{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T19:08:04Z","timestamp":1778526484436,"version":"3.51.4"},"reference-count":63,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,11,19]],"date-time":"2019-11-19T00:00:00Z","timestamp":1574121600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,19]],"date-time":"2019-11-19T00:00:00Z","timestamp":1574121600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s00180-019-00936-5","type":"journal-article","created":{"date-parts":[[2019,11,19]],"date-time":"2019-11-19T23:01:48Z","timestamp":1574204508000},"page":"111-133","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Adaptive method for indirect identification of the statistical properties of random fields in a Bayesian framework"],"prefix":"10.1007","volume":"35","author":[{"given":"Guillaume","family":"Perrin","sequence":"first","affiliation":[]},{"given":"Christian","family":"Soize","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,11,19]]},"reference":[{"issue":"6","key":"936_CR1","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","volume":"19","author":"H Akaike","year":"1974","unstructured":"Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716\u2013723","journal-title":"IEEE Trans Autom Control"},{"issue":"9","key":"936_CR2","doi-asserted-by":"crossref","first-page":"3134","DOI":"10.1016\/j.jcp.2009.12.033","volume":"229","author":"M Arnst","year":"2010","unstructured":"Arnst M, Ghanem R, Soize C (2010) Identification of bayesian posteriors for coefficients of chaos expansions. J Comput Phys 229(9):3134\u20133154","journal-title":"J Comput Phys"},{"issue":"1\u20133","key":"936_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0895-7177(00)00225-9","volume":"33","author":"J Atwell","year":"2001","unstructured":"Atwell J, King B (2001) Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations. Math Comput Modell 33(1\u20133):1\u201319","journal-title":"Math Comput Modell"},{"issue":"3","key":"936_CR4","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1007\/s11222-011-9273-9","volume":"22","author":"Y Auffray","year":"2012","unstructured":"Auffray Y, Barbillon P, Marin JM (2012) Maximin design on non hypercube domains and kernel interpolation. Stat Comput 22(3):703\u2013712","journal-title":"Stat Comput"},{"key":"936_CR5","volume-title":"Handbook of uncertainty quantification","author":"I Bilionis","year":"2015","unstructured":"Bilionis I, Zabaras N (2015) Bayesian uncertainty propagation using gaussian processes. In: Ghanem R, Higdon D, Owhadi H (eds) Handbook of uncertainty quantification. Springer, New York"},{"key":"936_CR6","volume-title":"Time series analysis: forecasting and control","author":"G Box","year":"1970","unstructured":"Box G, Jenkins G (1970) Time series analysis: forecasting and control. Holden-Day, San Francisco"},{"key":"936_CR7","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.cma.2015.08.006","volume":"297","author":"P Chen","year":"2015","unstructured":"Chen P, Schwab C (2015) Sparse-grid, reduced basis bayesian inversion. Comput Methods Appl Mech Eng 297:84\u2013115","journal-title":"Comput Methods Appl Mech Eng"},{"key":"936_CR8","doi-asserted-by":"crossref","first-page":"2415","DOI":"10.1016\/j.jsv.2012.10.011","volume":"332","author":"D Clouteau","year":"2013","unstructured":"Clouteau D, Cottereau R, Lombaert G (2013) Dynamics of structures coupled with elastic media\u2014a review of numerical models and methods. J Sound Vib 332:2415\u20132436","journal-title":"J Sound Vib"},{"key":"936_CR9","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1080\/01621459.2015.1096787","volume":"111","author":"PR Conrad","year":"2016","unstructured":"Conrad PR, Marzouk YM, Pillai NS, Smith A (2016) Accelerating asymptotically exact MCMC for computationally intensive models via local approximations. J Am Stat Assoc 111:1591\u20131607","journal-title":"J Am Stat Assoc"},{"issue":"1","key":"936_CR10","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1137\/16M1084080","volume":"6","author":"PR Conrad","year":"2018","unstructured":"Conrad PR, Davis A, Marzouk YM, Pillai NS, Smith A (2018) Parallel local approximation MCMC for expensive models. SIAM\/ASA J Uncertain Quantif 6(1):39\u2013373","journal-title":"SIAM\/ASA J Uncertain Quantif"},{"issue":"1","key":"936_CR11","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1137\/15M1033162","volume":"6","author":"G Damblin","year":"2013","unstructured":"Damblin G, Barbillonz P, Keller M, Pasanisi A, Parent E (2013) Adaptive numerical designs