메뉴 건너뛰기




Volumn 10, Issue 7, 2007, Pages 551-563

Data cloning: Easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods

Author keywords

Bayesian statistics; Density dependence; Fisher information; Frequentist statistics; Generalized linear mixed models; Hierarchical models; Markov chain Monte Carlo; State space models; Stochastic population models

Indexed keywords

ALGORITHM; BAYESIAN ANALYSIS; DATA ACQUISITION; DENSITY DEPENDENCE; ECOLOGICAL MODELING; MARKOV CHAIN; MAXIMUM LIKELIHOOD ANALYSIS; MONTE CARLO ANALYSIS; POPULATION MODELING; SOFTWARE; STOCHASTICITY;

EID: 34249822549     PISSN: 1461023X     EISSN: 14610248     Source Type: Journal    
DOI: 10.1111/j.1461-0248.2007.01047.x     Document Type: Article
Times cited : (212)

References (75)
  • 2
    • 0000073382 scopus 로고    scopus 로고
    • Bayesian capture-recapture methods for error detection and estimation of population size: Heterogeneity and dependence
    • Basu, S. Ebrahimi, N. (2001). Bayesian capture-recapture methods for error detection and estimation of population size: heterogeneity and dependence. Biometrika, 88, 269 279.
    • (2001) Biometrika , vol.88 , pp. 269-279
    • Basu, S.1    Ebrahimi, N.2
  • 3
    • 5244304444 scopus 로고
    • Efficient estimation of free energy differences from Monte Carlo data
    • Bennett, C.H. (1976). Efficient estimation of free energy differences from Monte Carlo data. J. Comput. Phys., 22, 245 268.
    • (1976) J. Comput. Phys. , vol.22 , pp. 245-268
    • Bennett, C.H.1
  • 4
    • 0003020981 scopus 로고
    • Bias correction in generalised linear mixed models with a single component of dispersion
    • Breslow, N.E. Lin, X. (1995). Bias correction in generalised linear mixed models with a single component of dispersion. Biometrika, 82, 81 91.
    • (1995) Biometrika , vol.82 , pp. 81-91
    • Breslow, N.E.1    Lin, X.2
  • 5
    • 0011241944 scopus 로고
    • Approximate inference in generalized linear mixed models
    • Breslow, N.E. Clayton, D.G. (1993). Approximate inference in generalized linear mixed models. J. Am. Stat. Assoc., 88, 9 25.
    • (1993) J. Am. Stat. Assoc. , vol.88 , pp. 9-25
    • Breslow, N.E.1    Clayton, D.G.2
  • 6
    • 0000728412 scopus 로고
    • Optimization using simulated annealing
    • Brooks, S.P. Morgan, B.J.T. (1995). Optimization using simulated annealing. Statistician, 44, 241 257.
    • (1995) Statistician , vol.44 , pp. 241-257
    • Brooks, S.P.1    Morgan, B.J.T.2
  • 8
    • 0037769488 scopus 로고    scopus 로고
    • Classical model selection via simulated annealing
    • Brooks, S.P., Friel, N. King, R. (2003). Classical model selection via simulated annealing. J. Roy. Stat. Soc. B, 65, 505 520.
    • (2003) J. Roy. Stat. Soc. B , vol.65 , pp. 505-520
    • Brooks, S.P.1    Friel, N.2    King, R.3
  • 9
    • 0742323619 scopus 로고    scopus 로고
    • State-space models for the dynamics of wild animal populations
    • Buckland, S.T., Newman, K.B., Thomas, L. Koesters, N.B. (2004). State-space models for the dynamics of wild animal populations. Ecol. Model., 171, 157 175.
    • (2004) Ecol. Model. , vol.171 , pp. 157-175
    • Buckland, S.T.1    Newman, K.B.2    Thomas, L.3    Koesters, N.B.4
  • 12
    • 84937730674 scopus 로고
    • Explaining the Gibbs sampler
    • Casella, G. George, E.I. (1992). Explaining the Gibbs sampler. Am. Stat., 46, 167 174.
    • (1992) Am. Stat. , vol.46 , pp. 167-174
