In this section, we will illustrate how to define the Sharpe ratio as a probability model and compare the resulting posterior distributions for different return series. The Bayesian estimation for two groups provides complete distributions of credible values for the effect size, group means and their difference, standard deviations and their difference, and the normality of the data.

Key use cases include the analysis of differences between alternative strategies, or between a strategy's in-sample return in relation to its out-of-sample return (see the bayesian_sharpe_ratio notebook for details). The Bayesian Sharpe ratio is also part of pyfolio's Bayesian tearsheet.