Thin film models with constant source: model selection in a stochastic setting

Abstract

Dunn and Tichenor [Atmospheric Environment, 22:885--894, 1988] proposed a class of differential equation models to describe the phenomenon of transient sink behaviour for organic emissions exhibited by interior surface films in state-of-the-art emission test chambers. The proposed model selection scheme embeds the derived models within a class of stochastic differential equations. The quality of model fit varies inversely with the strength of the stochastic forcing term; that is, if the model is adequate the stochastic forcing term should be small. Data from a particular application where the source can be considered to be constant demonstrates the approach. The approach can be applied to any phenomenon that is modelled by a class of linear differential equations where different models are embedded within a full model. References B. D. Anderson and J. B. Moore Optimal Filtering, Prentice--Hall, Inc., Englewood Cliffs, N. J., 1979. C. F. Ansley and R. Kohn A geometrical derivation of the fixed interval smoothing algorithm. Biometrika, 69:486--487. J. E. Dunn and B. A. Tichenor. Compensating for sink effects in emissions test chambers by mathematical modeling. Atmospheric Environment, 22:885--894, 1988. M. R. Osborne and T. Prvan. Smoothness and conditioning in generalised smoothing spline calculations. J. Austral. Math. Soc. Ser. B, 30:43--56, 1988. T. Prvan and M. R. Osborne. Model selection in a stochastic setting. ANZIAM J., 45(E) ppC787--C799, 2004. http://anziamj.austms.org.au/V45/CTAC2003/Prva/home.html H. E. Rauch, F. Tung and C. T. Striebel. Maximum Likelihood Estimates of Linear Dynamic Systems. AIAA J., 3: 1445--1450, 1965. G. Wahba. Improper priors, spline smoothing and the problem of guarding against model errors in regression. J. R. Statist. Assoc., 40:364--372, 1978. G. Wahba. A comparison of GCV and GML for choosing the smoothing parameter in the generalised spline smoothing problem. Ann. Statist., 13: 1378--1402, 1985. W. Wecker and C. F. Ansley. Signal extraction approach to non linear regression and spline smoothing. J. Amer. Statist. Assoc., 78: 81--89, 1983.