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Item An adaptive genetic algorithm for fitting DeGroot opinion diffusion models on social networks(Montana State University - Bozeman, College of Letters & Science, 2022) Johnson, Kara Layne; Chairperson, Graduate Committee: John J. BorkowskiWhile a variety of options are available for modeling opinion diffusion--the process through which opinions change and spread through a social network--current methods focus on modeling the process on online social networks where large quantities of opinion data are readily available. For in-person networks, where data are more difficult to collect, models that predict the opinions of the individuals in the network require that the structure of social influence--who is influenced by whom and to what degree--is specified by the researcher instead of informed by data. In order to fit data-driven opinion diffusion models on small networks with limited data, we developed a genetic algorithm for fitting the DeGroot opinion diffusion model. We detail the algorithm and present simulation studies to assess the algorithm's performance. We find the algorithm is able to recover model parameters across a variety of network and data set conditions, it continues to perform well under the assumption violations expected in practical applications, and the algorithm performance is robust to most choices of hyperparameters. Finally, we present an analysis of data from the study that motivated the methodological development.Item Robust and optimal design strategies for nonlinear models using genetic algorithms(Montana State University - Bozeman, College of Letters & Science, 2014) Akapame, Sydney Kwasi; Chairperson, Graduate Committee: John J. BorkowskiExperimental design pervades all areas of scientific inquiry. The central idea behind many designed experiments is to improve or optimize inference about the quantities of interest in a statistical model. Thus, the strengths of any inferences made will be dependent on the choice of the experimental design and the statistical model. Any design that optimizes some statistical property will be referred to as an optimal design. In the main, most of the literature has focused on optimal designs for linear models such as low-order polynomials. While such models are widely applicable in some areas, they are unsuitable as approximations for data generated by systems or mechanisms that are nonlinear. Unlike linear models, nonlinear models have the unique property that the optimal designs for estimating their model parameters depend on the unknown model parameters. This dissertation addresses several strategies to choose experimental designs in nonlinear model situations. Attempts at solving the nonlinear design problem have included locally optimal designs, sequential designs and Bayesian optimal designs. Locally optimal designs are optimal designs conditional on a particular guess of the parameter vector. Although these designs are useful in certain situations, they tend to be sub-optimal if the guess is far from the truth. Sequential designs are based on repeated experimentation and tend to be expensive. Bayesian optimal designs generalize locally optimal designs by averaging a design optimality criterion over a prior distribution, but tend to be sensitive to the choice of prior distribution. More importantly, in cases where multiple priors are elicited from a group of experts, designs are required that are robust to the class (or range) of prior distributions. New robust design criteria to address the issue of robustness are proposed in this dissertation. In addition, designs based on axiomatic methods for pooling prior distributions are obtained. Efficient algorithms for generating designs are also required. In this research, genetic algorithms (GAs) are used for design generation in the MATLAB® computing environment. A new genetic operator suited to the design problem is developed and used. Existing designs in the published literature are improved using GAs.Item Hybridizing statistics with genetic algorithms(Montana State University - Bozeman, College of Letters & Science, 1995) Pamplin, Trenton L.Item Generic properties of the infinite population genetic algorithm(Montana State University - Bozeman, College of Letters & Science, 2006) Hayes, Christina Savannah Maria; Chairperson, Graduate Committee: Tomas GedeonThe infinite population model for the genetic algorithm, where the iteration of the genetic algorithm corresponds to an iteration of a map G, is a discrete dynamical system. The map G is a composition of a selection operator and a mixing operator, where the latter models the effects of both mutation and crossover. This dissertation examines the finiteness and hyperbolicity of fixed points of this model. For a typical mixing operator, the fixed point set of G is finite and all fixed points are hyperbolic.