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Volumn 221, Issue 1, 2009, Pages 43-53

Sequential estimation for prescribed statistical accuracy in stochastic simulation of biological systems

Author keywords

Biological systems; Confidence intervals; Sequential estimation; Statistical accuracy; Stochastic simulation

Indexed keywords

CONFIDENCE INTERVALS; DEATH PROCESS; GENE REGULATORY NETWORKS; MATHEMATICAL STATISTICS; NUMERICAL EXAMPLE; SAMPLE PATH; SEQUENTIAL ESTIMATION; SIMULATION STUDIES; STATISTICAL ACCURACY; STOCHASTIC PROCESS; STOCHASTIC SIMULATION; STOCHASTIC SIMULATIONS; SYSTEM PROPERTY; TRAJECTORY GENERATION;

EID: 68849102665     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2009.06.006     Document Type: Article
Times cited : (7)

References (76)
  • 9
    • 0002024701 scopus 로고
    • On the generalized birth-and-death process
    • Kendall D.G. On the generalized birth-and-death process. Ann. Math. Stat. 19 (1948) 1
    • (1948) Ann. Math. Stat. , vol.19 , pp. 1
    • Kendall, D.G.1
  • 10
    • 0001697963 scopus 로고
    • Stochastic processes and population growth
    • Kendall D.G. Stochastic processes and population growth. J. R. Stat. Soc. B 11 (1949) 230
    • (1949) J. R. Stat. Soc. B , vol.11 , pp. 230
    • Kendall, D.G.1
  • 11
    • 0005511856 scopus 로고
    • An artificial realisation of a simple birth and death process
    • Kendall D.G. An artificial realisation of a simple birth and death process. J. R. Stat. Soc. B 12 (1950) 116
    • (1950) J. R. Stat. Soc. B , vol.12 , pp. 116
    • Kendall, D.G.1
  • 12
    • 84968465028 scopus 로고
    • The classification of birth and death processes
    • Karlin S., and McGregor J. The classification of birth and death processes. Trans. Am. Math. Soc. 86 2 (1957) 366
    • (1957) Trans. Am. Math. Soc. , vol.86 , Issue.2 , pp. 366
    • Karlin, S.1    McGregor, J.2
  • 13
    • 51249193124 scopus 로고
    • On the linear birth-and-death processes of biology as Markoff chains
    • Bartholomay A.F. On the linear birth-and-death processes of biology as Markoff chains. Bull. Math. Biophys. 20 (1958) 97
    • (1958) Bull. Math. Biophys. , vol.20 , pp. 97
    • Bartholomay, A.F.1
  • 14
    • 0012022109 scopus 로고
    • A simple stochastic epidemic
    • Bailey N.T.J. A simple stochastic epidemic. Biometrika 37 (1950) 194
    • (1950) Biometrika , vol.37 , pp. 194
    • Bailey, N.T.J.1
  • 16
    • 0000296912 scopus 로고
    • Statistical fluctuations in autocatalytic reactions
    • Delbrück M. Statistical fluctuations in autocatalytic reactions. J. Chem. Phys. 8 (1940) 120
    • (1940) J. Chem. Phys. , vol.8 , pp. 120
    • Delbrück, M.1
  • 17
    • 0009543725 scopus 로고
    • Application of the theory of stochastic processes to the study of irreproducible chemical reactions and nucleation processes
    • Singer K. Application of the theory of stochastic processes to the study of irreproducible chemical reactions and nucleation processes. J. R. Stat. Soc. B 15 1 (1953) 92
    • (1953) J. R. Stat. Soc. B , vol.15 , Issue.1 , pp. 92
    • Singer, K.1
  • 19
    • 0014051980 scopus 로고
    • The application of the theory of Markov processes to the reversible one substrate-one intermediate-one product enzymic mechanism
    • Darvey I.G., and Staff P.J. The application of the theory of Markov processes to the reversible one substrate-one intermediate-one product enzymic mechanism. J. Theor. Biol. 14 2 (1967) 157
    • (1967) J. Theor. Biol. , vol.14 , Issue.2 , pp. 157
    • Darvey, I.G.1    Staff, P.J.2
  • 20
    • 0001601301 scopus 로고
    • Stochastic approach to chemical kinetics
    • McQuarrie D.A. Stochastic approach to chemical kinetics. J. Appl. Prob. 4 (1967) 413
    • (1967) J. Appl. Prob. , vol.4 , pp. 413
    • McQuarrie, D.A.1
  • 21
    • 36849099546 scopus 로고
    • Stochastic and deterministic formulation of chemical rate equations
    • Oppenheim I., Shuler K.E., and Weiss G.H. Stochastic and deterministic formulation of chemical rate equations. J. Chem. Phys. 50 1 (1969) 460
    • (1969) J. Chem. Phys. , vol.50 , Issue.1 , pp. 460
    • Oppenheim, I.1    Shuler, K.E.2    Weiss, G.H.3
  • 22
    • 0014789591 scopus 로고
    • A stochastic development of the reversible Michaelis-Menten mechanism
