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Volumn 21, Issue 3, 2015, Pages 1760-1799

Statistical estimation of a growth-fragmentation model observed on a genealogical tree

Author keywords

Cell division equation; Growth fragmentation; Markov chain on a tree; Nonparametric estimation

Indexed keywords


EID: 84938635586     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/14-BEJ623     Document Type: Article
Times cited : (72)

References (38)
  • 1
    • 1642312988 scopus 로고    scopus 로고
    • A mean-field model for multiple TCP connections through a buffer implementing RED
    • Baccelli, F., McDonald, D.R. and Reynier, J. (2002). A mean-field model for multiple TCP connections through a buffer implementing RED. Performance Evaluation 49 77-97.
    • (2002) Performance Evaluation , vol.49 , pp. 77-97
    • Baccelli, F.1    McDonald, D.R.2    Reynier, J.3
  • 2
    • 84877072779 scopus 로고    scopus 로고
    • Fine asymptotics of profiles and relaxation to equilibrium for growth-fragmentation equations with variable drift rates
    • Balagué, D., Canizo, J. and Gabriel, P. (2013). Fine asymptotics of profiles and relaxation to equilibrium for growth-fragmentation equations with variable drift rates. Kinetic and Related Models 6 219-243.
    • (2013) Kinetic and Related Models , vol.6 , pp. 219-243
    • Balagué, D.1    Canizo, J.2    Gabriel, P.3
  • 4
    • 52949114580 scopus 로고    scopus 로고
    • Proliferating parasites in dividing cells: Kimmel's branching model revisited
    • MR2418235
    • Bansaye, V. (2008). Proliferating parasites in dividing cells: Kimmel's branching model revisited. Ann. Appl. Probab. 18 967-996. MR2418235
    • (2008) Ann. Appl. Probab. , vol.18 , pp. 967-996
    • Bansaye, V.1
  • 5
    • 82655181332 scopus 로고    scopus 로고
    • Limit theorems for Markov processes indexed by continuous time Galton-Watson trees
    • MR2895416
    • Bansaye, V., Delmas, J.-F., Marsalle, L. and Tran, V.C. (2011). Limit theorems for Markov processes indexed by continuous time Galton-Watson trees. Ann. Appl. Probab. 21 2263-2314. MR2895416
    • (2011) Ann. Appl. Probab. , vol.21 , pp. 2263-2314
    • Bansaye, V.1    Delmas, J.-F.2    Marsalle, L.3    Tran, V.C.4
  • 6
    • 14544277112 scopus 로고    scopus 로고
    • Renewal theory and computable convergence rates for geometrically ergodic Markov chains
    • MR2114987
    • Baxendale, P.H. (2005). Renewal theory and computable convergence rates for geometrically ergodic Markov chains. Ann. Appl. Probab. 15 700-738. MR2114987
    • (2005) Ann. Appl. Probab. , vol.15 , pp. 700-738
    • Baxendale, P.H.1
  • 7
    • 33846526778 scopus 로고    scopus 로고
    • Random fragmentation and coagulation processes
    • Cambridge: Cambridge Univ. Press. MR2253162
    • Bertoin, J. (2006). Random Fragmentation and Coagulation Processes. Cambridge Studies in Advanced Mathematics 102. Cambridge: Cambridge Univ. Press. MR2253162
    • (2006) Cambridge Studies in Advanced Mathematics , vol.102
    • Bertoin, J.1
  • 8
    • 80052611963 scopus 로고    scopus 로고
    • Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations
    • MR2832638
    • Cáceres, M.J., Ca?izo, J.A. and Mischler, S. (2011). Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations. J. Math. Pures Appl. (9) 96 334-362. MR2832638
    • (2011) J. Math Pures Appl. , vol.96 , Issue.9 , pp. 334-362
    • Cáceres, M.J.1    Caizo, J.A.2    Mischler, S.3
  • 11
    • 14544282666 scopus 로고    scopus 로고
    • Quantitative bounds on convergence of timeinhomogeneous Markov chains
    • MR2099647
    • Douc, R., Moulines, E. and Rosenthal, J.S. (2004). Quantitative bounds on convergence of timeinhomogeneous Markov chains. Ann. Appl. Probab. 14 1643-1665. MR2099647
    • (2004) Ann. Appl. Probab. , vol.14 , pp. 1643-1665
    • Douc, R.1    Moulines, E.2    Rosenthal, J.S.3
  • 12
    • 84861414830 scopus 로고    scopus 로고
    • Nonparametric estimation of the division rate of a size-structured population
    • Doumic, M., Hoffmann, M., Reynaud-Bouret, P. and Rivoirard, V. (2012). Nonparametric estimation of the division rate of a size-structured population. SIAM J. Numer. Anal. 50 925-950.
    • (2012) SIAM J. Numer. Anal. , vol.50 , pp. 925-950
