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Simulated Convergence Rates with Application to an Intractable alpha-Stable Inference Problem
Univ Cambridge, England.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. Univ Cambridge, England.
Athens Univ Econ and Business, Greece.
Univ Cambridge, England.
2017 (English)In: 2017 IEEE 7TH INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP), IEEE , 2017Conference paper, Published paper (Refereed)
Abstract [en]

We report the results of a series of numerical studies examining the convergence rate for some approximate representations of alpha-stable distributions, which are a highly intractable class of distributions for inference purposes. Our proposed representation turns the intractable inference for an infinite-dimensional series of parameters into an (approximately) conditionally Gaussian representation, to which standard inference procedures such as Expectation-Maximization (EM), Markov chain Monte Carlo (MCMC) and Particle Filtering can be readily applied. While we have previously proved the asymptotic convergence of this representation, here we study the rate of this convergence for finite values of a truncation parameter, c. This allows the selection of appropriate truncations for different parameter configurations and for the accuracy required for the model. The convergence is examined directly in terms of cumulative distribution functions and densities, through the application of the Berry theorems and Parseval theorems. Our results indicate that the behaviour of our representations is significantly superior to that of representations that simply truncate the series with no Gaussian residual term.

Place, publisher, year, edition, pages
IEEE , 2017.
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-147621DOI: 10.1109/CAMSAP.2017.8313170ISI: 000428438100114ISBN: 978-1-5386-1251-4 (print)OAI: oai:DiVA.org:liu-147621DiVA, id: diva2:1202360
Conference
7th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
Available from: 2018-04-27 Created: 2018-04-27 Last updated: 2018-04-27

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