Contributions to Bayesian inference via spectral methods

This thesis investigates Bayesian inference methods for time series and spatial models in the frequency domain. One of the main drawbacks of Bayesian inference in this setting is the computational burden, especially for large data. Using ideas from Fourier analysis, the original signal (data) domain can be transformed into the frequency domain, which portrays how the signal is decomposed across different frequencies, which is known as the spectrum. A key property of the spectrum is the asymptotic independence of the spectrum ordinates, which can be used to form an approximate likelihood known as the Whittle likelihood, which is computationally faster than the corresponding time domain likelihood. We explore this computationally faster likelihood for three Bayesian models. First, we explore linear dynamic regression with semi-long memory disturbance processes. Second, spectral subsampling of continuous-time models for large data. Third, the estimation of stationary random fields for latticed spatial data.

Author dc:creator

• Goodwin, Thomas

Statement dc:rights

• info:eu-repo/semantics/openAccess
• The author owns the copyright in this thesis including all reproduction and reuse rights for the work. The work may not be altered without the permission of the copyright owner. Attribution is essential when quoting or paraphrasing from this thesis.
• © 2024 Thomas Goodwin
• au.edu.uts.lib/cph

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10453/187555

OAI identifier oai:identifier

oai:opus.lib.uts.edu.au:10453/187555