论文标题
贝叶斯参数推断，用于部分观察到的部分由布朗运动驱动的SDE
Bayesian Parameter Inference for Partially Observed SDEs driven by Fractional Brownian Motion
论文作者
论文摘要
在本文中，我们考虑了部分观察到的分数布朗运动（FBM）模型的贝叶斯参数推断。我们遵循的方法是将隐藏的过程限制，然后设计Markov Chain Monte Carlo（MCMC）算法，以从给定数据的参数上的后密度进行采样。我们依赖于时间离散化的新颖表示，该表示旨在从后部的近似值中取样，然后通过重要性采样来纠正； O（t）将近似值减少（根据总观察时间t）。通过使用多级MCMC方法扩展此方法，该方法可以降低计算成本以达到给定的平方误差（MSE），而不是使用单个时间离散化。我们的方法在模拟和真实数据上进行了说明。
In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC) algorithms to sample from the posterior density on the parameters given data. We rely on a novel representation of the time discretization, which seeks to sample from an approximation of the posterior and then corrects via importance sampling; the approximation reduces the time (in terms of total observation time T) by O(T). This method is extended by using a multilevel MCMC method which can reduce the computational cost to achieve a given mean square error (MSE) versus using a single time discretization. Our methods are illustrated on simulated and real data.
