Journal of Medical Systems, Vol. 2. No. 3. 1978 Statistical Development Nonparametric Detection Scheme for Myocardial Infarction Larry H. Bernstein, Chris P. Tsokos, and John C. Turner Bernstein et al.~ have suggested a method for the detection of myocardial infarction using the combined measurement of serum LD activity and inhibition of LD by pyruvate (which depends on the amount of LD from damaged myocardium). This is another in the growing number of applications of discriminant analysis in medical diagnosis. As is often the case, the true underlying distribution of the data is not known. In this case, in particular, an attempt is made at defining the distribution to more accurately assess those patients among whom the diagnosis of myocardial infarction is suspect bui is not clearly identified. Tsokos and Welch 2 have shown that discriminant procedures based on incorrect assumptions of the underlying distribution led to substantially higher error rates. In this paper, we consider the application of a nonparametric probability density estimator recently developed by David W. Scott: This leads to a rather accurate discriminant procedure that is applicable to many other types of data. INTRODUCTION The standard discrimination problem consists of finding a function that classifies observations as having come from one of a number of populations. The criterion for choosing such a function is given in terms of a loss function, which is the loss incurred by incorrectly classifying an observation. The optimal discrimination is the one that minimizes the expected value of the loss function. However, to evaluate this expected value requires knowledge of the probability distributions of each of the populations. This paper addresses the problem of determining the probability distributions of the populations. In the past, there have been two major approaches to the determination of the probability distributions. The first is merely to assume that the distributions involved From the Department of Pathology, Iowa Methodist Medical Center, Des Moines, Iowa, and the Depart- ment of Mathematics, University of South Florida, Tampa, Florida. 2O3 0148-5598/78/0900-0203505.00/0 9 Plenum Publishing Corporation