Matching Items (2)
Filtering by
- All Subjects: Bootstrap (Statistics)
- Creators: Kang, Yun
- Creators: Sterner, Beckett
Description
Statistical model selection using the Akaike Information Criterion (AIC) and similar criteria is a useful tool for comparing multiple and non-nested models without the specification of a null model, which has made it increasingly popular in the natural and social sciences. De- spite their common usage, model selection methods are not driven by a notion of statistical confidence, so their results entail an unknown de- gree of uncertainty. This paper introduces a general framework which extends notions of Type-I and Type-II error to model selection. A theo- retical method for controlling Type-I error using Difference of Goodness of Fit (DGOF) distributions is given, along with a bootstrap approach that approximates the procedure. Results are presented for simulated experiments using normal distributions, random walk models, nested linear regression, and nonnested regression including nonlinear mod- els. Tests are performed using an R package developed by the author which will be made publicly available on journal publication of research results.
ContributorsCullan, Michael J (Author) / Sterner, Beckett (Thesis advisor) / Fricks, John (Committee member) / Kao, Ming-Hung (Committee member) / Arizona State University (Publisher)
Created2018
Description
This dissertation investigates the dynamics of evolutionary games based on the framework of interacting particle systems in which individuals are discrete, space is explicit, and dynamics are stochastic. Its focus is on 2-strategy games played on a d-dimensional integer lattice with a range of interaction M. An overview of related past work is given along with a summary of the dynamics in the mean-field model, which is described by the replicator equation. Then the dynamics of the interacting particle system is considered, first when individuals are updated according to the best-response update process and then the death-birth update process. Several interesting results are derived, and the differences between the interacting particle system model and the replicator dynamics are emphasized. The terms selfish and altruistic are defined according to a certain ordering of payoff parameters. In these terms, the replicator dynamics are simple: coexistence occurs if both strategies are altruistic; the selfish strategy wins if one strategy is selfish and the other is altruistic; and there is bistability if both strategies are selfish. Under the best-response update process, it is shown that there is no bistability region. Instead, in the presence of at least one selfish strategy, the most selfish strategy wins, while there is still coexistence if both strategies are altruistic. Under the death-birth update process, it is shown that regardless of the range of interactions and the dimension, regions of coexistence and bistability are both reduced. Additionally, coexistence occurs in some parameter region for large enough interaction ranges. Finally, in contrast with the replicator equation and the best-response update process, cooperators can win in the prisoner's dilemma for the death-birth process in one-dimensional nearest-neighbor interactions.
ContributorsEvilsizor, Stephen (Author) / Lanchier, Nicolas (Thesis advisor) / Kang, Yun (Committee member) / Motsch, Sebastien (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2016