{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T04:43:42Z","timestamp":1771044222902,"version":"3.50.1"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008,7,15]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Motivation: Low haplotype diversity and linkage disequilibrium are the rule in short genomic segments. This fact suggests that parsimony should be enforced in estimation of haplotype frequencies. The current article introduces a diversity penalty that automatically discards potential haplotypes with low explanatory power. The standard EM algorithm for haplotype frequency estimation can accommodate the penalty if one passes over to a more general minorize\u2013maximize (MM) scheme for estimation.<\/jats:p><jats:p>Results: Our new MM algorithm converges in fewer iterations, eliminates marginal haplotypes from further consideration and reduces the computational complexity of each iteration. Estimation by the MM algorithm also improves haplotyping and genotype imputation compared to naive application of the EM algorithm. Thus, the MM algorithm is a useful substitute for the EM algorithm. Compared to the most sophisticated current methods of haplotyping and genotype imputation, the MM algorithm is slightly less accurate but at least an order of magnitude faster.<\/jats:p><jats:p>Availability: Our software will be made available in the next release the program Mendel at http:\/\/www.genetics.ucla.edu\/software\/.<\/jats:p><jats:p>Contact: \u00a0kayers@ucla.edu<\/jats:p>","DOI":"10.1093\/bioinformatics\/btn236","type":"journal-article","created":{"date-parts":[[2008,5,17]],"date-time":"2008-05-17T00:26:02Z","timestamp":1210983962000},"page":"1596-1602","source":"Crossref","is-referenced-by-count":16,"title":["Penalized estimation of haplotype frequencies"],"prefix":"10.1093","volume":"24","author":[{"given":"Kristin L.","family":"Ayers","sequence":"first","affiliation":[{"name":"1 Department of Biomathematics, 2Department of Human Genetics and 3Department of Statistics, University of California, Los Angeles, CA 90095, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenneth","family":"Lange","sequence":"additional","affiliation":[{"name":"1 Department of Biomathematics, 2Department of Human Genetics and 3Department of Statistics, University of California, Los Angeles, CA 90095, USA"},{"name":"1 Department of Biomathematics, 2Department of Human Genetics and 3Department of Statistics, University of California, Los Angeles, CA 90095, USA"},{"name":"1 Department of Biomathematics, 2Department of Human Genetics and 3Department of Statistics, University of California, Los Angeles, CA 90095, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2008,5,16]]},"reference":[{"key":"2023020210490252600_B1","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1038\/sj.ejhg.5200619","article-title":"Haplotypes vs single marker linkage disequilibrium tests: what do we gain?","volume":"9","author":"Akey","year":"2001","journal-title":"Eur. J. Hum. Genet"},{"key":"2023020210490252600_B2","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1002\/gepi.20232","article-title":"A dictionary model for haplotyping, genotype calling, and association testing","volume":"31","author":"Ayers","year":"2007","journal-title":"Genet. Epi"},{"key":"2023020210490252600_B3","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1137\/S1064827596304010","article-title":"Atomic decomposition by basis pursuit","volume":"20","author":"Chen","year":"1998","journal-title":"SIAM J. Sci. Comput"},{"key":"2023020210490252600_B4","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1190\/1.1440378","article-title":"Robust modeling with erratic data","volume":"38","author":"Claerbout","year":"1973","journal-title":"Geophysics"},{"key":"2023020210490252600_B5","volume-title":"Geometric Representations of Relational Data","author":"De Leeuw","year":"1977"},{"key":"2023020210490252600_B6","first-page":"921","article-title":"Maximum likelihood estimation of molecular haplotype frequencies in a diploid population","volume":"12","author":"Excoffier","year":"1995","journal-title":"Mol. Biol. Evol"},{"key":"2023020210490252600_B7","volume-title":"The Majorization Approach to Multidimensional Scaling: Some Problems and Extensions","author":"Groenen","year":"1993"},{"key":"2023020210490252600_B8","doi-asserted-by":"crossref","first-page":"1842","DOI":"10.1093\/bioinformatics\/bth149","article-title":"Haplotype reconstruction from genotype data using imperfect