An Introduction to Inductive Statistical Inference -- from Parameter Estimation to Decision-Making
share
These lecture notes aim at a post-Bachelor audience with a backgound at an introductory level in Applied Mathematics and Applied Statistics. They discuss the logic and methodology of the Bayes-Laplace approach to inductive statistical inference that places common sense and the guiding lines of the scientific method at the heart of systematic analyses of quantitative-empirical data. Following an exposition of exactly solvable cases of single- and two-parameter estimation, the main focus is laid on Markov Chain Monte Carlo (MCMC) simulations on the basis of Gibbs sampling and Hamiltonian Monte Carlo sampling of posterior joint probability distributions for regression parameters occurring in generalised linear models. The modelling of fixed as well as of varying effects (varying intercepts) is considered, and the simulation of posterior predictive distributions is outlined. The issues of model comparison with Bayes factors and the assessment of models' relative posterior predictive accuracy with information entropy-based criteria DIC and WAIC are addressed. Concluding, a conceptual link to the behavioural subjective expected utility representation of a single decision-maker's choice behaviour in static one-shot decision problems is established. Codes for MCMC simulations of multi-dimensional posterior joint probability distributions with the JAGS and Stan packages implemented in the statistical software R are provided. The lecture notes are fully hyperlinked. They direct the reader to original scientific research papers and to pertinent biographical information.
READ FULL TEXT
