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CATEGORIES:CCIMI Seminars
SUMMARY:Adaptive and robust nonparametric Bayesian contrac
tion rates for discretely observed compound Poisso
n processes - Dr Alberto J. Coca
DTSTART;TZID=Europe/London:20181107T140000
DTEND;TZID=Europe/London:20181107T150000
UID:TALK113227AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/113227
DESCRIPTION:Compound Poisson processes (CPPs) are the textbook
example of pure jump stochastic processes\, and t
hey approximate arbitrarily well much richer class
es of processes such as Lévy processes. They are c
haracterised by the so-called Lévy jump distributi
on\, N\, driving the frequency at which jumps (ran
domly) occur and their (random) sizes. Hence\, the
y provide a simple\, yet fundamental\, model for r
andom shocks in a system applied in a myriad of pr
oblems within natural sciences\, engineering and e
conomics. In most applications\, the underlying CP
P is not perfectly observed: only discrete observa
tions over a finite-time interval are available. T
hus\, the process may jump several times between t
wo observations and we are effectively observing a
random variable corrupted by a sum of a random nu
mber of copies of itself. Consequently\, estimatin
g N is a non-linear statistical inverse problem.\n
\nIn the recent years\, understanding the frequent
ist asymptotic behaviour of the Bayesian method in
inverse\nproblems and\, in particular\, in this p
roblem has received considerable attention. In thi
s talk\, we will present ongoing results on poster
ior contraction rates for the nonparametric densit
y \\nu of N: we show two-sided stability estimates
that guarantee that the classical theory in Ghosa
l\, Ghosh\, van der Vaart (2000) can be transferre
d to our problem\, allowing us to use mixture and
Gaussian priors for \\nu multidimensional\; furthe
rmore\, the rates are robust to the observation in
terval\, i.e. optimal adaptive inference can be ma
de without specification of whether the regime is
of high- or low-frequency\; and\, lastly\, we prop
ose an efficient \\infty-MCMC procedure to draw fr
om the posterior for infinite dimensional priors.
Given the diversity of the CCIMI members\, we will
attempt to introduce all these concepts during th
e presentation.\n
LOCATION:CMS\, MR14
CONTACT:J.W.Stevens
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