  Accidental damage is a typical component of motor insurance claim. Modeling
of this nature generally involves analysis of past claim history and different
characteristics of the insured objects and the policyholders. Generalized
linear models (GLMs) have become the industry's standard approach for pricing
and modeling risks of this nature. However, the GLM approach utilizes a single
"best" model on which loss predictions are based, which ignores the uncertainty
among the competing models and variable selection. An additional characteristic
of motor insurance data sets is the presence of many categorical variables,
within which the number of levels is high. In particular, not all levels of
such variables may be statistically significant and rather some subsets of the
levels may be merged to give a smaller overall number of levels for improved
model parsimony and interpretability. A method is proposed for assessing the
optimal manner in which to collapse a factor with many levels into one with a
smaller number of levels, then Bayesian model averaging (BMA) is used to blend
model predictions from all reasonable models to account for factor collapsing
uncertainty. This method will be computationally intensive due to the number of
factors being collapsed as well as the possibly large number of levels within
factors. Hence a stochastic optimisation is proposed to quickly find the best
collapsing cases across the model space.
