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Continuous time Graphical Models and Decomposition Sampling
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0001-6684-8088
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Two topics in temporal graphical probabilistic models are studied. The topics are treated in separate papers, both with applications in finance. The first paper study inference in dynamic Bayesian networks using Monte Carlo methods. A new method for sampling random variables is proposed. The method divides the sample space into subspaces. This allows the sampling to be done in parallel with independent and distinct sampling methods on the subspaces. The methodology is demonstrated on a volatility model and some toy examples with promising results. The second paper treats probabilistic graphical models in continuous time —a class of models with the ability to express causality. Tools for inference in these models are developed and employed in the design of a causality measure. The framework is used to analyze tick-by-tick data from the foreign exchange market.

Abstract [sv]

Två teman inom temporala grafiska modeller betraktas. De behandlas i separata artiklar, båda med tillämpningar inom finans. Den första artikeln studerar inferens i dynamiska Bayesianska nätverk med Monte Carlo-metoder. En ny metod för att simulera slumptal föreslås. Metoden delar upp tillståndsrummet i underrum. Detta gör att simuleringarna kan utföras parallellt med oberoende och distinkta simuleringstekniker på underrummen. Metodiken demonstreras på en volatilitesmodell och ett par leksaksmodeller med lovande resultat. Den andra artikeln behandlar probabilistiska grafiska modeller i kontinuerlig tid. Dessa modeller har förmåga att uttrycka kausalitet. Verktyg för inferens i dessa modeller utvecklas och används för att designa ett kausalitets-mått. Ramverket tillämpas genom att analysera tick-data från valutamarknaden.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. , viii, 8 p.
Series
TRITA-MAT-A, 2015:01
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-159954ISBN: 978-91-7595-441-7 (print)OAI: oai:DiVA.org:kth-159954DiVA: diva2:787945
Presentation
2015-02-24, Rum 3721, Inst för Matematik, Lindstedtsvägen 25, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20150218

Available from: 2015-02-18 Created: 2015-02-12 Last updated: 2015-02-18Bibliographically approved
List of papers
1. Decomposition Sampling Applied to Parallelization of Metropolis-Hastings
Open this publication in new window or tab >>Decomposition Sampling Applied to Parallelization of Metropolis-Hastings
(English)Manuscript (preprint) (Other academic)
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-159952 (URN)
Note

QS 2015

Available from: 2015-02-12 Created: 2015-02-12 Last updated: 2016-10-13Bibliographically approved
2. Testing for Causality in Continuous time Bayesian Network Models of High-Frequency Data
Open this publication in new window or tab >>Testing for Causality in Continuous time Bayesian Network Models of High-Frequency Data
(English)Manuscript (preprint) (Other academic)
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-159953 (URN)
Note

QS 2015

Available from: 2015-02-12 Created: 2015-02-12 Last updated: 2016-10-13Bibliographically approved

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Licentiate Thesis(327 kB)308 downloads
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Hallgren, Jonas

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Output format
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