BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Miguel de Carvalho (University of Edinburgh) DTSTART:20200716T100000Z DTEND:20200716T110000Z DTSTAMP:20260423T003254Z UID:ProbStat/5 DESCRIPTION:Title: Elements of Bayesian geometry\nby Miguel de Carvalho (University of E dinburgh) as part of Probability & Statistics (IST-CEMAT\, FC-CEAUL\, ULi sbon)\n\n\nAbstract\nIn this talk\, I will discuss a geometric interpretat ion to Bayesian inference that will yield a natural measure of the level o f agreement between priors\, likelihoods\, and posteriors. The starting po int for the construction of the proposed geometry is the observation that the marginal likelihood can be regarded as an inner product between the pr ior and the likelihood. A key concept in our geometry is that of compatibi lity\, a measure which is based on the same construction principles as Pea rson correlation\, but which can be used to assess how much the prior agre es with the likelihood\, to gauge the sensitivity of the posterior to the prior\, and to quantify the coherency of the opinions of two experts. Esti mators for all the quantities involved in our geometric setup are discusse d\, which can be directly computed from the posterior simulation output. S ome examples are used to illustrate our methods\, including data related t o on-the-job drug usage\, midge wing length\, and prostate cancer.\n\nJoin t work with G. L. Page and with B. J. Barney\n LOCATION:https://researchseminars.org/talk/ProbStat/5/ END:VEVENT END:VCALENDAR