Computer-intensive algorithms such as iterative, sampling-based method, have become increasingly popular satatistical tools, both in applied and theoretical work.
The properties of such algorithms, however, may sometimes not be obvious.
Here we give...
Computer-intensive algorithms such as iterative, sampling-based method, have become increasingly popular satatistical tools, both in applied and theoretical work.
The properties of such algorithms, however, may sometimes not be obvious.
Here we give a simple explanation of how and why the iterative, sampling-based method works. We analytically establish its properties in a simple case and provide insight for more complicated cases. There are also a number of examples.
For the Bayesian, the Gibbs sampler is mainly used to generate posterior distributions, whereas for the classical statistician a major use is for calculation of the likelihood function and characteristics of likelihood estimators.