象。我们研究了在离散时刻观察解的某些分量的情况下这类过程的参数估计。由于过渡密度的精确似然通常不为人所知，因此使用了在小的样本间时间$δT$和大的总观察时间$NδT$的极限下可以很好地工作的近似方法。低椭圆性加上部分观测导致病态条件，需要对各种参数进行估计的近似似然的明智组合。我们在一个确定性扫描吉布斯采样器中结合这些，在未观察到的解分量中的缺失数据和参数之间交替。数值实验表明，该方法在模拟数据上具有渐近一致性。最后介绍了Gibbs采样器在分子动力学数据中的应用。
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英文标题：
《Parameter Estimation for Partially Observed Hypoelliptic Diffusions》
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作者：
Y. Pokern, A. M. Stuart, P. Wiberg
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最新提交年份：
2007
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
  Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some components of the solution at discrete times. Since exact likelihoods for the transition densities are typically not known, approximations are used that are expected to work well in the limit of small inter-sample times $\Delta t$ and large total observation times $N\Delta t$. Hypoellipticity together with partial observation leads to ill-conditioning requiring a judicious combination of approximate likelihoods for the various parameters to be estimated. We combine these in a deterministic scan Gibbs sampler alternating between missing data in the unobserved solution components, and parameters. Numerical experiments illustrate asymptotic consistency of the method when applied to simulated data. The paper concludes with application of the Gibbs sampler to molecular dynamics data.
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PDF链接：
https://arxiv.org/pdf/710.5442