Basic probability and statistics - obligatory
Bayesian inference is one of the fundamental paradigms of statistical inference. While it has a strong philosophical foundation which makes it conceptually distinct from other forms of statistical inference, it more importantly provides the theory that gives the unifying scientific foundation for the modern information sciences generally. Many inferential procedures and modern forms of information processing have their origins in Bayesian forms of thinking and analysis or can be understood as special applications or simplified forms of those. In this way it has become an essential component of the modern data scientist’s toolbox and education. Awareness of Bayesian forms of thinking is therefor also an important data scientific skill when engaging in collaborative research.
This course provides a basic introduction to Bayesian forms of inference. The concept of Bayesian belief updating is explained, with reference to Bayes theorem. The notions of prior and posterior density are discussed, as well as concepts and issues relating to prior belief specification. Basic forms and examples of Bayesian belief updating in both univariate and multivariate parameter problems are explained in detail, in particular with respect to the exponential family and basic linear regression models. Examples are discussed as well as applications of Bayesian concepts in approximate (non-Bayesian) forms of inference. We also introduce basic notions of Bayesian computation and apply these methods in examples and exercises. We introduce and discuss some key applications of Bayesian approaches to inference from the statistical literature.
You can explain the basic concepts of Bayesian inference and are able to recognize these in documented statistical analyses materials. You are able to apply basic methods of Bayesian inference in simple (data-based) examples. You are able to interpret output and formulated conclusions (results) from applications of Bayesian analyses. You are able to critically evaluate basic applications of and results from Bayesian analysis in simple examples and problem settings.
The schedule for the course can be found on MyTimeTable
Mode of instruction
Lectures and take-home exercises.
Written examination at end of the course.
There is no specific books required.
The course lectures are much inspired by the structure presented in “Bayesian Biostatistics” (Lesaffre and Lawson, Wiley). We will particularly use many of the examples discussed in that book. Referencing the book can therefore be useful to understand these better. Material from other sources will be added to the course as required.
Many other good introductory textbooks exist for Bayesian statistics which are regarded as standard references in the field. Some students may also prefer these because of the different writing styles used in those texts. Two additional references stand out among others:
Bayesian Data Analysis by Gelman, Carlin, Stern and Rubin (an absolute classic);
Bayesian Methods for Data Analysis by Carlin and Louis (again a classic, but includes more links to “frequentist thinking” and the so-called “empirical Bayes” approach – in addition discusses some key application areas and case studies in detail ) Note this is the third edition: the first two editions have a different title: “Bayesian methods for Data Analysis and Empirical Bayes Methods for Data Analysis”;
Finally, for an excellent hands-on discussion of practical use of the Bayesian idea in evaluation of hypotheses in observational and trials data generally, Bayesian Approaches to Clinical Trials and Health-Care Evaluation by Spiegelhalter, Abrams and Myles is recommended reading.
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