Bayesian statistics is the formal process of updating beliefs about uncertain quantities in light of new data. The uncertainty is quantified by subjective probabilities, leading to a natural and practical way to make predictions and optimal decisions under uncertainty.
Most statistical problems - for example, the handling of missing observations and techniques for preventing overfitting - have elegant Bayesian solutions. Bayesian methods are widely used in applications, partly due to advances in computationally efficient inference methods implemented in powerful and user-friendly probabilistic programming languages.
Bayesian statistics has a long tradition at the department, originating from Daniel Thorburn's work in the 1980s, and subsequently carried on by his PhD students. Many PhD theses at the department have had a Bayesian focus, and the area continues to be strong.
Some recent and ongoing Bayesian research themes at the department are:
- Bayesian models and methods for data with complex dependence structure, such as time series, spatial and network data.
- Bayesian analysis of non-linear and non-Gaussian time-varying parameter models
- Computationally efficient posterior simulation algorithms for large-scale Bayesian Inference based on data subsampling
- Bayesian optimization for hyperparameter estimation
- Variational inference for large-scale Bayesian inference and prediction
- Bayesian model Inference and selection
- Bayesian inference for survival data