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A Rao-Blackwellized particle filter for joint parameter estimation and biomass tracking in a stochastic predator-prey system
1. | Departamento de Física Aplicada, Universidad de Granada, Avda. Fuentenueva s/n, 18071 Granada, Spain, Spain |
2. | Department of Molecular and Translational Medicine, University of Brescia, Viale Europa 11, 25125 Brescia |
3. | CNR-IMATI, Via Bassini 15, 20133 Milano, Italy |
4. | Departamento de Teoría de la Señal y Comunicaciones, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid, Spain |
References:
[1] |
Y. Aït-Sahalia, Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach, Econometrica, 70 (2002), 223-262.
doi: 10.1111/1468-0262.00274. |
[2] |
B. D. O. Anderson and J. B. Moore, Optimal Filtering, Englewood Cliffs, 1979.
doi: 10.1109/TSMC.1982.4308806. |
[3] |
C. Andrieu, A. Doucet and R. Holenstein, Particle Markov chain Monte Carlo methods, Journal of the Royal Statistical Society Series B-Statistical Methodology, 72 (2010), 269-342.
doi: 10.1111/j.1467-9868.2009.00736.x. |
[4] |
C. Andrieu, A. Doucet, S. S. Singh and V. B. Tadić, Particle methods for change detection, system identification and control, Proceedings of the IEEE, 92 (2004), 423-438.
doi: 10.1109/JPROC.2003.823142. |
[5] |
A. Bain and D. Crisan, Fundamentals of Stochastic Filtering, Springer, 2008. |
[6] |
A. Beskos, O. Papaspiliopoulos, G. O. Roberts and P. Fearnhead, Exact an computationally efficient likelihood-based estimation for discretely observed diffusion processes, J. Roy. Stat. Soc. Ser. B, 68 (2006), 333-382.
doi: 10.1111/j.1467-9868.2006.00552.x. |
[7] |
G. Buffoni and G. Gilioli, A lumped parameter model for acarine predator-prey population interactions, Ecological Modelling, 170 (2003), 155-171.
doi: 10.1016/S0304-3800(03)00223-0. |
[8] |
O. Cappé, S. J. Godsill and E. Moulines, An overview of existing methods and recent advances in sequential Monte Carlo, Proceedings of the IEEE, 95 (2007), 899-924. |
[9] |
J. Carpenter, P. Clifford and P. Fearnhead, Improved particle filter for nonlinear problems, IEE Proceedings - Radar, Sonar and Navigation, 146 (1999), 2-7.
doi: 10.1049/ip-rsn:19990255. |
[10] |
S. R. Carpenter, K. L. Cottingham and C. A. Stow, Fitting predator-prey models to time series with observation errors, Ecology, 75 (1994), 1254-1264.
doi: 10.2307/1937451. |
[11] |
R. Chen and J. S. Liu, Mixture Kalman filters, Journal of the Royal Statistics Society B, 62 (2000), 493-508.
doi: 10.1111/1467-9868.00246. |
[12] |
N. Chopin, P. E. Jacob and O. Papaspiliopoulos, SMC2: An efficient algorithm for sequential analysis of state space models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), (2012).
doi: 10.1111/j.1467-9868.2012.01046.x. |
[13] |
J. A. Comiskey, F. Dallmeier and A. Alonso, Framework for Assessment and Monitoring of Biodiversity, Academic Press, New York, 1999. |
[14] |
R. Douc, O. Cappe and E. Moulines, Comparison of resampling schemes for particle filtering, in ISPA 2005: Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005, 64-69.
doi: 10.1109/ISPA.2005.195385. |
[15] |
A. Doucet, N. de Freitas and N. Gordon (eds.), Sequential Monte Carlo Methods in Practice, Springer, New York (USA), 2001. |
[16] |
A. Doucet, S. Godsill and C. Andrieu, On sequential Monte Carlo sampling methods for Bayesian filtering, Statistics and Computing, 10 (2000), 197-208. |
[17] |
M. Dowd, A sequential Monte Carlo approach to marine ecological prediction, Environmetrics, 17 (2006), 435-455.
doi: 10.1002/env.780. |
[18] |
M. Dowd, Estimating parameters for a stochastic dynamic marine ecological system, Environmetrics, 22 (2011), 501-515.
doi: 10.1002/env.1083. |
[19] |
M. Dowd and R. Joy, Estimating behavioral parameters in animal movement models using a state-augmented particle filter, Ecology, 92 (2011), 568-575.
doi: 10.1890/10-0611.1. |
[20] |
G. B. Durham and A. R. Gallant, Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes, J. Bus. Econ. Stat., 20 (2002), 297-316.
doi: 10.1198/073500102288618397. |
[21] |
O. Elerian, S. Chib and N. Shephard, Likelihood inference for discretely observed nonlinear diffusions, Econometrica, 69 (2001), 959-993.
