Hi, this link introduces a HMM.

The hyper-parameters (C, alpha, etc.) are pre-specified, and hence the a prior distribution of the parameters (A, pi, etc.). Given an observed sequence vector_x, the posterior distribution of the parameters (A, pi, etc.) can be inferred.

What if we have multiple observed sequences? How can we improve the inference using multiple observations?

I know in this
paper mentioned an approach that to generate various hyper-parameters from different observations, then sample from each hyper-parameter set, and finally MLE the hyper-parameters from the samples. But this is to combine from appliance instances into an
appliance type. That is, they combine (hyper-)parameters from different sources.

In our case, we observe the same appliance multiple times, hence the inherent (hyper-)parameters are the same.

In this case, is there any we to use multiple observations?

One possible approach is to update the hyper-parameters sequentially using each observation: Let C_0 be the hyper-parameter for a prior before any data are provided. 1. to learn posterior C_1 from obs_0 and a prior C_0, then update a prior by C_1; 2. to
learn posterior C_2 from obs_1 and a prior C_1, then update a prior by C_2; ...; M. to learn posterior C_M from obs_{M-1} and a prior C_{M-1}. Then let C_M be the final posterior.

Is this a reasonable way to use multiple observations? Or is there any better way?

Thanks!