{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T04:17:18Z","timestamp":1741839438392,"version":"3.38.0"},"reference-count":57,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T00:00:00Z","timestamp":1741737600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T00:00:00Z","timestamp":1741737600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["SN COMPUT. SCI."],"DOI":"10.1007\/s42979-025-03829-1","type":"journal-article","created":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T11:56:48Z","timestamp":1741780608000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Evaluation of Bayesian Deep Learning Methods for Quantifying Uncertainties in Forecasting Deaths from COVID-19"],"prefix":"10.1007","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8862-2431","authenticated-orcid":false,"given":"Andr\u00e9 Vin\u00edcius","family":"Gon\u00e7alves","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gustavo Medeiros","family":"de Ara\u00fajo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eug\u00eanio Monteiro da Silva","family":"J\u00fanior","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,12]]},"reference":[{"issue":"4","key":"3829_CR1","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1038\/s41579-021-00639-z","volume":"20","author":"RE Baker","year":"2022","unstructured":"Baker RE, Mahmud AS, Miller IF, Rajeev M, Rasambainarivo F, Rice BL, Takahashi S, Tatem AJ, Wagner CE, Wang L-F, et al. Infectious disease in an era of global change. Nat Rev Microbiol. 2022;20(4):193\u2013205. https:\/\/doi.org\/10.1038\/s41579-021-00639-z.","journal-title":"Nat Rev Microbiol"},{"key":"3829_CR2","unstructured":"WHO: WHO Coronavirus Disease (COVID-19) Dashboard 2020; https:\/\/covid19.who.int\/."},{"key":"3829_CR3","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/j.apm.2021.03.044","volume":"97","author":"Y Chen","year":"2021","unstructured":"Chen Y, Liu F, Yu Q, Li T. Review of fractional epidemic models. Appl Math Model. 2021;97:281\u2013307.","journal-title":"Appl Math Model"},{"key":"3829_CR4","doi-asserted-by":"crossref","unstructured":"Bansal A, Jayant U. COVID-19 outbreak modelling using regression techniques. In: 2021 international conference on innovative practices in technology and management (ICIPTM). IEEE; 2021. pp. 113\u2013118.","DOI":"10.1109\/ICIPTM52218.2021.9388347"},{"issue":"2","key":"3829_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.asej.2021.08.016","volume":"13","author":"MA Khan","year":"2022","unstructured":"Khan MA, Khan R, Algarni F, Kumar I, Choudhary A, Srivastava A. Performance evaluation of regression models for COVID-19: a statistical and predictive perspective. Ain Shams Eng J. 2022;13(2): 101574.","journal-title":"Ain Shams Eng J"},{"issue":"5","key":"3829_CR6","doi-asserted-by":"publisher","first-page":"1419","DOI":"10.1016\/j.dsx.2020.07.042","volume":"14","author":"AK Sahai","year":"2020","unstructured":"Sahai AK, Rath N, Sood V, Singh MP. Arima modelling & forecasting of COVID-19 in top five affected countries. Diabetes Metab Syndr Clin Res Rev. 2020;14(5):1419\u201327.","journal-title":"Diabetes Metab Syndr Clin Res Rev"},{"key":"3829_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2021.107161","volume":"103","author":"K ArunKumar","year":"2021","unstructured":"ArunKumar K, Kalaga DV, Kumar CMS, Chilkoor G, Kawaji M, Brenza TM. Forecasting the dynamics of cumulative COVID-19 cases (confirmed, recovered and deaths) for top-16 countries using statistical machine learning models: auto-regressive integrated moving average (arima) and seasonal auto-regressive integrated moving average (sarima). Appl Soft Comput. 