{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T14:17:43Z","timestamp":1778077063805,"version":"3.51.4"},"reference-count":59,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T00:00:00Z","timestamp":1773273600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computational Statistics & Data Analysis"],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1016\/j.csda.2026.108368","type":"journal-article","created":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T16:22:59Z","timestamp":1773332579000},"page":"108368","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Fast approximate posterior inference for modeling disease dynamics via state-space models"],"prefix":"10.1016","volume":"221","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5338-8772","authenticated-orcid":false,"given":"Meini","family":"Tang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6709-7191","authenticated-orcid":false,"given":"Raquel","family":"Prado","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"3","key":"10.1016\/j.csda.2026.108368_bib0001","doi-asserted-by":"crossref","first-page":"77","DOI":"10.3390\/risks8030077","article-title":"A poisson autoregressive model to understand COVID-19 contagion dynamics","volume":"8","author":"Agosto","year":"2020","journal-title":"Risks"},{"issue":"1","key":"10.1016\/j.csda.2026.108368_bib0002","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1186\/s12879-021-05950-x","article-title":"Serial interval and incubation period of COVID-19: a systematic review and meta-analysis","volume":"21(1)","author":"Alene","year":"2021","journal-title":"BMC Infect. Dis."},{"key":"10.1016\/j.csda.2026.108368_bib0003","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/1471082X0801000102","article-title":"Transfer functions in dynamic generalized linear models","volume":"10 (1)","author":"Alves","year":"2010","journal-title":"Stat. Model."},{"issue":"29","key":"10.1016\/j.csda.2026.108368_bib0004","doi-asserted-by":"crossref","first-page":"16732","DOI":"10.1073\/pnas.2006520117","article-title":"The challenges of modeling and forecasting the spread of COVID-19","volume":"117(29)","author":"Bertozzi","year":"2020","journal-title":"Proc. Natl. Acad. Sci."},{"key":"10.1016\/j.csda.2026.108368_bib0005","unstructured":"Betancourt, M., 2018. A conceptual introduction to Hamiltonian Monte Carlo. arXiv: 1701.02434 [stat.ME]."},{"issue":"1","key":"10.1016\/j.csda.2026.108368_bib0006","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s10463-009-0236-2","article-title":"Smoothing algorithms for state\u2013space models","volume":"62(1)","author":"Briers","year":"2010","journal-title":"Ann. Inst. Stat. Math."},{"issue":"1829","key":"10.1016\/j.csda.2026.108368_bib0007","doi-asserted-by":"crossref","DOI":"10.1098\/rstb.2020.0276","article-title":"Mapping social distancing measures to the reproduction number for COVID-19","volume":"376","author":"Brooks-Pollock","year":"2021","journal-title":"Philos. Trans. R. Soc. B Biol. Sci."},{"key":"10.1016\/j.csda.2026.108368_bib0008","article-title":"Simple discrete-time self-exciting models can describe complex dynamic processes: a case study of COVID-19","volume":"16(4)","author":"Browning","year":"2021","journal-title":"PLoS ONE"},{"issue":"548","key":"10.1016\/j.csda.2026.108368_bib0009","doi-asserted-by":"crossref","first-page":"2983","DOI":"10.1080\/01621459.2023.2296704","article-title":"Fitting latent non-Gaussian models using variational bayes and laplace approximations","volume":"119 (548)","author":"Cabral","year":"2024","journal-title":"J. Am. Stat. Assoc."},{"issue":"545","key":"10.1016\/j.csda.2026.108368_bib0010","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1080\/01621459.2022.2102019","article-title":"Latent network structure learning from high-dimensional multivariate point processes","volume":"119(545)","author":"Cai","year":"2024","journal-title":"J. Am. Stat. Assoc."},{"issue":"3","key":"10.1016\/j.csda.2026.108368_bib0011","doi-asserted-by":"crossref","DOI":"10.1002\/sta4.70000","article-title":"A joint temporal model for hospitalizations and ICU admissions due to COVID-19 in Quebec","volume":"13(3)","author":"Carmona-Baez","year":"2024","journal-title":"Stat"},{"issue":"2","key":"10.1016\/j.csda.2026.108368_bib0012","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/j.ijforecast.2021.07.001","article-title":"Hawkes process modeling of COVID-19 with mobility leading indicators and spatial covariates","volume":"38(2)","author":"Chiang","year":"2022","journal-title":"Int. J. Forecast."