Name
Title | ||
|---|---|---|
On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data |
Abstract | ||
|---|---|---|
This paper investigates the predictive accuracy of stochastic models. In particular, a formulation is presented for the impact of data limitations associated with the calibration of parameters for these models, on their overall predictive accuracy. In the course of this development, a new method for the characterization of stochastic processes from corresponding experimental observations is obtained. Specifically, polynomial chaos representations of these processes are estimated that are consistent, in some useful sense, with the data. The estimated polynomial chaos coefficients are themselves characterized as random variables with known probability density function, thus permitting the analysis of the dependence of their values on further experimental evidence. Moreover, the error in these coefficients, associated with limited data, is propagated through a physical system characterized by a stochastic partial differential equation (SPDE). This formalism permits the rational allocation of resources in view of studying the possibility of validating a particular predictive model. A Bayesian inference scheme is relied upon as the logic for parameter estimation, with its computational engine provided by a Metropolis-Hastings Markov chain Monte Carlo procedure. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.jcp.2006.01.037 | J. Comput. Physics |
Keywords | Field | DocType |
uncertainty quantification,particular predictive model,data limitation,stochastic partial differential equation,computational bayesian analysis,limited data,polynomial chaos,overall predictive accuracy,corresponding experimental observation,markov chain monte carlo,stochastic finite elements,stochastic process,predictive accuracy,estimated polynomial chaos coefficient,parameter estimation,karhunen–loeve,stochastic model,random variable,probability density function,metropolis hastings,karhunen loeve,prediction model,bayesian inference,bayesian analysis | Applied mathematics,Mathematical optimization,Uncertainty quantification,Bayesian inference,Markov chain Monte Carlo,Markov chain,Stochastic process,Polynomial chaos,Stochastic modelling,Stochastic partial differential equation,Mathematics,Calculus | Journal |
Volume | Issue | ISSN |
217 | 1 | Journal of Computational Physics |
Citations | PageRank | References |
24 | 1.82 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Roger Ghanem | 1 | 183 | 26.72 |
| Alireza Doostan | 2 | 188 | 15.57 |