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INTERDISCIPLINARY JOURNAL OF CONTEMPORARY RESEARCH IN BUSINESS
6. Markov Chain Monte Carlo (MCMC) Sampling
Ultimately, we are interested in the marginal posterior probability of the state sequences,
P(S|D), which requires a marginalization over the model parameters according to (eq. 8).
7. Conclusion
We applied both HMM-Bayes and RECPARS to the synthetic DNA sequence
alignmentThe objective of this simulation study was to test the performance of both
methods on different (a priori known) mosaic structures and for varying levels of
difficulty of the detection problem (which is related to the tree height, also discussed
When the tree height is sufficiently large (0.3, 0.2), HMM-Bayes predict the true mosaic
structure, but with two important differences. First sequence gives only an accurate
prediction if the recombination and substitute t, have been set "appropriately." Note that
these parameters can not be inferred from the data, but rather have to be chosen in
advance. It was suggested by Wiuf, Christensen, and Hein that a ratio of the
recombination and substitution costs works fine quite generally. However, this was not
confirmed in our simulations, where for the largest tree height of 0.3 the predictions with
this ratio were wrong, leading to a mosaic structure that is over-tessellated. Because
HMM-Bayes infers all the parameters from the data, it does not suffer from this
shortcoming . Second, even when predicts the nature of the mosaic structure correctly, it
is less accurate than HMM-Bayes in locating the breakpoints:it can be seen that the
breakpoints predicted with are typically misplaced by 20–30 nucleotides. This is a
consequence of the fact that uses only the topology-defining sites, and thus discards a
considerable proportion of sites in the DNA sequence alignment.
When the tree height is decreased to 0.1, not HMM-Bayes predicts the mosaic structure
of the alignment correctly.finds only one recombinant region, which for the first
alignment is even badly misplaced (fig. 3bottom right). HMM-Bayes detects both
recombinant regions and even locates them rather accurately, but it misclassifies the
topology change for one of these regions (fig. 4 bottom right; fig. 1 bottom right). This is
most likely a consequence of the fact that for small tree heights, the number of mutations
and, consequently, the number of polymorphic sites is small. Thus, there is less
information in the data, and any inference is inevitably less accurate.
For a more quantitative comparison between and HMM-Bayes, recall that the detection of
recombination is basically a classification problem: Each site in the sequence alignment is
assigned to one of the three possible tree topologies. this is done directly. For HMM-
Bayes, it is done by assigning each site to the mode of the posterior probability. We use
two criteria to rate the performance of the methods: The sensitivity, which is the
percentage of correctly classified recombinant sites, and the specificity, which measures
the percentage of correctly classified non-recombinant sites. Comparing the performance
of RECPARS and HMM-Bayes across all simulations, shown in figure 2 we found that
HMM-Bayes gives a consistent and significant improvement on sequence the accuracy of
locating and classifying the recombinant regions, as indicated by a systematically
increased sensitivity score.
COPY RIGHT © 2011 Institute of Interdisciplinary Business Research
JANUARY 2011
VOL 2, NO 9
537