Disputas: Reinaldo Antonio Gomes Marques
M.Sc. Reinaldo Antonio Gomes Marques ved Matematisk institutt vil forsvare sin avhandling for graden ph.d.:
On Monte Carlo Contributions for Real-time Probabilistic Inference
Reinaldo Antonio Gomes Marques
Tid og sted for prøveforelesning
Lecturer Christopher Nemeth, B81 Postgraduate Statistics Centre, Lancaster University
Professor Tore Selland Kleppe, Universitetet i Stavanger, Institutt for matematikk og fysikk
Associate Professor Riccardo De Bin, Matematisk institutt, Universitetet i Oslo
Leder av disputas
Professor Arne Bang Huseby Matematisk institutt, Universitet i Oslo
- Professor Geir Olve Storvik, Matematisk institutt, Universitet i Oslo
- Professor Arnoldo Frigessi Di Rattalma, Matematisk institutt, Universitet i Oslo
Statistical analysis has experienced an explosion due to technological capacity and performance for analysing complex problems. As consequence of this technological expansion, decision making in real-time scenarios under uncertainty has emerged in several fields, for instance, financial market, artificial intelligence, engineering, neuroscience, recommendation systems, insurance telematics, and many others. This has created a need for computational techniques to deal with the intractability statistical or mathematical models that are relevant to be used in real-time applications. Reinaldo A. G. Marques addresses current challenges in Sequential Monte Carlo (SMC) methods, one of the most important tools in computational statistics for inference on data collected over time.
This doctoral work is divided into two parts. The first part corresponds to a methodological investigation to deal with intractability in online Bayesian inference using particle filter algorithms. In particular, extensions of Sequential Monte Carlo techniques are introduced in order to reduce the sample impoverishment in dynamical models. A particle move scheme has been developed such that the particle weights are simultaneously updated, while taking a move step into account. This strategy has been discussed in detail previously within a Markov Chain Monte Carlo framework. The other investigation resulted in a novel particle filter algorithm for path and parameter estimation in general state space models. Since there are few options to perform online joint Bayesian inference, this algorithm demonstrates to be a considerable possibility for practitioners to implement when they have to deal with datasets of long time horizons. The main advantage of applying these strategies in the SMC algorithms is to maintain the sample diversity such that the approximations of the posterior distribution can be improved within a fixed computational cost.
In the last part, two articles present the implementation of the algorithms and methods developed in this thesis. In particular, these algorithms were implemented in relevant engineering problems in which real-time inference is required. Furthermore, a user-friendly R package is developed. This R package can be used to explore standard SMC algorithms, as well as their variants developed in this thesis, to carry out sequential inference in dynamic models where the latent variables follows a linear structure.
Overall this Ph.D. research contributes to mitigating key weakness of the Sequential Monte Carlo field and provides new computational tools and algorithms to the scientific community and practitioners.
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