2021;103: 107161.","journal-title":"Appl Soft Comput"},{"key":"3829_CR8","doi-asserted-by":"crossref","unstructured":"Germann TC, Smith MZ, Dauelsberg L, Fairchild G, Turton TL, Gorris ME, Ross CW, Ahrens JP, Hemphill DD, Manore C, et al. Using an agent-based model to assess k-12 school reopenings under different COVID-19 spread scenarios\u2013United States, school year 2020\/21. medRxiv, 2020;2020\u201310.","DOI":"10.1101\/2020.10.09.20208876"},{"key":"3829_CR9","unstructured":"Errica F, Bacciu D, Micheli A. Graph mixture density networks. In: International conference on machine learning. PMLR; 2021. pp. 3025\u20133035."},{"issue":"4","key":"3829_CR10","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1089\/hs.2019.0022","volume":"17","author":"AN Desai","year":"2019","unstructured":"Desai AN, Kraemer MU, Bhatia S, Cori A, Nouvellet P, Herringer M, Cohn EL, Carrion M, Brownstein JS, Madoff LC, et al. Real-time epidemic forecasting: challenges and opportunities. Health Secur. 2019;17(4):268\u201375.","journal-title":"Health Secur"},{"key":"3829_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2020.114077","volume":"166","author":"C Katris","year":"2021","unstructured":"Katris C. A time series-based statistical approach for outbreak spread forecasting: application of COVID-19 in Greece. Expert Syst Appl. 2021;166: 114077. https:\/\/doi.org\/10.1016\/j.eswa.2020.114077.","journal-title":"Expert Syst Appl"},{"key":"3829_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.ebiom.2023.104482","volume":"89","author":"H Du","year":"2023","unstructured":"Du H, Dong E, Badr HS, Petrone ME, Grubaugh ND, Gardner LM. Incorporating variant frequencies data into short-term forecasting for COVID-19 cases and deaths in the USA: a deep learning approach. Ebiomedicine. 2023;89:104482.","journal-title":"Ebiomedicine"},{"key":"3829_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.techfore.2021.120602","volume":"166","author":"J Luo","year":"2021","unstructured":"Luo J. Forecasting COVID-19 pandemic: unknown unknowns and predictive monitoring. Technol Forecast Soc Chang. 2021;166: 120602.","journal-title":"Technol Forecast Soc Chang"},{"issue":"19","key":"3829_CR14","doi-asserted-by":"publisher","first-page":"1893","DOI":"10.1001\/jama.2020.6585","volume":"323","author":"NP Jewell","year":"2020","unstructured":"Jewell NP, Lewnard JA, Jewell BL. Predictive mathematical models of the COVID-19 pandemic: underlying principles and value of projections. JAMA. 2020;323(19):1893\u20134.","journal-title":"JAMA"},{"issue":"2","key":"3829_CR15","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1016\/j.ijforecast.2020.08.004","volume":"38","author":"JP Ioannidis","year":"2022","unstructured":"Ioannidis JP, Cripps S, Tanner MA. Forecasting for COVID-19 has failed. Int J Forecast. 2022;38(2):423\u201338.","journal-title":"Int J Forecast"},{"issue":"2","key":"3829_CR16","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/j.neunet.2006.01.012","volume":"19","author":"DL Shrestha","year":"2006","unstructured":"Shrestha DL, Solomatine DP. Machine learning approaches for estimation of prediction interval for the model output. Neural Netw. 2006;19(2):225\u201335. https:\/\/doi.org\/10.1016\/j.neunet.2006.01.012.","journal-title":"Neural Netw"},{"issue":"2","key":"3829_CR17","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.strusafe.2008.06.020","volume":"31","author":"A Der Kiureghian","year":"2009","unstructured":"Der Kiureghian A, Ditlevsen O. Aleatory or epistemic? does it matter? Struct Saf. 2009;31(2):105\u201312.","journal-title":"Struct Saf"},{"issue":"11","key":"3829_CR18","doi-asserted-by":"publisher","first-page":"2463","DOI":"10.1109\/TKDE.2012.179","volume":"25","author":"Y Li","year":"2012","unstructured":"Li Y, Chen J, Feng L. Dealing with uncertainty: a survey of theories and practices. IEEE Trans