On the Analysis of Optical Mapping Data - University of Wisconsin ...

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68 Observed Inferred (Viterbi) mean 25 Hit counts 20 15 10 5 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 Decreased copy number Normal Increased copy number Posterior probabilities 1.0 0.8 0.6 0.4 0.2 0.0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 Location (Mb) Figure 4.2 Results of one simulation run. In the top panel. the grey curve plots observed counts in windows with “expected” counts of 15, and the black line represents the decoded most likely (Viterbi) path. The bottom panel shows the posterior probabilities of the 3 estimated states for each window. Solid grey bars indicate gaps in the sequence.
69 Estimated Copy Number in simulation: human chromosome 2 sub full true sub full true sub full true sub full true sub full true sub full true sub full true sub full true sub full true sub full true sub full true sub full true sub full true sub full true sub full true Run 15 Run 14 Run 13 Run 12 Run 11 Run 10 Run 09 Run 08 Run 07 Run 06 Run 05 Run 04 Run 03 Run 02 Run 01 20 40 60 80 100 120 140 160 180 200 220 Location (Mb) 2.0 1.5 1.0 0.5 0.0 Figure 4.3 Summary of several simulation runs. Each panel represents one simulation. Within each panel, the bottom row represents the true copy number and the remaining rows represent estimated copy number based on the Viterbi path. The two cases differ in the number of maps used in the analysis: for the “full” version more maps are available than would normally be the case, and the“sub”version uses random subsets that have roughly the same numbers of maps as the GM07535 vs. CHM example below. Generally speaking, both versions consistently detect copy number changes larger that 1 Mb, and the “full” version has fewer false positives.
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ON THE ANALYSIS OF OPTICAL MAPPING
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To my parents. i
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DISCARD THIS PAGE
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iv Page 3.3 Results . . . . . . . .
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v LIST OF TABLES Table Page 1.1 Sum
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vi LIST OF FIGURES Figure Page 1.1
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ON THE ANALYSIS OF OPTICAL MAPPING
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1 Chapter 1 Overview of Optical Map
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3 hard, do not always have a unique
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5 for microbial and other small gen
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7 Figure 1.2 Close-up of a typical
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9 0.96 0.98 1.00 1.02 1.04 Offset a
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11 direct glimpse at the underlying
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13 which is not surprising since we
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15 Gapped alignments: The above des
Page 31 and 32: Figure 1.5 A visualization of align
Page 33 and 34: 19 Assembly: For these examples, th
Page 35 and 36: 21 Chapter 2 Modeling Optical Map D
Page 37 and 38: 23 Alternatively, it can be thought
Page 39 and 40: 25 and V (X i ) = E(V (Y i R i |R i
Page 41 and 42: 27 affect inference. If necessary,
Page 43 and 44: 29 Quantiles of fragment lengths (K
Page 45 and 46: 31 as a function of the parameters.
Page 47 and 48: 33 by rejecting maps that do not al
Page 49 and 50: 35 30 0.700 − 0.005 0 50 100 150
Page 51 and 52: 37 Chapter 3 Significance of Optica
Page 53 and 54: 39 using optical mapping data from
Page 55 and 56: 41 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8
Page 57 and 58: 43 3.3.2 Simplifications Direct app
Page 59 and 60: 45 Mean spurious score 0 −10 −2
Page 61 and 62: 47 3.3.3 Simulation Given a generat
Page 63 and 64: 49 3.4 Discussion 3.4.1 Uses Alignm
Page 65 and 66: 51 The ability to simulate from the
Page 67 and 68: 53 maps, where the separation betwe
Page 69 and 70: Figure 3.10 Schematic representatio
Page 71 and 72: 57 especially a short noisy one, to
Page 73 and 74: 59 Test statistics: Variability due
Page 75 and 76: 61 in sequence assembly and validat
Page 77 and 78: 63 1988). However, due to sampling
Page 79 and 80: 65 and rate parameters Λ i = E(N i
Page 81: 67 with mean µ k for the k th stat
Page 85 and 86: 71 Posterior probabilities 1.0 0.8
Page 87 and 88: 73 (a) Observed counts and decoded
Page 89 and 90: 75 Conclusion: Copy number alterati
Page 91 and 92: 77 well in its current form, but th
Page 93 and 94: 79 Change in score 15 10 5 0 0.9 1.
Page 95 and 96: 81 will rarely be homozygous. It ma
Page 97 and 98: 83 E.T. Dimalanta, A. Lim, R. Runnh
Page 99 and 100: 85 Appendix A: Score functions for
Page 101 and 102: 87 Appendix B: Hidden Markov Model
Page 103 and 104: 89 which can be shown to have highe
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