{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T02:12:25Z","timestamp":1775614345071,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"S12","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"published-print":{"date-parts":[[2014,12]]},"DOI":"10.1186\/1471-2105-15-s12-s3","type":"journal-article","created":{"date-parts":[[2014,11,6]],"date-time":"2014-11-06T16:02:42Z","timestamp":1415289762000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Approximate Bayesian computation schemes for parameter inference of discrete stochastic models using simulated likelihood density"],"prefix":"10.1186","volume":"15","author":[{"given":"Qianqian","family":"Wu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kate","family":"Smith-Miles","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianhai","family":"Tian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,11,6]]},"reference":[{"key":"6674_CR1","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1186\/1752-0509-5-14","volume":"5","author":"C Zhan","year":"2011","unstructured":"Zhan C, Yeung LF: Parameter estimation in systems biology models using spline approximation. BMC systems biology. 2011, 5: 14-10.1186\/1752-0509-5-14.","journal-title":"BMC systems biology"},{"issue":"5","key":"6674_CR2","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1093\/bioinformatics\/btg027","volume":"19","author":"S Kikuchi","year":"2003","unstructured":"Kikuchi S, Tominaga D, Arita M, Takahashi K, Tomita M: Dynamic modeling of genetic networks using genetic algorithm and S-system. Bioinformatics. 2003, 19 (5): 643-650. 10.1093\/bioinformatics\/btg027.","journal-title":"Bioinformatics"},{"key":"6674_CR3","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1186\/1471-2105-6-155","volume":"6","author":"KG Gadkar","year":"2005","unstructured":"Gadkar KG, Gunawan R, Doyle FJ: Iterative approach to model identification of biological networks. BMC bioinformatics. 2005, 6: 155-10.1186\/1471-2105-6-155.","journal-title":"BMC bioinformatics"},{"issue":"4","key":"6674_CR4","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1093\/bioinformatics\/btl522","volume":"23","author":"OR Gonzalez","year":"2007","unstructured":"Gonzalez OR, K\u00fcper C, Jung K, Naval PC, Mendoza E: Parameter estimation using Simulated Annealing for S-system models of biochemical networks. Bioinformatics. 2007, 23 (4): 480-486. 10.1093\/bioinformatics\/btl522.","journal-title":"Bioinformatics"},{"key":"6674_CR5","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1186\/1471-2105-15-256","volume":"15","author":"Z Deng","year":"2014","unstructured":"Deng Z, Tian T: A continuous approach for inferring parameters in mathematical models of regulatory networks. BMC bioinformatics. 2014, 15: 256-10.1186\/1471-2105-15-256.","journal-title":"BMC bioinformatics"},{"issue":"S8","key":"6674_CR6","first-page":"S8","volume":"8","author":"T Tian","year":"2014","unstructured":"Tian T, Smith-Miles K: Mathematical modelling of GATA-switching for regulating the differentiation of hematopoietic stem cell. BMC bioinformatics. 2014, 8 (S8): S8-","journal-title":"BMC bioinformatics"},{"issue":"4598","key":"6674_CR7","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1126\/science.220.4598.671","volume":"220","author":"S Kirkpatrick","year":"1983","unstructured":"Kirkpatrick S, Gelatt CD, Vecchi MP: Optimization by Simulated Annealing. Science. 1983, 220 (4598): 671-680. 10.1126\/science.220.4598.671.","journal-title":"Science"},{"issue":"10","key":"6674_CR8","doi-asserted-by":"publisher","first-page":"869","DOI":"10.1093\/bioinformatics\/14.10.869","volume":"14","author":"P Mendes","year":"1998","unstructured":"Mendes P, Kell D: Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics. 1998, 14 (10): 869-883. 10.1093\/bioinformatics\/14.10.869.","journal-title":"Bioinformatics"},{"issue":"6","key":"6674_CR9","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1109\/2.294849","volume":"27","author":"M Srinivas","year":"1994","unstructured":"Srinivas M, Patnaik LM: Genetic algorithms: A survey. Computer. 1994, 27 (6): 17-26.","journal-title":"Computer"},{"key":"6674_CR10","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1186\/1752-0509-2-83","volume":"2","author":"M Ashyraliyev","year":"2008","unstructured":"Ashyraliyev M, Jaeger J, Blom J: Parameter estimation and determinability analysis applied to Drosophila gap gene circuits. BMC Systems Biology. 