Friday 23 November at 12:00
Lab 602, Maths & Physics Building, University of Malta Msida Campus
Viable Posteriors for Gaussian and Levy Priors is the title of a seminar by Prof. Lino Sant that will be held on Friday 23 November at 12:00 in Lab 602, Maths & Physics Building, University of Malta Msida Campus.
Lab 602, Maths & Physics Building, University of Malta Msida Campus
Viable Posteriors for Gaussian and Levy Priors is the title of a seminar by Prof. Lino Sant that will be held on Friday 23 November at 12:00 in Lab 602, Maths & Physics Building, University of Malta Msida Campus.
Bayesian Nonparametric statistics is a relatively recent area which is flourishing with great vigour and popularity. Its increasing applicability is widening over more areas of applied research, while its theoretical content is sharpened through the input of theoreticians, algorithm developers and statisticians involved in applied research.
In fact it is an excellent area of research to help one understand how theory and practice work hand in hand within the context of relevant, current research problems. For the mathematically inclined statistician, as well as the pure mathematician, it is a really exciting crucible of results and concepts from various areas like functional analysis, stochastic processes, Bayesian statistics and measure theory. Most statisticians need no further proselyticising - they have been practising it for quite some time.
In fact it is an excellent area of research to help one understand how theory and practice work hand in hand within the context of relevant, current research problems. For the mathematically inclined statistician, as well as the pure mathematician, it is a really exciting crucible of results and concepts from various areas like functional analysis, stochastic processes, Bayesian statistics and measure theory. Most statisticians need no further proselyticising - they have been practising it for quite some time.
In this talk we give a review and critique of methods which have been developed in Bayesian nonparametric statistics for generating prior probabilities. The success, or otherwise, of this enterprise is judged by the ability to derive comfortably posterior distributions. Two main methods making use of probabilities defined on function spaces as well as on spaces of signed measures are discussed. The Bayesian kernel method, which has wide appeal and great flexibility, is discussed before an alternative which uses a Hilbert subspace as starting point is proposed. Completely random measures (CRM) are also discussed with a clear exposition of how they are defined and exploited through their infinite divisibility property. Their limitation to discrete measures is pointed out and an alternative method for generating Gaussian random measures to include with CRMs proposed.
A few applications of these methods will be entertained.