Editing Baum–Welch algorithm (section)

====Copy-number variation detection====
[[Copy-number variation]]s (CNVs) are an abundant form of genome structure variation in humans. A discrete-valued bivariate HMM (dbHMM) was used assigning chromosomal regions to seven distinct states: unaffected regions, deletions, duplications and four transition states.  Solving this model using Baum-Welch demonstrated the ability to predict the location of CNV breakpoint to approximately 300 bp from [[DNA microarray|micro-array experiments]].<ref>{{cite journal |last1=Korbel |first1=Jan |author-link=Jan O. Korbel |first2=Alexander |last2=Urban |first3=Fabien |last3=Grubert |first4=Jiang |last4=Du |first5=Thomas |last5=Royce |first6=Peter |last6=Starr |first7=Guoneng |last7=Zhong |first8=Beverly |last8=Emanuel |first9=Sherman |last9=Weissman |first10=Michael |last10=Snyder |first11=Marg |last11=Gerstein |title=Systematic prediction and validation of breakpoints associated with copy-number variations in the human genome |journal=Proceedings of the National Academy of Sciences of the United States of America |date=12 June 2007 |volume=104 |issue=24 |pages=10110–5 |doi=10.1073/pnas.0703834104 |pmid=17551006 |pmc=1891248 |bibcode=2007PNAS..10410110K |doi-access=free }}</ref> This magnitude of resolution enables more precise correlations between different CNVs and [[structural variations|across populations]] than previously possible, allowing the study of CNV population frequencies. It also demonstrated a [[Mendelian inheritance|direct inheritance pattern for a particular CNV]].