@article{einstein,
author =       "Albert Einstein",
title =        "{Zur Elektrodynamik bewegter Körper}",
journal =      "Annalen der Physik",
volume =       "322",
number =       "10",
pages =        "891--921",
year =         "1905"}

@book{latexcompanion,
author    = "Michel Goossens and Frank Mittelbach and Alexander Samarin",
title     = "The \LaTeX\ Companion",
year      = "1993",
publisher = "Addison-Wesley"}


@article{Best2012OnProperties,
    title = {{On the fundamental dichotomy in the local radio-AGN population: accretion, evolution and host galaxy properties}},
    year = {2012},
    journal = {Monthly Notices of the Royal Astronomical Society},
    author = {Best, P N and Heckman, T M},
    number = {2},
    month = {4},
    pages = {1569--1582},
    volume = {421},
    url = {https://doi.org/10.1111/j.1365-2966.2012.20414.x},
    doi = {10.1111/j.1365-2966.2012.20414.x},
    issn = {0035-8711}
}

@article{Miraghaei2017TheEnvironment,
    title = {{The nuclear properties and extended morphologies of powerful radio galaxies: The roles of host galaxy and environment}},
    year = {2017},
    journal = {Monthly Notices of the Royal Astronomical Society},
    author = {Miraghaei, H. and Best, P. N.},
    number = {4},
    month = {5},
    pages = {4346--4363},
    volume = {466},
    publisher = {Oxford University Press},
    doi = {10.1093/mnras/stx007},
    issn = {13652966},
    arxivId = {1701.00919},
    keywords = {Galaxies: active, Galaxies: interactions, Radio continuum: galaxies}
}

@misc{Porter2020MiraBestDataset,
    title = {{MiraBest Batched Dataset}},
    year = {2020},
    author = {Porter, Fiona Alice May},
    month = {11},
    url = {https://zenodo.org/record/4288837},
    doi = {10.5281/ZENODO.4288837},
    keywords = {Fanaroff, Riley galaxies}
}

@article{fanaroff1974morphology,
  title={The morphology of extragalactic radio sources of high and low luminosity},
  author={Fanaroff, Bernard L and Riley, Julia M},
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  publisher={Oxford University Press Oxford, UK}
}

@article{Aniyan2017ClassifyingNetwork,
    title = {{Classifying Radio Galaxies with the Convolutional Neural Network}},
    year = {2017},
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    author = {Aniyan, A K and Thorat, K},
    number = {2},
    pages = {20},
    volume = {230},
    publisher = {American Astronomical Society},
    url = {http://dx.doi.org/10.3847/1538-4365/aa7333},
    doi = {10.3847/1538-4365/aa7333},
    issn = {1538-4365}
}

@article{tang2019,
    author = {Tang, H and Scaife, A M M and Leahy, J P},
    title = "{Transfer learning for radio galaxy classification}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {488},
    number = {3},
    pages = {3358-3375},
    year = {2019},
    month = {07},
    issn = {0035-8711},
    doi = {10.1093/mnras/stz1883},
    url = {https://doi.org/10.1093/mnras/stz1883},
    eprint = {https://academic.oup.com/mnras/article-pdf/488/3/3358/29025869/stz1883.pdf},
}

@ARTICLE{lukic2019,
       author = {{Lukic}, V. and {Br{\"u}ggen}, M. and {Mingo}, B. and {Croston}, J.~H. and
         {Kasieczka}, G. and {Best}, P.~N.},
        title = "{Morphological classification of radio galaxies: capsule networks versus convolutional neural networks}",
      journal = {Monthly Notices of the Royal Astronomical Society},
     keywords = {instrumentation: miscellaneous, methods: miscellaneous, methods: data analysis, surveys, radio continuum: galaxies, radio continuum: general, Astrophysics - Instrumentation and Methods for Astrophysics},
         year = 2019,
        month = aug,
       volume = {487},
       number = {2},
        pages = {1729-1744},
          doi = {10.1093/mnras/stz1289},
archivePrefix = {arXiv},
       eprint = {1905.03274},
 primaryClass = {astro-ph.IM},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.1729L},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{wu2018,
    author = {Wu, Chen and Wong, Oiwei Ivy and Rudnick, Lawrence and Shabala, Stanislav S and Alger, Matthew J and Banfield, Julie K and Ong, Cheng Soon and White, Sarah V and Garon, Avery F and Norris, Ray P and Andernach, Heinz and Tate, Jean and Lukic, Vesna and Tang, Hongming and Schawinski, Kevin and Diakogiannis, Foivos I},
    title = "{Radio Galaxy Zoo: Claran – a deep learning classifier for radio morphologies}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {482},
    number = {1},
    pages = {1211-1230},
    year = {2018},
    month = {10},
    issn = {0035-8711},
    doi = {10.1093/mnras/sty2646},
    url = {https://doi.org/10.1093/mnras/sty2646},
    eprint = {https://academic.oup.com/mnras/article-pdf/482/1/1211/26205089/sty2646.pdf},
}

