Class 2 - Bayesian Inference

An approach to count all the ways data can happen according to assumptions.

Bayesian data analysis uses probabilities to describe uncertainty. Importantly, in Bayesian data analysis probabilities describe degrees of belief. In contrast, a frequentist interpretation of probabilities would be as the frequencies of events in very large samples.

This leads to frequentist uncertainty being premised on imaginary resampling of data—if we were to repeat the measurement many many times, we would end up collecting a list of values that will have some pattern to it. It means also that parameters and models cannot have probability distributions, only measurements can.

They were originally developed (largely by Ronald Fisher) in the early 20th century for agricultural applications. They typically were for randomized experiments with large effects, in which measurement issues had been solved.

Such statistical tests produce inferences, not decisions.

Null hypotheses are not unique. Hypotheses do not imply unique models, and models do not imply unique hypotheses.

Models are not hypotheses; they are neither true or false. Models are “golems” that do as they are told. Ideally should compare performance across models (model comparison).

Popper: test (attempt to falsify) research hypothesis. Use theory, make a falsifiable prediction, and test that; not that nothing happened (aka null hypothesis).