Reviews: On Mixtures of Markov Chains

The paper is globally sound and makes a new contribution to an important topic. However some technicalities need to be addressed and a revised version should be encouraged. Major remarks: - There is a confusion on whether the Markov chains under consideration are supposed to be stationary or not. Indeed, the concept of t-trail either requires that the Markov chains under study are stationary or one should specify that all the trails start with same initial distribution, i.e. these trails are observations of (X_1,X_2,X_3) and not (X_s, X_{s 1},X_{s 2}) for some s. I first understood that you adopt the second approach (as you count the parameters of initial distributions as free parameters) but in the real data experiments, you take many (3001)-trails and break them into 3000 overlapping 3-trails (by the way, you need a 3002-trail to obtain these).