Course overview
The aim of this course is to achieve an understanding of the logic of Bayesian statistical inference, i.e. the use of probability models to quantify uncertainty in statistical conclusions, and acquire skills to perform practical Bayesian analysis relating to health research problems. Topics will include simple one-parameter models with conjugate prior distributions; standard models containing two or more parameters, including specifics for the normal location-scale model; the role of non-informative prior distributions; the relationship between Bayesian methods and standard 'classical' approaches to statistics, especially those based on likelihood methods; computational techniques for use in Bayesian analysis, especially the use of simulation from posterior distributions, with emphasis on the WinBUGS package as a practical tool; and application of Bayesian methods for fitting hierarchical models to complex data structures.
Course learning outcomes
- Explain the difference between Bayesian and frequentist concepts of statistical inference.
- Demonstrate how to specify and fit simple Bayesian models with appropriate attention to the role of the prior distribution and the data model.
- Explain how these generative models can be used for inference, prediction and model criticism.
- Demonstrate proficiency in using statistical software packages (R) to specify and fit models, assess model fit, detect and remediate non-convergence, and compare models.
- Engage in specifying, checking and interpreting Bayesian statistical analyses in practical problems using effective communication with health and medical investigators.