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Parameter estimation in models with hidden variables : An application to a biotech process
Author(s) -
Jang S. S.,
De la Hoz H.,
Benzvi A.,
McCaffrey W. C.,
Gopaluni R. B.
Publication year - 2012
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.20557
Subject(s) - gibbs sampling , sampling (signal processing) , bayesian probability , nonlinear system , process (computing) , stochastic process , mathematics , computer science , estimation theory , metropolis–hastings algorithm , algorithm , set (abstract data type) , mathematical optimization , artificial intelligence , statistics , markov chain monte carlo , physics , filter (signal processing) , quantum mechanics , computer vision , programming language , operating system
Biological processes are often characterised by significant nonlinearities, noisy measurements and hidden process variables. The dynamic behaviour of such processes can be represented by stochastic differential equations obtained from physical laws. We propose a Bayesian algorithm for parameter estimation in stochastic nonlinear biological processes with unmeasured (or hidden) variables. The proposed algorithm, involves drawing random samples iteratively from a posterior density functions of the parameters and the hidden variables. A Bayesian sampling techniques is used to approximate these posterior density functions. Both Metropolis–Hastings algorithm and Gibbs sampling are used for sample generation. The algorithm is extended to handle multiple data sets and missing observations. The algorithm is applied to an experimental data set collected from an algal bioreactor system. © 2011 Canadian Society for Chemical Engineering