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Research into Bayesian methods includes work on both generic issues, such as model selection, graphical models and default priors, and on application-specific models and methods in a wide variety of domains, including genetic epidemiology, econometrics, hydrology and traffic management.
The key characteristic of Bayesian methods is that all variables – data, parameters, latent variables etc – are treated as random and all uncertainties are expressed as probabilities.
This gives Bayesian analysis an attractive uniformity and coherence. Inferential tasks such as hypothesis testing and the construction of confidence intervals, which have to be performed indirectly in classical inference, can be replaced by direct probability statements about unknowns.
Bayesian methods are used in many different situations, such as traffic management, genetic epidemiology, econometrics and hydrology, as well as generic issues such as model selection, graphical models and default priors.
Inherently, Bayesian analysis is suited to complexity, prediction, sequential updating of information and nuisance parameters.
Developments in Monte Carlo Computation have dramatically eased the computational challenge of implementing Bayesian methods, particularly in complex models.