{"id":219,"date":"2017-04-18T03:03:33","date_gmt":"2017-04-18T03:03:33","guid":{"rendered":"http:\/\/sites.warnercnr.colostate.edu\/gwhite\/?page_id=219"},"modified":"2017-04-18T03:12:41","modified_gmt":"2017-04-18T03:12:41","slug":"statistical-theory","status":"publish","type":"page","link":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/statistical-theory\/","title":{"rendered":"Statistical Theory"},"content":{"rendered":"

Contents<\/a> – Index<\/a><\/span><\/p>\n

\n

Statistical Theory<\/b><\/span><\/p>\n

Much of modern statistical theory rests on Fisher’s likelihood principle.\u00a0 This theory continues to serve as the backbone of general statistical inference across nearly all areas of science.\u00a0 The past two decades have seen an explosion in advanced statistical methods.\u00a0 These advances include\u00a0 generalized linear models (McCullagh and Nelder 1989<\/a>) and new theory for the analysis of binary data (Cox and Snell 1989<\/a>).<\/span>
\n\u00a0 Quasi-likelihood methods for modeling the variance-covariance matrix and allowing empirical estimates of sampling variances (Wedderburn 1974<\/a>) have been developed and are particularly important in product-multinomial models.\u00a0 Profile likelihood intervals are now frequently used (Cormack 1992<\/a>). Use of general information theoretic methods in the selection of a parsimonious model (Akaike 1985<\/a>) has been a major theoretical advance.\u00a0 This theory, including Akaike’s Information Criterion (AIC<\/a>) is a substantial advance to the general likelihood theory.<\/span>
\nSeveral important statistical advances have resulted because of the greatly increased computational power of relatively inexpensive computers.\u00a0 This has lead to a number of computer intensive statistical methods.\u00a0 The concept of repeated resampling has lead to the bootstrap (Efron 1982<\/a>) for empirical estimates of the variance-covariance matrix and establishing confidence intervals.\u00a0 Procedures now exist to compute the exact P<\/i>-value for contingency tables where the data are sparse (i.e., the expected values are small).\u00a0 These procedures are relevant for goodness of fit tests for general multinomial models.<\/span>
\nThis body of theory then finds specific application in the analysis of data from capture-recapture and band recovery surveys and experiments.<\/span><\/p>\n

More information is available at <\/span>https:\/\/sites.warnercnr.colostate.edu\/gwhite\/analysis-marked-animal-encounter-data\/<\/span>.<\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Contents – Index Statistical Theory Much of modern statistical theory rests on Fisher’s likelihood principle.\u00a0 This theory continues to serve as the backbone of general statistical inference across nearly all areas of science.\u00a0 The past two decades have seen an …<\/p>\n

Statistical Theory<\/span> Read More »<\/a><\/p>\n","protected":false},"author":117,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-219","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/219","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/users\/117"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/comments?post=219"}],"version-history":[{"count":3,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/219\/revisions"}],"predecessor-version":[{"id":231,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/219\/revisions\/231"}],"wp:attachment":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/media?parent=219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}