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Abstract
The first part of this thesis proposes a method to determine the preferred number
of structures, their proportions and the corresponding geometrical shapes of an mmembered ring molecule. This is obtained by formulating a statistical model for the
data and constructing an algorithm which samples from a posterior distribution.
The sampling algorithm is constructed from a Markov chain which allows the
dimension of each sample to vary, this is obtained by utilizing the Reversible jumps
methology proposed by Peter Green. Each sample is constructed such that the
corresponding structures are physically realizable; this is obtained by utilizing the
geometry of the structures. Determining the shapes, number of structures and
proportions for an mmembered ring molecule is of interest, since these quantities
determine the chemical properties.
The second part of this thesis deals with parameter estimation for diffusions. The
first idea is in an optimal way to incorporate prior information in the estimation
equation G(;Xt1 ; : : : ;Xtn ) = 0, used to nd an estimator of the unknown parameter . The general idea is to introduce an new optimality criterion which
optimizes the correlation with the posterior score function. From an application
point of view this methology is easy to apply, since the optimal estimating function G(;Xt1 ; : : : ;Xtn ) is equal to the classical optimal estimating function, plus
a correction term which takes into account the prior information. The methology is particularly useful in situations where prior information is available and only
few observations are present. The resulting estimators in some sense have better
properties than the classical estimators. The second idea is to formulate Michael
Sørensens method "prediction based estimating function" for measurement error
models. This is obtained by constructing an estimating function through projections of some chosen function of Yti+1 onto functions of previous observations
Yti ; : : : ; Yt0 . The process of interest Xti+1 is partially observed through a measurement equation Yti+1 = h(Xti+1)+ noice, where h(:) is restricted to be a polynomial.
Through a simulation study we compare for the CIR process the obtained estimator with an estimator derived from utilizing the extended Kalman filter. The
simulation study shows that the two estimation methods perform equally well.
Original language  English 

Place of Publication  Kgs. Lyngby, Denmark 

Publisher  Technical University of Denmark, DTU Informatics, Building 321 
Publication status  Published  Jan 2007 
Series  IMMPHD2006168 

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Dive into the research topics of 'Application of Parameter Estimation for Diffusions and Mixture Models'. Together they form a unique fingerprint.Projects
 1 Finished

Estimationsteori for stokastiske differentialligninger
Nolsøe, K., Madsen, H., Kessler, M., Nielsen, B. F., Rydén, T. & Jørgensen, B.
01/10/2002 → 15/01/2007
Project: PhD