Increasingly refined cosmological observations, ranging from temperature anisotropies in the cosmic microwave background to the distribution of galaxies in the modern Universe, are leading to the formulation of a “concordance model” of cosmology. As the data sets beocme large and more complex in nature, the statistical tools used to analyse them have become correspondingly more refined, in order to deliver observational answers to many relevant theoretical questions, such as: is dark energy evolving with time? What can we say about the primordial spectrum of density fluctuations? Is the Universe flat? Have we detected hints of new physics in the sky?
In this talk I will present some ideas stemming from a Bayesian approach to statistical inference, which provides a consistent framework for answering model selection questions such as the ones above. I will discuss the notions of Bayesian evidence and model complexity, and will present some tools that can be used to decide which theoretical scenario is in better agreement with data. I will then apply those concepts to some outstanding questions in cosmology, regarding the nature of dark energy, the description of the primordial power spectrum and the initial conditions in the Universe.