@article{alger2018,
    author = {Alger, M J and Banfield, J K and Ong, C S and Rudnick, L and Wong, O I and Wolf, C and Andernach, H and Norris, R P and Shabala, S S},
    title = "{Radio Galaxy Zoo: machine learning for radio source host galaxy cross-identification}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {478},
    number = {4},
    pages = {5547-5563},
    year = {2018},
    month = {05},
    issn = {0035-8711},
    doi = {10.1093/mnras/sty1308},
    url = {https://doi.org/10.1093/mnras/sty1308},
    eprint = {https://academic.oup.com/mnras/article-pdf/478/4/5547/25204505/sty1308.pdf},
}

@article{bowles2021attention,
  title={Attention-gating for improved radio galaxy classification},
  author={Bowles, Micah and Scaife, Anna MM and Porter, Fiona and Tang, Hongming and Bastien, David J},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={501},
  number={3},
  pages={4579--4595},
  year={2021},
  publisher={Oxford University Press}
}

@article{scaife2021fanaroff,
  title={Fanaroff--Riley classification of radio galaxies using group-equivariant convolutional neural networks},
  author={Scaife, Anna MM and Porter, Fiona},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={503},
  number={2},
  pages={2369--2379},
  year={2021},
  publisher={Oxford University Press}
}

@article{bastien2021structured,
  title={Structured variational inference for simulating populations of radio galaxies},
  author={Bastien, David J and Scaife, Anna MM and Tang, Hongming and Bowles, Micah and Porter, Fiona},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={503},
  number={3},
  pages={3351--3370},
  year={2021},
  publisher={Oxford University Press}
}

@inbook{rumelhart1986,
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numpages = {45}
}

@inproceedings{bundell,
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year = {2015},
publisher = {JMLR.org},
booktitle = {Proceedings of the 32nd International Conference on International Conference on Machine Learning - Volume 37},
pages = {1613–1622},
numpages = {10},
location = {Lille, France},
series = {ICML'15}
}



@ARTICLE{vireview,
       author = {{Blei}, David M. and {Kucukelbir}, Alp and {McAuliffe}, Jon D.},
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         year = 2016,
        month = jan,
          eid = {arXiv:1601.00670},
        pages = {arXiv:1601.00670},
archivePrefix = {arXiv},
       eprint = {1601.00670},
 primaryClass = {stat.CO},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2016arXiv160100670B},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@inproceedings{practicalvi,
author = {Graves, Alex},
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year = {2011},
isbn = {9781618395993},
publisher = {Curran Associates Inc.},
address = {Red Hook, NY, USA},
booktitle = {Proceedings of the 24th International Conference on Neural Information Processing Systems},
pages = {2348–2356},
numpages = {9},
location = {Granada, Spain},
series = {NIPS'11}
}
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booktitle = {Proceedings of the Sixth Annual Conference on Computational Learning Theory},
pages = {5–13},
numpages = {9},
location = {Santa Cruz, California, USA},
series = {COLT '93}
}

@ARTICLE{stochasticvi,
       author = {{Hoffman}, Matt and {Blei}, David M. and {Wang}, Chong and {Paisley}, John},
        title = "{Stochastic Variational Inference}",
      journal = {arXiv e-prints},
     keywords = {Statistics - Machine Learning, Computer Science - Artificial Intelligence, Statistics - Computation, Statistics - Methodology},
         year = 2012,
        month = jun,
          eid = {arXiv:1206.7051},
        pages = {arXiv:1206.7051},
archivePrefix = {arXiv},
       eprint = {1206.7051},
 primaryClass = {stat.ML},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2012arXiv1206.7051H},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@inproceedings{tu2016reducing,
  title={Reducing the model order of deep neural networks using information theory},
  author={Tu, Ming and Berisha, Visar and Cao, Yu and Seo, Jae-sun},
  booktitle={2016 IEEE Computer Society Annual Symposium on VLSI (IifeLSI)},
  pages={93--98},
  year={2016},
  organization={IEEE}
}

