A Quantitative Occam's Razor

Abstract

This paper derives an objective Bayesian "prior" based on considerations of entropy/information. By this means, it produces a quantitative measure of goodness of fit (the "H-statistic") that balances higher likelihood against the number of fitting parameters employed. The method is intended for phenomenological applications where the underlying theory is uncertain or unknown. For example, it can help decide whether the large angle anomalies in the CMB data should be taken seriously. I am therefore posting it now, even though it was published before the arxiv existed.