Strikingly few Nobel laureates within medicine, natural and social sciences are women. Although it is obvious that there are fewer women researchers within these fields, does this gender ratio still fully account for the low number of female Nobel laureates? We examine whether women are awarded the Nobel Prizes less often than the gender ratio suggests. Based on historical data across four scientific fields and a Bayesian hierarchical model, we quantify any possible bias. The model reveals, with exceedingly large confidence, that indeed women are strongly under-represented among Nobel laureates across all disciplines examined.