In order to establish a brain-machine-interface (BMI) system that rehabilitates damaged cerebellum function of discrete motor learning, the detection of conditional and unconditional stimuli (CS and US) onset times based on electro-physiology recordings analysis is necessary. These signals are relayed through brainstem areas called Pontine Nucleus (PN) and the Inferior Olive (IO) respectively. In this paper we focus on the model based analysis of the PN and compare the expected model performance with the observed one with real samples. We suggest a model of multi-unit (MU) activity as filtered inhomogeneous Poisson pulses of evoked activity contaminated by homogenous spontaneous activity and thermal noise (Filtered Poisson-Poisson-Gaussian model). By assigning the likelihood into the generalize log likelihood test (GLRT), we show that the best expected feature is energy detection. The model parameters were estimated based on the recorded peri-stimuli-time-histogram (PSTH) by chi-square goodness-of-fit minimization. Monte Carlo simulation showed that the thermal noise can be neglected in respect to the spontaneous activity and also predicted the order of the observed empiric detection performance in terms of detection probability and area under the receiver operation characteristic (ROC) curve (AUC).