A Bayesian formulation of the problem of analysing data from a curvilinear regression of $y$ on $x_1, x_2, \cdots, x_r$ in order to predict a future value of $y$ is considered. The problem is to obtain a criterion to decide which is the best subset of $x_1, x_2, \cdots, x_r$ to perform this prediction. Under very strict assumptions the criterion obtained is shown to use the same statistic as the orthodox (least squares) approach.
"The Choice of Variables for Prediction in Curvilinear Multiple Regression." Ann. Statist. 1 (3) 506 - 516, May, 1973. https://doi.org/10.1214/aos/1176342416