17 Comparing frequentist and Bayesian statistics

Bayesian methods allow for probability distributions over latent variables, like model parameters or models themselves. Frequentist methods do not. That is the most striking difference between these two approaches to data analysis. At the heart, this difference is one based on conceptual considerations about what we may or may not attach probabilities to. Still, conceptual questions aside, there are also further consequences of this difference. The most obvious is that, usually, Bayesian approaches are more complex to compute or analyze but provide richer information, such as a full distribution rather than just a point- and an interval-estimate. This chapter will explore some of the more or less obvious differences in order to also contribute a better understanding of both approaches in isolation.