Perspectives on Randomness in Statistic

Most (frequentist) statistical methods are built on the assumption of independent and identically distributed data points; one may imagine that these are sampled from an infinite super-population or generated by some random mechanism. Survey sampling and design-based causal inference, to the contrary, consider an explicitly finite population and try to elicit information about it. Bayesian statistics treats the data points as fixed and perceives the parameters of a posited model as random. Lastly, chaos and ergodic theory examine deterministic dynamical systems but often need to resort to stochastic statements as the behaviour of many chaotic systems is not tractable.
In this course, we compare these different frameworks and how randomness arises in them. We provide historical perspectives, and discuss the different interpretations and their suitability for specific applications. The participants will study articles on a given topic, present them during the course and lead a group discussion.