{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T01:27:14Z","timestamp":1768699634182,"version":"3.49.0"},"reference-count":60,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,5,13]],"date-time":"2023-05-13T00:00:00Z","timestamp":1683936000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Najran University","award":["05R18P02820"],"award-info":[{"award-number":["05R18P02820"]}]},{"name":"Saudi Arabia Cultural Bureau","award":["05R18P02820"],"award-info":[{"award-number":["05R18P02820"]}]},{"name":"ERDF Deep Digital Cornwall","award":["05R18P02820"],"award-info":[{"award-number":["05R18P02820"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The epistemic uncertainty in coronavirus disease (COVID-19) model-based predictions using complex noisy data greatly affects the accuracy of pandemic trend and state estimations. Quantifying the uncertainty of COVID-19 trends caused by different unobserved hidden variables is needed to evaluate the accuracy of the predictions for complex compartmental epidemiological models. A new approach for estimating the measurement noise covariance from real COVID-19 pandemic data has been presented based on the marginal likelihood (Bayesian evidence) for Bayesian model selection of the stochastic part of the Extended Kalman filter (EKF), with a sixth-order nonlinear epidemic model, known as the SEIQRD (Susceptible\u2013Exposed\u2013Infected\u2013Quarantined\u2013Recovered\u2013Dead) compartmental model. This study presents a method for testing the noise covariance in cases of dependence or independence between the infected and death errors, to better understand their impact on the predictive accuracy and reliability of EKF statistical models. The proposed approach is able to reduce the error in the quantity of interest compared to the arbitrarily chosen values in the EKF estimation.<\/jats:p>","DOI":"10.3390\/s23104734","type":"journal-article","created":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T02:56:57Z","timestamp":1684119417000},"page":"4734","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Bayesian Noise Modelling for State Estimation of the Spread of COVID-19 in Saudi Arabia with Extended Kalman Filters"],"prefix":"10.3390","volume":"23","author":[{"given":"Lamia","family":"Alyami","sequence":"first","affiliation":[{"name":"Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn Campus, Penryn TR10 9FE, UK"},{"name":"Department of Mathematics, College of Science, Najran University, Najran 11001, Saudi Arabia"}]},{"given":"Deepak Kumar","family":"Panda","sequence":"additional","affiliation":[{"name":"Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn Campus, Penryn TR10 9FE, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8394-5303","authenticated-orcid":false,"given":"Saptarshi","family":"Das","sequence":"additional","affiliation":[{"name":"Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn Campus, Penryn TR10 9FE, UK"},{"name":"Institute for Data Science and Artificial Intelligence, University of Exeter, Exeter EX4 4QE, UK"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Alyami, L., and Das, S. 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