随机微分方程的统计推断

IF 4.4 2区 数学 Q1 STATISTICS & PROBABILITY
P. Craigmile, Radu Herbei, Geoffrey Liu, Grant Schneider
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引用次数: 6

摘要

许多科学领域都在使用随机微分方程(SDEs),也称为扩散过程,随着时间的推移来模拟科学现象。SDEs可以同时捕捉潜在感兴趣变量的已知确定性动态(例如,洋流、水体的化学和物理特征、疾病的存在、不存在和传播),同时使建模者能够捕捉随机环境中未知的随机动态。我们重点回顾了基于似然的频率推断和基于离散采样扩散的贝叶斯参数推断的广泛的统计推断方法。精确的参数推断通常是不可能的,因为跃迁密度不能以封闭形式得到。因此,我们回顾了关于近似数值方法(例如,Euler, Milstein,局部线性化和Aït‐Sahalia)和基于模拟的方法(例如,数据增强和精确抽样)的文献,这些方法用于对SDE过程进行参数统计推断。最后,我们简要讨论了其他推断SDE和更复杂的SDE过程(如时空SDE)的方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Statistical inference for stochastic differential equations
Many scientific fields have experienced growth in the use of stochastic differential equations (SDEs), also known as diffusion processes, to model scientific phenomena over time. SDEs can simultaneously capture the known deterministic dynamics of underlying variables of interest (e.g., ocean flow, chemical and physical characteristics of a body of water, presence, absence, and spread of a disease), while enabling a modeler to capture the unknown random dynamics in a stochastic setting. We focus on reviewing a wide range of statistical inference methods for likelihood‐based frequentist and Bayesian parametric inference based on discretely‐sampled diffusions. Exact parametric inference is not usually possible because the transition density is not available in closed form. Thus, we review the literature on approximate numerical methods (e.g., Euler, Milstein, local linearization, and Aït‐Sahalia) and simulation‐based approaches (e.g., data augmentation and exact sampling) that are used to carry out parametric statistical inference on SDE processes. We close with a brief discussion of other methods of inference for SDEs and more complex SDE processes such as spatio‐temporal SDEs.
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来源期刊
CiteScore
6.20
自引率
0.00%
发文量
31
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