},{"issue":"9","key":"10.1016\/j.csda.2026.108368_bib0013","doi-asserted-by":"crossref","first-page":"1505","DOI":"10.1093\/aje\/kwt133","article-title":"A new framework and software to estimate time-varying reproduction numbers during epidemics","volume":"178(9)","author":"Cori","year":"2013","journal-title":"Am. J. Epidemiol."},{"issue":"3","key":"10.1016\/j.csda.2026.108368_bib0014","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1007\/s00477-020-01781-5","article-title":"On the use of adaptive spatial weight matrices from disease mapping multivariate analyses","volume":"34(3)","author":"Corpas-Burgos","year":"2020","journal-title":"Stochas. Environ. Res. Risk Assess."},{"issue":"535","key":"10.1016\/j.csda.2026.108368_bib0015","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1080\/01621459.2021.1904957","article-title":"Count time series: a methodological review","volume":"116(535)","author":"Davis","year":"2021","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2026.108368_bib0016","series-title":"The Oxford Handbook of Nonlinear Filtering","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1093\/oxfordhb\/9780199571888.013.0010","article-title":"A tutorial on particle filtering and smoothing: fifteen years later","author":"Doucet","year":"2011"},{"key":"10.1016\/j.csda.2026.108368_bib0017","series-title":"Time Series Analysis by State Space Methods","author":"Durbin","year":"2012"},{"issue":"2","key":"10.1016\/j.csda.2026.108368_bib0018","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1093\/biomet\/asq013","article-title":"A sequential smoothing algorithm with linear computational cost","volume":"97(2)","author":"Fearnhead","year":"2010","journal-title":"Biometrika"},{"issue":"c","key":"10.1016\/j.csda.2026.108368_bib0019","article-title":"Statistical analysis of multivariate discrete-valued time series","volume":"188(C)","author":"Fokianos","year":"2022","journal-title":"J. Multivar. Anal."},{"issue":"3","key":"10.1016\/j.csda.2026.108368_bib0020","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1080\/10618600.2022.2134875","article-title":"Variational bayes in state space models: inferential and predictive accuracy","volume":"32(3)","author":"Frazier","year":"2023","journal-title":"J. Comput. Graph. Stat."},{"issue":"1","key":"10.1016\/j.csda.2026.108368_bib0021","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1080\/10618600.2024.2341899","article-title":"Loss-based variational bayes prediction","volume":"34(1)","author":"Frazier","year":"2025","journal-title":"J. Comput. Graph. Stat."},{"issue":"1","key":"10.1016\/j.csda.2026.108368_bib0022","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1093\/biomet\/85.1.215","article-title":"Markov chain Monte Carlo for dynamic generalised linear models","volume":"85(1)","author":"Gamerman","year":"1998","journal-title":"Biometrika"},{"key":"10.1016\/j.csda.2026.108368_bib0023","series-title":"Handbook of Discrete-Valued Time Series","first-page":"165","article-title":"Dynamic bayesian models for discrete-valued time series","author":"Gamerman","year":"2016"},{"issue":"3","key":"10.1016\/j.csda.2026.108368_bib0024","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1111\/j.2517-6161.1993.tb01928.x","article-title":"Dynamic hierarchical models","volume":"55","author":"Gamerman","year":"1993","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"10.1016\/j.csda.2026.108368_bib0025","doi-asserted-by":"crossref","DOI":"10.1016\/j.spasta.2019.100357","article-title":"Bayesian analysis of areal data with unknown adjacencies using the stochastic edge mixed effects model","volume":"31","author":"Gao","year":"2019","journal-title":"Spat. Stat."},{"issue":"4","key":"10.1016\/j.csda.2026.108368_bib0026","first-page":"733","article-title":"Posterior predictive assessment of model fitness via realized discrepancies","volume":"6(4)","author":"Gelman","year":"1996","journal-title":"Stat. Sin."},{"issue":"51","key":"10.1016\/j.csda.2026.108368_bib0027","first-page":"1","article-title":"Covariances, robustness, and variational bayes","volume":"19","author":"Giordano","year":"2018","journal-title":"J. Mach. Learn. Res."},{"issue":"1","key":"10.1016\/j.csda.2026.108368_bib0028","doi-asserted-by":"crossref","DOI":"10.1002\/bimj.202200054","article-title":"Bayesian time-varying autoregressive models of COVID-19 epidemics","volume":"65(1)","author":"Giudici","year":"2023","journal-title":"Biometr. J."},{"issue":"2","key":"10.1016\/j.csda.2026.108368_bib0029","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1049\/ip-f-2.1993.0015","article-title":"Novel approach to nonlinear\/non-Gaussian Bayesian state estimation","volume":"140(2)","author":"Gordon","year":"1993","journal-title":"IEE Proc. F (Radar and Signal Process.)"