  These lecture notes aim at a post-Bachelor audience with a background 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 problems, the main focus is laid on Markov Chain Monte
Carlo (MCMC) simulations on the basis of Hamiltonian Monte Carlo sampling of
posterior joint probability distributions for regression parameters occurring
in generalised linear models for a univariate outcome variable. The modelling
of fixed effects as well as of correlated varying effects via multi-level
models in non-centred parametrisation is considered. The simulation of
posterior predictive distributions is outlined. The assessment of a model's
relative out-of-sample posterior predictive accuracy with information
entropy-based criteria WAIC and LOOIC and model comparison with Bayes factors
are addressed. A brief discussion on the description of the generation of
stationary time series data by means of autoregressive models is contained.
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. Vectorised codes for MCMC simulations of
multi-dimensional posterior joint probability distributions with the Stan
probabilistic programming language implemented in the statistical software R
are provided. The lecture notes are fully hyperlinked. They direct the reader
to original scientific research papers, online resources on inductive
statistical inference, and to pertinent biographical information.
