Abstract
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<p class="MsoNormal" style="margin: 0in; font-size: 12pt; font-family: "Times New Roman", serif;"><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 12pt; font-family: "Times New Roman", serif;">The present thesis explores particle filter (PF) algorithms that enable the simultaneous state and parameter estimates (SSPE) of dynamic systems in-line. Such algorithms will monitor and track the changes in the performance of a dynamic system (state) and the factors that impact performance (parameters) simultaneously and in real-time. The monitoring/tracking problem is of singular importance in fields such as marketing, finance, and economics where it is required not only to identify how a system is evolving but why they are, i.e., researchers and practitioners are mostly interested in estimate concurrently both how a system is changing in time and what are the factors that influence such changes. First, an augmented state-space representation of a linear dynamic system is developed, enabling the in-line SSPE for linear systems using PF. Sampling algorithms, built upon the Markov Chain Monte Carlo (MCMC) sampling approaches, are presented and shown to be scalable and computationally efficient to enable the in-line estimation in large scale linear models. Second, the proposed PF method is extended to non-linear systems that can be represented in the Cobb-Douglas form, and the impact of each term on the dependent variable is convex. Though the Cobb-Douglas form is a small subset of the general class of non-linear systems, it finds numerous applications in modeling dynamic systems in marketing, economics, finance, and production/manufacturing. The proposed algorithm will be tested for scalability and precision using case studies from the field of marketing. Third, evolutionary algorithms (EA) are introduced in the base PF algorithm to tackle the curse of dimensionality and particle degeneracy in the context of SSPE. Fourth, the recursive non-parametric particle learning (RNPPL) method is introduced as an alternative to SSPE. Finally, an open-source software solution has been developed to enable researchers and practitioners to conduct in-line SSPE of Cobb-Douglas type of dynamic models. It will exploit the capabilities for multi-core and parallel processing to enable large scale estimation. The implementation has been developed in R in the novel package LMfilteR.<o:p></o:p></p></div></div></div>