@ARTICLE{adam,
       author = {{Kingma}, Diederik P. and {Ba}, Jimmy},
        title = "{Adam: A Method for Stochastic Optimization}",
      journal = {arXiv e-prints},
     keywords = {Computer Science - Machine Learning},
         year = 2014,
        month = dec,
          eid = {arXiv:1412.6980},
        pages = {arXiv:1412.6980},
archivePrefix = {arXiv},
       eprint = {1412.6980},
 primaryClass = {cs.LG},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2014arXiv1412.6980K},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@book{Goodfellow-et-al-2016,
    title={Deep Learning},
    author={Ian Goodfellow and Yoshua Bengio and Aaron Courville},
    publisher={MIT Press},
    note={\url{http://www.deeplearningbook.org}},
    year={2016}
}

@misc{lecunmnist,
  title = {MNIST handwritten digit database},
  author = {Yann LeCun and Corinna Cortes},
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  volume={},
  number={},
  pages={},
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}
@article{lecun2015lenet,
  title={LeNet-5, convolutional neural networks},
  author={LeCun, Yann and others},
  journal={URL: http://yann. lecun. com/exdb/lenet},
  volume={20},
  number={5},
  pages={14},
  year={2015}
}

@inproceedings{guo2017calibration,
  title={On calibration of modern neural networks},
  author={Guo, Chuan and Pleiss, Geoff and Sun, Yu and Weinberger, Kilian Q},
  booktitle={International Conference on Machine Learning},
  pages={1321--1330},
  year={2017},
  organization={PMLR}
}


@inproceedings{guo2017, author = {Guo, Chuan and Pleiss, Geoff and Sun, Yu and Weinberger, Kilian Q.}, title = {On Calibration of Modern Neural Networks}, year = {2017}, publisher = {JMLR.org}, abstract = {Confidence calibration - the problem of predicting probability estimates representative of the true correctness likelihood - is important for classification models in many applications. We discover that modern neural networks, unlike those from a decade ago, are poorly calibrated. Through extensive experiments, we observe that depth, width, weight decay, and Batch Normalization are important factors influencing calibration. We evaluate the performance of various post-processing calibration methods on state-of-the-art architectures with image and document classification datasets. Our analysis and experiments not only offer insights into neural network learning, but also provide a simple and straightforward recipe for practical settings: on most datasets, temperature scaling - a single-parameter variant of Platt Scaling - is surprisingly effective at calibrating predictions.}, booktitle = {Proceedings of the 34th International Conference on Machine Learning - Volume 70}, pages = {1321–1330}, numpages = {10}, location = {Sydney, NSW, Australia}, series = {ICML'17} 
}


@inbook{lecun1995convolutional,
author = {LeCun, Yann and Bengio, Yoshua},
title = {Convolutional Networks for Images, Speech, and Time Series},
year = {1998},
isbn = {0262511029},
publisher = {MIT Press},
address = {Cambridge, MA, USA},
booktitle = {The Handbook of Brain Theory and Neural Networks},
pages = {255–258},
numpages = {4}
}

@ARTICLE{lecun1998lenet5,
  author={Lecun, Y. and Bottou, L. and Bengio, Y. and Haffner, P.},
  journal={Proceedings of the IEEE}, 
  title={Gradient-based learning applied to document recognition}, 
  year={1998},
  volume={86},
  number={11},
  pages={2278-2324},
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@article{qian1999momentum,
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  author={Qian, Ning},
  journal={Neural networks},
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  number={1},
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  year={1999},
  publisher={Elsevier}
}

@article{polyak1964some,
  title={Some methods of speeding up the convergence of iteration methods},
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}

@misc{hochreiter2001gradient,
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  year={2001},
  publisher={A field guide to dynamical recurrent neural networks. IEEE Press}
}

