---
references:
- id: BhadraDefault2016
  accessed:
    - year: 2022
      month: 10
      day: 24
  author:
    - family: Bhadra
      given: Anindya
    - family: Datta
      given: Jyotishka
    - family: Polson
      given: Nicholas G.
    - family: Willard
      given: Brandon
  citation-key: BhadraDefault2016
  container-title: Biometrika
  container-title-short: Biometrika
  ISSN: 0006-3444
  issue: '4'
  issued:
    - year: 2016
  page: 955-969
  publisher: '[Oxford University Press, Biometrika Trust]'
  title: Default Bayesian analysis with global-local shrinkage priors
  type: article-journal
  URL: https://www.jstor.org/stable/26363497
  volume: '103'

- id: BondellConsistent2012
  accessed:
    - year: 2019
      month: 10
      day: 15
  author:
    - family: Bondell
      given: Howard D.
    - family: Reich
      given: Brian J.
  citation-key: BondellConsistent2012
  container-title: Journal of the American Statistical Association
  DOI: 10.1080/01621459.2012.716344
  ISSN: 0162-1459
  issue: '500'
  issued:
    - year: 2012
      month: 12
      day: 1
  page: 1610-1624
  PMID: '23482517'
  title: >-
    Consistent High-Dimensional Bayesian Variable Selection via Penalized
    Credible Regions
  type: article-journal
  volume: '107'

- id: BurknerApproximate2020
  accessed:
    - year: 2021
      month: 11
      day: 12
  author:
    - family: Bürkner
      given: Paul-Christian
    - family: Gabry
      given: Jonah
    - family: Vehtari
      given: Aki
  citation-key: BurknerApproximate2020
  container-title: Journal of Statistical Computation and Simulation
  container-title-short: 'null'
  DOI: 10.1080/00949655.2020.1783262
  ISSN: 0094-9655
  issue: '14'
  issued:
    - year: 2020
      month: 9
      day: 21
  page: 2499-2523
  publisher: Taylor & Francis
  title: >-
    Approximate leave-future-out cross-validation for Bayesian time series
    models
  type: article-journal
  volume: '90'

- id: CarvalhoHorseshoe2010
  accessed:
    - year: 2019
      month: 1
      day: 7
  author:
    - family: Carvalho
      given: Carlos M.
    - family: Polson
      given: Nicholas G.
    - family: Scott
      given: James G.
  citation-key: CarvalhoHorseshoe2010
  container-title: Biometrika
  container-title-short: Biometrika
  DOI: 10.1093/biomet/asq017
  ISSN: 0006-3444
  issue: '2'
  issued:
    - year: 2010
      month: 6
      day: 1
  language: en
  page: 465-480
  title: The horseshoe estimator for sparse signals
  type: article-journal
  volume: '97'

- id: CastilloBayesian2015
  accessed:
    - year: 2023
      month: 8
      day: 29
  author:
    - family: Castillo
      given: Ismaël
    - family: Schmidt-Hieber
      given: Johannes
    - family: Vaart
      given: Aad
      non-dropping-particle: van der
  citation-key: CastilloBayesian2015
  container-title: The Annals of Statistics
  container-title-short: Ann. Statist.
  DOI: 10.1214/15-AOS1334
  ISSN: 0090-5364
  issue: '5'
  issued:
    - year: 2015
      month: 10
      day: 1
  title: Bayesian linear regression with sparse priors
  type: article-journal
  URL: http://arxiv.org/abs/1403.0735
  volume: '43'

- id: ChipmanPractical2001
  accessed:
    - year: 2017
      month: 8
      day: 20
  author:
    - family: Chipman
      given: Hugh
    - family: George
      given: Edward I.
    - family: McCulloch
      given: Robert E.
    - family: Lahiri
      given: P
  citation-key: ChipmanPractical2001
  collection-title: IMS Lecture Notes - Monograph Series
  container-title: Model selection
  DOI: 10.1214/lnms/1215540964
  event-place: Beachwood, OH
  ISBN: 978-0-940600-52-2
  issued:
    - year: 2001
  publisher: Institute of Mathematical Statistics
  publisher-place: Beachwood, OH
  title: The Practical Implementation of Bayesian Model Selection
  type: chapter
  URL: >-
    http://www.rob-mcculloch.org/some_papers_and_talks/papers/published/IMSpaper3-31-01.pdf
  volume: '38'