for the calibration of computer codes. SIAM\/ASA J Uncertain Quantif 6(1):151\u2013179","journal-title":"SIAM\/ASA J Uncertain Quantif"},{"issue":"2","key":"936_CR12","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1080\/00401706.2012.676951","volume":"54","author":"D Dragulji\u0107","year":"2012","unstructured":"Dragulji\u0107 D, Santner TJ, Dean AM (2012) Noncollapsing space-filling designs for bounded nonrectangular regions. Technometrics 54(2):169\u2013178","journal-title":"Technometrics"},{"key":"936_CR13","doi-asserted-by":"crossref","first-page":"6395","DOI":"10.1016\/j.apm.2016.01.046","volume":"13\u201314","author":"J Emery","year":"2016","unstructured":"Emery J, Grigoriu M, Field RF Jr (2016) Bayesian methods for characterizing unknown parameters of material models. Appl Math Model 13\u201314:6395\u20136411","journal-title":"Appl Math Model"},{"key":"936_CR14","volume-title":"Design and modeling for computer experiments. Computer science and data analysis series","author":"K Fang","year":"2006","unstructured":"Fang K, Li R, Sudjianto A (2006) Design and modeling for computer experiments. Computer science and data analysis series. Chapman & Hall, London"},{"key":"936_CR15","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/S0169-7161(03)22006-X","volume":"22","author":"K Fang","year":"2003","unstructured":"Fang K, Lin D (2003) Uniform experimental designs and their applications in industry. Handb Stat 22:131\u2013178","journal-title":"Handb Stat"},{"issue":"1","key":"936_CR16","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1198\/TECH.2010.09195","volume":"53","author":"M Fielding","year":"2011","unstructured":"Fielding M, Nott DJ, Liong SY (2011) Efficient MCMC schemes for computationally expensive posterior distributions. Technometrics 53(1):16\u201328","journal-title":"Technometrics"},{"key":"936_CR17","volume-title":"Stochastic finite elements: a spectral approach","author":"R Ghanem","year":"2003","unstructured":"Ghanem R, Spanos PD (2003) Stochastic finite elements: a spectral approach, rev edn. Dover Publications, New York","edition":"rev"},{"key":"936_CR18","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s10659-012-9396-z","volume":"111","author":"J Guilleminot","year":"2013","unstructured":"Guilleminot J, Soize C (2013) On the statistical dependence for the components of random elasticity tensors exhibiting material symmetry properties. J Elast 111:109\u2013130","journal-title":"J Elast"},{"key":"936_CR19","first-page":"181","volume":"7","author":"D Higdon","year":"2003","unstructured":"Higdon D, Lee H, Holloman C (2003) Markov chain monte carlo based approaches for inference in computationally intensive inverse problems. Bayesian Stat 7:181\u2013197","journal-title":"Bayesian Stat"},{"issue":"482","key":"936_CR20","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1198\/016214507000000888","volume":"103","author":"D Higdon","year":"2008","unstructured":"Higdon D, Gattiker J, Williams B, Rightley M (2008) Computer model calibration using high-dimensional output. J Am Stat Assoc 103(482):570\u2013583","journal-title":"J Am Stat Assoc"},{"issue":"2","key":"936_CR21","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1093\/biomet\/asv002","volume":"102","author":"VR Joseph","year":"2015","unstructured":"Joseph VR, Gul E, Ba S (2015) Maximum projection designs for computer experiments. Biometrika 102(2):371\u2013380","journal-title":"Biometrika"},{"key":"936_CR22","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1111\/1467-9868.00294","volume":"63","author":"M Kennedy","year":"2001","unstructured":"Kennedy M, O\u2019Hagan A (2001) Bayesian calibration of computer models. J R Stat Soc 63:425\u2013464","journal-title":"J R Stat Soc"},{"key":"936_CR23","volume-title":"Introduction to continuum mechanics","author":"WM Lai","year":"2010","unstructured":"Lai WM, Rubin D, Krempl E (2010) Introduction to continuum mechanics. Elsevier, Inc, Amsterdam"},{"key":"936_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-90-481-3520-2","volume-title":"Spectral methods for uncertainty quantification","author":"O Le Ma\u00eetre","year":"2010","unstructured":"Le Ma\u00eetre O, Knio O (2010) Spectral methods for uncertainty quantification. Springer, New York"},{"issue":"5","key":"936_CR25","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1002\/qre.1640","volume":"31","author":"R Lekivetz","year":"2015","unstructured":"Lekivetz R, Jones B (2015) Fast flexible space-filling designs for nonrectangular regions. Qual