Kalman Filter Beginners Matlab Examples Pdf

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The prior information allowed for arbitrarly selecting markers at which we can measure the abundance of the tumor cells. In contrast, the employed HMM-based approach considers a fixed depth for the branching process and, therefore, a specific number of tumor progression stages. Since the depth is fixed only for a given patient, this method is not able to adjust its branching structure to the actual biomarker pattern or to a new biomarker pattern. In other words, our approach is not generalizable.

It turns out, that the branching structure of the process is a regular tree with a predefined branching depth. This fact enables the application of the re-rooting algorithm. As indicated above, the re-rooting tree is adjusted to the parameters of the Markov model. Unknown transition probabilities can be approximated by the conditional probabilities of the maximal subtrees.

The difference of the described approach to existing methods is its capability to infer the actual branching structure. In contrast to most published studies, the number of Markov stages and transition probabilities is not arbitrary but depends on the biomarker pattern. Therefore, the probabilities of the transitions can be inferred from the observed tumor progression and they are in accordance with the actual biology. d2c66b5586

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