Optimization of PRIM under normality

We modify the PRIM (Patient Rule Induction Method) algorithm for bump hunting used for finding modes in populations to obtain a converging region under normality, reducing the complexity of the algorithm to a single step. We prove several interesting results comparing forms of PRIM, including that the final region found by PRIM is more accurate on a rotation induced by the principal components. We illustrate the method via a variety of simulations.