---
references:
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    - year: 2020
      month: 11
      day: 25
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  citation-key: AdamsBayesian2007
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      month: 10
      day: 19
  title: Bayesian Online Changepoint Detection
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- id: AlvaradoEfficient2018
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  issued:
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      month: 11
      day: 16
  title: >-
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- id: AlvaradoSparse2019
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- id: BertolacciAdaptSPECX2020
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- id: BertolacciClimate2019
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  language: EN
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  publisher: Institute of Mathematical Statistics
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- id: BertolacciHierarchical2019
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      given: Michael
  citation-key: BertolacciHierarchical2019
  issued:
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  language: en
  title: >-
    Hierarchical Bayesian mixture models for spatiotemporal data with
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- id: BruinsmaLearning2018
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- id: CemgilBayesian2009
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  container-title: Computational Intelligence and Neuroscience
  DOI: 10.1155/2009/785152
  issued:
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  language: en
  PMID: '19536273'
  title: Bayesian Inference for Nonnegative Matrix Factorisation Models
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- id: ChengTime2015
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      month: 11
      day: 25
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- id: ChoudhuriBayesian2004
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      month: 10
      day: 26
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    - family: Roy
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  DOI: 10.1198/016214504000000557
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      month: 12
      day: 1
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  publisher: Taylor & Francis
  title: Bayesian Estimation of the Spectral Density of a Time Series
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- id: ChoudhuriContiguity2004
  accessed:
    - year: 2021
      month: 12
      day: 8
  author:
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      given: Nidhan
    - family: Ghosal
      given: Subhashis
    - family: Roy
      given: Anindya
  citation-key: ChoudhuriContiguity2004
  container-title: Biometrika
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      month: 3
      day: 1
  language: en
  page: 211-218
  publisher: Oxford Academic
  title: Contiguity of the Whittle measure for a Gaussian time series
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- id: CunninghamFast2008
  accessed:
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      month: 2
      day: 24
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    - family: Shenoy
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    - family: Sahani
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  citation-key: CunninghamFast2008
  collection-title: ICML '08
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  language: en
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  publisher: ACM Press
  publisher-place: New York, NY, USA
  title: Fast gaussian process methods for point process intensity estimation
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- id: CurtainInfiniteDimensional1975
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      month: 9
      day: 7
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      month: 1
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  publisher: Society for Industrial and Applied Mathematics
  title: Infinite-Dimensional Filtering
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- id: DuvenaudAdditive2011
  author:
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      given: David K.
    - family: Nickisch
      given: Hannes
    - family: Rasmussen
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  citation-key: DuvenaudAdditive2011
  container-title: Advances in neural information processing systems
  issued:
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  page: 226–234
  title: Additive gaussian processes
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- id: DymGaussian2008
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      given: H.
    - family: McKean
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  collection-title: Dover books on mathematics
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  ISBN: 978-0-486-46279-0
  issued:
    - year: 2008
  number-of-pages: '333'
  publisher: Dover Publications
  publisher-place: Mineola, N.Y
  title: Gaussian processes, function theory, and the inverse spectral problem
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- id: EdwardsBayesian2015
  accessed:
    - year: 2021
      month: 7
      day: 6
  author:
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      given: Matthew C.
    - family: Meyer
      given: Renate
    - family: Christensen
      given: Nelson
  citation-key: EdwardsBayesian2015
  DOI: 10.1103/PhysRevD.92.064011
  issued:
    - year: 2015
      month: 5
      day: 31
  language: en
  title: >-
    Bayesian semiparametric power spectral density estimation with applications
    in gravitational wave data analysis
  type: article-journal
  URL: https://arxiv.org/abs/1506.00185v2

- id: EdwardsBayesian2019
  accessed:
    - year: 2020
      month: 11
      day: 25
  author:
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      given: Matthew C.
    - family: Meyer
      given: Renate
    - family: Christensen
      given: Nelson
  citation-key: EdwardsBayesian2019
  container-title: Statistics and Computing
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  ISSN: 1573-1375
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      month: 1
      day: 1
  language: en
  page: 67-78
  title: Bayesian nonparametric spectral density estimation using B-spline priors
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  volume: '29'