    • Casella, G.1    George, E.I.2
  • 13
    • 32344446687 scopus 로고
    • Understanding the Metropolis-Hastings algorithm
    • Chib, S. Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. Am. Stat., 49, 327 335.
    • (1995) Am. Stat. , vol.49 , pp. 327-335
    • Chib, S.1    Greenberg, E.2
  • 14
    • 0042722200 scopus 로고    scopus 로고
    • Uncertainty in population growth rates calculated from demography: The hierarchical approach
    • Clark, J.S. (2003). Uncertainty in population growth rates calculated from demography: the hierarchical approach. Ecology, 84, 1370 1381.
    • (2003) Ecology , vol.84 , pp. 1370-1381
    • Clark, J.S.1
  • 15
    • 12944287801 scopus 로고    scopus 로고
    • Why environmental scientists are becoming Bayesians
    • Clark, J.S. (2005). Why environmental scientists are becoming Bayesians. Ecol. Lett., 8, 2 14.
    • (2005) Ecol. Lett. , vol.8 , pp. 2-14
    • Clark, J.S.1
  • 16
    • 9244230097 scopus 로고    scopus 로고
    • Population time series: Process variability, observation errors, missing values, lags, and hidden states
    • Clark, J.S. Bjørnstad, O.N. (2004). Population time series: process variability, observation errors, missing values, lags, and hidden states. Ecology, 85, 3140 3150.
    • (2004) Ecology , vol.85 , pp. 3140-3150
    • Clark, J.S.1    Bjørnstad, O.N.2
  • 17
    • 33745420790 scopus 로고    scopus 로고
    • A future for models and data in ecology
    • Clark, J.S. Gelfand, A.E. (2006). A future for models and data in ecology. Trends Ecol. Evol., 21, 375 380.
    • (2006) Trends Ecol. Evol. , vol.21 , pp. 375-380
    • Clark, J.S.1    Gelfand, A.E.2
  • 18
    • 0345447476 scopus 로고    scopus 로고
    • Estimating population spread: What can we forecast and how well
    • Clark, J.S., Lewis, M., McLachlan, J.S. Hille Ris Lambers J. (2003). Estimating population spread: what can we forecast and how well Ecology, 84, 1979 1988.
    • (2003) Ecology , vol.84 , pp. 1979-1988
    • Clark, J.S.1    Lewis, M.2    McLachlan, J.S.3    Hille Ris Lambers, J.4
  • 19
    • 23644450785 scopus 로고    scopus 로고
    • Hierarchical Bayes for structured and variable populations: From capture-recapture data to life-history prediction
    • Clark, J.S., Ferraz, G., Oguge, N., Hays, H. DiCostanzo, J. (2005). Hierarchical Bayes for structured and variable populations: from capture-recapture data to life-history prediction. Ecology, 86, 2232 2244.
    • (2005) Ecology , vol.86 , pp. 2232-2244
    • Clark, J.S.1    Ferraz, G.2    Oguge, N.3    Hays, H.4    Dicostanzo, J.5
  • 20
    • 1342287624 scopus 로고    scopus 로고
    • Better inferences from population-dynamics experiments using Monte Carlo state-space likelihood methods
    • De Valpine, P. (2003). Better inferences from population-dynamics experiments using Monte Carlo state-space likelihood methods. Ecology, 84, 3064 3077.
    • (2003) Ecology , vol.84 , pp. 3064-3077
    • De Valpine, P.1
  • 21
    • 2942538599 scopus 로고    scopus 로고
    • Monte Carlo state-space likelihoods by weighted posterior kernel density estimation
    • De Valpine, P. (2004). Monte Carlo state-space likelihoods by weighted posterior kernel density estimation. J. Am. Stat. Assoc., 99, 523 536.
    • (2004) J. Am. Stat. Assoc. , vol.99 , pp. 523-536
    • De Valpine, P.1
  • 22
    • 0036160013 scopus 로고    scopus 로고
    • Fitting population models incorporating process noise and observation error
