Prof. Mario Castro (Pontificia Comillas University, Madrid ) – Apology of the spherical cow: A probabilistic view of Occam's razor

Complex systems are often characterised by their intricate structures and behaviours, which can be challenging to analyse and understand. However, the principle of Occam’s Razor suggests that the simplest explanation is often the best. This idea, encapsulated in the concept of the toy model, is often perceived as a parsimonious or exploratory approach when dealing with problems involving many unknown mechanisms or restricted to aggregated data, and it is not always taken seriously. In this work, we connect the idea of model inference from data to rationalise our intuition about minimal models. Connecting ideas from information geometry and Bayesian inference, we show that toy models are often the optimal way to exploit the information in the data and, hence, are not only mathematically or computationally tractable but also optimal in the sense of information theory. We illustrate these ideas with examples from ecology, epidemiology, or astrochemistry. However, they can be applied to any field where data quality and quantity are limited, or the diversity is poor. We also discuss the implications of these ideas in the context of well-established ideas, such as the renormalisation group theory.