Experimental Approach

Let $p({\bf x}\vert H_a)$ stand for a theoretical PDF from which we can generate an unlimited amount of data. When another theoretical class $\log p({\bf x}\vert H_b)$ is introduced, we can determine the classification performance of the optimal Neyman-Pearson classifier: $\arg \max_k \left\{ p({\bf x}\vert H_k)\right\},$ which can be compared with the performance of the classifier that uses the projected PDFs in place of $p({\bf x}\vert H_k)$.