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theses

This dissertation presents an account of the Principle of Simplicity, a prominent idea in the philosophy of science. The principle states that when a simple model and a complex model both predict the data, and all else is equal, the data supports the simpler model more. The account, the “Predictive Focus Account,” states that simpler models are better confirmed in these contexts because they make narrower, more focused predictions. The introduction presents Principle of Simplicity and the Predictive Focus Account. It defines key terms and explains the dissertation's methodology. This section also flags background issues that go beyond the scope of the dissertation. Chapter 1 investigates the philosophical history of the Predictive Focus Account, and the relationship between a model's simplicity and its “global likelihood.” On this account, the explanation of the advantage of simplicity is grounded in relations of Bayesian confirmation between competing models. That is, the advantage of simplicity is a subtle, but inherent, feature of standard Bayesian model evaluation. This chapter argues that the Predictive Focus Account is incomplete without a method for fixing prior probabilities. It proposes a new approach to fixing objective priors, the “Data Window Prior,” grounded in experimental design. The proposed prior bounds the parameters of statistical models and reigns in their predictions, which are a priori unbounded and infinitely extended. So bounded, the models have definite prediction ranges and corresponding degrees of predictive focus. I apply the Data Window Prior to the historical case of Hubble's Law from cosmology, yielding a powerful, intuitive verdict about the confirmation relations between models of varying degree of complexity. Chapter 2 contrasts the Predictive Focus Account with the more popular Bayesian method of “prior-stacking,” whereby Bayesians privilege simpler models and hypotheses with higher prior probabilities. The Predictive Focus Account has distinct advantages over the prior-stacking approach: it shows how simplicity can be favored on a posteriori, empirical grounds, and how this favoring relation depends on the nature of the extant data. Chapter 3 contrasts my account with another, based in Akaike's Information Criterion (AIC), a contemporary, non-Bayesian alternative. The AIC is a statistical model selection criterion that describes estimation error. It is designed to quantify and resist “over-fitting” the data with complex models. The main advantage of the Predictive Focus Account (and corresponding Bayesian method) is its generality. It applies to a wider range of cases and supports a broader range of inferences than the AIC.

ETD_5910

Ph.D.

Includes bibliographical references

by Justin Sharber

doi:10.7282/T3TH8P92

ETD doctoral

The author owns the copyright to this work.