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A regularized bridge sampler for sparsely sampled diffusions

机译：用于稀疏采样扩散的正则化桥梁采样器

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摘要

Sparsely sampled diffusion processes, in this paper interpreted as data sampled sparsely in time relative to the time constant, is a challenging statistical problem. Most approximations of the transition kernel are derived under the assumption that data is frequently sampled and these approximations are often severely biased for sparsely sampled data. Monte Carlo methods can be used for this problem as the transition density can be estimated with arbitrary accuracy regardless of the sampling frequency, but this is computationally expensive or even prohibited unless effective variance reduction is applied. The state of art variance reduction technique for diffusion processes is the Durham-Gallant (modified) bridge sampler. Their importance sampler is derived using a linearized, Gaussian approximation of the dynamics, and have proved successful for frequently sampled data. However, the approximation is often not valid for sparsely sampled data. We present a flexible, alternative derivation of the modified bridge sampler for multivariate, discretely observed diffusion models and modify it by taking uncertainty into account. The resulting sampler can be viewed as a combination of the basic sampler and the Durham-Gallant sampler, using the sampler that is most appropriate for the given problem, while still being computationally efficient. Our sampler is providing effective variance reduction for frequently and sparsely sampled data.
机译：在本文中，稀疏采样的扩散过程被解释为相对于时间常数在时间上稀疏采样的数据，这是一个具有挑战性的统计问题。过渡内核的大多数近似值是在以下假设下得出的：数据经常被采样，而稀疏采样的数据通常会对这些近似值产生严重偏差。蒙特卡洛方法可用于此问题，因为无论采样频率如何，都可以以任意精度估算过渡密度，但是除非应用有效的方差降低，否则这在计算上是昂贵的，甚至是被禁止的。用于扩散过程的最先进的方差降低技术是Durham-Gallant（改进的）电桥采样器。它们的重要性采样器是使用动力学的线性化高斯近似导出的，并已证明对于频繁采样的数据是成功的。但是，这种近似通常对于稀疏采样的数据无效。对于多变量，离散观测的扩散模型，我们提出了修改后的桥梁采样器的灵活，替代性推导，并通过考虑不确定性对其进行了修改。使用最适合给定问题的采样器，同时仍具有计算效率，可以将结果采样器视为基本采样器和Durham-Gallant采样器的组合。我们的采样器可有效减少频繁且稀疏采样的数据。

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