{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T09:37:04Z","timestamp":1777196224576,"version":"3.51.4"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2022,9,30]],"date-time":"2022-09-30T00:00:00Z","timestamp":1664496000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,9,30]],"date-time":"2022-09-30T00:00:00Z","timestamp":1664496000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000266","name":"engineering and physical sciences research council","doi-asserted-by":"publisher","award":["EP\/J018317\/1"],"award-info":[{"award-number":["EP\/J018317\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"engineering and physical sciences research council","doi-asserted-by":"publisher","award":["PhD studentship"],"award-info":[{"award-number":["PhD studentship"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2022,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>One of the major challenges in Bayesian optimal design is to approximate the expected utility function in an accurate and computationally efficient manner. We focus on Shannon information gain, one of the most widely used utilities when the experimental goal is parameter inference. We compare the performance of various methods for approximating expected Shannon information gain in common nonlinear models from the statistics literature, with a particular emphasis on Laplace importance sampling (LIS) and approximate Laplace importance sampling (ALIS), a new method that aims to reduce the computational cost of LIS. Specifically, in order to centre the importance distributions LIS requires computation of the posterior mode for each of a large number of simulated possibilities for the response vector. ALIS substantially reduces the amount of numerical optimization that is required, in some cases eliminating all optimization, by centering the importance distributions on the data-generating parameter values wherever possible. Both methods are thoroughly compared with existing approximations including Double Loop Monte Carlo, nested importance sampling, and Laplace approximation. It is found that LIS and ALIS both give an efficient trade-off between mean squared error and computational cost for utility estimation, and ALIS can be up to 70% cheaper than LIS. Usually ALIS gives an approximation that is cheaper but less accurate than LIS, while still being efficient, giving a useful addition to the suite of efficient methods. However, we observed one case where ALIS is both cheaper and more accurate. In addition, for the first time we show that LIS and ALIS yield superior designs to existing methods in problems with large numbers of model parameters when combined with the approximate co-ordinate exchange algorithm for design optimization.<\/jats:p>","DOI":"10.1007\/s11222-022-10159-2","type":"journal-article","created":{"date-parts":[[2022,9,30]],"date-time":"2022-09-30T09:11:42Z","timestamp":1664529102000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Approximate Laplace importance sampling for the estimation of expected Shannon information gain in high-dimensional Bayesian design for nonlinear models"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2826-0501","authenticated-orcid":false,"given":"Yiolanda","family":"Englezou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8868-3146","authenticated-orcid":false,"given":"Timothy W.","family":"Waite","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7648-429X","authenticated-orcid":false,"given":"David C.","family":"Woods","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,9,30]]},"reference":[{"key":"10159_CR1","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316757","volume-title":"Nonlinear Regression Analysis and its Applications","author":"DM Bates","year":"1988","unstructured":"Bates, D.M., Watts, D.G.: Nonlinear Regression Analysis and its Applications. Wiley, New York (1988)"},{"key":"10159_CR2","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1016\/j.cma.2018.01.053","volume":"334","author":"J Beck","year":"2018","unstructured":"Beck, J., Dia, B.M., Espath, L.F., Long, Q., Tempone, R.: Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain. Comput. Methods Appl. Mech. Eng. 334, 523\u2013553 (2018)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10159_CR3","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1214\/aos\/1176344689","volume":"7","author":"JM Bernardo","year":"1979","unstructured":"Bernardo, J.M.: Expected information as expected utility. Ann. Stat. 7, 686\u2013690 (1979)","journal-title":"Ann. Stat."