},{"key":"10.1016\/j.csda.2026.108368_bib0030","doi-asserted-by":"crossref","DOI":"10.1016\/j.spasta.2021.100552","article-title":"Modelling the effect of a border closure between Switzerland and Italy on the spatiotemporal spread of COVID-19 in switzerland","volume":"49","author":"Grim\u00e9e","year":"2022","journal-title":"Spat. Stat."},{"issue":"3","key":"10.1016\/j.csda.2026.108368_bib0031","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1191\/1471082X05st098oa","article-title":"A statistical framework for the analysis of multivariate infectious disease surveillance counts","volume":"5(3)","author":"Held","year":"2005","journal-title":"Stat. Model."},{"key":"10.1016\/j.csda.2026.108368_bib0032","series-title":"Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics","article-title":"Validated variational inference via practical posterior error bounds","author":"Huggins","year":"2020"},{"issue":"1","key":"10.1016\/j.csda.2026.108368_bib0033","article-title":"Distributed lag inspired machine learning for predicting vaccine-induced changes in COVID-19 hospitalization and intensive care unit admission","volume":"12(1)","author":"Khan","year":"2022","journal-title":"Sci. Rep."},{"issue":"4","key":"10.1016\/j.csda.2026.108368_bib0034","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1007\/BF00773470","article-title":"The two-filter formula for smoothing and an implementation of the Gaussian-sum smoother","volume":"46(4)","author":"Kitagawa","year":"1994","journal-title":"Ann. Inst. Stat. Math."},{"issue":"1","key":"10.1016\/j.csda.2026.108368_bib0035","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/10618600.1996.10474692","article-title":"Monte Carlo filter and smoother for non-Gaussian nonlinear state space models","volume":"5","author":"Kitagawa","year":"1996","journal-title":"J. Comput. Graph. Stat."},{"key":"10.1016\/j.csda.2026.108368_bib0036","article-title":"Estimating the time-varying reproduction number of COVID-19 with a state-space method","volume":"17(1)","author":"Koyama","year":"2021","journal-title":"PLoS Comput. Biol."},{"key":"10.1016\/j.csda.2026.108368_bib0037","series-title":"Distributed Lags and Investment Analysis","author":"Koyck","year":"1954"},{"key":"10.1016\/j.csda.2026.108368_bib0038","article-title":"Mask wearing in community settings reduces SARS-CoV-2 transmission","volume":"119(23)","author":"Leech","year":"2022","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"2","key":"10.1016\/j.csda.2026.108368_bib0039","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1080\/10618600.2016.1237363","article-title":"Divide-and-conquer with sequential Monte Carlo","volume":"26(2)","author":"Lindsten","year":"2017","journal-title":"J. Comput. Graph. Stat."},{"issue":"2","key":"10.1016\/j.csda.2026.108368_bib0040","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.jeconom.2021.05.002","article-title":"Fast and accurate variational inference for models with many latent variables","volume":"230(2)","author":"Loaiza-Maya","year":"2022","journal-title":"J. Econom."},{"key":"10.1016\/j.csda.2026.108368_bib0041","series-title":"Proceedings of the 41st International Conference on Machine Learning","first-page":"35039","article-title":"Online variational sequential Monte Carlo","author":"Mastrototaro","year":"2024"},{"issue":"16","key":"10.1016\/j.csda.2026.108368_bib0042","doi-asserted-by":"crossref","first-page":"4177","DOI":"10.1109\/TSP.2019.2926035","article-title":"High-dimensional filtering using nested sequential Monte Carlo","volume":"67(16)","author":"Naesseth","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"10.1016\/j.csda.2026.108368_bib0043","series-title":"Handbook of Markov Chain Monte Carlo","article-title":"MCMC using hamiltonian dynamics","author":"Neal","year":"2011"},{"issue":"446","key":"10.1016\/j.csda.2026.108368_bib0044","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1080\/01621459.1999.10474153","article-title":"Filtering via simulation: auxiliary particle filters","volume":"94(446)","author":"Pitt","year":"1999","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2026.108368_bib0045","series-title":"Time Series: Modeling, Computation and Inference","author":"Prado","year":"2021"},{"issue":"2","key":"10.1016\/j.csda.2026.108368_bib0046","first-page":"1","article-title":"Toward accurate spatiotemporal COVID-19 risk scores using high-resolution real-world mobility data","volume":"8(2)","author":"Rambhatla","year":"2022","journal-title":"ACM Trans. Spatial Algo. Syst. (TSAS)"},{"key":"10.1016\/j.csda.2026.108368_bib0047","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1002\/asmb.628","article-title":"Revisiting distributed lag models through a Bayesian perspective","volume":"22(2)","author":"Ravines","year":"2006","journal-title":"Appl. Stoch. Models Bus. Ind."