Bayesian and Monte Carlo Methods
“The fundamental problem of scientific progress, and a fundamental one of everyday life, is that of learning from experience. Knowledge obtained in this way is partly merely description of what we have already observed, but partly consists of making inference from past experience to predict future experience" - Sir Harold Jeffreys, Theory of Probability.
The Bayesian approach to statistical modelling uses probability as a means to quantify the beliefs of the observer about the model parameters, given the data observed. Computationally intensive methods such as Markov chain Monte Carlo have facilitated the application of Bayesian methods to a diverse range of fields, including archaeology, ecology, engineering, medicine, epidemiology and biostatistics. Trans-dimensional Markov chains permit the Markov chain to traverse through varying dimensions over time. The simultaneous exploration of model and parameter space is particularly useful in the context of Bayesian model determination and model averaging. Performance of Markov chains has long been a contentious issue, and recent progress in adaptive algorithms and exact or perfect sampling have provided exciting avenues of research.
Specific research interests of this group include the application of Bayesian methods, simulation via trans-dimensional Markov chains, perfect or exact sampling algorithms, efficient and adaptive Markov chain Monte Carlo, and stochastic simulation in the absence of likelihoods.
Group Members
About the Bayesian Statistics and Monte Carlo Methods group
The group has strong ties with the School of Economics through Robert Kohn, and with the Australian Graduate School of Management through Sally Wood. There are a number of PhD and postdoctoral researchers between the schools.
Research in the group is sponsored by the Australian Research Council.
Some ongoing projects
Approximate Bayesian computation
There are many applications in which the likelihood for a model is not known, or is computationally prohibitive to evaluate, but where it is possible to efficiently simulate data. The group is currently active in developing so-called approximate Bayesian computation algorithms capable of simulating from the posterior distribution implied by such models.
Automating trans-dimensional Markov chains
Trans-dimensional samplers, such as the reversible jump algorithm, require specification of both within- and between- model transitions. Efficient transitions are difficult to find for generic models, in particular for the between-model moves. The group is currently active in developing techniques and algorithms to automate the selection of the most efficient transitions for such samplers.
Bayesian generalised linear mixed models
Linear models are able to handle an extraordinary range of complications in regression-type analyses. The group is interested in the development of Bayesian methods for GLMM's, particularly for binary and count responses where the models are hindered by the presence of intractable multivariate intervals.
Bayesian inference and computation for complex regression models
The Bayesian statistics and Monte Carlo methods group is also active in researching Bayesian approaches to inference and computation for complex regression models. Some particular interests of group members are flexible simultaneous modelling of mean and variance functions, Bayesian hierarchical modelling of data from gene expression studies and Bayesian hierarchical modelling of data sets arising in meteorology and environmental science.
MCMC and sampling methodology
The group is interested in the development of novel methodology concerning sampling algorithms. This includes the assessment of convergence properties and diagnostics, perfect or exact simulation, sequential Monte Carlo methods, model selection and transdimensional sampling schemes.
