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Short Course in Bayesian Non-Parametrics

Monday 21st January (1WN 3.11):

11:00-13:00: Introductory lectures in Bayesian non-parametrics given by Global Chair Prof. Rams´es Mena. Only basic stats/probability knowledge assumed. Primarily theoretical focus but the possibility of some programming pending time and interest.

13:00-14:00: Lunch provided for participants.

14:00-16:00: Introductory lectures continue from morning session.

Wednesday 23rd January (3E 3.5):

11:00-13:00 Practical programming session. 

Thursday 24th January (3E 3.5): 

11:00-13:00 Seminar from Dario Spano (https://warwick.ac.uk/fac/sci/statistics/staff/academic-research/spano/)

Title: Time-dependent non-parametric models via genealogies and duality.

Abstract. In many statistical problems (including financial econometrics,
filtering, genetics, meta-analysis) the parameter of interest depends on a
covariate which we can conveniently interpret as time. The observations
are taken at distinct time points thus they are, in general, not
exchangeable. From a Bayesian perspective, it is important to be able to
model  tractable and interpretable prior distributions on time-dependent
parameters to capture heterogeneity in the data.  The problem becomes
complicated when the parameter is, at each time, infinite-dimensional e.g.
a measure. I will illustrate how two families of measure-valued stochastic
processes, well-known in the area of population genetics, can be used to
generate continous-time-dependent variants of the popular Dirichlet
Process and the Gamma process nonparametric priors. I will illustrate how
genealogical processes embedded in the mentioned population models can be
used, in connection with various probabilistic notions of duality, to
describe dependence fairly explicitly, and to provide insight on the
so-called "borrowing strength" properties of the model.

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