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CATEGORIES:Signal Processing and Communications Lab Seminars
SUMMARY:Latent Variable Models for Bayesian Inference with
Stable Distributions and Processes - Marina Riabi
z\, King's College London
DTSTART;TZID=Europe/London:20190130T153000
DTEND;TZID=Europe/London:20190130T163000
UID:TALK114496AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/114496
DESCRIPTION:Extreme values and skewness are often observed in
engineering\, financial and biological time-series
. This talk summarizes my PhD work\, a study motiv
ated by the need of efficient and reliable Bayesia
n inference methods when the α-stable model is sel
ected to represent such data. While having a key r
ole as the limit of the generalized central limit
theorem (CLT)\, the class of stable distributions
is highly intractable\, given that it is not possi
ble to analytically express its pdf.\nSeveral appr
oximate methods are available in the literature\,
in both the frequentist and Bayesian paradigms\, b
ut they suffer from a number of deficiencies\, the
most relevant being the lack of quantification of
the approximation made.\n\nThis talk focuses on t
wo different latent variable models\, that provide
two marginal representations of the stable pdf. F
or the first model\, an exact parameter inference
scheme\, based on the pseudo-marginal Markov chain
Monte Carlo approach\, is developed\, providing r
esults comparable to a state of the art Bayesian s
ampler. The novel method does not introduce any ap
proximation\, while allowing for better control of
the quality of the inference.\nThe second model d
erives from an infinite series representation stab
le random variables.\nIn this setting\, we first f
ormulate a CLT for the series residual\, which ser
ves to justify existing approximations used in pre
vious literature. Moreover\, we present numerical
and theoretical results on the rate of convergence
for finite values of the series truncation parame
ter\, thus giving theoretical guarantees on the ac
curacy achieved. Finally\, we present extensions o
f this model to multivariate stable random variabl
es\, in the framework of simulation of continuous
time stochastic processes. This is at the basis of
inference methods to be developed in future work.
LOCATION:LT6\, Baker Building\, CUED
CONTACT:Dr Ramji Venkataramanan
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