Reliab Eng Int 31(5):829\u2013837","journal-title":"Qual Reliab Eng Int"},{"key":"936_CR26","doi-asserted-by":"crossref","first-page":"A1163","DOI":"10.1137\/130938189","volume":"36","author":"J Li","year":"2014","unstructured":"Li J, Marzouk YM (2014) Adaptive construction of surrogates for the bayesian solution of inverse problems. SIAM J Sci Comput 36:A1163\u2013A1186","journal-title":"SIAM J Sci Comput"},{"issue":"1","key":"936_CR27","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1080\/10618600.2017.1302881","volume":"27","author":"S Mak","year":"2018","unstructured":"Mak S, Joseph VR (2018) Minimax and minimax projection designs using clustering. J Comput Graph Stat 27(1):166\u2013178. https:\/\/doi.org\/10.1080\/10618600.2017.1302881","journal-title":"J Comput Graph Stat"},{"key":"936_CR28","volume-title":"Bayesian core","author":"JM Marin","year":"2007","unstructured":"Marin JM, Robert CP (2007) Bayesian core. Springer, New York"},{"issue":"6","key":"936_CR29","doi-asserted-by":"crossref","first-page":"1862","DOI":"10.1016\/j.jcp.2008.11.024","volume":"228","author":"YM Marzouk","year":"2009","unstructured":"Marzouk YM, Najm HN (2009) Dimensionality reduction and polynomial chaos acceleration of bayesian inference in inverse problems. J Comput Phys 228(6):1862\u20131902","journal-title":"J Comput Phys"},{"key":"936_CR30","doi-asserted-by":"crossref","first-page":"826","DOI":"10.4208\/cicp.2009.v6.p826","volume":"6","author":"YM Marzouk","year":"2009","unstructured":"Marzouk YM, Xiu D (2009) A stochastic collocation approach to bayesian inference in inverse problems. Commun Comput Phys 6:826\u2013847","journal-title":"Commun Comput Phys"},{"issue":"1","key":"936_CR31","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1186\/s40323-016-0075-7","volume":"3","author":"H Matthies","year":"2016","unstructured":"Matthies H, Zander E, Rosi B, Litvinenko A (2016) Parameter estimation via conditional expectation: a Bayesian inversion. Adv Model Simul Eng Sci 3(1):24","journal-title":"Adv Model Simul Eng Sci"},{"key":"936_CR32","first-page":"239","volume":"21","author":"M McKay","year":"1979","unstructured":"McKay M, Beckman R, Conover W (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21:239\u2013245","journal-title":"Technometrics"},{"issue":"4","key":"936_CR33","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1615\/IntJMultCompEng.2015011435","volume":"13","author":"MT Nguyen","year":"2015","unstructured":"Nguyen MT, Desceliers C, Soize C, Allain J, Gharbi H (2015) Multiscale identification of random elasticity field at mesoscale of a heterogeneous microstructure using multiscale experimental observations. J Multiscale Comput Eng 13(4):281\u2013295","journal-title":"J Multiscale Comput Eng"},{"key":"936_CR34","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/s11831-010-9054-1","volume":"17","author":"A Nouy","year":"2010","unstructured":"Nouy A (2010) Proper generalized decomposition and separated representations for the numerical solution of high dimensional stochastic problems. Arch Comput Methods Eng 17:403\u2013434","journal-title":"Arch Comput Methods Eng"},{"key":"936_CR35","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1017\/S0956792514000072","volume":"25","author":"A Nouy","year":"2014","unstructured":"Nouy A, Soize C (2014) Random fields representations for stochastic elliptic boundary value problems and statistical inverse problems. Eur J Appl Math 25:339\u2013373","journal-title":"Eur J Appl Math"},{"key":"936_CR36","doi-asserted-by":"publisher","first-page":"106728","DOI":"10.1016\/j.ress.2019.106728","volume":"196","author":"G. Perrin","year":"2020","unstructured":"Perrin G (2019) Adaptive calibration of a computer code with time-series output. Reliab Eng Syst Saf. https:\/\/doi.org\/10.1016\/j.ress.2019.106728","journal-title":"Reliability Engineering & System Safety"},{"issue":"1","key":"936_CR37","first-page":"37","volume":"158","author":"G Perrin","year":"2017","unstructured":"Perrin G, Cannamela C (2017) A repulsion-based method for the definition and the enrichment of opotimized space filling designs in constrained input spaces. J Soc Fr Stat 158(1):37\u201367","journal-title":"J Soc Fr Stat"},{"issue":"6","key":"936_CR38","doi-asserted-by":"crossref","first-page":"2917","DOI":"10.1137\/11084950X","volume":"34","author":"G Perrin","year":"2012","unstructured":"Perrin G, Soize C, Duhamel D, Funfschilling C (2012) Identification of polynomial chaos representations in high dimension from a set of