    • Staff P.J. A stochastic development of the reversible Michaelis-Menten mechanism. J. Theor. Biol. 27 2 (1970) 221
    • (1970) J. Theor. Biol. , vol.27 , Issue.2 , pp. 221
    • Staff, P.J.1
  • 23
    • 0001455869 scopus 로고
    • The relationship between stochastic and deterministic models for chemical reactions
    • Kurtz T.G. The relationship between stochastic and deterministic models for chemical reactions. J. Chem. Phys. 57 7 (1972) 2976
    • (1972) J. Chem. Phys. , vol.57 , Issue.7 , pp. 2976
    • Kurtz, T.G.1
  • 24
    • 0017030517 scopus 로고
    • A general method for numerically simulating the time evolution of coupled chemical reactions
    • Gillespie D.T. A general method for numerically simulating the time evolution of coupled chemical reactions. J. Comput. Phys. 22 (1976) 403
    • (1976) J. Comput. Phys. , vol.22 , pp. 403
    • Gillespie, D.T.1
  • 25
    • 33645429016 scopus 로고
    • Exact stochastic simulation of coupled chemical reactions
    • Gillespie D.T. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 71 25 (1977) 2340
    • (1977) J. Phys. Chem. , vol.71 , Issue.25 , pp. 2340
    • Gillespie, D.T.1
  • 26
    • 44049109914 scopus 로고
    • A rigorous derivation of the chemical master equation
    • Gillespie D.T. A rigorous derivation of the chemical master equation. Phys. A 188 (1992) 404
    • (1992) Phys. A , vol.188 , pp. 404
    • Gillespie, D.T.1
  • 31
    • 33750617708 scopus 로고    scopus 로고
    • Szallasi Z., Stelling J., and Periwal V. (Eds), The MIT
    • In: Szallasi Z., Stelling J., and Periwal V. (Eds). System Modeling in Cellular Biology (2006), The MIT
    • (2006) System Modeling in Cellular Biology
  • 34
    • 0037119578 scopus 로고    scopus 로고
    • Small numbers of big molecules
    • Fedoroff N., and Fontana W. Small numbers of big molecules. Science 297 (2002) 1129
    • (2002) Science , vol.297 , pp. 1129
    • Fedoroff, N.1    Fontana, W.2
  • 36
    • 0033083733 scopus 로고    scopus 로고
    • It's a noisy business!
    • McAdams H.H., and Arkin A. It's a noisy business!. Trends Genet. 15 2 (1999) 65
    • (1999) Trends Genet. , vol.15 , Issue.2 , pp. 65
    • McAdams, H.H.1    Arkin, A.2
  • 37
    • 0036400749 scopus 로고    scopus 로고
    • Stochastic vs. deterministic modeling of intracellular viral kinetics
    • Srivastava R., You L., Summers J., and Yin J. Stochastic vs. deterministic modeling of intracellular viral kinetics. J. Theor. Biol. 218 (2002) 309
    • (2002) J. Theor. Biol. , vol.218 , pp. 309
    • Srivastava, R.1    You, L.2    Summers, J.3    Yin, J.4
  • 54
    • 0000537133 scopus 로고
    • A two-sample test for a linear hypothesis whose power is independent of the variance
    • Stein C. A two-sample test for a linear hypothesis whose power is independent of the variance. Ann. Math. Stat. 16 (1945) 243
    • (1945) Ann. Math. Stat. , vol.16 , pp. 243
    • Stein, C.1
  • 55
    • 0001608054 scopus 로고
    • Asymptotic theory of triple sampling for sequential estimation of the mean
    • Hall P. Asymptotic theory of triple sampling for sequential estimation of the mean. Ann. Stat. 9 (1981) 1229
    • (1981) Ann. Stat. , vol.9 , pp. 1229
    • Hall, P.1
  • 57
    • 0001336620 scopus 로고
    • On the asymptotic theory of fixed-width sequential confidence intervals for the mean
    • Chow Y.S., and Robbins H. On the asymptotic theory of fixed-width sequential confidence intervals for the mean. Ann. Math. Stat. 36 (1965) 457
    • (1965) Ann. Math. Stat. , vol.36 , pp. 457
    • Chow, Y.S.1    Robbins, H.2
  • 58
    • 0002815335 scopus 로고
    • The performance of a statistical procedure for the fixed-width interval estimation for the mean
    • Starr N. The performance of a statistical procedure for the fixed-width interval estimation for the mean. Ann. Math. Stat. 37 (1966) 36
    • (1966) Ann. Math. Stat. , vol.37 , pp. 36
    • Starr, N.1
  • 59
    • 0009333505 scopus 로고
    • On the cost of not knowing the variance when making a fixed-width confidence interval for the mean
    • Simons G. On the cost of not knowing the variance when making a fixed-width confidence interval for the mean. Ann. Math. Stat. 39 (1968) 1946
    • (1968) Ann. Math. Stat. , vol.39 , pp. 1946
    • Simons, G.1
  • 60
    • 17644362944 scopus 로고
