Refining posterior Markov chain

We describe different approaches that were used to test and investigate potential improvements in various aspects of the posterior Markov chain. This includes different ways of combining Up and Down chains, and inclusion of all available transitions within a window. Additionally, an alternative algorithm for computing the posterior Markov chain was tested, relying on forward-backward algorithm, using a higher order chain to obtain the posterior Lfcs. Proposed approaches were tested on both PCube paper example and Volund dataset, and results from the latter are presented. First approaches yielded some changes, but not significant improvements implying that current approach is a robust and reasonable choice. On the other hand, the proposed alternative algorithm produced different results. However, it is not straightforward to conclude, whether the results are to be preferred over the ones produced by the existing approach.