{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T07:13:08Z","timestamp":1771657988792,"version":"3.50.1"},"reference-count":41,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2022,8,23]],"date-time":"2022-08-23T00:00:00Z","timestamp":1661212800000},"content-version":"am","delay-in-days":365,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#am"},{"start":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T00:00:00Z","timestamp":1629676800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS 1513657"],"award-info":[{"award-number":["DMS 1513657"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Biometrical J"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The self\u2010exciting Hawkes point process model (Hawkes, 1971) has been used to describe and forecast communicable diseases. A variant of the Hawkes model, called the recursive model, was proposed by Schoenberg et\u00a0al. (2019) and has been shown to fit well to various epidemic disease datasets. Unlike the Hawkes model, the recursive model allows the productivity to vary as the overall rate of incidence of the disease varies. Here, we extend the data\u2010driven nonparametric expectation\u2010maximization method of Marsan and Lenglin\u00e9 (2008) in order to fit the recursive model without assuming a particular functional form for the productivity. The nonparametric recursive model is trained to fit to weekly reported cases of mumps in Pennsylvania during the January 1970\u2013September 1990 time frame and then assessed using one week forecasts for the October 1990\u2013December 2001 time period. Both its training and predictive ability are evaluated compared to that of other candidate models, such as Hawkes and SVEILR (susceptible, vaccinated, exposed, infected, lightly infected, recovered) compartmental\u00a0models.<\/jats:p>","DOI":"10.1002\/bimj.202000245","type":"journal-article","created":{"date-parts":[[2021,8,24]],"date-time":"2021-08-24T06:34:28Z","timestamp":1629786868000},"page":"20-32","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Nonparametric estimation of recursive point processes with application to mumps in Pennsylvania"],"prefix":"10.1002","volume":"64","author":[{"given":"Andrew","family":"Kaplan","sequence":"first","affiliation":[{"name":"Department of Statistics University of California  Los Angeles CA USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junhyung","family":"Park","sequence":"additional","affiliation":[{"name":"Department of Statistics University of California  Los Angeles CA USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Conor","family":"Kresin","sequence":"additional","affiliation":[{"name":"Department of Statistics University of California  Los Angeles CA USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4791-7345","authenticated-orcid":false,"given":"Frederic","family":"Schoenberg","sequence":"additional","affiliation":[{"name":"Department of Statistics University of California  Los Angeles CA USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,8,23]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2011.641402"},{"key":"e_1_2_9_3_1","unstructured":"Centers for Disease Control and Prevention. (2011).Vaccine coverage levels \u2013 United States 1962\u20132009. The Pink Book (11th ed.). Author."},{"key":"e_1_2_9_4_1","unstructured":"Centers for Disease Control and Prevention. (2019)Epidemiology and prevention of vaccine\u2010preventable diseases. The Pink Book (13th ed.). Author."},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/env.2168"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1586\/14760584.2015.964212"},{"key":"e_1_2_9_7_1","unstructured":"Elflein J.(2019).New cases of mumps per 100 000 population in the U.S. from 1970 to 2017.Statista.https:\/\/www.statista.com\/statistics\/186404\/cases-of-mumps-in-the-us-since-1970"},{"key":"e_1_2_9_8_1","unstructured":"Gordon J.(2017).nphawkes R package version 0.1.https:\/\/github.com\/mrjoshuagordon\/nphawkes"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.spasta.2015.06.001"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/58.1.83"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.epidem.2019.100354"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1927.0118"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1080\/00949655.2017.1422126"},{"key":"e_1_2_9_14_1","doi-asserted-by":"crossref","unstructured":"Kong Q. Rizoiu M.\u2010A. Xie L.(2020).Modeling information cascades with self\u2010exciting processes via generalized epidemic models. InWSDM '20: ACM International Conference on Web Search and Data Mining Houston TX (pp.286\u2013294).ACM.","DOI":"10.1145\/3336191.3371821"},{"key":"e_1_2_9_15_1","unstructured":"Kresin C. Schoenberg F. &Mohler G.(2020).Comparison of Hawkes and SEIR models for the spread of Covid\u201019.Statistical Science. to appear."},{"issue":"1","key":"e_1_2_9_16_1","first-page":"1","article-title":"A nonparametric EM algorithm for multiscale Hawkes processes","volume":"1","author":"Lewis E.","year":"2011","journal-title":"Journal of Nonparametric Statistics"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1126\/scitranslmed.aao5945"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.3390\/ijerph15010033"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1148783"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2011.01684.x"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOAS743"},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijforecast.2014.01.004"},{"key":"e_1_2_9_23_1","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2011.ap09546"},{"key":"e_1_2_9_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02480216"},{"key":"e_1_2_9_25_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1988.10478560"},{"key":"e_1_2_9_26_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1003403601725"},{"key":"e_1_2_9_27_1","doi-asserted-by":"crossref","unstructured":"Park J. Chaffee A. Harrigan R. &Schoenberg F. P.(2020).A non\u2010parametric Hawkes model of the spread of Ebola in West Africa.Journal of Applied Statistics. Advance online publication.https:\/\/doi.org\/10.1080\/02664763.2020.1825646.","DOI":"10.1080\/02664763.2020.1825646"},{"key":"e_1_2_9_28_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2012.01809.x"},{"key":"e_1_2_9_29_1","doi-asserted-by":"crossref","unstructured":"Rizoiu M.\u2010A. Mishra S. Kong Q. Carman M. &Xie L.(2018).SIR\u2010Hawkes: Linking epidemic models and Hawkes processes to model diffusions in finite populations. 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Cross A. &Burke D.(2018).Counts of mumps reported in United States of America: 1923\u20102017 (version 2.0 April 1): Project Tycho data release https:\/\/doi.org\/10.25337\/T7\/ptycho.v2.0\/US.36989005"},{"key":"e_1_2_9_37_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214508000000148"},{"key":"e_1_2_9_38_1","unstructured":"Wang J.(2019).Point process models for the spread of coccidioidomycosis an infectious disease in California(master's thesis).Department of Statistics University of California Los Angeles CA."},{"key":"e_1_2_9_39_1","doi-asserted-by":"crossref","unstructured":"Wheatley S. Filimonov V. &Sornette D.(2014).Estimation of the Hawkes process with renewal immigration using the EM algorithm. Swiss Finance Institute Research Paper 14\u201353.","DOI":"10.2139\/ssrn.2477432"},{"key":"e_1_2_9_40_1","unstructured":"Yang A. S.(2019).Modeling the transmission dynamics of pertussis using recursive point process and SEIR model(master's thesis.Department of Statistics University of California Los Angeles CA."},{"key":"e_1_2_9_41_1","first-page":"4938","article-title":"Online learning for multivariate Hawkes processes","volume":"30","author":"Yang Y.","year":"2017","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_2_9_42_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssa.12429"}],"container-title":["Biometrical Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/bimj.202000245","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/bimj.202000245","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/am-pdf\/10.1002\/bimj.202000245","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/bimj.202000245","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T05:52:24Z","timestamp":1693201944000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/bimj.202000245"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,23]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["10.1002\/bimj.202000245"],"URL":"https:\/\/doi.org\/10.1002\/bimj.202000245","archive":["Portico"],"relation":{},"ISSN":["0323-3847","1521-4036"],"issn-type":[{"value":"0323-3847","type":"print"},{"value":"1521-4036","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,23]]},"assertion":[{"value":"2020-08-16","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-03-08","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-08-23","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}