- id: FevotteNonnegative2008
  accessed:
    - year: 2015
      month: 5
      day: 31
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      given: Cédric
    - family: Bertin
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    - family: Durrieu
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  citation-key: FevotteNonnegative2008
  container-title: Neural Computation
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  ISSN: 0899-7667
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  issued:
    - year: 2008
      month: 9
      day: 11
  page: 793-830
  title: >-
    Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With
    Application to Music Analysis
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  volume: '21'

- id: GirolamiHierarchic2005
  accessed:
    - year: 2019
      month: 10
      day: 4
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      given: Mark
    - family: Rogers
      given: Simon
  citation-key: GirolamiHierarchic2005
  container-title: >-
    Proceedings of the 22nd international conference on Machine learning  - ICML
    '05
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  event-place: Bonn, Germany
  event-title: the 22nd international conference
  ISBN: 978-1-59593-180-1
  issued:
    - year: 2005
  language: en
  page: 241-248
  publisher: ACM Press
  publisher-place: Bonn, Germany
  title: Hierarchic Bayesian models for kernel learning
  type: paper-conference
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    https://icml.cc/Conferences/2005/proceedings/papers/031_Hierarchic_GirolamiRogers.pdf

- id: GodsillProbabilistic2005
  author:
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      given: Simon J
    - family: Cemgil
      given: Ali Taylan
  citation-key: GodsillProbabilistic2005
  container-title: 2005 13th European Signal Processing Conference
  event-title: 2005 13th European Signal Processing Conference
  issued:
    - year: 2005
  language: en
  page: '4'
  title: >-
    Probabilistic Phase Vocoder and Its Application to Interpolation of Missing
    Values in Audio Signals
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    https://www.eurasip.org/Proceedings/Eusipco/Eusipco2005/defevent/papers/cr1319.pdf

- id: HartikainenKalman2010
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      given: J.
    - family: Särkkä
      given: S.
  citation-key: HartikainenKalman2010
  container-title: 2010 IEEE International Workshop on Machine Learning for Signal Processing
  DOI: 10.1109/MLSP.2010.5589113
  event-place: Kittila, Finland
  event-title: 2010 IEEE International Workshop on Machine Learning for Signal Processing
  ISBN: 978-1-4244-7875-0
  issued:
    - year: 2010
      month: 8
  page: 379-384
  publisher: IEEE
  publisher-place: Kittila, Finland
  title: >-
    Kalman filtering and smoothing solutions to temporal Gaussian process
    regression models
  type: paper-conference
  URL: https://users.aalto.fi/~ssarkka/pub/gp-ts-kfrts.pdf

- id: HensmanVariational2018
  accessed:
    - year: 2020
      month: 8
      day: 30
  author:
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      given: James
    - family: Durrande
      given: Nicolas
    - family: Solin
      given: Arno
  citation-key: HensmanVariational2018
  container-title: Journal of Machine Learning Research
  ISSN: 1533-7928
  issue: '151'
  issued:
    - year: 2018
  page: 1-52
  title: Variational Fourier Features for Gaussian Processes
  type: article-journal
  URL: http://jmlr.org/papers/v18/16-579.html
  volume: '18'

- id: HermansenBayesian2008
  accessed:
    - year: 2020
      month: 10
      day: 28
  author:
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      given: Gudmund Horn
  citation-key: HermansenBayesian2008
  issued:
    - year: 2008
  language: eng
  title: >-
    Bayesian nonparametric modelling of covariance functions, with application
    to time series and spatial statistics
  type: thesis
  URL: https://www.duo.uio.no/handle/10852/10811

- id: JesusInference2017
  accessed:
    - year: 2020
      month: 10
      day: 28
  author:
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      given: Joao
    - family: Chandler
      given: Richard E.
  citation-key: JesusInference2017
  container-title: Journal of Time Series Analysis
  DOI: 10.1111/jtsa.12225
  ISSN: 1467-9892
  issue: '2'
  issued:
    - year: 2017
  language: en
  page: 204-224
  title: >-
    Inference with the Whittle Likelihood: A Tractable Approach Using Estimating
    Functions
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  volume: '38'

