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Second, the problem is multi-modal (cf. Fig. 3), so that the sum-product algorithm doesn’t converge to the right answer. Hence, we had to invent a new method for solving this problem in detail in the following sections.

In the situation of multi-modal observations, an intuitive idea is to map observations to latent states. Namely, each LNL with a mass of $m$ corresponds to a latent state with a mass $m$. Now, the observation matrix specifies the probability of observing the corresponding latent state. From this, the state transition matrix can be inferred using an appropriate model like a two-state Hidden Markov Model.

In the following chapter, we will derive the parameters of the model for the transition matrix ({ arvec{A}}) in terms of the given parameters specifying the observation matrix for the healthy LNLs ({ arvec{B}}). The obtained values are used in the following to infer the transition matrix for the tumor-bearing LNLs ({ arvec{A}}={ arvec{C}}). It turns out that the obtained results are very close to the true value in all series. Nevertheless, each of the two values inferred by our method is biased and the bias quickly decreases with increasing tumor mass (cf. Fig. 4). d2c66b5586