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Model determination using sampling-based methods. (English) Zbl 0840.62003

Gilks, W. R. (ed.) et al., Markov chain Monte Carlo in practice. London: Chapman & Hall. 145-161 (1996).
Responsible data analysis must address the issue of model determination, which we take as consisting of two components: model assessment or checking and model choice or selection. Since in practice, apart from rare situations, a model specification is never ‘correct’ we must ask (i) is a given model adequate? and (ii) within a collection of models under consideration, which is the best?
This chapter describes how to perform model determination in practice. Our approach is informal, adopting an exploratory data analysis viewpoint and creating a variety of diagnostic tools for this purpose. We illustrate our approach with an example which, though simpler than usual applications, conveniently enables us to reveal the key ideas.
For the entire collection see [Zbl 0832.00018].

MSC:

62-07 Data analysis (statistics) (MSC2010)
62F15 Bayesian inference
62J02 General nonlinear regression
65C05 Monte Carlo methods