推论
非线性系统
应用数学
计算机科学
数学优化
波动性(金融)
扩散
随机波动
算法
数学
统计物理学
人工智能
计量经济学
物理
量子力学
热力学
作者
Cédric Archambeau,Manfred Opper,Yuan Shen,Dan Cornford,John Shawe‐Taylor
摘要
Diffusion processes are a family of continuous-time continuous-state stochastic processes that are in general only partially observed. The joint estimation of the forcing parameters and the system noise (volatility) in these dynamical systems is a crucial, but non-trivial task, especially when the system is nonlinear and multi-modal. We propose a variational treatment of diffusion processes, which allows us to compute type II maximum likelihood estimates of the parameters by simple gradient techniques and which is computationally less demanding than most MCMC approaches. We also show how a cheap estimate of the posterior over the parameters can be constructed based on the variational free energy.
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