    • An extension of the theorem of Chow and Robbins on sequential confidence intervals for the mean
    • Nadas A. An extension of the theorem of Chow and Robbins on sequential confidence intervals for the mean. Ann. Math. Stat. 40 (1969) 667
    • (1969) Ann. Math. Stat. , vol.40 , pp. 667
    • Nadas, A.1
  • 61
    • 0000467558 scopus 로고
    • Second order approximations for sequential point and interval estimation
    • Woodroofe M. Second order approximations for sequential point and interval estimation. Ann. Stat. 5 (1977) 985
    • (1977) Ann. Stat. , vol.5 , pp. 985
    • Woodroofe, M.1
  • 62
    • 84958364216 scopus 로고
    • Relative width sequential confidence intervals for the mean
    • Law A.M., Kelton W.D., and Koenig L.W. Relative width sequential confidence intervals for the mean. Commun. Stat. B 10 (1981) 29
    • (1981) Commun. Stat. B , vol.10 , pp. 29
    • Law, A.M.1    Kelton, W.D.2    Koenig, L.W.3
  • 65
    • 84952519631 scopus 로고
    • Algorithms for computing the sample variance: analysis and recommendations
    • Chan T.F., Golub G.H., and LeVeque R.J. Algorithms for computing the sample variance: analysis and recommendations. Am. Stat. 37 3 (1983) 242
    • (1983) Am. Stat. , vol.37 , Issue.3 , pp. 242
    • Chan, T.F.1    Golub, G.H.2    LeVeque, R.J.3
  • 66
    • 0016434592 scopus 로고
    • Stably updating mean and standard deviation of data
    • Hanson R.J. Stably updating mean and standard deviation of data. Commun. ACM 18 (1975) 57
    • (1975) Commun. ACM , vol.18 , pp. 57
    • Hanson, R.J.1
  • 67
    • 0018518780 scopus 로고
    • Updating mean and variance estimates: an improved method
    • West D.H.D. Updating mean and variance estimates: an improved method. Commun. ACM 22 (1979) 522
    • (1979) Commun. ACM , vol.22 , pp. 522
    • West, D.H.D.1
  • 70
    • 0000396393 scopus 로고
    • A Monte Carlo comparison of four estimators for a covariance matrix
    • Krishnaiah P.R. (Ed), North-Holland
    • Lin S.P., and Perlman M.D. A Monte Carlo comparison of four estimators for a covariance matrix. In: Krishnaiah P.R. (Ed). Multivariate Analysis VI (1985), North-Holland 411-429
    • (1985) Multivariate Analysis VI , pp. 411-429
    • Lin, S.P.1    Perlman, M.D.2
  • 71
    • 0346961488 scopus 로고    scopus 로고
    • A well-conditioned estimator for large-dimensional covariance matrices
    • Ledoit O., and Wolf M. A well-conditioned estimator for large-dimensional covariance matrices. J. Multivariate Anal. 88 2 (2004) 365
    • (2004) J. Multivariate Anal. , vol.88 , Issue.2 , pp. 365
    • Ledoit, O.1    Wolf, M.2
  • 72
    • 0000835233 scopus 로고
    • On fixed-width confidence bounds for regression parameters and mean vector
    • Srivastava M.S. On fixed-width confidence bounds for regression parameters and mean vector. J. R. Stat. Soc. B 29 (1967) 132
    • (1967) J. R. Stat. Soc. B , vol.29 , pp. 132
    • Srivastava, M.S.1
  • 73
    • 0003709525 scopus 로고
    • Accurate multivariate estimation using triple sampling
    • Lohr S. Accurate multivariate estimation using triple sampling. Ann. Stat. 18 (1990) 1615
    • (1990) Ann. Stat. , vol.18 , pp. 1615
    • Lohr, S.1
  • 74
    • 0343327401 scopus 로고
    • The asymptotic validity of sequential stopping rules for stochastic simulations
    • Glynn P.W., and Whitt W. The asymptotic validity of sequential stopping rules for stochastic simulations. Ann. Appl. Prob. 2 (1992) 180
    • (1992) Ann. Appl. Prob. , vol.2 , pp. 180
    • Glynn, P.W.1    Whitt, W.2
  • 75
    • 0036276492 scopus 로고    scopus 로고
    • Fixed width confidence region for the mean of a multivariate normal distribution
    • Nagao H., and Srivastava M.S. Fixed width confidence region for the mean of a multivariate normal distribution. J. Multivariate Anal. 81 (2002) 259
    • (2002) J. Multivariate Anal. , vol.81 , pp. 259
    • Nagao, H.1    Srivastava, M.S.2
  • 76
    • 0037217334 scopus 로고    scopus 로고
    • The role of dimerization in noise reduction of simple genetic networks
    • Bundschuh R., Hayot F., and Jayaprakash C. The role of dimerization in noise reduction of simple genetic networks. J. Theor. Biol. 220 (2003) 261
    • (2003) J. Theor. Biol. , vol.220 , pp. 261
    • Bundschuh, R.1    Hayot, F.2    Jayaprakash, C.3


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