Thursday 09 Oct 2014: Statistical Science Seminar
Diana Cole -
To be able to fit or examine a parametric model successfully all the parameters need to be identifiable. If the parameters are non-identifiable the model can be rewritten in terms of a smaller set of parameters, and is termed parameter redundant. Parameter redundancy is not always obvious, in which case the definitive method for detecting parameter redundancy involves calculating the rank of a matrix, which is expressed symbolically.
Models used in ecology are becoming more realistic but at the same time more complex. This poses a problem for this symbolic method as computers run out of memory calculating the rank of the appropriate matrix. We describe an extended symbolic method to solve this problem, which involves reparameterisation of the model and calculating the rank of a structurally simpler matrix. We demonstrate how this method works on various ecology models including multi-state mark recapture models and state-space models.
An alternative solution is a hybrid-symbolic numeric method. This method combines symbolic and numeric methods to create an algorithm that is extremely accurate compared to other numeric methods but is also more straightforward to use. We demonstrate the advantages of this method and show how it can be used in ecological models.