- id: KailathStructure1971
  accessed:
    - year: 2017
      month: 10
      day: 4
  author:
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      given: Thomas
  citation-key: KailathStructure1971
  container-title: The Annals of Mathematical Statistics
  ISSN: 0003-4851
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  page: 1054-1067
  title: >-
    The Structure of Radon-Nikodym Derivatives with Respect to Wiener and
    Related Measures
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- id: KalmanGeneral1959
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    - year: 2014
      month: 7
      day: 19
  author:
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      given: R.
  citation-key: KalmanGeneral1959
  container-title: IRE Transactions on Automatic Control
  DOI: 10.1109/TAC.1959.1104873
  ISSN: 0096-199X
  issue: '3'
  issued:
    - year: 1959
  page: 110–110
  title: On the general theory of control systems
  type: article-journal
  URL: http://www.control.utoronto.ca/~broucke/ece557f/kalman.pdf
  volume: '4'

- id: KalmanNew1960
  accessed:
    - year: 2014
      month: 5
      day: 14
  author:
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      given: R. E.
  citation-key: KalmanNew1960
  container-title: Journal of Basic Engineering
  DOI: 10.1115/1.3662552
  ISSN: '00219223'
  issue: '1'
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    - year: 1960
  language: en
  page: '35'
  title: A New Approach to Linear Filtering and Prediction Problems
  type: article-journal
  URL: >-
    http://FluidsEngineering.asmedigitalcollection.asme.org/article.aspx?articleid=1430402
  volume: '82'

- id: KarvonenApproximate2016
  accessed:
    - year: 2019
      month: 7
      day: 30
  author:
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      given: Toni
    - family: Särkkä
      given: Simo
  citation-key: KarvonenApproximate2016
  container-title: >-
    2016 IEEE 26th International Workshop on Machine Learning for Signal
    Processing (MLSP)
  DOI: 10.1109/MLSP.2016.7738812
  event-place: Vietri sul Mare, Salerno, Italy
  event-title: >-
    2016 IEEE 26th International Workshop on Machine Learning for Signal
    Processing (MLSP)
  ISBN: 978-1-5090-0746-2
  issued:
    - year: 2016
      month: 9
  language: en
  page: 1-6
  publisher: IEEE
  publisher-place: Vietri sul Mare, Salerno, Italy
  title: Approximate state-space Gaussian processes via spectral transformation
  type: paper-conference
  URL: https://users.aalto.fi/~karvont2/pdf/KarvonenSarkka2016-MLSP.pdf

- id: KirchWhittle2019
  accessed:
    - year: 2020
      month: 10
      day: 26
  author:
    - family: Kirch
      given: Claudia
    - family: Edwards
      given: Matthew C.
    - family: Meier
      given: Alexander
    - family: Meyer
      given: Renate
  citation-key: KirchWhittle2019
  container-title: Bayesian Analysis
  container-title-short: Bayesian Anal.
  DOI: 10.1214/18-BA1126
  ISSN: 1936-0975, 1931-6690
  issue: '4'
  issued:
    - year: 2019
      month: 12
  language: EN
  page: 1037-1073
  publisher: International Society for Bayesian Analysis
  title: >-
    Beyond Whittle: Nonparametric Correction of a Parametric Likelihood with a
    Focus on Bayesian Time Series Analysis
  type: article-journal
  URL: http://arxiv.org/abs/1701.04846
  volume: '14'

- id: LindgrenExplicit2011
  accessed:
    - year: 2019
      month: 7
      day: 30
  author:
    - family: Lindgren
      given: Finn
    - family: Rue
      given: Håvard
    - family: Lindström
      given: Johan
  citation-key: LindgrenExplicit2011
  container-title: 'Journal of the Royal Statistical Society: Series B (Statistical Methodology)'
  container-title-short: 'Journal of the Royal Statistical Society: Series B (Statistical Methodology)'
  DOI: 10.1111/j.1467-9868.2011.00777.x
  ISSN: 1369-7412
  issue: '4'
  issued:
    - year: 2011
      month: 9
      day: 1
  page: 423-498
  title: >-
    An explicit link between Gaussian fields and Gaussian Markov random fields:
    the stochastic partial differential equation approach
  type: article-journal
  volume: '73'

