While the formalism with the observation matrix B and the data matrix C is quite elegant and general, it comes with significant performance issues as soon as one wants to use more than two diagnostic modalities. This is mainly because they grow really quickly with the number of modalities.
There might be a simple solution though: Instead of computing the probability for every possible combination of diagnoses given any possible hidden state, only compute the likelihood of the actually observed diagnoses given all possible hidden states. This would be a process carried out once, when the data is loaded and result in a matrix of size 2^N x P where N is the number of LNLs and P the number of patients.
While the formalism with the observation matrix B and the data matrix C is quite elegant and general, it comes with significant performance issues as soon as one wants to use more than two diagnostic modalities. This is mainly because they grow really quickly with the number of modalities.
There might be a simple solution though: Instead of computing the probability for every possible combination of diagnoses given any possible hidden state, only compute the likelihood of the actually observed diagnoses given all possible hidden states. This would be a process carried out once, when the data is loaded and result in a matrix of size 2^N x P where N is the number of LNLs and P the number of patients.