@article{hochreiter1991untersuchungen,
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  author={Hochreiter, Sepp},
  journal={Diploma, Technische Universit{\"a}t M{\"u}nchen},
  volume={91},
  number={1},
  year={1991}
}

@article{rosenblatt1958perceptron,
  title={The perceptron: a probabilistic model for information storage and organization in the brain.},
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  number={6},
  pages={386},
  year={1958},
  publisher={American Psychological Association}
}

@ARTICLE{shridhar2019,
       author = {{Shridhar}, Kumar and {Laumann}, Felix and {Liwicki}, Marcus},
        title = "{A Comprehensive guide to Bayesian Convolutional Neural Network with Variational Inference}",
      journal = {arXiv e-prints},
     keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
         year = 2019,
        month = jan,
          eid = {arXiv:1901.02731},
        pages = {arXiv:1901.02731},
archivePrefix = {arXiv},
       eprint = {1901.02731},
 primaryClass = {cs.LG},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2019arXiv190102731S},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{hinton2012dropout,
       author = {{Hinton}, Geoffrey E. and {Srivastava}, Nitish and {Krizhevsky}, Alex and {Sutskever}, Ilya and {Salakhutdinov}, Ruslan R.},
        title = "{Improving neural networks by preventing co-adaptation of feature detectors}",
      journal = {arXiv e-prints},
     keywords = {Computer Science - Neural and Evolutionary Computing, Computer Science - Computer Vision and Pattern Recognition, Computer Science - Machine Learning},
         year = 2012,
        month = jul,
          eid = {arXiv:1207.0580},
        pages = {arXiv:1207.0580},
archivePrefix = {arXiv},
       eprint = {1207.0580},
 primaryClass = {cs.NE},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2012arXiv1207.0580H},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{srivastava2014dropout,
  title={Dropout: a simple way to prevent neural networks from overfitting},
  author={Srivastava, Nitish and Hinton, Geoffrey and Krizhevsky, Alex and Sutskever, Ilya and Salakhutdinov, Ruslan},
  journal={The journal of machine learning research},
  volume={15},
  number={1},
  pages={1929--1958},
  year={2014},
  publisher={JMLR. org}
}

@article{hornik1989multilayer,
  title={Multilayer feedforward networks are universal approximators},
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  journal={Neural networks},
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  number={5},
  pages={359--366},
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  publisher={Elsevier}
}

@incollection{bengio2012practical,
  title={Practical recommendations for gradient-based training of deep architectures},
  author={Bengio, Yoshua},
  booktitle={Neural networks: Tricks of the trade},
  pages={437--478},
  year={2012},
  publisher={Springer}
}

@incollection{prechelt1998early,
  title={Early stopping-but when?},
  author={Prechelt, Lutz},
  booktitle={Neural Networks: Tricks of the trade},
  pages={55--69},
  year={1998},
  publisher={Springer}
}

@incollection{lecun2012efficient,
  title={Efficient backprop},
  author={LeCun, Yann A and Bottou, L{\'e}on and Orr, Genevieve B and M{\"u}ller, Klaus-Robert},
  booktitle={Neural networks: Tricks of the trade},
  pages={9--48},
  year={2012},
  publisher={Springer}
}

@incollection{gal2016uncertainty,
  title={Uncertainty in deep learning},
  author={Gal, Yarin},
  year={2016},
  url={http://mlg.eng.cam.ac.uk/yarin/thesis/thesis.pdf},
  journal={},
  volume={},
  number={},
  pages={},
  publisher={PhD thesis, University of Cambridge}
}

@article{masters2018revisiting,
  title={Revisiting small batch training for deep neural networks},
  author={Masters, Dominic and Luschi, Carlo},
  journal={arXiv preprint arXiv:1804.07612},
  year={2018},
  volume={},
  number={},
  pages={}
}

@article{peterson1987mean,
  title={A mean field theory learning algorithm for neural networks},
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  journal={Complex systems},
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  year={1987}
}

@inbook{jordan1999,
author = {Jordan, Michael I. and Ghahramani, Zoubin and Jaakkola, Tommi S. and Saul, Lawrence K.},
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year = {1999},
isbn = {0262600323},
publisher = {MIT Press},
address = {Cambridge, MA, USA},
booktitle = {Learning in Graphical Models},
pages = {105–161},
numpages = {57}
}

