BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Adaptive and robust nonparametric Bayesian contraction rates for d
 iscretely observed compound Poisson processes - Dr Alberto J. Coca
DTSTART:20181107T140000Z
DTEND:20181107T150000Z
UID:TALK113227@talks.cam.ac.uk
CONTACT:J.W.Stevens
DESCRIPTION:Compound Poisson processes (CPPs) are the textbook example of 
 pure jump stochastic processes\, and they approximate arbitrarily well muc
 h richer classes of processes such as Lévy processes. They are characteri
 sed by the so-called Lévy jump distribution\, N\, driving the frequency a
 t which jumps (randomly) occur and their (random) sizes. Hence\, they prov
 ide a simple\, yet fundamental\, model for random shocks in a system appli
 ed in a myriad of problems within natural sciences\, engineering and econo
 mics. In most applications\, the underlying CPP is not perfectly observed:
  only discrete observations over a finite-time interval are available. Thu
 s\, the process may jump several times between two observations and we are
  effectively observing a random variable corrupted by a sum of a random nu
 mber of copies of itself. Consequently\, estimating N is a non-linear stat
 istical inverse problem.\n\nIn the recent years\, understanding the freque
 ntist asymptotic behaviour of the Bayesian method in inverse\nproblems and
 \, in particular\, in this problem has received considerable attention. In
  this talk\, we will present ongoing results on posterior contraction rate
 s for the nonparametric density \\nu of N: we show two-sided stability est
 imates that guarantee that the classical theory in Ghosal\, Ghosh\, van de
 r Vaart (2000) can be transferred to our problem\, allowing us to use mixt
 ure and Gaussian priors for \\nu multidimensional\; furthermore\, the rate
 s are robust to the observation interval\, i.e. optimal adaptive inference
  can be made without specification of whether the regime is of high- or lo
 w-frequency\; and\, lastly\, we propose an efficient \\infty-MCMC procedur
 e to draw from the posterior for infinite dimensional priors. Given the di
 versity of the CCIMI members\, we will attempt to introduce all these conc
 epts during the presentation.\n
LOCATION:CMS\, MR14
END:VEVENT
END:VCALENDAR