MODEL SELECTION, SIMPLICITY AND THE CONSERVATIVE TREATMENT OF DATA

Abstract

This dissertation consists of three related essays in philosophy of science, which employ statistical results revolving the notion of simplicity as a theoretic virtue. The most significant statistical result bearing on the nature and epistemic significance of simplicity has been achieved in the so-called “model selection” problem. This is the problem of determining the ‘optimal’ family of hypotheses, given a body of data and a host of background knowledge. There are various model selection criteria for various goals of statistical inference. Interestingly, despite their many differences, these criteria all emphasize the significance of the simplicity on a number of epistemically valuable features of a theory, viz, its predictive accuracy and probability of truth.

The first essay, which is co-authored with Kasra Alishahi, offers a solution to a purported problem for model selection criteria, called the “sub-family” problem. This problem arises if one uses model selection criteria in an ad hoc way. We show that a deeper understanding of model selection criteria disallows such ad hoc use of them.

In the second essay, I show how model selection criteria justify an extremely strong version of predictionism: the thesis that successfully predicting a given body of data typically provides stronger evidence for a theory than merely accommodating the same body of data.

In the third essay, I show how various facts about the nature of error together with general principles of practical rationality demand (or license) disregarding disconfirming data when its size is small or its credibility is suspect. However, those same considerations demand that we scrutinize counterevidence more than confirming evidence when the size of disconfirming data is large. I also show how demands of simplicity and precision help mitigate the worry that if we follow such conservative practices our conclusions will reflect the order in which our evidence arrives.