{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T23:55:22Z","timestamp":1781913322555,"version":"3.54.5"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2003,1,1]],"date-time":"2003-01-01T00:00:00Z","timestamp":1041379200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2003,1,1]],"date-time":"2003-01-01T00:00:00Z","timestamp":1041379200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Machine Learning"],"published-print":{"date-parts":[[2003,1]]},"DOI":"10.1023\/a:1020297828025","type":"journal-article","created":{"date-parts":[[2003,3,15]],"date-time":"2003-03-15T08:37:24Z","timestamp":1047717444000},"page":"73-94","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":51,"title":["Mixtures of Factor Analysers. Bayesian Estimation and Inference by Stochastic Simulation"],"prefix":"10.1007","volume":"50","author":[{"given":"Ernest","family":"Fokou\u00e9","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D.M.","family":"Titterington","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"5096738_CR1","doi-asserted-by":"crossref","first-page":"{pp475","DOI":"10.1007\/BF02294568","volume":"64","author":"G. Arminger","year":"1999","unstructured":"Arminger, G., Stein, P., &; Wittenberg, J. (1999). Mixtures of conditional mean and covariance structure models. Psychometrika, 64, {pp475-494.","journal-title":"Psychometrika"},{"key":"5096738_CR2","first-page":"584","volume":"56","author":"A. J. Baddeley","year":"1994","unstructured":"Baddeley, A. J. (1994). Discussion on representation of knowledge in complex systems by Grenander and Miller. Journal of the Royal Statistical Society, Series B, 56, 584-585.","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"5096738_CR3","series-title":"Monographs on Statistics and Applied Probability","volume-title":"Stochastic geometry: Likelihood and computation","author":"O. E. Barndorff-Nielsen","year":"1999","unstructured":"Barndorff-Nielsen, O. E., Kendall, W. S., &; van Lieshout, M. N. M. (1999). Stochastic geometry: Likelihood and computation. Monographs on Statistics and Applied Probability. London: Chapman and Hall."},{"key":"5096738_CR4","unstructured":"Bartholomew, D. J. (1987). Latent variable models and factor analysis, Griffin's Statistical Monographs and Courses. Charles Griffin &; Company Limited."},{"key":"#cr-split#-5096738_CR5.1","doi-asserted-by":"crossref","unstructured":"Celeux, G. (1998). Bayesian inference for mixtures: The label switching problem. In J. Payne, &","DOI":"10.1007\/978-3-662-01131-7_26"},{"key":"#cr-split#-5096738_CR5.2","unstructured":"P. Green (Eds.), Proceedings in Computational Statistics 1998. pp. 227-232, Physica-Verlag."},{"key":"5096738_CR6","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1080\/01621459.2000.10474285","volume":"95","author":"G. Celeux","year":"2000","unstructured":"Celeux, G., Hurn, M., &; Robert, C. P. (2000). Computational and inferential difficulties with mixture posterior distributions. Journal of the American Statistical Association, 95, 957-970.","journal-title":"Journal of the American Statistical Association"},{"key":"5096738_CR7","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1111\/j.2517-6161.1994.tb01985.x","volume":"56","author":"J. Diebolt","year":"1994","unstructured":"Diebolt, J., &; Robert, C. P. (1994). Estimation of finite mixture distributions through Bayesian sampling. Journal of the Royal Statistical Society, Series B, 56, 363-375.","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"5096738_CR8","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF02294853","volume":"63","author":"C. V. Dolan","year":"1998","unstructured":"Dolan, C. V., &; Van der Maas, H. L. J. (1998). Fitting multivariate normal finite mixtures subject to structural equation modelling. Psychometrika, 63, 227-253.","journal-title":"Psychometrika"},{"key":"5096738_CR9","first-page":"707","volume":"90","author":"K. K. Dong","year":"1995","unstructured":"Dong, K. K., &; Taylor, J. M. G. (1995). The restricted EM algorithm for maximum likelihood estimation under linear restrictions on the parameters. Journal of the American Statistical Association, 90, 707-716.","journal-title":"Journal of the American Statistical Association"},{"key":"5096738_CR10","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1080\/01621459.1995.10476550","volume":"90","author":"M. D. Escobar","year":"1995","unstructured":"Escobar, M. D., &; West, M. (1995). Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association, 90, 577-588.","journal-title":"Journal of the American Statistical Association"},{"key":"5096738_CR11","doi-asserted-by":"crossref","unstructured":"Everitt, B. S. (1984). An introduction to latent variable models. Monographs on Statistics and Applied Probability. Chapman and Hall.","DOI":"10.1007\/978-94-009-5564-6"},{"key":"5096738_CR12","doi-asserted-by":"crossref","unstructured":"Everitt, B. S., &; Hand, D. J. (1981). Finite mixture distributions. Monographs on Statistics and Applied Probability. Chapman and Hall.","DOI":"10.1007\/978-94-009-5897-5"},{"key":"#cr-split#-5096738_CR13.1","unstructured":"Fokou\u00e9, E. (2000). A Markov chain Monte Carlo (MCMC) approach to the Bayesian analysis of mixtures of factor analysers. In W. Jansen, &"},{"key":"#cr-split#-5096738_CR13.2","doi-asserted-by":"crossref","unstructured":"J. G. Bethlehem (Eds.), Proceedings in Computational Statistics 2000, Short Communication and Posters (pp. 29-30), Statistics The Netherlands.","DOI":"10.1007\/978-3-642-57678-2"},{"key":"5096738_CR14","series-title":"Technical Report","volume-title":"Bayesian sampling for mixtures of factor analysers","author":"E. Fokou\u00e9","year":"2000","unstructured":"Fokou\u00e9, E., &; Titterington, D. M. (2000a). Bayesian sampling for mixtures of factor analysers. Technical Report No. 00-3, Department of Statistics, University of Glasgow, Glasgow, G12 8QW, Scotland, UK."},{"key":"5096738_CR15","series-title":"Technical Report","volume-title":"Mixtures of factor analysers with fixed observed covariates","author":"E. Fokou\u00e9","year":"2000","unstructured":"Fokou\u00e9, E., &; Titterington, D. M. (2000b). Mixtures of factor analysers with fixed observed covariates. Technical Report No. 00-4, Department of Statistics, University of Glasgow, Glasgow, G12 8QW, Scotland, UK."},{"key":"5096738_CR16","series-title":"Technical Report","volume-title":"Stochastic model selection for mixtures of factor analysers","author":"E. Fokou\u00e9","year":"2000","unstructured":"Fokou\u00e9, E., &; Titterington, D. M. (2000c). Stochastic model selection for mixtures of factor analysers. Technical Report No. 00-5, Department of Statistics, University of Glasgow, Glasgow, G12 8QW, Scotland, UK."},{"key":"5096738_CR17","first-page":"733","volume":"6","author":"A. Gelman","year":"1996","unstructured":"Gelman, A., Meng, S. L., &; Stern, H. (1996). Posterior predictive assessment of model fitness via realised discrepancies. Statistica Sinica, 6, 733-759.","journal-title":"Statistica Sinica"},{"key":"5096738_CR18","series-title":"Technical Report","volume-title":"The EM algorithm for mixtures of factor analysers","author":"Z. Ghahramani","year":"1997","unstructured":"Ghahramani, Z., &; Hinton, G. E. (1997). The EM algorithm for mixtures of factor analysers. Technical Report CRG-TR-96-1, Department of Computer Science, University of Toronto, 6 King's College Road, Toronto, Canada, M5S 1A4."},{"key":"5096738_CR19","volume-title":"Advanced in neural information processing systems","author":"Z. Ghahramani","year":"2000","unstructured":"Ghahramani, Z., &; Beal, M. (2000). Variational inference for Bayesian mixture of factor analysers. In S. A. Solla, T. K. Leen, &; K.-R. M\u00fcller (Eds.) Advanced in neural information processing systems 12. Cambridge, MA: MIT Press."},{"key":"5096738_CR20","doi-asserted-by":"crossref","unstructured":"Gilks, W. R., Richardson, S., &; Spiegelhalter, D. J. (1996). Markov chain Monte Carlo in practice. Interdisciplinary Statistics. Chapman and Hall.","DOI":"10.1201\/b14835"},{"key":"5096738_CR21","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1111\/j.2517-6161.1994.tb02000.x","volume":"56","author":"U. Grenander","year":"1994","unstructured":"Grenander, U., &; Miller, M. I. (1994). Representation of knowledge in complex systems. Journal of the Royal Statistical Society, Series B, 56, 549-603.","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"5096738_CR22","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1093\/biomet\/82.4.711","volume":"82","author":"P. J. Green","year":"1995","unstructured":"Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711-732.","journal-title":"Biometrika"},{"key":"5096738_CR23","series-title":"Technical Report","volume-title":"Estimating mixtures of regressions","author":"M. Hurn","year":"2000","unstructured":"Hurn, M., Justel, A., &; Robert, C. P. (2000). Estimating mixtures of regressions. Technical Report, Department of Mathematical Sciences, University of Bath, UK."},{"key":"5096738_CR24","unstructured":"Krzanowski, W. J., &; Marriott, F. H. C. (1994). Multivariate analysis,Part 1: Distribution, ordination and inference, Kendall's Library of Statistics 1. Arnorld."},{"key":"5096738_CR25","unstructured":"Krzanowski, W. J., &; Marriott, F. H. C. (1995). Multivariate analysis, Part 2: Classification, covariance structures and repeated measurements, Kendall's Library of Statistics 2. Arnorld."},{"key":"5096738_CR26","first-page":"585","volume":"56","author":"M. N. M. van Lieshout","year":"1994","unstructured":"van Lieshout, M. N. M. (1994). Discussion on representation of knowledge in complex systems by Grenander and Miller. Journal of the Royal Statistical Society, Series B, 56, 585.","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"5096738_CR27","series-title":"Technical Report","volume-title":"Model uncertainty in factor analysis","author":"H. F. Lopes","year":"1999","unstructured":"Lopes, H. F., &; West, M. (1999). Model uncertainty in factor analysis. Technical Report, Institute of Statistics and Decision Sciences, Duke University, USA."