In this paper, we propose a two-part approach to robust optimization to derive the set of worst-case trajectories of any random process. First, we approximate its distribution using a set of concurrent multivariate distributions and tools from Bayesian inference. This can be done by using a mixture of multivariate Gaussian distributions, where concurrent distributions correspond to different numbers of mixture components. For each concurrent model and possible path that can be taken by the random process, we associate a "local" Poisson distribution with parameter defined as a function of its probability. Then, we can compute the minimum number of trials that is required for this path to be taken at least once by the random process.

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