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First, the dimension of the generated sample space ({ arvec{B}}) is very large, namely, 10({}^{6}) for tumor tissue and 10({}^{8}) for LNLs. In addition, the number of transitions is not small. Both of those facts drastically reduce the chances that we can find a sample vector, which delivers a very precise estimate of ({ arvec{A}}). Instead, we are interested in an estimate which allows to reproduce a series of problems. This estimate is a middle point between an estimate where { arvec{A}} is inferred very precisely from a small sample of observations and an estimate where the inferences never results in a unique state sequence belonging to { arvec{B}}. Thus, we didn't use any specific iterative algorithm, we simply initialized our search algorithm at the starting state and ran it for variable amounts of time. We basically run the algorithm and see if 10({}^{6}) consecutive samples resemble the matrix of model derivation ({ arvec{B}}). If they do, the algorithm has converged, otherwise, it is still running. If it runs for 2 hours, it means that after 2 hours our algorithm has yet not been able to deliver the correct transition matrix ({ arvec{A}}).
The fact that our algorithm has not been able to converge in 2 hours should not be surprising. In theory, the starting state is already located within the observed area in ({ arvec{B}}) and the typical time it takes to identify the matrix { arvec{A}} is related to the dimension of the sample space: the greater the dimension of the sample space, the longer it takes for our algorithm to converge. In our case, we have 10({}^{6}) samples to choose from, spending only a small amount of time is impossible. Moreover, the dimension of { arvec{B}} is approximately 5 times larger than the dimension of { arvec{A}}. Due to that, our algorithm is stuck for quite a long time and we generally could not afford more than 20 minutes of running time for a single sample. d2c66b5586