2008, 2: 83-10.1186\/1752-0509-2-83.","journal-title":"BMC Systems Biology"},{"issue":"11","key":"6674_CR11","doi-asserted-by":"publisher","first-page":"2467","DOI":"10.1101\/gr.1262503","volume":"13","author":"CG Moles","year":"2003","unstructured":"Moles CG, Mendes P, Banga JR: Parameter estimation in biochemical pathways: a comparison of global optimization methods. Genome research. 2003, 13 (11): 2467-2474. 10.1101\/gr.1262503.","journal-title":"Genome research"},{"issue":"5","key":"6674_CR12","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/j.compbiolchem.2005.08.001","volume":"29","author":"R Lall","year":"2005","unstructured":"Lall R, Voit EO: Parameter estimation in modulated, unbranched reaction chains within biochemical systems. Computational biology and chemistry. 2005, 29 (5): 309-318. 10.1016\/j.compbiolchem.2005.08.001.","journal-title":"Computational biology and chemistry"},{"issue":"3","key":"6674_CR13","doi-asserted-by":"publisher","first-page":"el000696","DOI":"10.1371\/journal.pcbi.1000696","volume":"6","author":"G Lillacci","year":"2010","unstructured":"Lillacci G, Khammash M: Parameter estimation and model selection in computational biology. PLoS computational biology. 2010, 6 (3): el000696-","journal-title":"PLoS computational biology"},{"issue":"21","key":"6674_CR14","doi-asserted-by":"publisher","first-page":"2505","DOI":"10.1093\/bioinformatics\/btn470","volume":"24","author":"G Goel","year":"2008","unstructured":"Goel G, Chou IC, Voit EO: System estimation from metabolic time-series data. Bioinformatics. 2008, 24 (21): 2505-2511. 10.1093\/bioinformatics\/btn470.","journal-title":"Bioinformatics"},{"issue":"2","key":"6674_CR15","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/j.cell.2008.09.050","volume":"135","author":"A Raj","year":"2008","unstructured":"Raj A, van Oudenaarden A: Nature, nurture, or chance: stochastic gene expression and its consequences. Cell. 2008, 135 (2): 216-226. 10.1016\/j.cell.2008.09.050.","journal-title":"Cell"},{"issue":"2","key":"6674_CR16","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1093\/bib\/bbm007","volume":"8","author":"DJ Wilkinson","year":"2007","unstructured":"Wilkinson DJ: Bayesian methods in bioinformatics and computational systems biology. Briefings in, bioinformatics. 2007, 8 (2): 109-116.","journal-title":"Briefings in, bioinformatics"},{"issue":"31","key":"6674_CR17","doi-asserted-by":"publisher","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 MP: Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. Journal of the Royal Society Interface. 2009, 6 (31): 187-202. 10.1098\/rsif.2008.0172.","journal-title":"Journal of the Royal Society Interface"},{"issue":"26","key":"6674_CR18","doi-asserted-by":"publisher","first-page":"16904","DOI":"10.1073\/pnas.262658899","volume":"99","author":"D Battogtokh","year":"2002","unstructured":"Battogtokh D, Asch DK, Case ME, Arnold J, Sch\u00fcttler HB: An ensemble method for identifying regulatory circuits with special reference to the qa gene cluster of Neurospora crassa. Proceedings of the National Academy of Sciences. 2002, 99 (26): 16904-16909. 10.1073\/pnas.262658899. [http:\/\/www.pnas.org\/content\/99\/26\/16904.abstract]","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"6","key":"6674_CR19","doi-asserted-by":"publisher","first-page":"1760","DOI":"10.1073\/pnas.0607208104","volume":"104","author":"SA Sisson","year":"2007","unstructured":"Sisson SA, Fan Y, Tanaka MM: Sequential monte carlo without likelihoods. Proceedings of the National Academy of Sciences. 2007, 104 (6): 1760-1765. 10.1073\/pnas.0607208104.","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"4","key":"6674_CR20","doi-asserted-by":"crossref","first-page":"2025","DOI":"10.1093\/genetics\/162.4.2025","volume":"162","author":"MA Beaumont","year":"2002","unstructured":"Beaumont MA, Zhang W, Balding DJ: Approximate Bayesian Computation in Population Genetics. Genetics. 2002, 162 (4): 2025-2035.","journal-title":"Genetics"},{"issue":"26","key":"6674_CR21","doi-asserted-by":"publisher","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. Proceedings of the National Academy of Sciences. 