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SUMMARY:Latent Variable Models for Bayesian Inference with Stable Distribu
 tions and Processes - Marina Riabiz\, King's College London
DTSTART:20190130T153000Z
DTEND:20190130T163000Z
UID:TALK114496@talks.cam.ac.uk
CONTACT:Prof. Ramji Venkataramanan
DESCRIPTION:Extreme values and skewness are often observed in engineering\
 , financial and biological time-series. This talk summarizes my PhD work\,
  a study motivated by the need of efficient and reliable Bayesian inferenc
 e methods when the α-stable model is selected to represent such data. Whi
 le having a key role as the limit of the generalized central limit theorem
  (CLT)\, the class of stable distributions is highly intractable\, given t
 hat it is not possible to analytically express its pdf.\nSeveral approxima
 te methods are available in the literature\, in both the frequentist and B
 ayesian paradigms\, but they suffer from a number of deficiencies\, the mo
 st relevant being the lack of quantification of the approximation made.\n\
 nThis talk focuses on two different latent variable models\, that provide 
 two marginal representations of the stable pdf. For the first model\, an e
 xact parameter inference scheme\, based on the pseudo-marginal Markov chai
 n Monte Carlo approach\, is developed\, providing results comparable to a 
 state of the art Bayesian sampler. The novel method does not introduce any
  approximation\, while allowing for better control of the quality of the i
 nference.\nThe second model derives from an infinite series representation
  stable random variables.\nIn this setting\, we first formulate a CLT for 
 the series residual\, which serves to justify existing approximations used
  in previous literature. Moreover\, we present numerical and theoretical r
 esults on the rate of convergence for finite values of the series truncati
 on parameter\, thus giving theoretical guarantees on the accuracy achieved
 . Finally\, we present extensions of this model to multivariate stable ran
 dom variables\, in the framework of simulation of continuous time stochast
 ic processes. This is at the basis of inference methods to be developed in
  future work.  
LOCATION:LT6\, Baker Building\, CUED
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