doi: 10.1111/1468-0262.00226. |
[22] |
B. Eraker, MCMC analysis of diffusion models with application to finance, J. Bus. Econ. Stat., 19 (2001), 177-191.
doi: 10.1198/073500101316970403. |
[23] |
G. Gilioli, S. Pasquali and F. Ruggeri, Bayesian inference for functional response in a stochastic predator-prey system, Bulletin of Mathematical Biology, 70 (2008), 358-381.
doi: 10.1007/s11538-007-9256-3. |
[24] |
G. Gilioli, S. Pasquali and F. Ruggeri, Nonlinear functional response parameter estimation in a stochastic predator-prey model, Mathematical Biosciences and Engineering, 9 (2012), 75-96.
doi: 10.3934/mbe.2012.9.75. |
[25] |
G. Gilioli and V. Vacante, Aspetti della dinamica di popolazione del sistema tetranychus urticae- phytoseiulus persimilis in pieno campo: implicazioni per le strategie di lotta biologica, in Atti del Convegno "La difesa delle colture in agricoltura biologica" - Notiziario sulla protezione delle piante, vol. 13, 2001. |
[26] |
A. Golightly and D. J. Wilkinson, Bayesian inference for stochastic kinetic models using a diffusion approximations, Biometrics, 61 (2005), 781-788.
doi: 10.1111/j.1541-0420.2005.00345.x. |
[27] |
A. Golightly and D. J. Wilkinson, Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo, Interface Focus, 1 (2011), 807-820.
doi: 10.1098/rsfs.2011.0047. |
[28] |
N. Gordon, D. Salmond and A. F. M. Smith, Novel approach to nonlinear and non-Gaussian Bayesian state estimation, IEE Proceedings-F, 140 (1993), 107-113.
doi: 10.1049/ip-f-2.1993.0015. |
[29] |
C. Jost and S. P. Ellner, Testing for predator dependence in predator-prey dynamics: a non-parametric approach, Proc. Roy. Soc. Lond. B, 267 (2000), 1611-1620.
doi: 10.1098/rspb.2000.1186. |
[30] |
R. E. Kalman, A new approach to linear filtering and prediction problems, Journal of Basic Engineering, 82 (1960), 35-45.
doi: 10.1115/1.3662552. |
[31] |
J. Knape and P. de Valpine, Fitting complex population models by combining particle filters with Markov chain Monte Carlo, Ecology, 93 (2012), 256-263.
doi: 10.1890/11-0797.1. |
[32] |
J. Liu and M. West, Combined parameter and state estimation in simulation-based filtering, in Sequential Monte Carlo Methods in Practice (eds. A. Doucet, N. de Freitas and N. Gordon), chap. 10, Springer, 2001, 197-223. |
[33] |
J. S. Liu and R. Chen, Sequential Monte Carlo methods for dynamic systems, Journal of the American Statistical Association, 93 (1998), 1032-1044.
doi: 10.1080/01621459.1998.10473765. |
[34] |
J. Míguez, D. Crisan and P. M. Djurić, On the convergence of two sequential Monte Carlo methods for maximum a posteriori sequence estimation and stochastic global optimization, Statistics and Computing. |
[35] |
P. D. Moral, Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications, Springer, 2004.
doi: 10.1007/978-1-4684-9393-1. |
[36] |
M. A. Pascual and K. Kareiva, Predicting the outcome of competition using experimental data: maximum likelihood and Bayesian approaches, Ecology, 77 (1996), 337-349.
doi: 10.2307/2265613. |
[37] |
A. R. Pedersen, A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations, Scand. J. Stat., 22 (1995), 55-71. |
[38] |
M. K. Pitt and N. Shephard, Filtering via simulation: Auxiliary particle filters, Journal of the American statistical association, 94 (1999), 590-599.
doi: 10.1080/01621459.1999.10474153. |
[39] |
B. L. S. Prakasa Rao, Statistical Inference for Diffusion Type Processes, Arnold, London, 1999. |
[40] |
C. P. Robert and G. Casella, Monte Carlo Statistical Methods, Springer, 2004. |
[41] |
2.0.CO;2] K. Shea, H. P. Possingham, W. W. Murdoch and R. Roush, Active adaptive management in insect pest and weed control: intervention with a plan for learning, Ecological Applications, 12 (2002), 927-936. |
[42] |
H. Sorensen, Parametric inference for diffusion processes observed at discrete points in time: a survey, Int. Stat. Rev., 72 (2004), 337-354.
doi: 10.1111/j.1751-5823.2004.tb00241.x. |
[43] |
O. Stramer and J. Yan, On simulated likelihood of discretely observed diffusion processes and comparison to closed-form approximation, J. Comput. Graph. Stat., 16 (2007).
