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Epsilon machines have received a lot of attention lately as models of stochastic processes. When modeling stochastic processes, researchers often face the problem of inferring epsilon machines from finite data. Accordingly, studying the mechanisms and the difficulties in inference could give us insight into how to perform it more accurately. We propose to choose two inference methods, the classic Baum Welch Estimation and the recent Bayesian Structural Inference and outline a comparison framework. We present our numerical results and show how this led to identification of how the two methods solve the same objective in parameter inference. We further outline comparisons of how the methods do topology selection.

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