Monte Carlo algorithms for performing Bayesian inference on Piecewise Deterministic Processes

Monte Carlo algorithms for performing Bayesian inference on Piecewise Deterministic Processes

Mignacco, Chiara (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Delft Institute of Applied Mathematics; TU Delft Statistics)

Bierkens, G.N.J.C. (mentor)
Duncan, Andrew (mentor)
Meester, L.E. (graduation committee)

Delft University of Technology

Applied Mathematics

2022-09-22

Since their introduction in 1993, particle filters are amongst the most popular algorithms for performing Bayesian inference on state space models that do not admit an analytical solution. In this thesis, we will present several particle filtering algorithms adapted to a class of models known as Piecewise Deterministic Markov Processes (PDMP), i.e. processes governed by one or more parameters that admit random jumps in their value at random times. Our work will focus on object tracking, the estimation of a target’s kinematic state over time from a sequence of noisy or incomplete measurements. Moreover, we will combine these techniques with Markov Chain Monte Carlo methods in order to infer the model parameters. We will perform sequential inference on both parameters and states by introducing an adaptation of the SMC2 to PDMPs. Finally, all algorithms will be tested both on simulated and real-world data (Piraeus AIS Dataset).

Particle Filters
Sequential Monte Carlo
Hidden Markov Model
Piecewise Deterministic Process
Object Tracking
Markov Chains Monte Carlo

http://resolver.tudelft.nl/uuid:59633bf0-d981-4821-b66c-6f7e610797ef

Student theses

master thesis

© 2022 Chiara Mignacco