phylogeny","volume":"20","author":"Halperin","year":"2004","journal-title":"Bioinformatics"},{"key":"2023020210490252600_B9","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1093\/oxfordjournals.jhered.a111613","article-title":"Haplo: a program using the EM algorithm to estimate the frequencies of multi-site haplotypes","volume":"86","author":"Hawley","year":"1995","journal-title":"J. Hered"},{"key":"2023020210490252600_B10","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1198\/0003130042836","article-title":"A tutorial on MM algorithms","volume":"58","author":"Hunter","year":"2004","journal-title":"Am. Stat"},{"key":"2023020210490252600_B11","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21750-5","volume-title":"Mathematical and Statistical Methods for Genetic Analysis","author":"Lange","year":"2002"},{"key":"2023020210490252600_B12","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4182-7","volume-title":"Optimization","author":"Lange","year":"2004"},{"key":"2023020210490252600_B13","first-page":"250","article-title":"An algorithm for automatic genotype elimination","volume":"40","author":"Lange","year":"1987","journal-title":"Am. J. Hum. Genet"},{"key":"2023020210490252600_B14","first-page":"A1886","article-title":"Mendel version 4.0: a complete package for the exact genetic analysis of discrete traits in pedigree and population data sets","volume":"69","author":"Lange","year":"2001","journal-title":"Am. J. Hum. Genet"},{"key":"2023020210490252600_B15","first-page":"225","article-title":"An E-M algorithm and testing strategy for multiple-locus haplotypes","volume":"56","author":"Long","year":"1995","journal-title":"Am. J. Hum. Genet"},{"key":"2023020210490252600_B16","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1086\/500808","article-title":"A comparison of phasing algorithms for trios and unrelated individuals","volume":"78","author":"Marchini","year":"2006","journal-title":"Am. J. Hum. Genet"},{"key":"2023020210490252600_B17","doi-asserted-by":"crossref","first-page":"1242","DOI":"10.1086\/344207","article-title":"Partition-ligation-expectation-maximization algorithm for haplotype inference with single-nucleotide polymorphisms","volume":"71","author":"Qin","year":"2002","journal-title":"Am. J. Hum. Genet"},{"key":"2023020210490252600_B18","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1137\/0907087","article-title":"Linear inversion of band-limited reflection seismograms","volume":"7","author":"Santosa","year":"1986","journal-title":"SIAM J. Sci. Stat. Comput"},{"key":"2023020210490252600_B19","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1086\/502802","article-title":"A fast and flexible statistical model for large-scale population genotype data: applications to inferring missing genotypes and haplotypic phase","volume":"78","author":"Scheet","year":"2006","journal-title":"Am. J. Hum. Genet"},{"key":"2023020210490252600_B20","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1086\/428594","article-title":"Accounting for decay of linkage disequilibrium in haplotype inference and missing-data imputation","volume":"76","author":"Stephens","year":"2005","journal-title":"Am. J. Hum. Genet"},{"key":"2023020210490252600_B21","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1086\/319501","article-title":"A new statistical method for haplotype reconstruction from population data","volume":"68","author":"Stephens","year":"2001","journal-title":"Am. J. Hum. Genet"},{"key":"2023020210490252600_B22","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1190\/1.1440921","article-title":"Deconvolution with the \u21131norm","volume":"44","author":"Taylor","year":"1979","journal-title":"Geophysics"},{"key":"2023020210490252600_B23","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the Lasso","volume":"58","author":"Tibshirani","year":"1996","journal-title":"JRSS-B"}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/24\/14\/1596\/49048975\/bioinformatics_24_14_1596.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/24\/14\/1596\/49048975\/bioinformatics_24_14_1596.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,30]],"date-time":"2025-01-30T09:48:23Z","timestamp":1738230503000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/24\/14\/1596\/181704"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,5,16]]},"references-count":23,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2008,7,15]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btn236","relation":{},"ISSN":["1367-4811","1367-4803"],"issn-type":[{"value":"1367-4811","type":"electronic"},{"value":"1367-4803","type":"print"}],"subject":[],"published-other":{"date-parts":[[2008,7,15]]},"published":{"date-parts":[[2008,5,16]]}}}