{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T10:43:58Z","timestamp":1772793838862,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,11,29]],"date-time":"2013-11-29T00:00:00Z","timestamp":1385683200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/2.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2015,3]]},"DOI":"10.1007\/s11222-013-9432-2","type":"journal-article","created":{"date-parts":[[2013,11,28]],"date-time":"2013-11-28T11:31:10Z","timestamp":1385638270000},"page":"289-301","source":"Crossref","is-referenced-by-count":12,"title":["Piecewise Approximate Bayesian Computation: fast inference for discretely observed Markov models using a factorised posterior distribution"],"prefix":"10.1007","volume":"25","author":[{"given":"S. R.","family":"White","sequence":"first","affiliation":[]},{"given":"T.","family":"Kypraios","sequence":"additional","affiliation":[]},{"given":"S. P.","family":"Preston","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,11,29]]},"reference":[{"key":"9432_CR1","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1111\/1468-0262.00274","volume":"70","author":"Y. A\u00eft-Sahalia","year":"2002","unstructured":"A\u00eft-Sahalia, Y.: Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach. Econometrica 70, 223\u2013262 (2002)","journal-title":"Econometrica"},{"issue":"3","key":"9432_CR2","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1111\/j.1467-9892.1987.tb00438.x","volume":"8","author":"M.A. Al-Osh","year":"1987","unstructured":"Al-Osh, M.A., Alzaid, A.A.: First-order integer-valued autoregressive (INAR(1)) process. J. Time Ser. Anal. 8(3), 261\u2013275 (1987)","journal-title":"J. Time Ser. Anal."},{"issue":"3","key":"9432_CR3","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1111\/j.1467-9868.2009.00736.x","volume":"72","author":"C. Andrieu","year":"2010","unstructured":"Andrieu, C., Doucet, A., Holenstein, R.: Particle Markov chain Monte Carlo methods. J. R. Stat. Soc., Ser. B, Stat. Methodol. 72(3), 269\u2013342 (2010)","journal-title":"J. R. Stat. Soc., Ser. B, Stat. Methodol."},{"key":"9432_CR4","unstructured":"Barthelm\u00e9, S., Chopin, N.: Expectation-Propagation for Summary-Less, Likelihood-Free Inference. J. Acoust. Soc. Am. ArXiv e-prints (2011, to appear)"},{"issue":"4","key":"9432_CR5","doi-asserted-by":"crossref","first-page":"2025","DOI":"10.1093\/genetics\/162.4.2025","volume":"162","author":"M.A. Beaumont","year":"2002","unstructured":"Beaumont, M.A., Zhang, W., Balding, D.J.: Approximate Bayesian Computation in population genetics. Genetics 162(4), 2025\u20132035 (2002)","journal-title":"Genetics"},{"key":"9432_CR6","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s11222-009-9116-0","volume":"20","author":"M.G.B. Blum","year":"2010","unstructured":"Blum, M.G.B., Fran\u00e7ois, O.: Non-linear regression models for approximate Bayesian computation. Stat. Comput. 20, 63\u201373 (2010)","journal-title":"Stat. Comput."},{"issue":"2","key":"9432_CR7","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/s11222-007-9043-x","volume":"18","author":"R.J. Boys","year":"2008","unstructured":"Boys, R.J., Wilkinson, D.J., Kirkwood, T.B.: Bayesian inference for a discretely observed stochastic kinetic model. Stat. Comput. 18(2), 125\u2013135 (2008)","journal-title":"Stat. Comput."},{"issue":"2","key":"9432_CR8","doi-asserted-by":"crossref","first-page":"385","DOI":"10.2307\/1911242","volume":"53","author":"J.C. Cox","year":"1985","unstructured":"Cox, J.C., Ingersoll, J.E., Ross, S.A.: A theory of the term structure of interest rates. Econometrica 53(2), 385\u2013407 (1985)","journal-title":"Econometrica"},{"key":"9432_CR9","unstructured":"Dean, T., Singh, S.: Asymptotic behaviour of approximate Bayesian estimators. Technical report, University of Cambridge (2011)"},{"key":"9432_CR10","unstructured":"Dean, T.A., Singh, S.S., Jasra, A., Peters, G.W.: Parameter Estimation for Hidden Markov Models with Intractable Likelihoods. ArXiv e-prints (2011)"},{"key":"9432_CR11","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1198\/073500102288618397","volume":"20","author":"G.B. Durham","year":"2002","unstructured":"Durham, G.B., Gallant, A.R.: Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes. J. Bus. Econ. Stat. 20, 297\u2013338 (2002)","journal-title":"J. Bus. Econ. Stat."