realizations. SIAM J Sci Comput 34(6):2917\u20132945","journal-title":"SIAM J Sci Comput"},{"key":"936_CR39","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1016\/j.jcp.2013.02.036","volume":"242","author":"G Perrin","year":"2013","unstructured":"Perrin G, Soize C, Duhamel D, Funfschilling C (2013) Karhunen\u2013lo\u00e9ve expansion revisited for vector-valued random fields: scaling, errors and optimal basis. J Comput Phys 242:607\u2013622","journal-title":"J Comput Phys"},{"key":"936_CR40","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1137\/130905095","volume":"2","author":"G Perrin","year":"2014","unstructured":"Perrin G, Soize C, Duhamel D, Funfschilling C (2014) A posteriori error and optimal reduced basis for stochastic processes defined by a finite set of realizations. SIAM\/ASA J Uncertain Quantif 2:745\u2013762","journal-title":"SIAM\/ASA J Uncertain Quantif"},{"key":"936_CR41","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/j.jcp.2017.05.051","volume":"346","author":"G Perrin","year":"2017","unstructured":"Perrin G, Soize C, Marque-Pucheu S, Garnier J (2017) Nested polynomial trends for the improvement of gaussian process-based predictors. J Comput Phys 346:389\u2013402","journal-title":"J Comput Phys"},{"key":"936_CR42","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.csda.2017.10.005","volume":"119","author":"G Perrin","year":"2018","unstructured":"Perrin G, Soize C, Ouhbi N (2018) Data-driven kernel representations for sampling with an unknown block dependence structure under correlation constraints. J Comput Stat Data Anal 119:139\u2013154","journal-title":"J Comput Stat Data Anal"},{"key":"936_CR43","first-page":"651","volume":"7","author":"CE Rasmussen","year":"2003","unstructured":"Rasmussen CE (2003) Gaussian processes to speed up hybrid monte carlo for expensive bayesian integrals. Bayesian Stat 7:651\u2013659","journal-title":"Bayesian Stat"},{"key":"936_CR44","volume-title":"Simulation and the Monte Carlo method","author":"RT Rubinstein","year":"2008","unstructured":"Rubinstein RT, Kroese D (2008) Simulation and the Monte Carlo method. Wiley, Hoboken"},{"key":"936_CR45","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3799-8","volume-title":"The design and analysis of computer experiments","author":"TJ Santner","year":"2003","unstructured":"Santner TJ, Williams B, Notz W (2003) The design and analysis of computer experiments. Springer, New York"},{"key":"936_CR46","first-page":"229","volume-title":"Handbook of Statistics","author":"David W. Scott","year":"2005","unstructured":"Scott DW, Sain SR (2004) Multidimensional density estimation. In: Handbook of statistics, vol 24, pp 229\u2013261"},{"key":"936_CR47","doi-asserted-by":"crossref","first-page":"640","DOI":"10.1137\/15M1047659","volume":"5","author":"M Sinsbeck","year":"2017","unstructured":"Sinsbeck M, Nowak W (2017) Sequential design of computer experiments for the solution of Bayesian inverse. SIAM\/ASA J Uncertain Quantif 5:640\u2013664","journal-title":"SIAM\/ASA J Uncertain Quantif"},{"key":"936_CR48","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.cma.2004.12.014","volume":"195","author":"C Soize","year":"2006","unstructured":"Soize C (2006) Non-gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators. Comput Methods Appl Mech Eng 195:26\u201364","journal-title":"Comput Methods Appl Mech Eng"},{"key":"936_CR49","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.probengmech.2007.12.019","volume":"23","author":"C Soize","year":"2008","unstructured":"Soize C (2008) Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size. Probab Eng Mech 23:307\u2013323","journal-title":"Probab Eng Mech"},{"issue":"33\u201336","key":"936_CR50","doi-asserted-by":"crossref","first-page":"2150","DOI":"10.1016\/j.cma.2010.03.013","volume":"199","author":"C Soize","year":"2010","unstructured":"Soize C (2010) Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data. Comput Methods Appl Mech Eng 199(33\u201336):2150\u20132164","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"45\u201346","key":"936_CR51","doi-asserted-by":"crossref","first-page":"3083","DOI":"10.1016\/j.cma.2011.07.005","volume":"200","author":"C Soize","year":"2011","unstructured":"Soize C (2011) A computational inverse method for identification of non-Gaussian random fields using the Bayesian approach in very high dimension. Comput Methods Appl Mech Eng 200(45\u201346):3083\u20133099","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"September 