MCMC methods for diffusion bridges
MCMC methods for diffusion bridges
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DOI：
10.1142/s0219493708002378
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发表时间：
2008-09
影响因子：
1.1
通讯作者：
A. Beskos;G. Roberts;A. Stuart;J. Voss
中科院分区：
文献类型：
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作者：
A. Beskos;G. Roberts;A. Stuart;J. Voss
提出并研究了一种非线性扩散桥采样的Langevin MCMC方法。该方法是基于最近的理论随机偏微分方程（SPDE）可逆的目标桥梁，通过应用朗之万的想法桥路径空间。在此过程中，还得到了随机行走大都会算法和独立采样器。本文的新颖算法思想是，MCMC算法的建议移动是通过使用隐式格式在时间方向上离散SPDE来确定的，参数为θ ∈ [0，1]。当MCMC方法具有正确的二次变差时，我们证明了当θ = 1/2时，所得到的无限维MCMC采样器是定义良好的.之前基于Langevin的MCMC方法使用显式方案，对应于θ = 0。选择θ = 1/2的意义是由实际使用的算法的有限维近似继承的。我们提出的数值结果说明的现象和理论，解释it. Diffusion桥（加性噪声）是代表家庭的法律定义为一个变化的措施，从高斯分布在任意可分离的希尔伯特空间，本文的分析可以很容易地扩展到目标法律从这个家庭和信号处理的一个例子说明了这一事实。
We present and study a Langevin MCMC approach for sampling nonlinear diffusion bridges. The method is based on recent theory concerning stochastic partial differential equations (SPDEs) reversible with respect to the target bridge, derived by applying the Langevin idea on the bridge pathspace. In the process, a Random-Walk Metropolis algorithm and an Independence Sampler are also obtained. The novel algorithmic idea of the paper is that proposed moves for the MCMC algorithm are determined by discretising the SPDEs in the time direction using an implicit scheme, parametrised by θ ∈ [0,1]. We show that the resulting infinite-dimensional MCMC sampler is well-defined only if θ = 1/2, when the MCMC proposals have the correct quadratic variation. Previous Langevin-based MCMC methods used explicit schemes, corresponding to θ = 0. The significance of the choice θ = 1/2 is inherited by the finite-dimensional approximation of the algorithm used in practice. We present numerical results illustrating the phenomenon and the theory that explains it. Diffusion bridges (with additive noise) are representative of the family of laws defined as a change of measure from Gaussian distributions on arbitrary separable Hilbert spaces; the analysis in this paper can be readily extended to target laws from this family and an example from signal processing illustrates this fact.