Parameter estimation and inference in dynamic systems described by linear partial differential equations

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• 作者：Gianluca Frasso ; Jonathan Jaeger ; Philippe Lambert
• 刊名：AStA Advances in Statistical Analysis
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：100
• 期：3
• 页码：259-287
• 全文大小：22,050 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Econometrics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1863-818X
• 卷排序：100

文摘

Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications, the parameters involved in the DE models are usually unknown and need to be estimated from the available measurements together with the state function. In this paper, we present frequentist and Bayesian approaches for the joint estimation of the parameters and of the state functions involved in linear PDEs. We also propose two strategies to include state (initial and/or boundary) conditions in the estimation procedure. We evaluate the performances of the proposed strategy through simulated examples and a real data analysis involving (known and necessary) state conditions.KeywordsLinear partial differential equationsParameter estimation Penalized tensor B-spline smoothingState conditions