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Working with over-parameterized models

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A parametric representation of a statistical model may involve some redundancy; that is, the mapping from parameter space to family of distributions may be many-to-one. Such over-parameterized representations are often very useful conceptually, but can cause computational and inferential problems (ridges in the likelihood, non-estimable parameter combinations). For linear and generalized-linear models, well known approaches use either a reduced basis or a generalized matrix inverse. In this talk I will discuss how to work with over-parameterized nonlinear models. Aspects covered will include maximum-likelihood computation, detection of non-identifiability, and presentation of results. Some implications for Bayesian analysis will also be touched upon. The work is motivated by the design and implementation of the R package “gnm” (written jointly with Dr Heather Turner).

This talk is part of the Statistics series.

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