Single molecule experiments study the kinetics of molecular biological systems. Many such studies generate data that can be described by aggregated hidden Markov models, whereby there is a need of doing inference on such data and models. In this study, model selection in aggregated Hidden Markov models was performed with a criterion of maximum Bayesian evidence. Variational Bayes inference was seen to underestimate the evidence for aggregated model fits. Estimation of the evidence integral by brute force Monte Carlo integration theoretically always converges to the correct value, but it converges in far from tractable time. Nested sampling is a promising method for solving this problem by doing faster Monte Carlo integration, but it was here seen to have difficulties generating uncorrelated samples.