Effect of Geometric Complexity on Intuitive Model Selection

Occam's razor is the principle stating that, all else being equal, simpler explanations for a set of observations are to be preferred to more complex ones. This idea can be made precise in the context of statistical inference, where a geometrical characterization of statistical model complexity emerges naturally from an approach based on Bayesian model selection. The broad applicability of this formulation suggests a normative reference point for decision making under uncertainty. However, little is known about if and how humans intuitively quantify the complexity of competing interpretations of noisy data. In this work, first, we extend the geometrical characterization of model complexity to apply to models with bounded parameters, and second, we measure the sensitivity of naive human subjects to statistical model complexity. Our data show that human subjects bias their decisions in favor of simple explanations based not only on the dimensionality of the alternatives (number of model parameters), but also on finer-grained aspects of their geometry, such as volume, curvature, and presence of prominent boundaries. Our results imply that principled notions of statistical model complexity have direct quantitative relevance to human decision making.