- id: LiutkusGaussian2011
  author:
    - family: Liutkus
      given: Antoine
    - family: Badeau
      given: Roland
    - family: Richard
      given: Gäel
  citation-key: LiutkusGaussian2011
  container-title: IEEE Transactions on Signal Processing
  DOI: 10.1109/TSP.2011.2119315
  ISSN: 1053-587X, 1941-0476
  issue: '7'
  issued:
    - year: 2011
      month: 7
  number: '7'
  page: 3155-3167
  title: Gaussian Processes for Underdetermined Source Separation
  type: article-journal
  URL: https://hal.archives-ouvertes.fr/hal-00643951
  volume: '59'

- id: LiutkusKernel2014
  accessed:
    - year: 2016
      month: 6
      day: 16
  author:
    - family: Liutkus
      given: Antoine
    - family: Rafii
      given: Zafar
    - family: Pardo
      given: Bryan
    - family: Fitzgerald
      given: Derry
    - family: Daudet
      given: Laurent
  citation-key: LiutkusKernel2014
  DOI: 10.1109/HSCMA.2014.6843240
  ISBN: 978-1-4799-3109-5
  issued:
    - year: 2014
      month: 5
  page: 6-10
  publisher: IEEE
  title: Kernel spectrogram models for source separation
  type: paper-conference

- id: MacaroSpectral2014
  accessed:
    - year: 2020
      month: 10
      day: 28
  author:
    - family: Macaro
      given: Christian
    - family: Prado
      given: Raquel
  citation-key: MacaroSpectral2014
  container-title: Psychometrika
  container-title-short: Psychometrika
  DOI: 10.1007/s11336-013-9354-0
  ISSN: 0033-3123
  issue: '1'
  issued:
    - year: 2014
  page: 105-129
  PMCID: PMC3925306
  PMID: '24154824'
  title: >-
    Spectral Decompositions of Multiple Time Series: A Bayesian Non-parametric
    Approach
  type: article-journal
  URL: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3925306/
  volume: '79'

- id: MeierBayesian2020
  accessed:
    - year: 2020
      month: 10
      day: 26
  author:
    - family: Meier
      given: Alexander
    - family: Kirch
      given: Claudia
    - family: Meyer
      given: Renate
  citation-key: MeierBayesian2020
  container-title: Journal of Multivariate Analysis
  container-title-short: Journal of Multivariate Analysis
  DOI: 10.1016/j.jmva.2019.104560
  ISSN: 0047-259X
  issued:
    - year: 2020
      month: 1
      day: 1
  language: en
  page: '104560'
  title: >-
    Bayesian nonparametric analysis of multivariate time series: A matrix Gamma
    Process approach
  type: article-journal
  URL: http://arxiv.org/abs/1811.10292
  volume: '175'

- id: MeyerComputational2020
  accessed:
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      month: 7
      day: 6
  author:
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      given: Renate
    - family: Edwards
      given: Matthew C.
    - family: Maturana-Russel
      given: Patricio
    - family: Christensen
      given: Nelson
  citation-key: MeyerComputational2020
  container-title: WIREs Computational Statistics
  DOI: 10.1002/wics.1532
  ISSN: 1939-0068
  issue: n/a
  issued:
    - year: 2020
      month: 9
      day: 22
  language: en
  page: e1532
  title: >-
    Computational techniques for parameter estimation of gravitational wave
    signals
  type: article-journal
  URL: https://arxiv.org/abs/2009.10316v1
  volume: n/a

- id: NickischState2018
  accessed:
    - year: 2019
      month: 9
      day: 17
  author:
    - family: Nickisch
      given: Hannes
    - family: Solin
      given: Arno
    - family: Grigorevskiy
      given: Alexander
  citation-key: NickischState2018
  container-title: International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  issued:
    - year: 2018
      month: 7
      day: 3
  language: en
  page: 3789-3798
  title: State Space Gaussian Processes with Non-Gaussian Likelihood
  type: paper-conference
  URL: http://proceedings.mlr.press/v80/nickisch18a.html

- id: OsborneBayesian2010
  accessed:
    - year: 2020
      month: 11
      day: 25
  author:
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      given: Michael A.
  citation-key: OsborneBayesian2010
  genre: http://purl.org/dc/dcmitype/Text
  issued:
    - year: 2010
  language: en
  publisher: Oxford University, UK
  title: >-
    Bayesian Gaussian processes for sequential prediction, optimisation and
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- id: RemesNonStationary2017
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- id: SarkkaApplied2019
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- id: SarkkaNonlinear2013
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...
