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We propose a method to ease the challenges of exploring multi-dimensional parameter spaces in beyond-the-Standard Model theories. We evaluate the model likelihood for any choice of parameters by sampling the theory parameters intelligently and building a Kernel Density Estimator. By reducing the number of expensive Monte-Carlo simulations, this method provides a more efficient way to test complex theories. We illustrate our technique to set new limits on a short-lived heavy neutrino $N$, proposed as an explanation of anomalies in neutrino experiments. Using a search for lepton pairs in the T2K near detector, we find exclusion limits on the model parameters in a vast region of parameter space, fully exploiting the advantages of our new method. With a single Monte Carlo simulation, we obtain the differential event rate for arbitrary choices of model parameters, allowing us to cast limits on any slice of the model parameter space. We conclude that $N$ particles with lifetimes greater than $c τ^0 \gtrsim 3~$cm are excluded by T2K data. We also derive model-independent constraints in terms of the total rate, lifetime, and $N$ mass and provide an approximated analytical formula. This method can be applied in other branches of physics to explore the landscape of theory parameters efficiently.