@book{wainwright2008graphical,
  title={Graphical models, exponential families, and variational inference},
  author={Wainwright, Martin J and Jordan, Michael Irwin},
  year={2008},
  publisher={Now Publishers Inc}
}

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  title={On information and sufficiency},
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@article{kingma2013auto,
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  year={2013}
}

@article{kingma2015variational,
  title={Variational dropout and the local reparameterization trick},
  author={Kingma, Durk P and Salimans, Tim and Welling, Max},
  journal={Advances in neural information processing systems},
  volume={28},
  pages={2575--2583},
  year={2015}
}
 
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location = {Denver, Colorado},
series = {NIPS'91}
}

@article{gal2015bayesian,
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  year={2015}
}

@article{jospin2020hands,
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  journal={arXiv preprint arXiv:2007.06823},
  year={2020}
}

@article{saul1996mean,
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@incollection{neal1998view,
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  pages={355--368},
  year={1998},
  publisher={Springer}
}


@inproceedings{wenzel2020good,
author = {Wenzel, Florian and Roth, Kevin and Veeling, Bastiaan S. and Swi\k{a}tkowski, Jakub and Tran, Linh and Mandt, Stephan and Snoek, Jasper and Salimans, Tim and Jenatton, Rodolphe and Nowozin, Sebastian},
title = {How good is the bayes posterior in deep neural networks really?},
year = {2020},
publisher = {JMLR.org},
abstract = {During the past five years the Bayesian deep learning community has developed increasingly accurate and efficient approximate inference procedures that allow for Bayesian inference in deep neural networks. However, despite this algorithmic progress and the promise of improved uncertainty quantification and sample efficiency there are--as of early 2020--no publicized deployments of Bayesian neural networks in industrial practice. In this work we cast doubt on the current understanding of Bayes posteriors in popular deep neural networks: we demonstrate through careful MCMC sampling that the posterior predictive induced by the Bayes posterior yields systematically worse predictions compared to simpler methods including point estimates obtained from SGD. Furthermore, we demonstrate that predictive performance is improved significantly through the use of a "cold posterior" that overcounts evidence. Such cold posteriors sharply deviate from the Bayesian paradigm but are commonly used as heuristic in Bayesian deep learning papers. We put forward several hypotheses that could explain cold posteriors and evaluate the hypotheses through experiments. Our work questions the goal of accurate posterior approximations in Bayesian deep learning: If the true Bayes posterior is poor, what is the use of more accurate approximations? Instead, we argue that it is timely to focus on understanding the origin of the improved performance of cold posteriors.},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
articleno = {949},
numpages = {12},
series = {ICML'20}
}

  


@inproceedings{aitchison2020statistical,
  title={A statistical theory of cold posteriors in deep neural networks},
  author={Aitchison, Laurence},
  booktitle={International Conference on Learning Representations},
  year={2020}
}

@inproceedings{lecun1990optimal,
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  volume={182},
  number={2},
  pages={543},
  year={2009},
  publisher={IOP Publishing}
}
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}

@ARTICLE{mackay1992b,
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@article{mackay1992a,
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@article{wang2019pulsar,
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@article{mesarcik2020deep,
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@article{george2018classification,
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@article{naul2018recurrent,
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@article{nguyen2014,
  author    = {Anh Mai Nguyen and
               Jason Yosinski and
               Jeff Clune},
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@article{hein2019,
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@ARTICLE{2005best,
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@ARTICLE{2009donoson,
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% new 2022

@article{metropolis1953equation,
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@inproceedings{izmailov2021bayesian,
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}

