Materials for a course given at the Kavli Institute in Tokyo, Japan, in 2018.
These lectures will complement those of Prof. Koike by focusing on foundational issues in statistics, statistical inferential thinking, the interpretation of statistical calculations, and nonparametric and exact methods. Topics will include types of uncertainty; theories of probability and their shortcomings; systematic and stochastic errors; frequentist and Bayesian approaches to estimation and inference and their shortcomings; confounding; the method of comparison; the importance of experimental/observational design; assessing estimators; interpreting p-values, confidence sets, posterior probabilities, and credible sets; common fallacies in statistical inference; the Neyman model for causal inference; interference in experiments; abstract permutation methods; pseudo-random number generation; computational implementation of permutation methods and resampling methods in Python. Examples will be drawn from physical, social, and health sciences.