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Inhalt:
State space models enjoy wide popularity in mathematical and statistical modelling across disciplines and research fields. Frequent solutions to problems of estimation and forecasting of a latent signal such as the celebrated Kalman filter hereby rely on a set of strong assumptions such as linearity of system dynamics and Gaussianity of noise terms. We investigate fallacy in mis-specification of the noise terms, that is signal noise and observation noise, regarding heavy tailedness in that the true dynamic frequently produces observation outliers or abrupt jumps of the signal state due to realizations of these heavy tails not considered by the model. We propose a formalisation of observation noise mis-specification in terms of Huber’s ε-contamination as well as a computationally cheap solution via generalised Bayesian posteriors with a diffusion Stein divergence loss resulting in the diffusion score matching Kalman filter - a modified algorithm akin in complexity to the regular Kalman filter. For this new filter interpretations of ...
Anmerkung:
Masterarbeit Universität Potsdam 2024
Sprache:
Englisch
Schlagwort(e):
Hochschulschrift
DOI:
10.25932/publishup-64946
URN:
urn:nbn:de:kobv:517-opus4-649469
Mehr zum Autor:
Carpentier, Alexandra 1987-