@inproceedings{welling2011bayesian,
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@article{neal2011mcmc,
  title={MCMC using Hamiltonian dynamics},
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  number={11},
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  year={2011},
  publisher={Chapman and Hall/CRC}
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@article{papamarkou2022challenges,
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@inproceedings{cobb2021scaling,
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@article{gelman1992inference,
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@book{nalisnick2018priors,
  title={On priors for Bayesian neural networks},
  author={Nalisnick, Eric Thomas},
  year={2018},
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@inproceedings{krishnan2020specifying,
  title={Specifying weight priors in bayesian deep neural networks with empirical bayes},
  author={Krishnan, Ranganath and Subedar, Mahesh and Tickoo, Omesh},
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  year={2020}
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@article{mohan2022quantifying,
  title={Quantifying uncertainty in deep learning approaches to radio galaxy classification},
  author={Mohan, Devina and Scaife, Anna MM and Porter, Fiona and Walmsley, Mike and Bowles, Micah},
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  volume={511},
  number={3},
  pages={3722--3740},
  year={2022},
  publisher={Oxford University Press}
}

article{neal1994improved,
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  volume={111},
  number={1},
  pages={194--203},
  year={1994},
  publisher={Elsevier}
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@article{newphysicsincosmobnn,
  title = {Seeking new physics in cosmology with Bayesian neural networks: Dark energy and modified gravity},
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  url = {https://link.aps.org/doi/10.1103/PhysRevD.105.023531}
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@article{moller2020supernnova,
  title={SuperNNova: an open-source framework for Bayesian, neural network-based supernova classification},
  author={M{\"o}ller, Anais and de Boissi{\`e}re, Thibault},
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  number={3},
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@article{LINKA2022115346,
title = {Bayesian Physics Informed Neural Networks for real-world nonlinear dynamical systems},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {402},
pages = {115346},
year = {2022},
note = {A Special Issue in Honor of the Lifetime Achievements of J. Tinsley Oden},
issn = {0045-7825},
doi = {https://doi.org/10.1016/j.cma.2022.115346},
url = {https://www.sciencedirect.com/science/article/pii/S0045782522004327},
author = {Kevin Linka and Amelie Schäfer and Xuhui Meng and Zongren Zou and George Em Karniadakis and Ellen Kuhl},
keywords = {Dynamical systems, Machine learning, Neural Networks, Physics Informed Neural Networks, Bayesian Inference, Bayesian Neural Networks}

}


@article{
cranmerplanetary,
author = {Miles Cranmer  and Daniel Tamayo  and Hanno Rein  and Peter Battaglia  and Samuel Hadden  and Philip J. Armitage  and Shirley Ho  and David N. Spergel },
title = {A Bayesian neural network predicts the dissolution of compact planetary systems},
journal = {Proceedings of the National Academy of Sciences},
volume = {118},
number = {40},
pages = {e2026053118},
year = {2021},
doi = {10.1073/pnas.2026053118},
URL = {https://www.pnas.org/doi/abs/10.1073/pnas.2026053118},
eprint = {https://www.pnas.org/doi/pdf/10.1073/pnas.2026053118}}

@article{sun2022alpha,
  title={$\alpha$-Deep Probabilistic Inference ($\alpha$-DPI): efficient uncertainty quantification from exoplanet astrometry to black hole feature extraction},
  author={Sun, He and Bouman, Katherine L and Tiede, Paul and Wang, Jason J and Blunt, Sarah and Mawet, Dimitri},
  journal={The Astrophysical Journal},
  volume={932},
  number={2},
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  year={2022},
  publisher={IOP Publishing}
}

@article{pearsonbnnlens,
    author = {Pearson, James and Maresca, Jacob and Li, Nan and Dye, Simon},
    title = "{Strong lens modelling: comparing and combining Bayesian neural networks and parametric profile fitting}",
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    volume = {505},
    number = {3},
    pages = {4362-4382},
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    eprint = {https://academic.oup.com/mnras/article-pdf/505/3/4362/39395417/stab1547.pdf},
}

@article{cobb2019ensemble,
  title={An ensemble of bayesian neural networks for exoplanetary atmospheric retrieval},
  author={Cobb, Adam D and Himes, Michael D and Soboczenski, Frank and Zorzan, Simone and O’Beirne, Molly D and Baydin, At{\i}l{\i}m G{\"u}ne{\c{s}} and Gal, Yarin and Domagal-Goldman, Shawn D and Arney, Giada N and Angerhausen, Daniel and others},
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  volume={158},
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@inproceedings{sun2021deep,
  title={Deep probabilistic imaging: Uncertainty quantification and multi-modal solution characterization for computational imaging},
  author={Sun, He and Bouman, Katherine L},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={35},
  number={3},
  pages={2628--2637},
  year={2021}
}