Knowl Data Eng. 2012;25(11):2463\u201382.","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"4","key":"3829_CR19","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1111\/j.1539-6924.1994.tb00266.x","volume":"14","author":"JC Helton","year":"1994","unstructured":"Helton JC. Treatment of uncertainty in performance assessments for complex systems. Risk Anal. 1994;14(4):483\u2013511.","journal-title":"Risk Anal"},{"key":"3829_CR20","doi-asserted-by":"crossref","unstructured":"Meeker WQ, Hahn GJ, Escobar LA. Statistical intervals: a guide for practitioners and researchers vol. 541. John Wiley & Sons; 2017.","DOI":"10.1002\/9781118594841"},{"key":"3829_CR21","unstructured":"Pearce T, Brintrup A, Zaki M, Neely A. High-quality prediction intervals for deep learning: A distribution-free, ensembled approach. In: International conference on machine learning. PMLR; 2018. pp. 4075\u20134084."},{"key":"3829_CR22","doi-asserted-by":"crossref","unstructured":"Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian data analysis. Chapman and Hall\/CRC; 2013.","DOI":"10.1201\/b16018"},{"key":"3829_CR23","unstructured":"Murphy KP. Machine learning: a probabilistic perspective. MIT press; 2012."},{"key":"3829_CR24","unstructured":"Gal Y, Ghahramani Z. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In: International conference on machine learning. PMLR; 2016. pp. 1050\u20131059."},{"key":"3829_CR25","unstructured":"Gal Y, Hron J, Kendall A. Concrete dropout. Adv Neural Inf Process Syst 2017;30"},{"issue":"1","key":"3829_CR26","doi-asserted-by":"publisher","first-page":"5458","DOI":"10.1038\/s41598-021-84854-x","volume":"11","author":"A Mobiny","year":"2021","unstructured":"Mobiny A, Yuan P, Moulik SK, Garg N, Wu CC, Van Nguyen H. Dropconnect is effective in modeling uncertainty of Bayesian deep networks. Sci Rep. 2021;11(1):5458.","journal-title":"Sci Rep"},{"key":"3829_CR27","unstructured":"Chen T, Fox E, Guestrin C. Stochastic gradient hamiltonian monte carlo. In: International conference on machine learning. PMLR. 2014; pp. 1683\u20131691. https:\/\/proceedings.mlr.press\/v32\/cheni14.html."},{"key":"3829_CR28","unstructured":"Maddox WJ, Izmailov P, Garipov T, Vetrov DP, Wilson AG. A simple baseline for Bayesian uncertainty in deep learning. Adv Neural Inf Process Syst 2019;32"},{"issue":"Suppl 1","key":"3829_CR29","doi-asserted-by":"publisher","first-page":"1513","DOI":"10.1007\/s10462-023-10562-9","volume":"56","author":"J Gawlikowski","year":"2023","unstructured":"Gawlikowski J, Tassi CRN, Ali M, Lee J, Humt M, Feng J, Kruspe A, Triebel R, Jung P, Roscher R, et al. A survey of uncertainty in deep neural networks. Artif Intell Rev. 2023;56(Suppl 1):1513\u201389. https:\/\/doi.org\/10.1007\/s10462-023-10562-9.","journal-title":"Artif Intell Rev"},{"key":"3829_CR30","unstructured":"Mukhoti J, Stenetorp P, Gal Y. On the importance of strong baselines in Bayesian deep learning. 2018; arXiv preprint arXiv:1811.09385."},{"issue":"1","key":"3829_CR31","volume":"2","author":"J Caldeira","year":"2020","unstructured":"Caldeira J, Nord B. Deeply uncertain: comparing methods of uncertainty quantification in deep learning algorithms. Mach Learn: Sci Technol. 2020;2(1): 015002.","journal-title":"Mach Learn: Sci Technol"},{"issue":"2","key":"3829_CR32","volume":"1","author":"K Tran","year":"2020","unstructured":"Tran K, Neiswanger W, Yoon J, Zhang Q, Xing E, Ulissi ZW. Methods for comparing uncertainty quantifications for material property predictions. Mach Learn: Sci Technol. 