2003, 100 (26): 15324-15328. 10.1073\/pnas.0306899100.","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"12","key":"6674_CR22","doi-asserted-by":"publisher","first-page":"1791","DOI":"10.1093\/oxfordjournals.molbev.a026091","volume":"16","author":"JK Pritchard","year":"1999","unstructured":"Pritchard JK, Seielstad MT, Perez-Lezaun A, Feldman MW: Population growth of human Y chromosomes: a study of Y chromosome microsatellites. Molecular Biology and Evolution. 1999, 16 (12): 1791-1798. 10.1093\/oxfordjournals.molbev.a026091.","journal-title":"Molecular Biology and Evolution"},{"issue":"3","key":"6674_CR23","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1111\/j.1467-9868.2011.01010.x","volume":"74","author":"P Fearnhead","year":"2012","unstructured":"Fearnhead P, Prangle D: Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2012, 74 (3): 419-474. 10.1111\/j.1467-9868.2011.01010.x.","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"10","key":"6674_CR24","doi-asserted-by":"publisher","first-page":"759","DOI":"10.1038\/nrg1961","volume":"7","author":"P Marjoram","year":"2006","unstructured":"Marjoram P, Tavar\u00e9 S: Modern computational approaches for analysing molecular genetic variation data. Nature Reviews Genetics. 2006, 7 (10): 759-770. 10.1038\/nrg1961.","journal-title":"Nature Reviews Genetics"},{"issue":"3","key":"6674_CR25","doi-asserted-by":"publisher","first-page":"1511","DOI":"10.1534\/genetics.106.055574","volume":"173","author":"MM Tanaka","year":"2006","unstructured":"Tanaka MM, Francis AR, Luciani F, Sisson S: Using approximate Bayesian computation to estimate tuberculosis transmission parameters from genotype data. Genetics. 2006, 173 (3): 1511-1520. 10.1534\/genetics.106.055574.","journal-title":"Genetics"},{"issue":"3","key":"6674_CR26","doi-asserted-by":"publisher","first-page":"1607","DOI":"10.1534\/genetics.105.048223","volume":"172","author":"K Thornton","year":"2006","unstructured":"Thornton K, Andolfatto P: Approximate Bayesian inference reveals evidence for a recent, severe bottleneck in a Netherlands population of Drosophila melanogaster. Genetics. 2006, 172 (3): 1607-1619.","journal-title":"Genetics"},{"key":"6674_CR27","volume-title":"Journal of Computational and Graphical Statistics in press","author":"UL Picchini","year":"2014","unstructured":"Picchini UL: Inference for SDE models via Approximate Bayesian Computation. Journal of Computational and Graphical Statistics in press. 2014"},{"key":"6674_CR28","first-page":"416","volume-title":"Bioinformatics and Biomedicine (BIBM)","author":"Q Wu","year":"2013","unstructured":"Wu Q, Smith-Miles K, Tian T: Approximate Bayesian computation for estimating rate constants in biochemical reaction systems. Bioinformatics and Biomedicine (BIBM). 2013, 416-421. IEEE International Conference on 2013"},{"key":"6674_CR29","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1186\/1471-2105-13-68","volume":"13","author":"BJ Daigle","year":"2012","unstructured":"Daigle BJ, Roh MK, Petzold LR, Niemi J: Accelerated maximum likelihood parameter estimation for stochastic biochemical systems. BMC bioinformatics. 2012, 13: 68-10.1186\/1471-2105-13-68.","journal-title":"BMC bioinformatics"},{"issue":"25","key":"6674_CR30","doi-asserted-by":"publisher","first-page":"2340","DOI":"10.1021\/j100540a008","volume":"81","author":"DT Gillespie","year":"1977","unstructured":"Gillespie DT: Exact stochastic simulation of coupled chemical reactions. The journal of physical chemistry. 1977, 81 (25): 2340-2361. 10.1021\/j100540a008.","journal-title":"The journal of physical chemistry"},{"key":"6674_CR31","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1093\/bioinformatics\/btl552","volume":"23","author":"T Tian","year":"2007","unstructured":"Tian T, Xu S, Gao J, Burrage K: Simulated maximum likelihood method for estimating kinetic rates in gene expression. Bioinformatics. 2007, 23: 84-91. 10.1093\/bioinformatics\/btl552.","journal-title":"Bioinformatics"},{"key":"6674_CR32","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1186\/1752-0509-4-99","volume":"4","author":"Y Wang","year":"2010","unstructured":"Wang Y, Christley S, Mjolsness E, Xie X: Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent. BMC systems biology. 