{"id":{"repo_id":"uts","oai_identifier":"oai:opus.lib.uts.edu.au:10453/187555"},"canonical_url":"https://search.dev.ndltd.org/etd/uts/oai:opus.lib.uts.edu.au:10453/187555","repository":{"repo_id":"uts","name":"University of Technology Sydney","base_url":"https://opus.lib.uts.edu.au/oai/request"},"display":{"title":"Contributions to Bayesian inference via spectral methods","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Goodwin, Thomas"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024","date_published":"2024","updated_at":"2026-07-24T06:32:35Z","subjects":[],"languages":["en_US"],"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"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10453/187555","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Goodwin, Thomas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-05-29T03:26:21Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-05-29T03:26:21Z"]},{"key":"dc:date.issued","label":"Date","values":["2024"]},{"key":"dc:relation","label":"Dc Relation","values":["https://opus.lib.uts.edu.au/bitstream/10453/187555/1/thesis.pdf"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["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"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10453/187555"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["University of Technology Sydney. Faculty of Science."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format","label":"Dc Format","values":["Thesis (PhD)"]},{"key":"dc:title","label":"Title","values":["Contributions to Bayesian inference via spectral methods"]}]}],"canonical_facts":{"dc:creator":["Goodwin, Thomas"],"dc:date.accessioned":["2025-05-29T03:26:21Z"],"dc:date.available":["2025-05-29T03:26:21Z"],"dc:date.issued":["2024"],"dc:description":["University of Technology Sydney. Faculty of Science."],"dc:description.abstract":["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."],"dc:format":["Thesis (PhD)"],"dc:identifier.uri":["http://hdl.handle.net/10453/187555"],"dc:language.iso":["en_US"],"dc:relation":["https://opus.lib.uts.edu.au/bitstream/10453/187555/1/thesis.pdf"],"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"],"dc:title":["Contributions to Bayesian inference via spectral methods"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T06:32:35Z"}