},{"key":"10159_CR4","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1137\/141000671","volume":"59","author":"J Bezanson","year":"2017","unstructured":"Bezanson, J., Edelman, A., Karpinski, S., Shah, V.B.: Julia: a fresh approach to numerical computing. SIAM Rev. 59, 65\u201398 (2017)","journal-title":"SIAM Rev."},{"key":"10159_CR5","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1214\/ss\/1177009939","volume":"10","author":"K Chaloner","year":"1995","unstructured":"Chaloner, K., Verdinelli, I.: Bayesian experimental design: a review. Stat. Sci. 10, 273\u2013304 (1995)","journal-title":"Stat. Sci."},{"key":"10159_CR6","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1214\/aoms\/1177728915","volume":"24","author":"H Chernoff","year":"1953","unstructured":"Chernoff, H.: Locally optimal designs for estimating parameters. Ann. Math. Stat. 24, 586\u2013602 (1953)","journal-title":"Ann. Math. Stat."},{"key":"10159_CR7","doi-asserted-by":"publisher","first-page":"903","DOI":"10.1080\/01621459.1997.10474045","volume":"92","author":"TJ DiCiccio","year":"1997","unstructured":"DiCiccio, T.J., Kass, R.E., Raftery, A., Wasserman, L.: Computing Bayes factors by combining simulation and asymptotic approximations. J. Am. Stat. Assoc. 92, 903\u2013915 (1997)","journal-title":"J. Am. Stat. Assoc."},{"key":"10159_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v040.i08","volume":"40","author":"D Eddelbuettel","year":"2011","unstructured":"Eddelbuettel, D., Fran\u00e7ois, R., Allaire, J., Ushey, K., Kou, Q., Russel, N., Chambers, J., Bates, D.: Rcpp: Seamless R and C++ integration. J. Stat. Softw. 40, 1\u201318 (2011)","journal-title":"J. Stat. Softw."},{"key":"10159_CR9","doi-asserted-by":"publisher","first-page":"1054","DOI":"10.1016\/j.csda.2013.02.005","volume":"71","author":"D Eddelbuettel","year":"2014","unstructured":"Eddelbuettel, D., Sanderson, C.: RcppArmadillo: accelerating R with high-performance C++ linear algebra. Comput. Stat. Data Anal. 71, 1054\u20131063 (2014)","journal-title":"Comput. Stat. Data Anal."},{"key":"10159_CR10","unstructured":"Englezou, Y.: Bayesian design for calibration of physical models, PhD thesis, University of Southampton. (2018) https:\/\/eprints.soton.ac.uk\/427145\/"},{"key":"10159_CR11","unstructured":"Feng, C.: Optimal Bayesian experimental design in the presence of model error, Master\u2019s thesis, Center for Computational Engineering, Massachussets Institute of Technology (2015)"},{"key":"10159_CR12","unstructured":"Feng, C., Marzouk, Y.M.: A layered multiple importance sampling scheme for focused optimal Bayesian experimental design. (2019) arXiv preprintarXiv:1903.11187"},{"key":"10159_CR13","unstructured":"Foster, A., Jankowiak, M., Bingham, E., Horsfall, P., Teh, Y.\u00a0W., Rainforth, T., Goodman, N.: Variational Bayesian optimal experimental design (2019). arXiv preprintarXiv:1903.05480"},{"key":"10159_CR14","unstructured":"Ge, H., Xu, K., Ghahramani, Z.: Turing: a language for flexible probabilistic inference, in \u2018International Conference on Artificial Intelligence and Statistics, AISTATS 2018, 9-11 April 2018, Playa Blanca, Lanzarote, Canary Islands, Spain\u2019, pp.\u00a01682\u20131690 (2018). http:\/\/proceedings.mlr.press\/v84\/ge18b.html"},{"key":"10159_CR15","doi-asserted-by":"publisher","DOI":"10.1201\/b16018","volume-title":"Bayesian Data Analysis","author":"A Gelman","year":"2013","unstructured":"Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B.: Bayesian Data Analysis, 3rd edn. Chapman and Hall\/CRC, Boca Raton (2013)","edition":"3"},{"key":"10159_CR16","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1016\/j.jcp.2012.08.013","volume":"232","author":"X Huan","year":"2013","unstructured":"Huan, X., Marzouk, Y.M.: Simulation-based optimal Bayesian experimental design for nonlinear systems. J. Comput. Phys. 232, 288\u2013317 (2013)","journal-title":"J. Comput. Phys."