@article{cai2018uncertainty,
  title={Uncertainty quantification for radio interferometric imaging--I. Proximal MCMC methods},
  author={Cai, Xiaohao and Pereyra, Marcelo and McEwen, Jason D},
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  volume={480},
  number={3},
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  year={2018},
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}

@article{arras2021comparison,
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  author={Arras, Philipp and Bester, Hertzog L and Perley, Richard A and Leike, Reimar and Smirnov, Oleg and Westermann, R{\"u}diger and En{\ss}lin, Torsten A},
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  volume={646},
  pages={A84},
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}

@article{repetti2019scalable,
  title={Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimization},
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}

@inproceedings{pourzanjani2017improving,
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  author={Pourzanjani, Arya A and Jiang, Richard M and Petzold, Linda R},
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@article{vadera2022ursabench,
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@article{ho2022dynamical,
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@article{foreman2017fast,
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  volume={154},
  number={6},
  pages={220},
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}

@article{scaife2020big,
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  author={Scaife, AMM},
  journal={Philosophical Transactions of the Royal Society A},
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  number={2166},
  pages={20190060},
  year={2020},
  publisher={The Royal Society Publishing}
}

@article{an2019science,
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  author={An, Tao},
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  year={2019},
  publisher={Springer}
}

@article{bonaldi2021square,
  title={Square kilometre array science data challenge 1: analysis and results},
  author={Bonaldi, A and An, T and Br{\"u}ggen, M and Burkutean, SANDRA and Coelho, B and Goodarzi, H and Hartley, P and Sandhu, PK and Wu, C and Yu, L and others},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={500},
  number={3},
  pages={3821--3837},
  year={2021},
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}

@article{hartley2023ska,
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  author={Hartley, P and Bonaldi, A and Braun, R and Aditya, JNHS and Aicardi, S and Alegre, L and Chakraborty, A and Chen, X and Choudhuri, S and Clarke, AO and others},
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  year={2023}
}

@ARTICLE{fr1974,
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}
@ARTICLE{blundell,
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}

@article{slijepcevic2022radio,
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@article{tang2022radio,
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  journal={Monthly Notices of the Royal Astronomical Society},
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}

@inproceedings{yao2018yes,
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@inproceedings{chan2020unlabelled,
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  year={2020},
  organization={PMLR}
}

@inproceedings{chen2014stochastic,
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@article{hoffman2014no,
  title={The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo.},
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}

@article{betancourt2017conceptual,
  title={A conceptual introduction to Hamiltonian Monte Carlo},
  author={Betancourt, Michael},
  journal={arXiv preprint arXiv:1701.02434},
  year={2017}
}

@article{casella1992explaining,
  title={Explaining the Gibbs sampler},
  author={Casella, George and George, Edward I},
  journal={The American Statistician},
  volume={46},
  number={3},
  pages={167--174},
  year={1992},
  publisher={Taylor \& Francis}
}


@article{kobyzev2020normalizing,
  title={Normalizing flows: An introduction and review of current methods},
  author={Kobyzev, Ivan and Prince, Simon JD and Brubaker, Marcus A},
  journal={IEEE transactions on pattern analysis and machine intelligence},
  volume={43},
  number={11},
  pages={3964--3979},
  year={2020},
  publisher={IEEE}
}

@article{lakshminarayanan2017simple,
  title={Simple and scalable predictive uncertainty estimation using deep ensembles},
  author={Lakshminarayanan, Balaji and Pritzel, Alexander and Blundell, Charles},
  journal={Advances in neural information processing systems},
  volume={30},
  year={2017}
}

@article{maddox2019simple,
  title={A simple baseline for bayesian uncertainty in deep learning},
  author={Maddox, Wesley J and Izmailov, Pavel and Garipov, Timur and Vetrov, Dmitry P and Wilson, Andrew Gordon},
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@article{wilson2020bayesian,
  title={Bayesian deep learning and a probabilistic perspective of generalization},
  author={Wilson, Andrew G and Izmailov, Pavel},
  journal={Advances in neural information processing systems},
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  year={2020}
}

@article{hogg2018data,
  title={Data analysis recipes: Using markov chain monte carlo},
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  journal={The Astrophysical Journal Supplement Series},
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}

@book{murphy2012machine,
  title={Machine learning: a probabilistic perspective},
  author={Murphy, Kevin P},
  year={2012},
  publisher={MIT press}
}

