Uncertainty & Surprise in the Exact Sciences
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There will be three speakers:
Jan-Willem Romeijn (Groningen): Model uncertainty and implicit complexity
ABSTRACT: Statistical model selection is a technique that is routinely used by social scientists when they need to choose among rivalling models of a target system. Arguably, it provides a statistical answer to what is often called model uncertainty, i.e., uncertainty that can perhaps not be expressed in the usual probabilistic fashion. Evaluation criteria for models include proximity to a hypothesized truth, and past or expected predictive performance. Remarkably, almost all such criteria lead to a built-in disadvantage for complex models. This paper concerns a hitherto untargeted problem with the notion of complexity that shows up in statistical model selection, specifically in curve fitting. It turns out that we can fit any scatter plot exactly at little cost in complexity, by choosing a family of highly versatile curves. The paper presents a diagnosis of this problem and investigates if and how current model selection tools can be used to resolve it. The upshot is that the evaluation of models must occur against a shared theoretical background. This reflects negatively on the use of model selection for resolving model uncertainty.
Liesbeth de Mol (Ghent): Unpredictability in computer-assisted mathematics.
ABSTRACT: In a paper from 1965, computer pioneer and mathematician Richard Hamming points at a fundamental misconception about computers, viz. that they can only do what they are told to do. Hamming's objection against this misconception is the inherent unpredictability of (the behavior of) computer programs. The aim of this talk is twofold. On the one hand, I will show how such unpredictability lies at the core of computer-assisted mathematical experiments. On the other, I will show how it is this unpredictability and the new (local and global) problems it results in for the mathematicians, which offers one possible way to tackle the still difficult question of the impact of the computer on mathematics. One hypothesis which will be suggested on the basis of several historical case studies is that this unpredictability is (re-)injecting time into mathematics.
Peter Streufert (University of Western Ontario, London): "Off-equilibrium beliefs in a game, and off-paradigm beliefs in a science"
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