doi: 10.1198/106186007X237306. |
[44] |
J. Y. Xia, R. Rabbinge and W. van der Werf, Multistage functional responses in a leadybeetle-aphid system: scaling up from the laboratory to the field, Environmental Entomology, 32 (2003), 151-162.
doi: 10.1603/0046-225X-32.1.151. |
show all references
References:
[1] |
Y. Aït-Sahalia, Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach, Econometrica, 70 (2002), 223-262.
doi: 10.1111/1468-0262.00274. |
[2] |
B. D. O. Anderson and J. B. Moore, Optimal Filtering, Englewood Cliffs, 1979.
doi: 10.1109/TSMC.1982.4308806. |
[3] |
C. Andrieu, A. Doucet and R. Holenstein, Particle Markov chain Monte Carlo methods, Journal of the Royal Statistical Society Series B-Statistical Methodology, 72 (2010), 269-342.
doi: 10.1111/j.1467-9868.2009.00736.x. |
[4] |
C. Andrieu, A. Doucet, S. S. Singh and V. B. Tadić, Particle methods for change detection, system identification and control, Proceedings of the IEEE, 92 (2004), 423-438.
doi: 10.1109/JPROC.2003.823142. |
[5] |
A. Bain and D. Crisan, Fundamentals of Stochastic Filtering, Springer, 2008. |
[6] |
A. Beskos, O. Papaspiliopoulos, G. O. Roberts and P. Fearnhead, Exact an computationally efficient likelihood-based estimation for discretely observed diffusion processes, J. Roy. Stat. Soc. Ser. B, 68 (2006), 333-382.
doi: 10.1111/j.1467-9868.2006.00552.x. |
[7] |
G. Buffoni and G. Gilioli, A lumped parameter model for acarine predator-prey population interactions, Ecological Modelling, 170 (2003), 155-171.
doi: 10.1016/S0304-3800(03)00223-0. |
[8] |
O. Cappé, S. J. Godsill and E. Moulines, An overview of existing methods and recent advances in sequential Monte Carlo, Proceedings of the IEEE, 95 (2007), 899-924. |
[9] |
J. Carpenter, P. Clifford and P. Fearnhead, Improved particle filter for nonlinear problems, IEE Proceedings - Radar, Sonar and Navigation, 146 (1999), 2-7.
doi: 10.1049/ip-rsn:19990255. |
[10] |
S. R. Carpenter, K. L. Cottingham and C. A. Stow, Fitting predator-prey models to time series with observation errors, Ecology, 75 (1994), 1254-1264.
doi: 10.2307/1937451. |
[11] |
R. Chen and J. S. Liu, Mixture Kalman filters, Journal of the Royal Statistics Society B, 62 (2000), 493-508.
doi: 10.1111/1467-9868.00246. |
[12] |
N. Chopin, P. E. Jacob and O. Papaspiliopoulos, SMC2: An efficient algorithm for sequential analysis of state space models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), (2012).
doi: 10.1111/j.1467-9868.2012.01046.x. |
[13] |
J. A. Comiskey, F. Dallmeier and A. Alonso, Framework for Assessment and Monitoring of Biodiversity, Academic Press, New York, 1999. |
[14] |
R. Douc, O. Cappe and E. Moulines, Comparison of resampling schemes for particle filtering, in ISPA 2005: Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005, 64-69.
doi: 10.1109/ISPA.2005.195385. |
[15] |
A. Doucet, N. de Freitas and N. Gordon (eds.), Sequential Monte Carlo Methods in Practice, Springer, New York (USA), 2001. |
[16] |
A. Doucet, S. Godsill and C. Andrieu, On sequential Monte Carlo sampling methods for Bayesian filtering, Statistics and Computing, 10 (2000), 197-208. |
[17] |
M. Dowd, A sequential Monte Carlo approach to marine ecological prediction, Environmetrics, 17 (2006), 435-455.
doi: 10.1002/env.780. |
[18] |
M. Dowd, Estimating parameters for a stochastic dynamic marine ecological system, Environmetrics, 22 (2011), 501-515.
doi: 10.1002/env.1083. |
[19] |
M. Dowd and R. Joy, Estimating behavioral parameters in animal movement models using a state-augmented particle filter, Ecology, 92 (2011), 568-575.
doi: 10.1890/10-0611.1. |
[20] |
G. B. Durham and A. R. Gallant, Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes, J. Bus. Econ. Stat., 20 (2002), 297-316.
doi: 10.1198/073500102288618397. |
[21] |
O. Elerian, S. Chib and N. Shephard, Likelihood inference for discretely observed nonlinear diffusions, Econometrica, 69 (2001), 959-993.
doi: 10.1111/1468-0262.00226. |
[22] |
B. Eraker, MCMC analysis of diffusion models with application to finance, J. Bus. Econ. Stat., 19 (2001), 177-191.
doi: 10.1198/073500101316970403. |
[23] |
G. Gilioli, S. Pasquali and F. Ruggeri, Bayesian inference for functional response in a stochastic predator-prey system, Bulletin of Mathematical Biology, 70 (2008), 358-381.