2020;1(2): 025006.","journal-title":"Mach Learn: Sci Technol"},{"issue":"4","key":"3829_CR33","doi-asserted-by":"publisher","first-page":"0250417","DOI":"10.1371\/journal.pone.0250417","volume":"16","author":"T Murayama","year":"2021","unstructured":"Murayama T, Shimizu N, Fujita S, Wakamiya S, Aramaki E. Predicting regional influenza epidemics with uncertainty estimation using commuting data in Japan. PLoS ONE. 2021;16(4):0250417.","journal-title":"PLoS ONE"},{"key":"3829_CR34","doi-asserted-by":"crossref","unstructured":"Zhu L, Laptev N. Deep and confident prediction for time series at uber. In: 2017 IEEE International Conference on Data Mining Workshops (ICDMW). IEEE. 2017; pp. 103\u2013110.","DOI":"10.1109\/ICDMW.2017.19"},{"issue":"1","key":"3829_CR35","doi-asserted-by":"publisher","first-page":"13058","DOI":"10.1038\/s41598-021-92634-w","volume":"11","author":"Q Li","year":"2021","unstructured":"Li Q, Yang Y, Wang W, Lee S, Xiao X, Gao X, Oztekin B, Fan C, Mostafavi A. Unraveling the dynamic importance of county-level features in trajectory of COVID-19. Sci Rep. 2021;11(1):13058.","journal-title":"Sci Rep"},{"key":"3829_CR36","unstructured":"CDC: Centers for Disease Control and Prevention 2022; https:\/\/www.cdc.gov\/."},{"key":"3829_CR37","doi-asserted-by":"publisher","DOI":"10.3389\/fpubh.2020.580057","volume":"8","author":"N Ali","year":"2020","unstructured":"Ali N, Islam F. The effects of air pollution on COVID-19 infection and mortality\u2014a review on recent evidence. Front Public Health. 2020;8: 580057.","journal-title":"Front Public Health"},{"issue":"2","key":"3829_CR38","doi-asserted-by":"publisher","first-page":"396","DOI":"10.3390\/ijerph18020396","volume":"18","author":"H McClymont","year":"2021","unstructured":"McClymont H, Hu W. Weather variability and COVID-19 transmission: a review of recent research. Int J Environ Res Public Health. 2021;18(2):396.","journal-title":"Int J Environ Res Public Health"},{"issue":"12","key":"3829_CR39","doi-asserted-by":"publisher","first-page":"4204","DOI":"10.3390\/ijerph17124204","volume":"17","author":"A Mollalo","year":"2020","unstructured":"Mollalo A, Rivera KM, Vahedi B. Artificial neural network modeling of novel coronavirus (COVID-19) incidence rates across the continental united states. Int J Environ Res Public Health. 2020;17(12):4204.","journal-title":"Int J Environ Res Public Health"},{"key":"3829_CR40","unstructured":"NCEI: National Centers for Environmental Information 2022; https:\/\/www.ncei.noaa.gov\/."},{"key":"3829_CR41","unstructured":"US EPA: U.S. Environmental Protection Agency 2022; https:\/\/www.epa.gov\/."},{"key":"3829_CR42","unstructured":"Google: Google COVID-19 Community Mobility Reports 2020; https:\/\/www.google.com\/covid19\/mobility\/."},{"key":"3829_CR43","unstructured":"Apple: Mobility Trends Reports 2020; https:\/\/www.apple.com\/covid19\/mobility."},{"key":"3829_CR44","unstructured":"OxCGRT: Oxford COVID-19 Government Response Tracker 2022; https:\/\/www.bsg.ox.ac.uk\/research\/research-projects\/covid-19-government-response-tracker."},{"key":"3829_CR45","unstructured":"CMS: Centers for Medicare & Medicaid Services (CMS) 2020; https:\/\/data.cms.gov\/."},{"issue":"6","key":"3829_CR46","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.jinf.2020.03.005","volume":"80","author":"K Liu","year":"2020","unstructured":"Liu K, Chen Y, Lin R, Han K. Clinical features of covid-19 in elderly patients: a comparison with young and middle-aged patients. J Infect. 2020;80(6):14\u20138.","journal-title":"J Infect"},{"key":"3829_CR47","doi-asserted-by":"publisher","DOI":"10.1016\/j.mad.2020.111255","volume":"188","author":"C Leung","year":"2020","unstructured":"Leung C. Risk factors for predicting mortality in elderly patients with COVID-19: a review of clinical data in China. Mech Ageing Dev. 2020;188: 111255.","journal-title":"Mech Ageing Dev"},{"key":"3829_CR48","unstructured":"CDC: Centers for Disease Control and Prevention. https:\/\/data.cdc.gov\/Laboratory-Surveillance\/SARS-CoV-2-Variant-Proportions\/jr58-6ysp."