Recursive Bayesian inference in dynamic models: Advances and applications

Branislav Rudic

Recursive Bayesian inference in dynamic models: Advances and applications

Titel in Übersetzung: Rekursive Bayes'sche Inferenz in dynamischen Modellen: Fortschritte und Anwendungen

Branislav Rudic

Institut für Stochastik

Publikation: Abschlussarbeiten › Dissertation

Abstract

Bei der Analyse fehlerbehafteter Beobachtungsreihen dynamischer Systeme ergeben sich je nach Anwendungszweck unterschiedliche Schätzprobleme. Dazu zählen die statistische Inferenz über Wahrscheinlichkeitsverteilungen zukünftiger, aktueller oder vergangener Systemzustände sowie die Schätzung der wahrscheinlichsten Zustände oder Zustandsfolgen. Diese Arbeit abstrahiert derartige Fragestellungen im Rahmen der Bayesschen Inferenz zu
probabilistischen Zustandsbeobachtungsmodellen. Es werden sowohl zustandsdiskrete als auch zustandskontinuierliche Modelle unter Gaußschen und nicht-Gaußschen Annahmen betrachtet. Die Arbeit leistet praktische Beiträge zur Positionsverfolgung und Trajektoriendekodierung in drahtlosen Sensornetzwerken, etwa durch die Einbettung geometrischer Restriktionen
in die Modellparameter oder durch hierarchische Datenassoziation zur robusten Verfolgung mehrerer Ziele bei unmarkierten Beobachtungen. Der zentrale Beitrag besteht in der Entwicklung grundlegender Inferenztechniken. Im Gegensatz zu bestehenden Verfahren ermöglichen diese eine rekursive Dekodierung von kohärenten Zuständen bzw. plausiblen Zustandsfolgen für allgemeine Modelle, während bestehende Verfahren nur für zustandsdiskrete
Modelle oder Gaußsche Modelle anwendbar sind. Im Zuge der Herleitung dieser rekursiven Bayesschen Dekodierer wurde zudem das rekursive Bayessche Glätten für Mischmodelle analytisch gelöst. Diese Fragestellung galt seit über
drei Jahrezehnten als offen.

Titel in Übersetzung	Rekursive Bayes'sche Inferenz in dynamischen Modellen: Fortschritte und Anwendungen
Originalsprache	Englisch
Qualifikation	Doktorat
Betreuung / Begutachtung	Efrosinin, Dmitry, Betreuerin Sztrik, Janos, Betreuerin, Externe Person Pichler-Scheder, Markus, Mitbetreuer*in
Datum der Bewilligung	20 Okt. 2025
Publikationsstatus	Veröffentlicht - 20 Okt. 2025

Wissenschaftszweige

101019 Stochastik
101 Mathematik
101018 Statistik
101014 Numerische Mathematik
101024 Wahrscheinlichkeitstheorie

JKU-Schwerpunkte

Digital Transformation

Zugriff auf Dokument

https://epub.jku.at/urn/urn:nbn:at:at-ubl:1-94646

Dieses zitieren

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abstract = "When analyzing noisy observation sequences of dynamical systems, various estimation problems arise depending on the application. These include statistical inference over the probability distributions of future, current, or past system states, as well as the estimation of the most likely states or state sequences. This work abstracts such problems in the framework of Bayesian inference to probabilistic state observation models. Both discrete-state and continuous-state models are considered, under Gaussian and non-Gaussian assumptions. The thesis makes practical contributions to position tracking and trajectory decoding in wireless sensor networks, for example through the integration of geometric constraints into model parameters or through hierarchical data association for robust multiple object tracking with unlabeled observations. The main contribution is the development of foundational inference techniques. In contrast to existing methods, these techniques enable recursive decoding of coherent states or plausible state sequences for the general model case, whereas existing techniques are limited to special cases of discrete-state models or Gaussian models. In the course of deriving these recursive Bayesian decoders, the problem of recursive Bayesian smoothing for mixture models was solved analytically, which had been considered open for over three decades.",

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N2 - When analyzing noisy observation sequences of dynamical systems, various estimation problems arise depending on the application. These include statistical inference over the probability distributions of future, current, or past system states, as well as the estimation of the most likely states or state sequences. This work abstracts such problems in the framework of Bayesian inference to probabilistic state observation models. Both discrete-state and continuous-state models are considered, under Gaussian and non-Gaussian assumptions. The thesis makes practical contributions to position tracking and trajectory decoding in wireless sensor networks, for example through the integration of geometric constraints into model parameters or through hierarchical data association for robust multiple object tracking with unlabeled observations. The main contribution is the development of foundational inference techniques. In contrast to existing methods, these techniques enable recursive decoding of coherent states or plausible state sequences for the general model case, whereas existing techniques are limited to special cases of discrete-state models or Gaussian models. In the course of deriving these recursive Bayesian decoders, the problem of recursive Bayesian smoothing for mixture models was solved analytically, which had been considered open for over three decades.

AB - When analyzing noisy observation sequences of dynamical systems, various estimation problems arise depending on the application. These include statistical inference over the probability distributions of future, current, or past system states, as well as the estimation of the most likely states or state sequences. This work abstracts such problems in the framework of Bayesian inference to probabilistic state observation models. Both discrete-state and continuous-state models are considered, under Gaussian and non-Gaussian assumptions. The thesis makes practical contributions to position tracking and trajectory decoding in wireless sensor networks, for example through the integration of geometric constraints into model parameters or through hierarchical data association for robust multiple object tracking with unlabeled observations. The main contribution is the development of foundational inference techniques. In contrast to existing methods, these techniques enable recursive decoding of coherent states or plausible state sequences for the general model case, whereas existing techniques are limited to special cases of discrete-state models or Gaussian models. In the course of deriving these recursive Bayesian decoders, the problem of recursive Bayesian smoothing for mixture models was solved analytically, which had been considered open for over three decades.

M3 - Doctoral thesis

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