- id: ClaeskensModel2008
  author:
    - family: Claeskens
      given: Gerda
    - family: Hjort
      given: Nils Lid
  call-number: QA276.18 .C53 2008
  citation-key: ClaeskensModel2008
  collection-title: Cambridge series in statistical and probabilistic mathematics
  event-place: Cambridge ; New York
  ISBN: 978-0-521-85225-8
  issued:
    - year: 2008
  number-of-pages: '312'
  publisher: Cambridge University Press
  publisher-place: Cambridge ; New York
  title: Model selection and model averaging
  type: book

- id: EfronBayesian2012
  accessed:
    - year: 2015
      month: 6
      day: 24
  author:
    - family: Efron
      given: Bradley
  citation-key: EfronBayesian2012
  container-title: The Annals of Applied Statistics
  container-title-short: Ann. Appl. Stat.
  DOI: 10.1214/12-AOAS571
  ISSN: 1932-6157, 1941-7330
  issue: '4'
  issued:
    - year: 2012
      month: 12
  language: EN
  page: 1971-1997
  title: Bayesian inference and the parametric bootstrap
  type: article-journal
  volume: '6'

- id: FilipponeEnabling2015
  accessed:
    - year: 2022
      month: 10
      day: 21
  author:
    - family: Filippone
      given: Maurizio
    - family: Engler
      given: Raphael
  citation-key: FilipponeEnabling2015
  container-title: Proceedings of the 32nd International Conference on Machine Learning
  DOI: 10.48550/arXiv.1501.05427
  event-title: International Conference on Machine Learning
  ISSN: 1938-7228
  issued:
    - year: 2015
      month: 6
      day: 1
  language: en
  page: 1015-1024
  publisher: PMLR
  title: >-
    Enabling scalable stochastic gradient-based inference for Gaussian processes
    by employing the Unbiased LInear System SolvEr (ULISSE)
  type: paper-conference
  URL: https://arxiv.org/abs/1501.05427v4

- id: FongMarginal2019
  accessed:
    - year: 2019
      month: 7
      day: 22
  author:
    - family: Fong
      given: Edwin
    - family: Holmes
      given: Chris
  citation-key: FongMarginal2019
  container-title: arXiv:1905.08737 [stat]
  issued:
    - year: 2019
      month: 5
      day: 21
  publisher: Oxford Academic
  title: On the marginal likelihood and cross-validation
  type: article-journal
  URL: http://arxiv.org/abs/1905.08737

- id: GelmanAvoiding1995
  accessed:
    - year: 2019
      month: 8
      day: 12
  archive: JSTOR
  author:
    - family: Gelman
      given: Andrew
    - family: Rubin
      given: Donald B.
  citation-key: GelmanAvoiding1995
  container-title: Sociological Methodology
  DOI: 10.2307/271064
  ISSN: 0081-1750
  issued:
    - year: 1995
  page: 165-173
  title: Avoiding Model Selection in Bayesian Social Research
  type: article-journal
  URL: http://www.stat.columbia.edu/%7Egelman/research/published/avoiding.pdf
  volume: '25'

- id: GeorgeApproaches1997
  accessed:
    - year: 2019
      month: 1
      day: 7
  author:
    - family: George
      given: Edward I.
    - family: McCulloch
      given: Robert
  citation-key: GeorgeApproaches1997
  container-title: Statistica Sinica
  ISSN: 1017-0405
  issue: '2'
  issued:
    - year: 1997
      month: 4
  language: English (US)
  page: 339-373
  title: Approaches for bayesian variable selection
  type: article-journal
  URL: >-
    http://www.rob-mcculloch.org/some_papers_and_talks/papers/published/fastN96.pdf
  volume: '7'

