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Clinical outcome prediction from high-dimensional data is problematic in thecommon setting where there is only a relatively small number of samples. Theimbalance causes data overfitting, and outcome prediction becomescomputationally expensive or even impossible. We propose a Bayesian outcomeprediction method that can be applied to data of arbitrary dimension d, from 2outcome classes, and reduces overfitting without any approximations atparameter level. This is achieved by avoiding numerical integration orapproximation, and solving the Bayesian integrals analytically. We therebyreduce the dimension of numerical integrals from 2d dimensions to 4, for any d.For large d, this is reduced further to 3, and we obtain a simple outcomeprediction formula without integrals in leading order for very large d. Wecompare our method to the mclustDA method (Fraley and Raftery 2002), usingsimulated and real data sets. Our method perform as well as or better thanmclustDA in low dimensions d. In large dimensions d, mclustDA breaks down dueto computational limitations, while our method provides a feasible andcomputationally efficient alternative.

Overcoming computational inability to predict clinical outcome from high-dimensional patient data using Bayesian methods