Classical and Bayesian Inference

Two primary approaches to interpreting predictions and estimates:

• Classical

  • Traditional approach focused on summarizing the information in the data

  • Estimates should be correct on average (unbiased), and confidence intervals should cover the true parameter value 95% of the time (coverage). (When same statistical procedure is applied to many different problems.)

  • Strength: Emphasizes ‘objectivity’ over prior information - data ‘speaks’ for itself.

  • Weakness: Difficulty with small studies and indirect / highly variable data.

• Bayesian

  • Incorporates prior information into inferences to go beyond merely summarizing data

  • Strength: Can provide valid predictions even with weak data.

  • Weakness: Requires prior information - ‘Subjective’

  • Practical advantage: Inferences can be represented by random simulations.

No correct answer - be aware of your options. However we can use Bayesian methods (stan_glm) with noninformative or weakly informative priors to obtain results similar to classical methods (and still get simulation draws to express uncertainty!).

More on incorporating prior information in the Bayesian approach in chapter 9