Speaker: Prof. Mahmoud Zarepour, University of Ottawa
Title: New Development in Nonparametric Bayesian Inference
Abstract:
Ferguson's Dirichlet process introduces a prior <g class="gr_ gr_34 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar replaceWithoutSep" id="34" data-gr-id="34">on</g> space of all probability measures. This prior is a random discrete probability measure which is dense over the space of all probability measures. The Dirichlet prior works like frequentist's empirical process and this can be confirmed through <g class="gr_ gr_37 gr-alert gr_gramm gr_inline_cards gr_run_anim Style multiReplace" id="37" data-gr-id="37">asymptotic theory</g> as well. For example, the Bayesian bootstrap shows asymptotic equivalence and an analogous m out of n Bayesian bootstrap can also be introduced which works like the frequentists' regular "m out of n Bayesian bootstrap". The goal is to present an overview of topics from nonparametric Bayesian inference such as Bayesian testing. Some other important priors that work like Dirichlet process but with more flexibility will be introduced and a brief historical overview will be provided. We also present <g class="gr_ gr_33 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar only-ins replaceWithoutSep" id="33" data-gr-id="33">few</g> <g class="gr_ gr_38 gr-alert gr_gramm gr_hide gr_inline_cards gr_run_anim Style multiReplace replaceWithoutSep replaceWithoutSep" id="38" data-gr-id="38">semi-parametric models</g> and introduce a data augmentation technique to use the results it in Machine Learning.
Where: Katharine R. Cudahy Hall Room 401 (1313 W. Wisconsin Avenue, Milwaukee WI 53233)
When: 2:00 PM, Thursday, February 28, 2019------------------------------
Mehdi Maadooliat
Assistant Professor
Marquette University
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