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We provide, within a general Markovian context, sufficient conditions under which estimators from the variational approximations are asymptotically equivalent to maximum likelihood estimators, and we show empirically, for the simple example of a first-order autoregressive model with missing values, that the lower bound surface can be very similar in shape to the true log-likelihood in non-asymptotic situations.<\/jats:p>","DOI":"10.1111\/1467-9868.00350","type":"journal-article","created":{"date-parts":[[2003,3,12]],"date-time":"2003-03-12T19:37:22Z","timestamp":1047497842000},"page":"549-564","source":"Crossref","is-referenced-by-count":16,"title":["On the Adequacy of Variational Lower Bound Functions for Likelihood-based Inference in Markovian Models with Missing Values"],"prefix":"10.1093","volume":"64","author":[{"given":"Peter","family":"Hall","sequence":"first","affiliation":[{"name":"Australian National University , Canberra , Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"K.","family":"Humphreys","sequence":"additional","affiliation":[{"name":"Karolinska Institutet , Stockholm , Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D. 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