Simulation and Inference for Stochastic Processes with YUIMA: A Comprehensive R Framework for SDEs and Other Stochastic Processes
Simulation and Inference for Stochastic Processes with YUIMA: A Comprehensive R Framework for SDEs and Other Stochastic Processes
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使用 YUIMA 进行随机过程的模拟和推理：SDE 和其他随机过程的综合 R 框架
DOI：
10.1007/978-3-319-55569-0
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Nakahiro Yoshida
中科院分区：
文献类型：
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作者：
S. Iacus;Nakahiro Yoshida
随机过程统计学正在迅速发展。它形成了数学科学的一个分支，涉及理论统计学、概率论、软件开发和实际数据分析。随着随机过程统计推断的一般理论框架的建立，统计推断已适用于各种随机系统，其范围也越来越广泛，从遍历过程到非遍历过程，从低频正则采样方案到高频不规则采样方案，从线性模型到非线性模型，等等。该理论提供的公式往往相当复杂，这使得非专家很难在自己的领域中使用它们。例如，由Malliavin演算导出的渐近展开公式涉及数百项，最近在理论上得到验证的Bayesian估计量在实际计算中需要现代MCMC方法，一些用于模拟lsamv驱动的随机微分方程的随机数生成器使用了相当复杂的算法。在这种情况下，软件实现是一个问题。YUIMA是一个用于统计分析和模拟随机过程的计算框架，特别是根据随机分析描述的对象。YUIMA旨在实现数据分析、建模、拟合、仿真和预测的循环。通过YUIMA，用户可以轻松地享受到随机过程理论统计的最新发展，而无需依赖于他/她的专业知识。
Statistics for stochastic processes is rapidly developing. It forms a branch of mathematical sciences, spreading over theoretical statistics, probability theory, software development and real data analysis. Since a general theoretical framework of statistical inference for stochastic processes was recently established, statistical inference has been applicable to various stochastic systems and its scope is expanding more and more from ergodic to nonergodic processes, from low-frequency regular to high-frequency irregular sampling schemes, from linear to nonlinear models, and so on.The formulas provided by the theory are often fairly complicated, and it makes it difficult for nonexperts to use them in their own fields. For example, an asymptotic expansion formula derived by the Malliavin calculus involves hundreds of terms, the Bayesian estimator theoretically validated recently needs modern MCMC methods for computation in practice, and some random number generators for simulation of Lévy-driven stochastic differential equations use quite sophisticated algorithms. Software implementation is an issue in such circumstances. YUIMA is a computational framework for statistical analysis and simulation for stochastic processes, especially objects described in terms of the stochastic analysis. YUIMA is designed to realize a circle of data analysis, modelling, fitting, simulation, and prediction. Through YUIMA, the user enjoys easily, without depending on his/her expertise, the latest developments in theoretical statistics for stochastic processes.