},{"key":"3829_CR49","doi-asserted-by":"publisher","DOI":"10.15585\/mmwr.mm7224a2","author":"KC Ma","year":"2023","unstructured":"Ma KC. Genomic surveillance for sars-cov-2 variants: circulation of omicron lineages-United States, January 2022-May 2023. MMWR. Morb Mortal Weekly Rep. 2023 https:\/\/doi.org\/10.15585\/mmwr.mm7224a2","journal-title":"MMWR Morb Mortal Weekly Rep"},{"key":"3829_CR50","unstructured":"Blundell C, Cornebise J, Kavukcuoglu K, Wierstra D. Weight uncertainty in neural network. In: International conference on machine learning. PMLR; 2015. pp. 1613\u20131622."},{"key":"3829_CR51","unstructured":"Amini A, Soleimany A, Karaman S, Rus D. Spatial uncertainty sampling for end-to-end control. 2018; arXiv preprint arXiv:1805.04829"},{"key":"3829_CR52","unstructured":"Krueger D, Huang C-W, Islam R, Turner R, Lacoste A, Courville A. Bayesian hypernetworks. 2017; arXiv preprint arXiv:1710.04759"},{"key":"3829_CR53","unstructured":"Kendall A, Gal Y. What uncertainties do we need in Bayesian deep learning for computer vision? Adv Neural Inf Process Syst 2017;30"},{"issue":"7697","key":"3829_CR54","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1038\/d41586-018-02473-5","volume":"555","author":"M Eisenstein","year":"2018","unstructured":"Eisenstein M. Infection forecasts powered by big data. Nature. 2018;555(7697):2\u20132.","journal-title":"Nature"},{"issue":"3","key":"3829_CR55","doi-asserted-by":"publisher","first-page":"2377","DOI":"10.1016\/j.eswa.2009.07.059","volume":"37","author":"A Khosravi","year":"2010","unstructured":"Khosravi A, Nahavandi S, Creighton D. A prediction interval-based approach to determine optimal structures of neural network metamodels. Expert Syst Appl. 2010;37(3):2377\u201387.","journal-title":"Expert Syst Appl"},{"issue":"3","key":"3829_CR56","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1109\/TNN.2010.2096824","volume":"22","author":"A Khosravi","year":"2010","unstructured":"Khosravi A, Nahavandi S, Creighton D, Atiya AF. Lower upper bound estimation method for construction of neural network-based prediction intervals. IEEE Trans Neural Networks. 2010;22(3):337\u201346.","journal-title":"IEEE Trans Neural Networks"},{"issue":"15","key":"3829_CR57","doi-asserted-by":"publisher","first-page":"2113561119","DOI":"10.1073\/pnas.2113561119","volume":"119","author":"EY Cramer","year":"2022","unstructured":"Cramer EY, Ray EL, Lopez VK, Bracher J, Brennen A, Castro Rivadeneira AJ, Gerding A, Gneiting T, House KH, Huang Y, et al. Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the united states. Proc Natl Acad Sci. 2022;119(15):2113561119.","journal-title":"Proc Natl Acad Sci"}],"container-title":["SN Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42979-025-03829-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42979-025-03829-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42979-025-03829-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T11:57:06Z","timestamp":1741780626000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42979-025-03829-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,12]]},"references-count":57,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["3829"],"URL":"https:\/\/doi.org\/10.1007\/s42979-025-03829-1","relation":{},"ISSN":["2661-8907"],"issn-type":[{"value":"2661-8907","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,12]]},"assertion":[{"value":"4 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 March 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}},{"value":"No animal or human experimentation was involved in this study.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}],"article-number":"276"}}