Seismic monitoring for underground nuclear explosions answers three questions for all global seismic activity: Where is the seismic event located? What is the event source type (event identification)? If the event is an explosion, what is the yield? The answers to these questions involves processing seismometer waveforms with propagation paths predominately in the mantle. Four discriminants commonly used to identify teleseismic events are depth from travel time, presence of long-period surface energy (mb vs. MS), depth from reflective phases, and polarity of first motion. The seismic theory for these discriminants is well established in the literature (see, for example, Blandford  and Pomeroy et al. ). However, the physical basis of each has not been formally integrated into probability models to account for statistical error and provide discriminant calculations appropriate, in general, for multidimensional event identification. This article develops a mathematical statistics formulation of these discriminants and offers a novel approach to multidimensional discrimination that is readily extensible to other discriminants. For each discriminant a probability model is formulated under a general null hypothesis of H0: Explosion Characteristics. The veracity of the hypothesized model is measured with a p-value calculation (see Freedman et al.  and Stuart et al. ) that can be filtered to be approximately normally distributed and is in the range [0, 1]. A value near zero rejects H0 and a moderate to large value indicates consistency with H0. The hypothesis test formulation ensures that seismic phenomenology is tied to the interpretation of the p-value. These p-values are then embedded into a multidiscriminant algorithm that is developed from regularized discrimination methods proposed by DiPillo (1976), Smidt and McDonald (1976), and Friedman (1989). Performance of the methods is demonstrated with 102 teleseismic events with magnitudes (mb) ranging from 5 to 6.5. Example p-value calculations are given for two of these events.