Inherent Complexity: a problem for Statistical Model Evaluation

This paper investigates a problem for statistical model evaluation, in particular for curve fitting: by employing a different family of curves we can fit a scatter plot almost perfectly at apparently minor costs in terms of model complexity. The problem is resolved by an appeal to prior probabilities. This leads to some general lessons about how to approach model evaluation

New Theory about Old Evidence:A framework for open-minded Bayesianism

We present a conservative extension of a Bayesian account of confirmation that can deal with the problem of old evidence and new theories. So-called open-minded Bayesianism challenges the assumption-implicit in standard Bayesianism-that the correct empirical hypothesis is among the ones currently under consideration. It requires the inclusion of a catch-all hypothesis, which is characterized by means of sets of probability assignments. Upon the introduction of a new theory, the former catch-all is decomposed into a new empirical hypothesis and a new catch-all. As will be seen, this motivates a second update rule, besides Bayes' rule, for updating probabilities in light of a new theory. This rule conserves probability ratios among the old hypotheses. This framework allows for old evidence to confirm a new hypothesis due to a shift in the theoretical context. The result is a version of Bayesianism that, in the words of Earman, "keep[s] an open mind, but not so open that your brain falls out"

Inherent Complexity: a problem for Statistical Model Evaluation

This paper investigates a problem for statistical model evaluation, in particular for curve fitting: by employing a different family of curves we can fit a scatter plot almost perfectly at apparently minor costs in terms of model complexity. The problem is resolved by an appeal to prior probabilities. This leads to some general lessons about how to approach model evaluation

Philosophy of science and the formalization of psychological theory

One of the original aims of this journal was to promote theory in psychology. Nowadays more and more psychological researchers are calling for more theory development, and articles on the "theory crisis" have also found their way into mainstream journals. In this article, we provide a further perspective to this theory debate. Over the past century, philosophy of science has staged extensive discussions on the mathematization of nature and on the role of mathematics in the development of theory and the connection of theory to empirical facts. We show that these discussions are highly relevant for the current debate in psychology. In particular, we emphasize the importance of conceptual work in the process of mathematization, and the role of mathematics in co-ordinating theory and observations. We then discuss the implications that these points have for statistically oriented psychology in general and for the recent theory debate in psychology

When is an example a counterexample?

In this extended abstract, we carefully examine a purported counterexample to a postulate of iterated belief revision. We suggest that the example is better seen as a failure to apply the theory of belief revision in sufficient detail. The main contribution is conceptual aiming at the literature on the philosophical foundations of the AGM theory of belief revision [1]. Our discussion is centered around the observation that it is often unclear whether a specific example is a "genuine" counterexample to an abstract theory or a misapplication of that theory to a concrete case.Comment: 10 pages, Contributed talk at TARK 2013 (arXiv:1310.6382) http://www.tark.or