},{"key":"9432_CR12","unstructured":"Fan, Y., Nott, D.J., Sisson, S.A.: Approximate Bayesian computation via regression density estimation. Technical report (2012). arXiv:1212.1479"},{"key":"9432_CR13","author":"P. Fearnhead","year":"2012","unstructured":"Fearnhead, P., Prangle, D.: Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation. RSS Series B (2012). doi: 10.1111\/j.1467-9868.2011.01010.x","journal-title":"RSS Series B"},{"key":"9432_CR14","volume-title":"Introduction to Statistical Pattern Recognition. Electrical Science Series","author":"K. Fukunaga","year":"1972","unstructured":"Fukunaga, K.: Introduction to Statistical Pattern Recognition. Electrical Science Series. Academic Press, San Diego (1972)"},{"key":"9432_CR15","doi-asserted-by":"crossref","first-page":"1384","DOI":"10.1017\/S0950268810000488","volume":"138","author":"E. Gabriel","year":"2010","unstructured":"Gabriel, E., Wilson, D.J., Leatherbarrow, A.J., Cheesbrough, J., Gee, S., Bolton, E., Fox, A., Fearnhead, P., Hart, C.A., Diggle, P.J.: Spatio-temporal epidemiology of campylobacter jejuni enteritis, in an area of northwest England, 2000\u20132002. Epidemiol. Infect., 138, 1384\u20131390 (2010)","journal-title":"Epidemiol. Infect."},{"issue":"6","key":"9432_CR16","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1098\/rsfs.2011.0047","volume":"1","author":"A. Golightly","year":"2011","unstructured":"Golightly, A., Wilkinson, D.J.: Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo. Interface Focus 1(6), 807\u2013820 (2011)","journal-title":"Interface Focus"},{"key":"9432_CR17","series-title":"Probability and Mathematical Statistics: a Series of Monographs and Textbooks.","isbn-type":"print","volume-title":"Multivariate Analysis","author":"K.V. Mardia","year":"1979","unstructured":"Mardia, K.V., Kent, J.T., Bibby, J.M.: Multivariate Analysis. Probability and Mathematical Statistics: a Series of Monographs and Textbooks. Academic Press, London (1979). ISBN 0-12-471250-9","ISBN":"https:\/\/id.crossref.org\/isbn\/0124712509"},{"issue":"5","key":"9432_CR18","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1007\/s11222-011-9271-y","volume":"22","author":"J.M. Marin","year":"2012","unstructured":"Marin, J.M., Pudlo, P., Robert, C., Ryder, R.: Approximate Bayesian computational methods. Stat. Comput. 22(5), 1009\u20131020 (2012)","journal-title":"Stat. Comput."},{"issue":"26","key":"9432_CR19","doi-asserted-by":"crossref","first-page":"15324","DOI":"10.1073\/pnas.0306899100","volume":"100","author":"P. Marjoram","year":"2003","unstructured":"Marjoram, P., Molitor, J., Plagnol, V., Tavar\u00e9, S.: Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. USA 100(26), 15324 (2003)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"9432_CR20","series-title":"Handbook of Statist","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/S0169-7161(03)21018-X","volume-title":"Stochastic Processes: Modelling and Simulation","author":"E. McKenzie","year":"2003","unstructured":"McKenzie, E.: Discrete variate time series. In: Stochastic Processes: Modelling and Simulation. Handbook of Statist, vol. 21, pp. 573\u2013606. North-Holland, Amsterdam (2003)"},{"key":"9432_CR21","doi-asserted-by":"crossref","first-page":"24","DOI":"10.2202\/1557-4679.1171","volume":"5","author":"T. McKinley","year":"2009","unstructured":"McKinley, T., Cook, A., Deardon, R.: Inference in epidemic models without likelihoods. Int. J. Biostat. 5, 24 (2009)","journal-title":"Int. J. Biostat."},{"key":"9432_CR22","isbn-type":"print","first-page":"362","volume-title":"Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence, UAI\u201901","author":"T.P. Minka","year":"2001","unstructured":"Minka, T.P.: Expectation propagation for approximate Bayesian inference. In: Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence, UAI\u201901, pp. 362\u2013369. Morgan Kaufmann, San Francisco (2001). ISBN 1-55860-800-1. http:\/\/dl.acm.org\/citation.cfm?id=647235.720257","ISBN":"https:\/\/id.crossref.org\/isbn\/1558608001"},{"issue":"26","key":"9432_CR23","doi-asserted-by":"crossref","first-page":"3125","DOI":"10.1002\/sim.4336","volume":"30","author":"D. Mori\u00f1a","year":"2011","unstructured":"Mori\u00f1a, D., Puig, P., R\u00edos, J., Vilella, A., Trilla, A.: A statistical model for hospital admissions caused by seasonal diseases. Stat. Med. 30(26), 3125\u20133136 (2011)","journal-title":"Stat. Med."