    • Doumic, M.1    Hoffmann, M.2    Reynaud-Bouret, P.3    Rivoirard, V.4
  • 13
    • 78349308271 scopus 로고    scopus 로고
    • On the calibration of a size-structured population model from experimental data
    • Doumic, M., Maia, P. and Zubelli, J.P. (2010). On the calibration of a size-structured population model from experimental data. Acta Biotheor. 58 405-413.
    • (2010) Acta Biotheor. , vol.58 , pp. 405-413
    • Doumic, M.1    Maia, P.2    Zubelli, J.P.3
  • 14
    • 70350325431 scopus 로고    scopus 로고
    • Numerical solution of an inverse problem in sizestructured population dynamics
    • MR2482159
    • Doumic, M., Perthame, B. and Zubelli, J.P. (2009). Numerical solution of an inverse problem in sizestructured population dynamics. Inverse Problems 25 1-22. MR2482159
    • (2009) Inverse Problems , vol.25 , pp. 1-22
    • Doumic, M.1    Perthame, B.2    Zubelli, J.P.3
  • 15
    • 84878949906 scopus 로고    scopus 로고
    • Estimating the division rate for the growth-fragmentation equation
    • Doumic, M. and Tine, L.M. (2012). Estimating the division rate for the growth-fragmentation equation. J. Math. Biol. 67 69-103.
    • (2012) J. Math Biol. , vol.67 , pp. 69-103
    • Doumic, M.1    Tine, L.M.2
  • 16
    • 77953191728 scopus 로고    scopus 로고
    • Eigenelements of a general aggregation-fragmentation model
    • MR2652618
    • Doumic, M. and Gabriel, P. (2010). Eigenelements of a general aggregation-fragmentation model. Math. Models Methods Appl. Sci. 20 757-783. MR2652618
    • (2010) Math. Models Methods Appl Sci. , vol.20 , pp. 757-783
    • Doumic, M.1    Gabriel, P.2
  • 17
    • 33748890124 scopus 로고    scopus 로고
    • Analysis of a model for the dynamics of prions. II
    • MR2262459
    • Engler, H., Prüss, J. and Webb, G.F. (2006). Analysis of a model for the dynamics of prions. II. J. Math. Anal. Appl. 324 98-117. MR2262459
    • (2006) J. Math. Anal Appl. , vol.324 , pp. 98-117
    • Engler, H.1    Prüss, J.2    Webb, G.F.3
  • 18
    • 84864051612 scopus 로고    scopus 로고
    • Convergence of adaptive and interacting markov chain monte carlo algorithms
    • MR3012408
    • Fort, G., Moulines, E. and Priouret, P. (2011). Convergence of adaptive and interacting Markov chain Monte Carlo algorithms. Ann. Statist. 39 3262-3289. MR3012408
    • (2011) Ann Statist. , vol.39 , pp. 3262-3289
    • Fort, G.1    Moulines, E.2    Priouret, P.3
  • 19
    • 24344441592 scopus 로고    scopus 로고
    • Nonparametric estimation of scalar diffusions based on low frequency data
    • MR2102509
    • Gobet, E., Hoffmann, M. and Rei?, M. (2004). Nonparametric estimation of scalar diffusions based on low frequency data. Ann. Statist. 32 2223-2253. MR2102509
    • (2004) Ann Statist. , vol.32 , pp. 2223-2253
    • Gobet, E.1    Hoffmann, M.2    Rei, M.3
  • 20
    • 84858749056 scopus 로고    scopus 로고
    • Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality
    • MR2850214
    • Goldenshluger, A. and Lepski, O. (2011). Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality. Ann. Statist. 39 1608-1632. MR2850214
    • (2011) Ann Statist. , vol.39 , pp. 1608-1632
    • Goldenshluger, A.1    Lepski, O.2
  • 21
    • 0037524295 scopus 로고    scopus 로고
    • Loss of mass in deterministic and random fragmentations
    • MR1989629
    • Haas, B. (2003). Loss of mass in deterministic and random fragmentations. Stochastic Process. Appl. 106 245-277. MR1989629
    • (2003) Stochastic Process Appl. , vol.106 , pp. 245-277
    • Haas, B.1
  • 23
    • 19544379881 scopus 로고    scopus 로고
    • Stochasticity in gene expression: From theories to phenotypes
    • Kaern, M., Elston, T.C., Blake, W.J. and Collins, J.J. (2005). Stochasticity in gene expression: From theories to phenotypes. Nat. Rev. Genet. 6 451-464.
    • (2005) Nat. Rev. Genet. , vol.6 , pp. 451-464
    • Kaern, M.1    Elston, T.C.2    Blake, W.J.3    Collins, J.J.4
  • 24
    • 0014528269 scopus 로고
    • Growth during the bacterial cell cycle: Analysis of cell size distribution
    • Kubitschek, H.E. (1969). Growth during the bacterial cell cycle: Analysis of cell size distribution. Biophys. J. 9 792-809.
    • (1969) Biophys. J. , vol.9 , pp. 792-809
    • Kubitschek, H.E.1
  • 25
