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UBC Theses and Dissertations

Parameter estimation of stochastic nonlinear dynamic processes using multiple experimental data sets : with biological applications Jang, Seunghee Shelly


The dynamic behavior of many chemical and biological processes is defined by a set of nonlinear differential equations that constitute a model. These models typically contain parameters that need to be estimated using experimental data. A number of factors such as sampling intervals, number of measurements and noise level characterize the quality of data, and have a direct effect on the quality of estimated parameters. The quality of experimental data is rather poor in many processes due to instrument limitations or other physical and economical constraints. Traditional parameter estimation methods either yield inaccurate results or are not applicable when applied to such data. Despite this, it is common practice to apply them on a merged data set obtained by pooling together data from multiple experiments. Considering the difficulties in maintaining consistent experimental conditions, straightforward integration of multiple data sets will not provide the best estimates of parameters. In this thesis, a new approach to estimate parameters of nonlinear dynamic models using multiple experimental data is proposed. The approach uses Bayesian inference, and sequentially updates prior probability distribution of parameters for systematic integration of multiple data sets. An expression for posterior probability distribution of parameters conditional on all experimental data sets is derived. This expression is often analytically intractable; therefore two instances of numerical approximation method called Markov Chain Monte Carlo - Metropolis-Hastings (MH) algorithm and Gibbs sampler (GS) - are implemented. The two algorithms form inner and outer levels of iterations, where the MH algorithm is used in the inner level to estimate conditional probability distributions of individual parameters, which is used in the outer level in conjunction with the GS to estimate joint probability distributions of the parameters. The proposed method is applied to three nonlinear biological processes to estimate probability distribution of parameters with a small number of irregular samples. The approximated probability distribution provides a straightforward tool to calculate confidence interval of parameter estimates and is robust to initial guess of parameter value. Correlation among model parameters, quality of each model, and the approach taken to optimize the high cost of MCMC sampling are discussed.

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