Model selection for determining the number of basis functions

Develop model-selection methods to determine the number of basis functions required for a given dataset in the proposed Gibbs and Poisson point-process basis-expansion framework, including approaches such as stochastic search variable selection or the Bayesian Lasso.

Background

The paper models the global and pairwise interaction effects of general Gibbs point processes using finite Bernstein polynomial basis expansions. The number of basis functions controls the flexibility of both effect functions, but the paper does not provide a principled procedure for selecting that number for a particular dataset.

The authors explicitly identify model selection for determining the required number of basis functions as an open problem and mention stochastic search variable selection and the Bayesian Lasso as possible approaches to be studied in future work. Such a procedure would address the trade-off between approximation accuracy, model complexity, and identifiability in the proposed framework.