{"success":1,"msg":"","color":"rgb(28, 35, 49)","title":"Approximate Laplace approximation<\/b>","description":"webinar","title2":"","start":"2021-02-19 15:00","end":"2021-02-19 16:00","responsable":"Botond Szabo <\/i><\/a>","speaker":"David Rossell (Univ. Pompeu Fabra in Barcelona)","id":"25","type":"webinar","timezone":"Europe\/Amsterdam","activity":"International Bayes Club seminar (https:\/\/www.math.vu.nl\/thebayesclub\/)\r\n\r\nZoom link:\r\nTopic: International Bayes club\r\nTime: Feb 19, 2021 03:00 PM Amsterdam\r\n\r\nJoin Zoom Meeting\r\nhttps:\/\/vu-live.zoom.us\/j\/97567928223?pwd=Vm1SOTRuTzVsbjNrZkdBVHg1MTFrZz09\r\n\r\nMeeting ID: 975 6792 8223\r\nPasscode: 504799\r\n\r\n","abstract":"Bayesian model selection has desirable properties to recover structure, e.g. we discuss strong control of frequentist error probabilities in hypothesis tests. However, BMS requires evaluating integrals to assign posterior model probabilities to each candidate model. The computation is cumbersome when the integral has no closed-form, particularly when the sample size or the number of models are large. We present a simple yet powerful idea based on the Laplace approximation (LA) to an integral. LA uses a quadratic Taylor expansion at the mode of the integrand and is typically quite accurate, but requires cumbersome likelihood evaluations (for large n) an optimization (for large p). We propose the approximate Laplace approximation (ALA), which uses an Taylor expansion at the null parameter value. ALA brings significant speed-ups by avoiding optimizations altogether, and evaluating likelihoods via sufficient statistics. ALA is an approximate inference method equipped with strong model selection properties in the family of non-linear GLMs, attaining comparable rates to exact computation that also hold when all models are misspecified. In fact, it is questionable whether one should target exact calculations when (inevitably) the model is never exactly corret. We show examples in non-linear Gaussian regression with non-local priors, for which no closed-form integral exists, as well as non-linear logistic, Poisson and survival regression."}