2010, 4: 99-10.1186\/1752-0509-4-99.","journal-title":"BMC systems biology"},{"issue":"3","key":"6674_CR33","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1111\/j.1541-0420.2005.00345.x","volume":"61","author":"A Golightly","year":"2005","unstructured":"Golightly A, Wilkinson DJ: Bayesian inference for stochastic kinetic models using a diffusion approximation. Biometrics. 2005, 61 (3): 781-788. 10.1111\/j.1541-0420.2005.00345.x.","journal-title":"Biometrics"},{"issue":"4","key":"6674_CR34","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1049\/ip-syb:20050105","volume":"153","author":"S Reinker","year":"2006","unstructured":"Reinker S, Altman R, Timmer J: Parameter estimation in stochastic biochemical reactions. IEE Proceedings-Systems Biology. 2006, 153 (4): 168-178. 10.1049\/ip-syb:20050105.","journal-title":"IEE Proceedings-Systems Biology"},{"issue":"21","key":"6674_CR35","doi-asserted-by":"publisher","first-page":"10356","DOI":"10.1063\/1.1810475","volume":"121","author":"T Tian","year":"2004","unstructured":"Tian T, Burrage K: Binomial leap methods for simulating stochastic chemical kinetics. The Journal of chemical physics. 2004, 121 (21): 10356-10364. 10.1063\/1.1810475.","journal-title":"The Journal of chemical physics"},{"key":"6674_CR36","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1093\/bib\/bbn050","volume":"10","author":"J Pahle","year":"2009","unstructured":"Pahle J: Biochemical simulations: stochastic, approximate stochastic and hybrid approaches. Briefings in bioinformatics. 2009, 10: 53-64.","journal-title":"Briefings in bioinformatics"},{"issue":"2","key":"6674_CR37","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.pbiomolbio.2004.01.014","volume":"85","author":"K Burrage","year":"2004","unstructured":"Burrage K, Tian T, Burrage P: A multi-scaled approach for simulating chemical reaction systems. Progress in biophysics and molecular biology. 2004, 85 (2): 217-234.","journal-title":"Progress in biophysics and molecular biology"},{"issue":"2","key":"6674_CR38","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s11222-007-9043-x","volume":"18","author":"RJ Boys","year":"2008","unstructured":"Boys RJ, Wilkinson DJ, Kirkwood TB: Bayesian inference for a discretely observed stochastic kinetic model. Statistics and Computing. 2008, 18 (2): 125-135. 10.1007\/s11222-007-9043-x.","journal-title":"Statistics and Computing"},{"issue":"6","key":"6674_CR39","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1098\/rsfs.2011.0047","volume":"1","author":"A Golightly","year":"2011","unstructured":"Golightly A, Wilkinson DJ: Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo. Interface Focus. 2011, 1 (6): 807-820. 10.1098\/rsfs.2011.0047.","journal-title":"Interface Focus"},{"issue":"3","key":"6674_CR40","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1093\/jjfinec\/nbm009","volume":"5","author":"AS Hurn","year":"2007","unstructured":"Hurn AS, Jeisman J, Lindsay KA: Seeing the wood for the trees: A critical evaluation of methods to estimate the parameters of stochastic differential equations. Journal of Financial Econometrics. 2007, 5 (3): 390-455. 10.1093\/jjfinec\/nbm009.","journal-title":"Journal of Financial Econometrics"},{"issue":"4","key":"6674_CR41","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1016\/S0378-4754(99)00017-8","volume":"48","author":"A Hurn","year":"1999","unstructured":"Hurn A, Lindsay K: Estimating the parameters of stochastic differential equations. Mathematics and computers in simulation. 1999, 48 (4): 373-384.","journal-title":"Mathematics and computers in simulation"}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1471-2105-15-S12-S3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T18:55:20Z","timestamp":1630608920000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcbioinformatics.biomedcentral.com\/articles\/10.1186\/1471-2105-15-S12-S3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,6]]},"references-count":41,"journal-issue":{"issue":"S12","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["6674"],"URL":"https:\/\/doi.org\/10.1186\/1471-2105-15-s12-s3","relation":{},"ISSN":["1471-2105"],"issn-type":[{"value":"1471-2105","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,6]]},"assertion":[{"value":"6 November 2014","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"S3"}}