- id: HirshSparsifying2022
  accessed:
    - year: 2023
      month: 3
      day: 14
  author:
    - family: Hirsh
      given: Seth M.
    - family: Barajas-Solano
      given: David A.
    - family: Kutz
      given: J. Nathan
  citation-key: HirshSparsifying2022
  container-title: Royal Society Open Science
  DOI: 10.1098/rsos.211823
  issue: '2'
  issued:
    - year: 2022
      month: 2
      day: 23
  page: '211823'
  publisher: Royal Society
  title: >-
    Sparsifying priors for Bayesian uncertainty quantification in model
    discovery
  type: article-journal
  volume: '9'

- id: IshwaranSpike2005
  accessed:
    - year: 2018
      month: 12
      day: 14
  author:
    - family: Ishwaran
      given: Hemant
    - family: Rao
      given: J. Sunil
  citation-key: IshwaranSpike2005
  container-title: The Annals of Statistics
  DOI: 10.1214/009053604000001147
  ISSN: 0090-5364
  issue: '2'
  issued:
    - year: 2005
      month: 4
  language: en
  page: 730-773
  title: 'Spike and slab variable selection: Frequentist and Bayesian strategies'
  type: article-journal
  URL: http://arxiv.org/abs/math/0505633
  volume: '33'

- id: KadaneMethods2004
  accessed:
    - year: 2017
      month: 8
      day: 20
  author:
    - family: Kadane
      given: Joseph B.
    - family: Lazar
      given: Nicole A.
  citation-key: KadaneMethods2004
  container-title: Journal of the American statistical Association
  DOI: 10.1198/016214504000000269
  ISSN: 0162-1459
  issue: '465'
  issued:
    - year: 2004
  page: 279–290
  title: Methods and criteria for model selection
  type: article-journal
  URL: http://repository.cmu.edu/statistics/202
  volume: '99'

- id: LaudPredictive1995
  accessed:
    - year: 2022
      month: 12
      day: 21
  author:
    - family: Laud
      given: Purushottam W.
    - family: Ibrahim
      given: Joseph G.
  citation-key: LaudPredictive1995
  container-title: Journal of the Royal Statistical Society. Series B (Methodological)
  ISSN: 0035-9246
  issue: '1'
  issued:
    - year: 1995
  page: 247-262
  publisher: '[Royal Statistical Society, Wiley]'
  title: Predictive Model Selection
  type: article-journal
  URL: https://www.jstor.org/stable/2346098
  volume: '57'

- id: LiFramework2016
  author:
    - family: Li
      given: Meng
    - family: Dunson
      given: David B.
  citation-key: LiFramework2016
  container-title: arXiv:1611.01241 [stat]
  issued:
    - year: 2016
      month: 11
      day: 3
  title: A framework for probabilistic inferences from imperfect models
  type: article-journal
  URL: http://arxiv.org/abs/1611.01241

- id: LorchDiBS2021
  accessed:
    - year: 2021
      month: 12
      day: 15
  author:
    - family: Lorch
      given: Lars
    - family: Rothfuss
      given: Jonas
    - family: Schölkopf
      given: Bernhard
    - family: Krause
      given: Andreas
  citation-key: LorchDiBS2021
  event-title: Thirty-Fifth Conference on Neural Information Processing Systems
  issued:
    - year: 2021
      month: 5
      day: 21
  language: en
  title: 'DiBS: Differentiable Bayesian Structure Learning'
  type: paper-conference
  URL: https://openreview.net/forum?id=YqYt54gU-XV

