Probability distributions over many variables occur frequently in Bayesian inference, statistical physics and simulation studies. Samples from distributions give insight into their typical behavior and can allow approximation of any quantity of interest, such as expectations or normalizing constants. Markov chain Monte Carlo (MCMC), introduced by Metropolis et al. (1953), allows sampling from d...

The ingredients to a Bayesian analysis comprise the sampling model {Pθ : θ ∈ Ω} for the response X, the prior Π for the parameter θ, and the observed value X = x. This is equivalent to specifying the joint model Pθ ×Π for (X, θ) and the observed value X = x. In many situations we may also have a loss function but we ignore this here as it is not material to our discussion. We refer to Pθ ×Π as ...

Benichou and Gail (1995, Biometrics 51, 182-194) describe methods for estimating the absolute risk of developing disease given a set of covariate values over a specified time interval from a case-control study within a cohort. The methods are most suitable for unmatched case-control studies, and are restricted to categorical covariates. Expanding on methods for estimating relative mortality fro...