@article{brooks1998general,
  title={General methods for monitoring convergence of iterative simulations},
  author={Brooks, Stephen P and Gelman, Andrew},
  journal={Journal of computational and graphical statistics},
  volume={7},
  number={4},
  pages={434--455},
  year={1998},
  publisher={Taylor \& Francis}
}

@article{ciprijanovic2021deepmerge,
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  publisher={Oxford University Press}
}

@article{gretton2012kernel,
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@article{noci2021disentangling,
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@article{porter2023mirabest,
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@inproceedings{immer2021scalable,
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  year={2021},
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}


@article{10.5555/3586589.3586721,
author = {Knoblauch, Jeremias and Jewson, Jack and Damoulas, Theodoros},
title = {An Optimization-Centric View on Bayes' Rule: Reviewing and Generalizing Variational Inference},
year = {2022},
issue_date = {January 2022},
publisher = {JMLR.org},
volume = {23},
number = {1},
issn = {1532-4435},
abstract = {We advocate an optimization-centric view of Bayesian inference. Our inspiration is the representation of Bayes' rule as infinite-dimensional optimization (Csisz´r, 1975; Donsker and Varadhan, 1975; Zellner, 1988). Equipped with this perspective, we study Bayesian inference when one does not have access to (1) well-specified priors, (2) well-specified likelihoods, (3) infinite computing power. While these three assumptions underlie the standard Bayesian paradigm, they are typically inappropriate for modern Machine Learning applications. We propose addressing this through an optimization-centric generalization of Bayesian posteriors that we call the Rule of Three (RoT). The RoT can be justified axiomatically and recovers Bayesian, PAC-Bayesian and VI posteriors as special cases. While the RoT is primarily a conceptual and theoretical device, it also encompasses a novel sub-class of tractable posteriors which we call Generalized Variational Inference (GVI) posteriors. Just as the RoT, GVI posteriors are specified by three arguments: a loss, a divergence and a variational family. They also possess a number of desirable properties, including modularity, Frequentist consistency and an interpretation as approximate ELBO. We explore applications of GVI posteriors, and show that they can be used to improve robustness and posterior marginals on Bayesian Neural Networks and Deep Gaussian Processes.},
journal = {J. Mach. Learn. Res.},
month = {jan},
articleno = {132},
numpages = {109},
keywords = {deep Gaussian proceses, Bayesian neural networks, Bayesian inference, variational inference, generalized Bayesian inference}
}

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  booktitle={NeurIPS 2021 Competitions and Demonstrations Track},
  pages={113--124},
  year={2022},
  organization={PMLR}
}

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  year={2023}
}

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  year={2017},
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}

@article{nickl2023memory,
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}

@inproceedings{kong2021resolving,
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  year={2021}
}

@article{heywood2022mightee,
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  publisher={Oxford University Press}
}

@article{qiu2023should,
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  year={2023}
}

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  year={2019}
}

@article{kim2023convergence,
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  year={2023}
}

@article{mohan2023mcmc,
  title={MCMC to address model misspecification in Deep Learning classification of Radio Galaxies},
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  journal={arXiv preprint arXiv:2311.08243},
  year={2023}
}

@article{yang2021generalized,
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  year={2021}
}

@inproceedings{wimmer2023quantifying,
  title={Quantifying aleatoric and epistemic uncertainty in machine learning: Are conditional entropy and mutual information appropriate measures?},
  author={Wimmer, Lisa and Sale, Yusuf and Hofman, Paul and Bischl, Bernd and H{\"u}llermeier, Eyke},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={2282--2292},
  year={2023},
  organization={PMLR}
}

@article{giordano2018covariances,
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  number={1},
  pages={19--32},
  year={2024},
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@article{walmsley2022galaxy,
  title={Galaxy Zoo DECaLS: Detailed visual morphology measurements from volunteers and deep learning for 314 000 galaxies},
  author={Walmsley, Mike and Lintott, Chris and G{\'e}ron, Tobias and Kruk, Sandor and Krawczyk, Coleman and Willett, Kyle W and Bamford, Steven and Kelvin, Lee S and Fortson, Lucy and Gal, Yarin and others},
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}

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}
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  organization={PMLR}
}
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}