},{"key":"10.1016\/j.csda.2026.108368_bib0048","series-title":"BIN models for trade-by-trade data","author":"Rydberg","year":"2000"},{"issue":"2","key":"10.1016\/j.csda.2026.108368_bib0049","doi-asserted-by":"crossref","first-page":"393","DOI":"10.2307\/1907729","article-title":"On a family of lag distributions","volume":"28(2)","author":"Solow","year":"1960","journal-title":"Econometrica"},{"issue":"2","key":"10.1016\/j.csda.2026.108368_bib0050","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1093\/biomet\/asy054","article-title":"Calibrating general posterior credible regions","volume":"106","author":"Syring","year":"2019","journal-title":"Biometrika"},{"issue":"1","key":"10.1016\/j.csda.2026.108368_bib0051","doi-asserted-by":"crossref","DOI":"10.1007\/s11222-021-10062-2","article-title":"Updating variational bayes: fast sequential posterior inference","volume":"32(1)","author":"Tomasetti","year":"2022","journal-title":"Stat. Comput."},{"issue":"6","key":"10.1016\/j.csda.2026.108368_bib0052","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1093\/aje\/kwh255","article-title":"Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures","volume":"160(6)","author":"Wallinga","year":"2004","journal-title":"Am. J. Epidemiol."},{"key":"10.1016\/j.csda.2026.108368_bib0053","series-title":"Proceedings of the 25th International Conference on Artificial Intelligence and Statistics","first-page":"8884","article-title":"Structured variational inference in bayesian state-space models","author":"Wang","year":"2022"},{"issue":"550","key":"10.1016\/j.csda.2026.108368_bib0054","doi-asserted-by":"crossref","first-page":"1014","DOI":"10.1080\/01621459.2024.2392907","article-title":"Statistical inference for networks of high-dimensional point processes","volume":"120(550)","author":"Wang","year":"2025","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2026.108368_bib0055","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1111\/j.1541-0420.2007.01039.x","article-title":"Bayesian distributed lag models: estimating effects of particulate matter air pollution on daily mortality","volume":"65(1)","author":"Welty","year":"2009","journal-title":"Biometrics"},{"key":"10.1016\/j.csda.2026.108368_bib0056","series-title":"Bayesian Forecasting and Dynamic Models","author":"West","year":"1997"},{"issue":"389","key":"10.1016\/j.csda.2026.108368_bib0057","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1080\/01621459.1985.10477131","article-title":"Dynamic generalized linear models and bayesian forecasting","volume":"80(389)","author":"West","year":"1985","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"10.1016\/j.csda.2026.108368_bib0058","doi-asserted-by":"crossref","DOI":"10.1007\/s11222-023-10356-7","article-title":"Stochastic variational inference for GARCH models","volume":"34(1)","author":"Xuan","year":"2024","journal-title":"Stat. Comput."},{"issue":"6","key":"10.1016\/j.csda.2026.108368_bib0059","doi-asserted-by":"crossref","DOI":"10.1007\/s11222-024-10488-4","article-title":"Natural gradient hybrid variational inference with application to deep mixed models","volume":"34(6)","author":"Zhang","year":"2024","journal-title":"Stat. Comput."}],"container-title":["Computational Statistics & Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S016794732600037X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S016794732600037X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T13:42:09Z","timestamp":1778074929000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S016794732600037X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9]]},"references-count":59,"alternative-id":["S016794732600037X"],"URL":"https:\/\/doi.org\/10.1016\/j.csda.2026.108368","relation":{},"ISSN":["0167-9473"],"issn-type":[{"value":"0167-9473","type":"print"}],"subject":[],"published":{"date-parts":[[2026,9]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Fast approximate posterior inference for modeling disease dynamics via state-space models","name":"articletitle","label":"Article Title"},{"value":"Computational Statistics & Data Analysis","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.csda.2026.108368","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"108368"}}