MCMC Analysis Of Classical Time Series Algorithms

Identification of order of an Autoregressive Moving Average Model (ARMA) by the usual graphical method is subjective. Hence, there is a need of developing a technique to identify the order without employing the graphical investigation of series autocorrelations. To avoid subjectivity, this thesis focuses on determining the order of the Autoregressive Moving Average Model using Reversible Jump Markov Chain Monte Carlo (RJMCMC). The RJMCMC selects the model from a set of the models suggested by better fitting, standard deviation errors and the frequency of accepted data. Together with deep analysis of the classical Box-Jenkins modeling methodology the integration with MCMC algorithms has been focused through parameter estimation and model fitting of ARMA models. This helps to verify how well the MCMC algorithms can treat the ARMA models, by comparing the results with graphical method. It has been seen that the MCMC produced better results than the classical time series approach.

Implementation of Quantitative Reaction-based Model Refinement

Building a computational model for complex biological systems is an iterative process. It starts from an abstraction of the process and then incorporates more details regarding the specific biochemical reactions which results in the change of the model fit. Meanwhile, the model’s numerical properties such as its numerical fit and validation should be preserved. However, refitting the model after each refinement iteration is computationally expensive resource-wise. There is an alternative approach which ensures the model fit preservation without the need to refit the model after each refinement iteration. And this approach is known as quantitative model refinement. The aim of this thesis is to develop and implement a tool called ModelRef which does the quantitative model refinement automatically. It is both implemented as a stand-alone Java application and as one of Anduril framework components. ModelRef performs data refinement of a model and generates the results in two different well known formats (SBML and CPS formats). The development of this tool successfully reduces the time and resource needed and the errors generated as well by traditional reiteration of the whole model to perform the fitting procedure.