Minimum bias designs under random contamination: application to polynomial spline models

Description/Abstract

Minimising the bias due to model misspecification has long been a
method for choosing designs. An approach is presented that
incorporates prior knowledge of the possible form of the true
model via an additive contamination term, regarded as a
realisation of a random variable. This induces a random bias term
for any given design. A prior distribution for the contamination
is obtained either directly or from prior distributions for the
individual elements of the contamination. A search technique is
used to find designs, where properties of the bias distribution
are estimated by simulation.

Several different criteria for choosing a design are proposed,
motivated by the distribution of the bias. These criteria are
investigated for models where the contamination has a polynomial
spline form with uncertainty in the number of knots and their
locations. The sensitivity of the resulting designs to the prior
distributions is examined.