On model expansion, model contraction, identifiability and prior information: two illustrative scenarios involving mismeasured variables. (English) Zbl 1087.62037

Gustafson, Paul

Stat. Sci. 20, No. 2, 111-140 (2005).

Summary: When a candidate model for data is nonidentifiable, conventional wisdom dictates that the model must be simplified somehow so as to gain identifiability. We explore two scenarios involving mismeasured variables where, in fact, model expansion, as opposed to model contraction, might be used to obtain identifiability. We compare the merits of model contraction and model expansion. We also investigate whether it is necessarily a good idea to alter the model for the sake of identifiability. In particular, estimators obtained from identifiable models are compared to those obtained from nonidentifiable models in tandem with crude prior distributions.
Both asymptotic theory and simulations with Markov chain Monte Carlo-based estimators are used to draw comparisons. A technical point which arises is that the asymptotic behavior of a posterior mean from a nonidentifiable model can be investigated using standard asymptotic theory, once the posterior mean is described in terms of the identifiable part of the model only.

MSC:

62F15	Bayesian inference
62F12	Asymptotic properties of parametric estimators
65C40	Numerical analysis or methods applied to Markov chains

Keywords:

Bayes analysis; identifiability; measurement error; misclassification; nested models; prior information

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