2015","key":"936_CR52","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.jcp.2016.05.044","volume":"321","author":"C Soize","year":"2016","unstructured":"Soize C, Ghanem R (2016) Data-driven probability concentration and sampling on manifold. J Comput Phys 321(September 2015):242\u2013258","journal-title":"J Comput Phys"},{"key":"936_CR53","first-page":"1","volume":"2017","author":"C Soize","year":"2017","unstructured":"Soize C, Ghanem R (2017) Probabilistic learning on manifold for optimization under uncertainties. Proc Uncecomp 2017:1\u201315","journal-title":"Proc Uncecomp"},{"issue":"4","key":"936_CR54","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1198\/004017003000000168","volume":"45","author":"E Stinstra","year":"2003","unstructured":"Stinstra E, den Hertog D, Stehouwer P, Vestjens A (2003) Constrained maximin designs for computer experiments. Technometrics 45(4):340\u2013346","journal-title":"Technometrics"},{"issue":"1","key":"936_CR55","first-page":"219","volume":"51","author":"E Stinstra","year":"2010","unstructured":"Stinstra E, den Hertog D, Stehouwer P, Vestjens A (2010) Uniform designs over general input domains with applications to target region estimation in computer experiments. Comput Stat Data Anal 51(1):219\u2013232","journal-title":"Comput Stat Data Anal"},{"key":"936_CR56","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1017\/S0962492910000061","volume":"19","author":"AM Stuart","year":"2010","unstructured":"Stuart AM (2010) Inverse problems: a bayesian perspective. Acta Numerica 19:451\u2013559","journal-title":"Acta Numerica"},{"key":"936_CR57","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.enggeo.2016.05.013","volume":"210","author":"M Tian","year":"2016","unstructured":"Tian M, Li D, Cao Z, Phoon K, Wang Y (2016) Bayesian identification of random field model using indirect test data. Eng Geol 210:197\u2013211","journal-title":"Eng Geol"},{"key":"936_CR58","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1137\/15M1043303","volume":"5","author":"P Tsilifis","year":"2017","unstructured":"Tsilifis P, Ghanem RG, Hajali P (2017) Efficient Bayesian experimentation using an expected information gain lower bound. SIAM\/ASA J Uncertain Quantif 5:30\u201362","journal-title":"SIAM\/ASA J Uncertain Quantif"},{"key":"936_CR59","doi-asserted-by":"crossref","first-page":"105004","DOI":"10.1088\/0266-5611\/27\/10\/105004","volume":"27","author":"J Wan","year":"2011","unstructured":"Wan J, Zabaras N (2011) A Bayesian approach to multiscale inverse problems using the sequential Monte Carlo method. Inverse Probl 27:105004","journal-title":"Inverse Probl"},{"issue":"60","key":"936_CR60","first-page":"212","volume":"60","author":"MP Wand","year":"1995","unstructured":"Wand MP, Jones MC (1995) Kernel smoothing. Encycl Stat Behav Sci 60(60):212","journal-title":"Encycl Stat Behav Sci"},{"key":"936_CR61","unstructured":"Whittle P (1951) Hypothesis testing in time series, Ph.D. thesis. University of Uppsala"},{"key":"936_CR62","volume-title":"Prediction and regulation by linear least-square methods","author":"P Whittle","year":"1983","unstructured":"Whittle P (1983) Prediction and regulation by linear least-square methods. University of Minnesota Press, Minneapolis"},{"key":"936_CR63","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.probengmech.2010.07.009","volume":"26","author":"M Williams","year":"2011","unstructured":"Williams M (2011) The eigenfunctions of the Karhunen\u2013Loeve integral equation for a spherical system. Propab Eng Mech 26:202\u2013207","journal-title":"Propab Eng Mech"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-019-00936-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00180-019-00936-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-019-00936-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,4]],"date-time":"2021-02-04T04:53:25Z","timestamp":1612414405000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00180-019-00936-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,19]]},"references-count":63,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["936"],"URL":"https:\/\/doi.org\/10.1007\/s00180-019-00936-5","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"value":"0943-4062","type":"print"},{"value":"1613-9658","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,19]]},"assertion":[{"value":"26 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 November 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 November 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}