Abstract
In this chapter, the CIP is formulated in a statistical framework. Byusing the Bayesian inference theory, we cast the CIP asaninformation transfer problem, in which the prior information andtheinformation transferred from state observations are combinedtoreduce uncertainty in the estimated parameters. The priorinformationis modeled using a probability density function (PDF)called the priorPDF and the inverse solution is also a PDF known asthe posteriorPDF. Because it is a PDF, the inverse solution is alwaysexistent andunique but with uncertainty. When the posterior PDF is ina relativelysimple form, point estimates of the unknown parameterscan bereadily obtained by solving an optimization problem, just as wehavedone in the deterministic framework. When the posterior PDFhas acomplex multimodal shape, however, the non-uniquenessandinstability issues associated with the inverse solution arise again.Forsuch cases, Monte Carlo sampling methods provide powerfultoolsfor learning the posterior PDFs without requiring theiractualfunctional forms be known. Two popular Markov Chain MonteCarlo(MCMC) algorithms are introduced. The application of MCMCforinverse solution and global optimization is also discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Sun, NZ., Sun, A. (2015). Statistical Methods for Parameter Estimation. In: Model Calibration and Parameter Estimation. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2323-6_4
Download citation
DOI: https://doi.org/10.1007/978-1-4939-2323-6_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2322-9
Online ISBN: 978-1-4939-2323-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)