},{"issue":"1","key":"9432_CR24","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1111\/j.1467-9892.2006.00500.x","volume":"28","author":"P. Neal","year":"2007","unstructured":"Neal, P., Subba Rao, T.: MCMC for integer-valued ARMA processes. J. Time Ser. Anal. 28(1), 92\u2013110 (2007)","journal-title":"J. Time Ser. Anal."},{"issue":"12","key":"9432_CR25","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1093\/oxfordjournals.molbev.a026091","volume":"16","author":"J.K. Pritchard","year":"1999","unstructured":"Pritchard, J.K., Seielstad, M.T., Perez-Lezaun, A., Feldman, M.W.: Population growth of human Y chromosomes: a study of Y chromosome microsatellites. Mol. Biol. Evol. 16(12), 1791\u20131798 (1999)","journal-title":"Mol. Biol. Evol."},{"key":"9432_CR26","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3324-9","volume-title":"Density Estimation for Statistics and Data Analysis","author":"B.W. Silverman","year":"1986","unstructured":"Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Chapman & Hall, London (1986)"},{"key":"9432_CR27","first-page":"605","volume":"1","author":"E.B. Sudderth","year":"2003","unstructured":"Sudderth, E.B., Ihler, A.T., Freeman, W.T., Willsky, A.S.: Nonparametric belief propagation. Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. 1, 605 (2003)","journal-title":"Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit."},{"issue":"1","key":"9432_CR28","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.jmva.2003.12.002","volume":"93","author":"G.J. Sz\u00e9kely","year":"2005","unstructured":"Sz\u00e9kely, G.J., Rizzo, M.L.: A new test for multivariate normality. J.\u00a0Multivar. Anal. 93(1), 58\u201380 (2005)","journal-title":"J.\u00a0Multivar. Anal."},{"key":"9432_CR29","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1098\/rsif.2008.0172","volume":"6","author":"T. Toni","year":"2009","unstructured":"Toni, T., Welch, D., Strelkowa, N., Ipsen, A., Stumpf, M.P.: Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface 6, 187\u2013202 (2009)","journal-title":"J. R. Soc. Interface"},{"key":"9432_CR30","volume-title":"Stochastic Processes in Physics and Chemistry","author":"N.G. Kampen Van","year":"2007","unstructured":"Van Kampen, N.G.: Stochastic Processes in Physics and Chemistry. North-Holland Personal Library, Amsterdam (2007)"},{"key":"9432_CR31","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-4493-1","volume-title":"Kernel Smoothing. Monographs on Statistics and Applied Probability","author":"P. Wand","year":"1995","unstructured":"Wand, P., Jones, C.: Kernel Smoothing. Monographs on Statistics and Applied Probability. Chapman & Hall, London (1995)"},{"key":"9432_CR32","doi-asserted-by":"crossref","DOI":"10.1201\/b11812","volume-title":"Stochastic Modelling for Systems Biology","author":"D.J. Wilkinson","year":"2011","unstructured":"Wilkinson, D.J.: Stochastic Modelling for Systems Biology, 2nd edn. Chapman & Hall, London (2011a)","edition":"2"},{"key":"9432_CR33","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1093\/acprof:oso\/9780199694587.003.0023","volume":"9","author":"D.J. Wilkinson","year":"2011","unstructured":"Wilkinson, D.J.: Parameter inference for stochastic kinetic models of bacterial gene regulation: a Bayesian approach to systems biology. Bayesian Stat. 9, 679\u2013690 (2011b)","journal-title":"Bayesian Stat."},{"key":"9432_CR34","author":"R.D. Wilkinson","year":"2013","unstructured":"Wilkinson, R.D.: Approximate Bayesian computation (ABC) gives exact results under the assumption of model error. Stat. Appl. Genet. Mol. Biol. (2013). Available online as arXiv:0811.3355 . doi: 10.1515\/sagmb-2013-0010","journal-title":"Stat. Appl. Genet. Mol. Biol."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-013-9432-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11222-013-9432-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-013-9432-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,17]],"date-time":"2022-03-17T23:17:07Z","timestamp":1647559027000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11222-013-9432-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,29]]},"references-count":34,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,3]]}},"alternative-id":["9432"],"URL":"https:\/\/doi.org\/10.1007\/s11222-013-9432-2","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,29]]}}}