- id: MacKayComparison1999
  accessed:
    - year: 2014
      month: 12
      day: 19
  author:
    - family: MacKay
      given: David JC
  citation-key: MacKayComparison1999
  container-title: Neural computation
  DOI: 10.1162/089976699300016331
  ISSN: 0899-7667
  issue: '5'
  issued:
    - year: 1999
  page: 1035–1068
  title: Comparison of approximate methods for handling hyperparameters
  type: article-journal
  URL: http://www.mitpressjournals.org/doi/abs/10.1162/089976699300016331
  volume: '11'

- id: MackayProbable1995
  accessed:
    - year: 2017
      month: 10
      day: 3
  author:
    - family: Mackay
      given: David J. C.
  citation-key: MackayProbable1995
  container-title: 'Network: Computation in Neural Systems'
  DOI: 10.1088/0954-898X_6_3_011
  ISSN: 0954-898X
  issue: '3'
  issued:
    - year: 1995
      month: 1
      day: 1
  page: 469-505
  title: >-
    Probable networks and plausible predictions — a review of practical Bayesian
    methods for supervised neural networks
  type: article-journal
  volume: '6'

- id: MadiganModel1994
  accessed:
    - year: 2019
      month: 1
      day: 7
  author:
    - family: Madigan
      given: David
    - family: Raftery
      given: Adrian E.
  citation-key: MadiganModel1994
  container-title: Journal of the American Statistical Association
  container-title-short: Journal of the American Statistical Association
  DOI: 10.1080/01621459.1994.10476894
  ISSN: 0162-1459
  issue: '428'
  issued:
    - year: 1994
      month: 12
      day: 1
  page: 1535-1546
  title: >-
    Model Selection and Accounting for Model Uncertainty in Graphical Models
    Using Occam's Window
  type: article-journal
  volume: '89'

- id: NavarroDevil2019
  accessed:
    - year: 2020
      month: 9
      day: 30
  author:
    - family: Navarro
      given: Danielle J.
  citation-key: NavarroDevil2019
  container-title: Computational Brain & Behavior
  container-title-short: Comput Brain Behav
  DOI: 10.1007/s42113-018-0019-z
  ISSN: 2522-087X
  issue: '1'
  issued:
    - year: 2019
      month: 3
      day: 1
  language: en
  page: 28-34
  title: >-
    Between the Devil and the Deep Blue Sea: Tensions Between Scientific
    Judgement and Statistical Model Selection
  type: article-journal
  volume: '2'

- id: OhnAdaptive2021
  accessed:
    - year: 2021
      month: 11
      day: 17
  author:
    - family: Ohn
      given: Ilsang
    - family: Lin
      given: Lizhen
  citation-key: OhnAdaptive2021
  container-title: arXiv:2109.03204 [math, stat]
  issued:
    - year: 2021
      month: 9
      day: 7
  title: 'Adaptive variational Bayes: Optimality, computation and applications'
  type: article-journal
  URL: http://arxiv.org/abs/2109.03204

- id: OhnPosterior2021
  accessed:
    - year: 2021
      month: 11
      day: 9
  author:
    - family: Ohn
      given: Ilsang
    - family: Kim
      given: Yongdai
  citation-key: OhnPosterior2021
  container-title: Bayesian Analysis
  container-title-short: Bayesian Anal.
  DOI: 10.1214/21-BA1261
  ISSN: 1936-0975
  issued:
    - year: 2021
      month: 1
      day: 1
  language: en
  title: >-
    Posterior Consistency of Factor Dimensionality in High-Dimensional Sparse
    Factor Models
  type: article-journal

- id: OrmerodBayesian2017
  accessed:
    - year: 2018
      month: 11
      day: 28
  author:
    - family: Ormerod
      given: John T.
    - family: Stewart
      given: Michael
    - family: Yu
      given: Weichang
    - family: Romanes
      given: Sarah E.
  citation-key: OrmerodBayesian2017
  container-title: arXiv:1710.09146 [math, stat]
  issued:
    - year: 2017
      month: 10
      day: 25
  title: >-
    Bayesian hypothesis tests with diffuse priors: Can we have our cake and eat
    it too?
  type: article-journal
  URL: http://arxiv.org/abs/1710.09146

