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Each dice has one probability mass function (pmf). In a discrete HMM, a pmf is assigned to each state. So my first remark is when you say: "The transition matrix for each individual die's unfair prob …

Taylor answer is accurate. I do not see HMM as suited to the data set you propose as is however. It seems to me that the number of samples in the time series is too little... To answer your question …

As the sequences are generated by HMM1 you will expect most of the data sequences to have a higher likelihood with respect to HMM1 than with respect to HMM2 as your first sentence suggests. The exper …

A Gaussian is not only represented by its mean but also by its variance. The variances will be very different for each Gaussian in this case and they are taking into account in the HMM. Basically, if …

I am not familiar with what you call mixture Markov models. However, as I say further in this answer, some people call hidden Markov models, dynamical mixture model. It is possible that other people r …

HMMs model ordered sequences of observations or time-series $X = \{x_1, x_2,..., x_T\}$, where each $x_i$ can be a discrete or continuous, uni-dimensional or multi-dimensional observation/data sample. …

One option: I worked on this exact same problem couple of years ago. The mixed data I was working with were multivariate with some of the dimensions being categorical and some other continuous. The …

For the number of hidden states, many estimation methods rely on trial/error, computing a score (like the BIC, AIC, or MML) and decide the final topology from these scores. The drawback of these scor …

We usually call multivariate HMM an HMM that model multidimensional observations. If you have time series in the form: X = [1 2 3 4 5 1 2] (each value corresponding to a time step), you will model t …

I am missing some information about your problem for a complete answer, but assuming that you have a finite number of known containers that can be used and that this number is not too big, here is wha …

The HMM parameters are estimated using a forward-backward algorithm also called the Baum-Welch algorithm. The Viterbi algorithm is used to get the most likely states sequnce for a given observation s …