},{"key":"10159_CR17","volume-title":"Monte Carlo and Quasi-Monte Carlo Sampling","author":"C Lemieux","year":"2009","unstructured":"Lemieux, C.: Monte Carlo and Quasi-Monte Carlo Sampling. Springer, New York (2009)"},{"key":"10159_CR18","doi-asserted-by":"publisher","first-page":"986","DOI":"10.1214\/aoms\/1177728069","volume":"27","author":"DV Lindley","year":"1956","unstructured":"Lindley, D.V., et al.: On a measure of the information provided by an experiment. Ann. Math. Stat. 27, 986\u20131005 (1956)","journal-title":"Ann. Math. Stat."},{"key":"10159_CR19","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/j.cma.2013.02.017","volume":"259","author":"Q Long","year":"2013","unstructured":"Long, Q., Scavino, M., Tempone, R., Wang, S.: Fast estimation of expected information gains for Bayesian experimental designs based on Laplace approximations. Comput. Methods Appl. Mech. Eng. 259, 24\u201339 (2013)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10159_CR20","doi-asserted-by":"publisher","first-page":"788","DOI":"10.1198\/016214504000001123","volume":"99","author":"P M\u00fcller","year":"2004","unstructured":"M\u00fcller, P., Sans\u00f3, B., De Iorio, M.: Optimal Bayesian design by inhomogeneous Markov chain simulation. J. Am. Stat. Assoc. 99, 788\u2013798 (2004)","journal-title":"J. Am. Stat. Assoc."},{"key":"10159_CR21","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/s11222-017-9734-x","volume":"28","author":"AM Overstall","year":"2018","unstructured":"Overstall, A.M., McGree, J.M., Drovandi, C.C.: An approach for finding fully Bayesian optimal designs using normal-based approximations to loss functions. Stat. Comput. 28, 343\u2013358 (2018)","journal-title":"Stat. Comput."},{"key":"10159_CR22","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1080\/00401706.2016.1251495","volume":"59","author":"AM Overstall","year":"2017","unstructured":"Overstall, A.M., Woods, D.C.: Bayesian design of experiments using approximate coordinate exchange. Technometrics 59, 458\u2013470 (2017)","journal-title":"Technometrics"},{"issue":"13","key":"10159_CR23","first-page":"1","volume":"95","author":"A Overstall","year":"2019","unstructured":"Overstall, A., Woods, D., Adamou, M.: acebayes: An R package for Bayesian optimal design of experiments via approximate coordinate exchange. J. Stat. Softw. 95(13), 1\u201333 (2019)","journal-title":"J. Stat. Softw."},{"key":"10159_CR24","doi-asserted-by":"publisher","first-page":"1063","DOI":"10.3390\/e17031063","volume":"17","author":"E Ryan","year":"2015","unstructured":"Ryan, E., Drovandi, C., Pettitt, A.: Fully Bayesian experimental design for pharmacokinetic studies. Entropy 17, 1063\u20131089 (2015)","journal-title":"Entropy"},{"key":"10159_CR25","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1198\/1061860032012","volume":"12","author":"KJ Ryan","year":"2003","unstructured":"Ryan, K.J.: Estimating expected information gains for experimental designs with application to the random fatigue-limit model. J. Comput. Graph. Stat. 12, 585\u2013603 (2003)","journal-title":"J. Comput. Graph. Stat."},{"key":"10159_CR26","doi-asserted-by":"publisher","first-page":"1183","DOI":"10.1007\/s11222-020-09938-6","volume":"30","author":"S Senarathne","year":"2020","unstructured":"Senarathne, S., Drovandi, C.C., McGree, J.M.: A Laplace-based algorithm for Bayesian adaptive design. Stat. Comput. 30, 1183\u20131208 (2020)","journal-title":"Stat. Comput."},{"key":"10159_CR27","unstructured":"Stan Development Team (2021) Stan Modeling Language Users Guide and Reference Manual, 2.27. https:\/\/mc-stan.org"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-022-10159-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-022-10159-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-022-10159-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T12:32:37Z","timestamp":1667219557000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-022-10159-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,30]]},"references-count":27,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["10159"],"URL":"https:\/\/doi.org\/10.1007\/s11222-022-10159-2","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,30]]},"assertion":[{"value":"27 July 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 September 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 September 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"82"}}