{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:35:24Z","timestamp":1787340924052,"version":"build-2736575974"},"reference-count":41,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM\/ASA J. Uncertainty Quantification"],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>We investigate nonlinear state-space models without a closed-form transition density and propose reformulating such models over their latent noise variables rather than their latent state variables. In doing so the tractable noise density emerges in place of the intractable transition density. For importance sampling methods such as the auxiliary particle filter, this enables importance weights to be computed where they could not be otherwise. As case studies we take two multivariate marine biogeochemical models and perform state and parameter estimation using the particle marginal Metropolis--Hastings sampler. For the particle filter within this sampler, we compare several proposal strategies over noise variables, all based on lookaheads with the unscented Kalman filter. These strategies are compared using conventional means for assessing Metropolis--Hastings efficiency, as well as with a novel metric called the conditional acceptance rate for assessing the consequences of using an estimated, and not exact, likelihood. Results indicate the utility of reformulating the model over noise variables, particularly for fast-mixing process models.<\/jats:p>","DOI":"10.1137\/130915376","type":"journal-article","created":{"date-parts":[[2013,12,5]],"date-time":"2013-12-05T12:49:12Z","timestamp":1386247752000},"page":"494-521","source":"Crossref","is-referenced-by-count":12,"title":["On Disturbance State-Space Models and the Particle Marginal Metropolis-Hastings Sampler"],"prefix":"10.1137","volume":"1","author":[{"given":"Lawrence M.","family":"Murray","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emlyn M.","family":"Jones","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John","family":"Parslow","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,12,5]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2009.00736.x"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2006.00552.x"},{"key":"atypb3","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1080\/10618600.1998.10474787","volume":"7","author":"Brooks S. P.","year":"1998","journal-title":"J. Comput. Graph. Statist."},{"key":"atypb4","unstructured":"M. H. Carpenter and C. A. Kennedy,\n                      Fourth-Order \\textup2N-Storage Runge-Kutta Schemes\n                      , Technical memorandum 109112, NASA, Washington, DC, 1994."},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"P. Del Moral,\n                      Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications\n                      , Springer, New York, 2004.","DOI":"10.1007\/978-1-4684-9393-1"},{"key":"atypb6","unstructured":"A. Doucet, N. de Freitas, K. Murphy, and S. Russel,\n                      Rao-Blackwellised particle filtering for dynamic Bayesian networks\n                      , in Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann, San Francisco, CA, 2000, pp. 176-183."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1029\/94JC00572"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2009.932223"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2008.00661.x"},{"key":"atypb10","unstructured":"A. Gelman, W. Gilks, and G. Roberts,\n                      Efficient Metropolis Jumping Rules\n                      , Technical report 94-10, University of Cambridge, Cambridge, UK, 1994."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2007.05.019"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1098\/rsfs.2011.0047"},{"key":"atypb13","first-page":"107","volume":"140","author":"Gordon N.","year":"1993","journal-title":"IEE Proc. F"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/57.1.97"},{"key":"atypb15","first-page":"60","volume":"45","author":"Holling C. S.","year":"1966","journal-title":"Mem. Entomology Soc. Canada"},{"key":"atypb16","doi-asserted-by":"crossref","first-page":"7","DOI":"10.22499\/2.5901.003","volume":"59","author":"Jones E.","year":"2010","journal-title":"Australian Meteorological Oceanographic J."},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"S. J. Julier and J. K. Uhlmann,\n                      A new extension of the Kalman filter to nonlinear systems\n                      , in Proceedings of AeroSense: The 11th International Symposium on Aerospace\/Defense Sensing, Simulation and Controls, Multi Sensor Fusion, Tracking and Resource Management, Orlando, FL, 1997.","DOI":"10.1117\/12.280797"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1080\/00031305.1998.10480547"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(99)00141-5"},{"key":"atypb20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/10618600.1996.10474692","volume":"5","author":"Kitagawa G.","year":"1996","journal-title":"J. Comput. Graph. Statist."},{"key":"atypb21","unstructured":"A. Lee,\n                      Towards Smooth Particle Filters for Likelihood Estimation with Multivariate Latent Variables\n                      , Master's thesis, University of British Columbia, Vancouver, Canada, 2008."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1214\/12-STS401"},{"key":"atypb23","unstructured":"A. Lotka,\n                      Elements of Physical Biology\n                      , Williams & Wilkins, Baltimore, MD, 1925."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1063\/1.1699114"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1109\/TPDS.2011.61"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2010.2096418"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1080\/00207179308934379"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1890\/12-0312.1"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1999.10474153"},{"key":"atypb30","unstructured":"M. K. Pitt,\n                      Smooth Particle Filters for Likelihood Evaluation and Maximisation\n                      , Technical report 651, Department of Economics, The University of Warwick, Coventry, UK, 2002."},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.06.004"},{"key":"atypb32","unstructured":"C. E. Rasmussen and H. Nickisch,\n                      GPML MATLAB Code\n                      , http:\/\/www.gaussianprocess.org\/gpml\/ code\/ (2011)."},{"key":"atypb33","doi-asserted-by":"crossref","unstructured":"C. E. Rasmussen and C. K. I. Williams,\n                      Gaussian Processes for Machine Learning\n                      , MIT Press, Cambridge, MA, 2006.","DOI":"10.7551\/mitpress\/3206.001.0001"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/88.3.603"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2008.919531"},{"key":"atypb36","unstructured":"G. L. Smith, S. F. Schmidt, and L. A. McGee,\n                      Application of Statistical Filter Theory to the Optimal Estimation of Position and Velocity on Board a Circumlunar Vehicle\n                      , Technical report, NASA, Washington, DC, 1962."},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1007\/BF00386670"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1093\/plankt\/14.1.157"},{"key":"atypb39","first-page":"584","author":"van der Merwe R.","year":"2000","journal-title":"UK"},{"key":"atypb40","first-page":"409","author":"Volterra V.","year":"1931","journal-title":"New York"},{"key":"atypb41","first-page":"153","author":"Wan E. 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