},{"key":"5096738_CR28","doi-asserted-by":"crossref","unstructured":"McLachlan, G., &; Peel, D. (2000). Finite mixture models, Wiley Series in Probability and Mathematical Statistics. John Wiley &; Sons.","DOI":"10.1002\/0471721182"},{"key":"5096738_CR29","unstructured":"Phillips, D. B., &; Smith, A. F. M. (1996). Bayesian model comparison via jump diffusions. In W. R. Gilks, S. Richardson, &; D. J. Spiegelhalter (Eds.), Markov chain Monte Carlo in practice. Interdisciplinary Statistics (ch. 13, pp. 215-239). Chapman and Hall."},{"key":"5096738_CR30","unstructured":"Press, S. J. (1972). Applied multivariate analysis. Holt, Rinehart and Winston."},{"key":"5096738_CR31","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1111\/1467-9868.00095","volume":"59","author":"S. Richardson","year":"1997","unstructured":"Richardson, S., &; Green, P. J. (1997). On the Bayesian analysis of mixtures with an unknown number of components (with discussion). Journal of the Royal Statistical Society, Series B, 59, 731-792.","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"5096738_CR32","unstructured":"Robert, C. P. (1996a). Mixtures of distributions: Inference and estimation. In W. R. Gilks, S. Richardson, &; D. J. Spiegelhalter (Eds.), Markov chain Monte Carlo in practice, Interdisciplinary Statistics (ch. 24, pp. 441-464). Chapman &; Hall."},{"key":"5096738_CR33","unstructured":"Robert, C. P. (1996b).M\u00e9thodes de Monte Carlo par Chaines de Markov, Statistique Math\u00e9matique et Probabilit\u00e9. Economica."},{"key":"5096738_CR34","doi-asserted-by":"crossref","unstructured":"Robert, C. P., &; Casella, G. (1999). Monte Carlo statistical methods. Springer.","DOI":"10.1007\/978-1-4757-3071-5"},{"key":"5096738_CR35","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1111\/1467-9868.00265","volume":"62","author":"M. Stephens","year":"2000","unstructured":"Stephens, M. (2000a). Dealing with label switching in mixture models. Journal of the Royal Statistical Society, Series B, 62, 795-809.","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"5096738_CR36","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1214\/aos\/1016120364","volume":"28","author":"M. Stephens","year":"2000","unstructured":"Stephens, M. (2000b). Bayesian analysis of mixtures models with an unknown number of components-an alternative to reversible jump methods. Annals of Statistics, 28, 40-74.","journal-title":"Annals of Statistics"},{"key":"5096738_CR37","unstructured":"Stoyan, D., Kendall, W. S., &; Mecke, J. (1995). Stochastic geometry and its applications, 2nd edn., Wiley Series in Probability and Statistics. John Wiley and Sons."},{"key":"5096738_CR38","first-page":"529","volume":"82","author":"M. A. Tanner","year":"1987","unstructured":"Tanner, M. A., &; Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82, 529-550.","journal-title":"Journal of the American Statistical Association"},{"key":"5096738_CR39","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1111\/1467-9868.00196","volume":"61","author":"M. Tipping","year":"1999","unstructured":"Tipping, M., &; Bishop, C. M. (1999). Probabilistic principal component analysis. Journal of the Royal Statistical Society B, 61, 611-622.","journal-title":"Journal of the Royal Statistical Society B"},{"key":"5096738_CR40","unstructured":"Titterington, D. M., Smith, A. F. M., &; Makov, U. E. (1985). Statistical analysis of finite mixture distributions, Wiley Series in Probability and Mathematical Statistics. John Wiley &; Sons."},{"key":"5096738_CR41","doi-asserted-by":"crossref","first-page":"2109","DOI":"10.1162\/089976600300015088","volume":"12","author":"N. Ueda","year":"2000","unstructured":"Ueda, N., Nakano, R., Ghahramani, Z., &; Hinton, G. E. (2000). SMEM for mixture models. Neural Computation, 12, 2109-2128.","journal-title":"Neural Computation"},{"key":"5096738_CR42","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1162\/08997660151134299","volume":"13","author":"A. Utsugi","year":"2001","unstructured":"Utsugi, A., &; Kumagai, T. (2001). Bayesian analysis of mixture of factor analysers. Neural Computation, 13, 993-1002.","journal-title":"Neural Computation"},{"key":"5096738_CR43","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF02294554","volume":"62","author":"Y. F. Yung","year":"1997","unstructured":"Yung, Y. F. (1997). Finite mixtures in confirmatory factor analysis models. Psychometrika, 62, 297-330.","journal-title":"Psychometrika"}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1020297828025.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1020297828025\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1020297828025.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T11:41:45Z","timestamp":1752147705000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1020297828025"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":45,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["5096738"],"URL":"https:\/\/doi.org\/10.1023\/a:1020297828025","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"value":"0885-6125","type":"print"},{"value":"1573-0565","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]},"assertion":[{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}