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SUMMARY:Nonparametric Bayesian intensity estimation for covariate-driven p
 oint processes - Matteo Giordano (Università degli Studi di Torino)
DTSTART:20260206T140000Z
DTEND:20260206T150000Z
UID:TALK243040@talks.cam.ac.uk
CONTACT:Po-Ling Loh
DESCRIPTION:A central task in the statistical analysis of spatial point pa
 tterns is to infer the relationship between the point distribution and a c
 ollection of covariates of interest. This talk will present recent theoret
 ical and methodological advances for covariate-based nonparametric Bayesia
 n intensity estimation\, in the two relevant asymptotic regimes for the pr
 oblem: large domains and replicated observations. On large domains\, it is
  shown how the presence of covariates allows to borrow information from fa
 r away locations in the observation window\, leading to minimax-optimal po
 sterior contraction rates in both global and point-wise loss functions\, u
 nder different classes of priors. For the replicated observations regime\,
  we consider the case of “anisotropic” intensity functions\, which is 
 common in applications where the covariates have different physical nature
 . We devise a “multi-bandwidth” Gaussian process method\, and prove th
 at it achieves optimal and adaptive posterior contraction rates. We furthe
 r show how posterior inference can be implemented in practice via a suitab
 le Metropolis-within-Gibbs sampling algorithm. Lastly\, we will illustrate
  the performance of the method via numerical simulations\, and present an 
 application to a Canadian wildfire dataset. Joint works with Alisa Kiriche
 nko\, Judith Rousseau and Patric Dolmeta.
LOCATION:MR12\, Centre for Mathematical Sciences
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