2. The additive version of the partial linear model may be too restrictive in some applications. This motivates interest in specifications which are more general, but less likely to suffer from the curse of dimensionality than the partial linear model. One such specification includes interaction terms between explanatory variables. In the case where p D 2, we would have the model yi D f1.xi1/ C f2.xi2/ C f3.xi1xi2/ C "i

(a) Describe how the methods of Section 10.2.3 can be extended to allow for Bayesian analysis of this model.

(b) Using artificial data sets of your choice, investigate the empirical performance of the methods developed in part (a).