- id: PiironenComparison2017
  author:
    - family: Piironen
      given: Juho
    - family: Vehtari
      given: Aki
  citation-key: PiironenComparison2017
  container-title: Statistics and Computing
  container-title-short: Stat Comput
  DOI: 10.1007/s11222-016-9649-y
  ISSN: 0960-3174, 1573-1375
  issue: '3'
  issued:
    - year: 2017
      month: 5
      day: 1
  language: en
  page: 711-735
  title: Comparison of Bayesian predictive methods for model selection
  type: article-journal
  volume: '27'

- id: PolsonLocal2012
  accessed:
    - year: 2022
      month: 10
      day: 24
  author:
    - family: Polson
      given: Nicholas G.
    - family: Scott
      given: James G.
  citation-key: PolsonLocal2012
  container-title: 'Journal of the Royal Statistical Society: Series B (Statistical Methodology)'
  DOI: 10.1111/j.1467-9868.2011.01015.x
  ISSN: 1467-9868
  issue: '2'
  issued:
    - year: 2012
  language: en
  page: 287-311
  title: Local shrinkage rules, Lévy processes and regularized regression
  type: article-journal
  URL: http://arxiv.org/abs/1010.3390
  volume: '74'

- id: RafteryBayesian1995
  accessed:
    - year: 2019
      month: 8
      day: 12
  archive: JSTOR
  author:
    - family: Raftery
      given: Adrian E.
  citation-key: RafteryBayesian1995
  container-title: Sociological Methodology
  DOI: 10.2307/271063
  ISSN: 0081-1750
  issued:
    - year: 1995
  page: 111-163
  title: Bayesian Model Selection in Social Research
  type: article-journal
  URL: https://glandfried.github.io/files/posts/bic.pdf
  volume: '25'

- id: RockovaSpikeandSlab2018
  accessed:
    - year: 2018
      month: 12
      day: 14
  author:
    - family: Ročková
      given: Veronika
    - family: George
      given: Edward I.
  citation-key: RockovaSpikeandSlab2018
  container-title: Journal of the American Statistical Association
  container-title-short: Journal of the American Statistical Association
  DOI: 10.1080/01621459.2016.1260469
  ISSN: 0162-1459
  issue: '521'
  issued:
    - year: 2018
      month: 1
      day: 2
  page: 431-444
  title: The Spike-and-Slab LASSO
  type: article-journal
  volume: '113'

- id: SchmidtLogScale2020
  accessed:
    - year: 2022
      month: 10
      day: 24
  author:
    - family: Schmidt
      given: Daniel F.
    - family: Makalic
      given: Enes
  citation-key: SchmidtLogScale2020
  DOI: 10.48550/arXiv.1801.02321
  issued:
    - year: 2020
      month: 1
      day: 30
  number: arXiv:1801.02321
  publisher: arXiv
  title: >-
    Log-Scale Shrinkage Priors and Adaptive Bayesian Global-Local Shrinkage
    Estimation
  type: article
  URL: http://arxiv.org/abs/1801.02321

- id: SimchoniIntegrating2023
  accessed:
    - year: 2023
      month: 8
      day: 29
  author:
    - family: Simchoni
      given: Giora
    - family: Rosset
      given: Saharon
  citation-key: SimchoniIntegrating2023
  DOI: 10.48550/arXiv.2206.03314
  issued:
    - year: 2023
      month: 1
      day: 27
  number: arXiv:2206.03314
  publisher: arXiv
  title: Integrating Random Effects in Deep Neural Networks
  type: article
  URL: http://arxiv.org/abs/2206.03314

- id: SteinModeling2008
  accessed:
    - year: 2017
      month: 10
      day: 3
  author:
    - family: Stein
      given: Michael L.
  citation-key: SteinModeling2008
  container-title: Journal of the Korean Statistical Society
  container-title-short: Journal of the Korean Statistical Society
  DOI: 10.1016/j.jkss.2007.09.001
  ISSN: 1226-3192
  issue: '1'
  issued:
    - year: 2008
      month: 3
      day: 1
  page: 3-10
  title: A modeling approach for large spatial datasets
  type: article-journal
  volume: '37'