doi: 10.1007/s11538-007-9256-3. |
[24] |
G. Gilioli, S. Pasquali and F. Ruggeri, Nonlinear functional response parameter estimation in a stochastic predator-prey model, Mathematical Biosciences and Engineering, 9 (2012), 75-96.
doi: 10.3934/mbe.2012.9.75. |
[25] |
G. Gilioli and V. Vacante, Aspetti della dinamica di popolazione del sistema tetranychus urticae- phytoseiulus persimilis in pieno campo: implicazioni per le strategie di lotta biologica, in Atti del Convegno "La difesa delle colture in agricoltura biologica" - Notiziario sulla protezione delle piante, vol. 13, 2001. |
[26] |
A. Golightly and D. J. Wilkinson, Bayesian inference for stochastic kinetic models using a diffusion approximations, Biometrics, 61 (2005), 781-788.
doi: 10.1111/j.1541-0420.2005.00345.x. |
[27] |
A. Golightly and D. J. Wilkinson, Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo, Interface Focus, 1 (2011), 807-820.
doi: 10.1098/rsfs.2011.0047. |
[28] |
N. Gordon, D. Salmond and A. F. M. Smith, Novel approach to nonlinear and non-Gaussian Bayesian state estimation, IEE Proceedings-F, 140 (1993), 107-113.
doi: 10.1049/ip-f-2.1993.0015. |
[29] |
C. Jost and S. P. Ellner, Testing for predator dependence in predator-prey dynamics: a non-parametric approach, Proc. Roy. Soc. Lond. B, 267 (2000), 1611-1620.
doi: 10.1098/rspb.2000.1186. |
[30] |
R. E. Kalman, A new approach to linear filtering and prediction problems, Journal of Basic Engineering, 82 (1960), 35-45.
doi: 10.1115/1.3662552. |
[31] |
J. Knape and P. de Valpine, Fitting complex population models by combining particle filters with Markov chain Monte Carlo, Ecology, 93 (2012), 256-263.
doi: 10.1890/11-0797.1. |
[32] |
J. Liu and M. West, Combined parameter and state estimation in simulation-based filtering, in Sequential Monte Carlo Methods in Practice (eds. A. Doucet, N. de Freitas and N. Gordon), chap. 10, Springer, 2001, 197-223. |
[33] |
J. S. Liu and R. Chen, Sequential Monte Carlo methods for dynamic systems, Journal of the American Statistical Association, 93 (1998), 1032-1044.
doi: 10.1080/01621459.1998.10473765. |
[34] |
J. Míguez, D. Crisan and P. M. Djurić, On the convergence of two sequential Monte Carlo methods for maximum a posteriori sequence estimation and stochastic global optimization, Statistics and Computing. |
[35] |
P. D. Moral, Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications, Springer, 2004.
doi: 10.1007/978-1-4684-9393-1. |
[36] |
M. A. Pascual and K. Kareiva, Predicting the outcome of competition using experimental data: maximum likelihood and Bayesian approaches, Ecology, 77 (1996), 337-349.
doi: 10.2307/2265613. |
[37] |
A. R. Pedersen, A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations, Scand. J. Stat., 22 (1995), 55-71. |
[38] |
M. K. Pitt and N. Shephard, Filtering via simulation: Auxiliary particle filters, Journal of the American statistical association, 94 (1999), 590-599.
doi: 10.1080/01621459.1999.10474153. |
[39] |
B. L. S. Prakasa Rao, Statistical Inference for Diffusion Type Processes, Arnold, London, 1999. |
[40] |
C. P. Robert and G. Casella, Monte Carlo Statistical Methods, Springer, 2004. |
[41] |
2.0.CO;2] K. Shea, H. P. Possingham, W. W. Murdoch and R. Roush, Active adaptive management in insect pest and weed control: intervention with a plan for learning, Ecological Applications, 12 (2002), 927-936. |
[42] |
H. Sorensen, Parametric inference for diffusion processes observed at discrete points in time: a survey, Int. Stat. Rev., 72 (2004), 337-354.
doi: 10.1111/j.1751-5823.2004.tb00241.x. |
[43] |
O. Stramer and J. Yan, On simulated likelihood of discretely observed diffusion processes and comparison to closed-form approximation, J. Comput. Graph. Stat., 16 (2007).
doi: 10.1198/106186007X237306. |
[44] |
J. Y. Xia, R. Rabbinge and W. van der Werf, Multistage functional responses in a leadybeetle-aphid system: scaling up from the laboratory to the field, Environmental Entomology, 32 (2003), 151-162.
doi: 10.1603/0046-225X-32.1.151. |
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