    • 70350447393 scopus 로고    scopus 로고
    • Exponential decay for the growth-fragmentation/cell-division equation
    • MR2536450
    • Lauren?ot, P. and Perthame, B. (2009). Exponential decay for the growth-fragmentation/cell-division equation. Commun. Math. Sci. 7 503-510. MR2536450
    • (2009) Commun. Math Sci. , vol.7 , pp. 503-510
    • Laurenot, P.1    Perthame, B.2
  • 26
    • 0003157238 scopus 로고
    • The dynamics of physiologically structured populations
    • Berlin: Springer. Papers from the colloquium held in Amsterdam, 1983 MR0860959
    • Metz, J.A.J. and Diekmann, O., eds. (1986). The Dynamics of Physiologically Structured Populations. Lecture Notes in Biomathematics 68. Berlin: Springer. Papers from the colloquium held in Amsterdam, 1983. MR0860959
    • (1986) Lecture Notes in Biomathematics , vol.68
    • Metz, J.A.J.1    Diekmann, O.2
  • 28
    • 33750058285 scopus 로고    scopus 로고
    • Existence of a solution to the cell division eigenproblem
    • MR2250122
    • Michel, P. (2006). Existence of a solution to the cell division eigenproblem. Math. Models Methods Appl. Sci. 16 1125-1153. MR2250122
    • (2006) Math. Models Methods Appl Sci. , vol.16 , pp. 1125-1153
    • Michel, P.1
  • 29
    • 24044522878 scopus 로고    scopus 로고
    • General relative entropy inequality: An illustration on growth models
    • MR2162224
    • Michel, P., Mischler, S. and Perthame, B. (2005). General relative entropy inequality: An illustration on growth models. J. Math. Pures Appl. (9) 84 1235-1260. MR2162224
    • (2005) J. Math Pures Appl. , vol.84 , Issue.9 , pp. 1235-1260
    • Michel, P.1    Mischler, S.2    Perthame, B.3
  • 30
    • 0033245858 scopus 로고    scopus 로고
    • Non-self-similar behavior in the LSW theory of Ostwald ripening
    • MR1712441
    • Niethammer, B. and Pego, R.L. (1999). Non-self-similar behavior in the LSW theory of Ostwald ripening. J. Stat. Phys. 95 867-902. MR1712441
    • (1999) J. Stat Phys. , vol.95 , pp. 867-902
    • Niethammer, B.1    Pego, R.L.2
  • 33
    • 12344315077 scopus 로고    scopus 로고
    • Exponential decay for the fragmentation or cell-division equation
    • MR2114128
    • Perthame, B. and Ryzhik, L. (2005). Exponential decay for the fragmentation or cell-division equation. J. Differential Equations 210 155-177. MR2114128
    • (2005) J. Differential Equations , vol.210 , pp. 155-177
    • Perthame, B.1    Ryzhik, L.2
  • 34
    • 34249659464 scopus 로고    scopus 로고
    • On the inverse problem for a size-structured population model
    • MR2329931
    • Perthame, B. and Zubelli, J.P. (2007). On the inverse problem for a size-structured population model. Inverse Problems 23 1037-1052. MR2329931
    • (2007) Inverse Problems , vol.23 , pp. 1037-1052
    • Perthame, B.1    Zubelli, J.P.2
  • 35
    • 13944272143 scopus 로고    scopus 로고
    • Aging and death in an organism that reproduces by morphologically symmetric division
    • Stewart, E.J., Madden, R., Paul, G. and Taddei, F. (2005). Aging and death in an organism that reproduces by morphologically symmetric division. PLoS Comput. Biol. 3 e45.
    • (2005) PLoS Comput. Biol. , vol.3 , pp. e45
    • Stewart, E.J.1    Madden, R.2    Paul, G.3    Taddei, F.4
  • 36
    • 79960941334 scopus 로고    scopus 로고
    • The cost of virulence: Retarded growth of Salmonella typhimurium cells expressing type III secretion system 1
    • Sturm, A., Heinemann, M., Arnoldini, M., Benecke, A., Ackermann, M., Benz, M., Dormann, J. and Hardt, W.-D. (2011). The cost of virulence: Retarded growth of Salmonella typhimurium cells expressing type III secretion system 1. PLoS Pathog. 7 e1002143.
    • (2011) PLoS Pathog. , vol.7 , pp. e1002143
    • Sturm, A.1    Heinemann, M.2    Arnoldini, M.3    Benecke, A.4    Ackermann, M.5    Benz, M.6    Dormann, J.7    Hardt, W.-D.8
  • 37
    • 70350324632 scopus 로고    scopus 로고
    • Emergent bistability by a growth-modulating positive feedback circuit
    • Tan, C., Marguet, P. and You, L. (2009). Emergent bistability by a growth-modulating positive feedback circuit. Nat. Chem. Biol. 5 842-848.
    • (2009) Nat. Chem. Biol. , vol.5 , pp. 842-848
    • Tan, C.1    Marguet, P.2    You, L.3


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