- id: TangBayesian2016
  accessed:
    - year: 2022
      month: 10
      day: 24
  author:
    - family: Tang
      given: Xueying
    - family: Xu
      given: Xiaofan
    - family: Ghosh
      given: Malay
    - family: Ghosh
      given: Prasenjit
  citation-key: TangBayesian2016
  DOI: 10.48550/arXiv.1605.07981
  issued:
    - year: 2016
      month: 5
      day: 25
  number: arXiv:1605.07981
  publisher: arXiv
  title: >-
    Bayesian Variable Selection and Estimation Based on Global-Local Shrinkage
    Priors
  type: article
  URL: http://arxiv.org/abs/1605.07981

- id: vanderLindenNo2017
  accessed:
    - year: 2019
      month: 8
      day: 12
  author:
    - family: Linden
      given: Sander
      non-dropping-particle: van der
    - family: Chryst
      given: Breanne
  citation-key: vanderLindenNo2017
  container-title: Frontiers in Applied Mathematics and Statistics
  container-title-short: Front. Appl. Math. Stat.
  DOI: 10.3389/fams.2017.00012
  ISSN: 2297-4687
  issued:
    - year: 2017
  language: English
  title: 'No Need for Bayes Factors: A Fully Bayesian Evidence Synthesis'
  type: article-journal
  volume: '3'

- id: vanWieringenLecture2021
  accessed:
    - year: 2022
      month: 2
      day: 15
  author:
    - family: Wieringen
      given: Wessel N.
      non-dropping-particle: van
  citation-key: vanWieringenLecture2021
  container-title: arXiv:1509.09169 [stat]
  issued:
    - year: 2021
      month: 5
      day: 31
  language: en
  title: Lecture notes on ridge regression
  type: article-journal
  URL: http://arxiv.org/abs/1509.09169

- id: VehtariSurvey2012
  author:
    - family: Vehtari
      given: Aki
    - family: Ojanen
      given: Janne
  citation-key: VehtariSurvey2012
  container-title: Statistics Surveys
  container-title-short: Statist. Surv.
  DOI: 10.1214/12-SS102
  ISSN: 1935-7516
  issued:
    - year: 2012
  language: EN
  page: 142-228
  title: >-
    A survey of Bayesian predictive methods for model assessment, selection and
    comparison
  type: article-journal
  volume: '6'

- id: XuBayesian2017
  accessed:
    - year: 2022
      month: 10
      day: 24
  author:
    - family: Xu
      given: Zemei
    - family: Schmidt
      given: Daniel F.
    - family: Makalic
      given: Enes
    - family: Qian
      given: Guoqi
    - family: Hopper
      given: John L.
  citation-key: XuBayesian2017
  DOI: 10.48550/arXiv.1709.04333
  issued:
    - year: 2017
      month: 11
      day: 3
  number: arXiv:1709.04333
  publisher: arXiv
  title: >-
    Bayesian Sparse Global-Local Shrinkage Regression for Selection of Grouped
    Variables
  type: article
  URL: http://arxiv.org/abs/1709.04333

- id: ZanellaScalable2019
  accessed:
    - year: 2023
      month: 8
      day: 29
  author:
    - family: Zanella
      given: Giacomo
    - family: Roberts
      given: Gareth
  citation-key: ZanellaScalable2019
  container-title: 'Journal of the Royal Statistical Society Series B: Statistical Methodology'
  DOI: 10.1111/rssb.12316
  ISSN: 1369-7412, 1467-9868
  issue: '3'
  issued:
    - year: 2019
      month: 7
      day: 1
  page: 489-517
  title: Scalable Importance Tempering and Bayesian Variable Selection
  type: article-journal
  URL: http://arxiv.org/abs/1805.00541
  volume: '81'
...
