{"id":375,"date":"2019-01-01T04:59:33","date_gmt":"2019-01-01T04:59:33","guid":{"rendered":"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=375"},"modified":"2019-01-01T04:59:59","modified_gmt":"2019-01-01T04:59:59","slug":"he-expectation-maximisation-emalgorithm","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/chapter\/he-expectation-maximisation-emalgorithm\/","title":{"rendered":"he Expectation Maximisation (EM)Algorithm"},"content":{"raw":"<div><\/div>\r\n<div><img class=\"aligncenter size-full wp-image-376\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-03.jpg\" alt=\"\" width=\"461\" height=\"221\" \/> <img class=\"aligncenter size-full wp-image-377\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-04.jpg\" alt=\"\" width=\"866\" height=\"435\" \/> <img class=\"aligncenter size-full wp-image-378\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-05.jpg\" alt=\"\" width=\"804\" height=\"397\" \/> <img class=\"aligncenter size-full wp-image-379\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-06.jpg\" alt=\"\" width=\"847\" height=\"327\" \/> <img class=\"aligncenter size-full wp-image-380\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-07.jpg\" alt=\"\" width=\"821\" height=\"431\" \/> <img class=\"aligncenter size-full wp-image-381\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-08.jpg\" alt=\"\" width=\"865\" height=\"495\" \/> <img class=\"aligncenter size-full wp-image-382\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-09.jpg\" alt=\"\" width=\"870\" height=\"633\" \/> <img class=\"aligncenter size-full wp-image-383\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-10.jpg\" alt=\"\" width=\"877\" height=\"597\" \/> <img class=\"aligncenter size-full wp-image-384\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-11.jpg\" alt=\"\" width=\"868\" height=\"554\" \/> <img class=\"aligncenter size-full wp-image-385\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-12.jpg\" alt=\"\" width=\"875\" height=\"451\" \/> <img class=\"aligncenter size-full wp-image-386\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-13.jpg\" alt=\"\" width=\"864\" height=\"317\" \/> <img class=\"aligncenter size-full wp-image-387\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-14.jpg\" alt=\"\" width=\"797\" height=\"375\" \/><\/div>\r\n<div><\/div>\r\n<div><\/div>\r\n<div>References<\/div>\r\n<div><\/div>\r\n<ul>\r\n \t<li style=\"text-align: justify\">Little, R.J.A. and Rubin, D.B. (1987). Statistical Analysis with Missing Data. New York: Wiley; Chapter 7<\/li>\r\n \t<li style=\"text-align: justify\">McLachlan, G.J and Krishnan T (1997). The EM Algorithm and Extensions.John Wiley Sons, Inc.<\/li>\r\n \t<li style=\"text-align: justify\">Dempster, A.P., Laird, N.M., and Rubin, D.B. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm. Journal of The Royal Statistical Society, Series B, 39, 1-38<\/li>\r\n<\/ul>","rendered":"<div><\/div>\n<div><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-376\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-03.jpg\" alt=\"\" width=\"461\" height=\"221\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-03.jpg 461w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-03-300x144.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-03-65x31.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-03-225x108.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-03-350x168.jpg 350w\" sizes=\"auto, (max-width: 461px) 100vw, 461px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-377\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-04.jpg\" alt=\"\" width=\"866\" height=\"435\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-04.jpg 866w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-04-300x151.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-04-768x386.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-04-65x33.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-04-225x113.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-04-350x176.jpg 350w\" sizes=\"auto, (max-width: 866px) 100vw, 866px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-378\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-05.jpg\" alt=\"\" width=\"804\" height=\"397\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-05.jpg 804w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-05-300x148.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-05-768x379.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-05-65x32.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-05-225x111.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-05-350x173.jpg 350w\" sizes=\"auto, (max-width: 804px) 100vw, 804px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-379\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-06.jpg\" alt=\"\" width=\"847\" height=\"327\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-06.jpg 847w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-06-300x116.jpg 300w, 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src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-09.jpg\" alt=\"\" width=\"870\" height=\"633\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-09.jpg 870w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-09-300x218.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-09-768x559.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-09-65x47.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-09-225x164.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-09-350x255.jpg 350w\" sizes=\"auto, (max-width: 870px) 100vw, 870px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-383\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-10.jpg\" alt=\"\" width=\"877\" height=\"597\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-10.jpg 877w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-10-300x204.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-10-768x523.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-10-65x44.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-10-225x153.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-10-350x238.jpg 350w\" sizes=\"auto, (max-width: 877px) 100vw, 877px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-384\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-11.jpg\" alt=\"\" width=\"868\" height=\"554\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-11.jpg 868w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-11-300x191.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-11-768x490.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-11-65x41.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-11-225x144.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-11-350x223.jpg 350w\" sizes=\"auto, (max-width: 868px) 100vw, 868px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-385\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-12.jpg\" alt=\"\" width=\"875\" height=\"451\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-12.jpg 875w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-12-300x155.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-12-768x396.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-12-65x34.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-12-225x116.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-12-350x180.jpg 350w\" sizes=\"auto, (max-width: 875px) 100vw, 875px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-386\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-13.jpg\" alt=\"\" width=\"864\" height=\"317\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-13.jpg 864w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-13-300x110.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-13-768x282.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-13-65x24.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-13-225x83.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-13-350x128.jpg 350w\" sizes=\"auto, (max-width: 864px) 100vw, 864px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-387\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-14.jpg\" alt=\"\" width=\"797\" height=\"375\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-14.jpg 797w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-14-300x141.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-14-768x361.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-14-65x31.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-14-225x106.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9498_et_missing_data_4_em-14-350x165.jpg 350w\" sizes=\"auto, (max-width: 797px) 100vw, 797px\" \/><\/div>\n<div><\/div>\n<div><\/div>\n<div>References<\/div>\n<div><\/div>\n<ul>\n<li style=\"text-align: justify\">Little, R.J.A. and Rubin, D.B. (1987). Statistical Analysis with Missing Data. New York: Wiley; Chapter 7<\/li>\n<li style=\"text-align: justify\">McLachlan, G.J and Krishnan T (1997). The EM Algorithm and Extensions.John Wiley Sons, Inc.<\/li>\n<li style=\"text-align: justify\">Dempster, A.P., Laird, N.M., and Rubin, D.B. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm. Journal of The Royal Statistical Society, Series B, 39, 1-38<\/li>\n<\/ul>\n","protected":false},"author":3,"menu_order":18,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["souvik-kumar-bandyopadhyay"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-375","chapter","type-chapter","status-publish","hentry","contributor-souvik-kumar-bandyopadhyay"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/chapters\/375","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":1,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/chapters\/375\/revisions"}],"predecessor-version":[{"id":388,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/chapters\/375\/revisions\/388"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/chapters\/375\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/wp\/v2\/media?parent=375"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/chapter-type?post=375"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/wp\/v2\/contributor?post=375"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/wp\/v2\/license?post=375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}