    • De Valpine, P. Hastings, A. (2002). Fitting population models incorporating process noise and observation error. Ecol. Monogr., 72, 57 76.
    • (2002) Ecol. Monogr. , vol.72 , pp. 57-76
    • De Valpine, P.1    Hastings, A.2
  • 23
    • 0028180186 scopus 로고
    • Density dependence in time series observations of natural populations: Estimation and testing
    • Dennis, B. Taper, M.L. (1994). Density dependence in time series observations of natural populations: estimation and testing. Ecol. Monogr., 64, 205 224.
    • (1994) Ecol. Monogr. , vol.64 , pp. 205-224
    • Dennis, B.1    Taper, M.L.2
  • 24
    • 0028976114 scopus 로고
    • Nonlinear demographic dynamics: Mathematical models, statistical methods, and biological experiments
    • Dennis, B., Desharnais, R.A., Cushing, J.M. Costantino, R.F. (1995). Nonlinear demographic dynamics: mathematical models, statistical methods, and biological experiments. Ecol. Monogr., 65, 261 281.
    • (1995) Ecol. Monogr. , vol.65 , pp. 261-281
    • Dennis, B.1    Desharnais, R.A.2    Cushing, J.M.3    Costantino, R.F.4
  • 25
    • 33747072045 scopus 로고    scopus 로고
    • Estimating density dependence, process noise, and observation error
    • Dennis, B., Ponciano, J.M., Lele, S.R. Taper, M.L. (2006). Estimating density dependence, process noise, and observation error. Ecol. Monogr., 76, 323 341.
    • (2006) Ecol. Monogr. , vol.76 , pp. 323-341
    • Dennis, B.1    Ponciano, J.M.2    Lele, S.R.3    Taper, M.L.4
  • 26
    • 15444367312 scopus 로고    scopus 로고
    • Confronting different models of community structure to species abundance data: A Bayesian model comparison
    • Etienne, R.S. Olff, H. (2005). Confronting different models of community structure to species abundance data: a Bayesian model comparison. Ecol. Lett., 8, 493 504.
    • (2005) Ecol. Lett. , vol.8 , pp. 493-504
    • Etienne, R.S.1    Olff, H.2
  • 27
    • 0033472991 scopus 로고    scopus 로고
    • Classical multilevel and Bayesian approaches to population size estimation using multiple lists
    • Feinberg, S.E., Johnson, M.S. Junker, B.W. (1999). Classical multilevel and Bayesian approaches to population size estimation using multiple lists. J. Roy. Stat. Soc. A, 62, 383 406.
    • (1999) J. Roy. Stat. Soc. a , vol.62 , pp. 383-406
    • Feinberg, S.E.1    Johnson, M.S.2    Junker, B.W.3
  • 29
    • 84950453304 scopus 로고
    • Sampling-based approaches to calculating marginal densities
    • Gelfand, A.E. Smith, A.F.M. (1990). Sampling-based approaches to calculating marginal densities. J. Am. Stat. Assoc., 85, 398 409.
    • (1990) J. Am. Stat. Assoc. , vol.85 , pp. 398-409
    • Gelfand, A.E.1    Smith, A.F.M.2
  • 31
    • 0000736067 scopus 로고    scopus 로고
    • Simulating normalizing constants: From importance sampling to bridge sampling to path sampling
    • Gelman, A. Meng, X.L. (1998). Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Statist. Sci., 13, 163 185.
    • (1998) Statist. Sci. , vol.13 , pp. 163-185
    • Gelman, A.1    Meng, X.L.2
  • 32
    • 0000085642 scopus 로고
    • Capture-recapture estimation via Gibbs sampling
    • George, E.I. Robert, C.P. (1992). Capture-recapture estimation via Gibbs sampling. Biometrika, 79, 677 683.
    • (1992) Biometrika , vol.79 , pp. 677-683
    • George, E.I.1    Robert, C.P.2
  • 33
    • 2542593163 scopus 로고    scopus 로고
    • Discovering disease genes: Multipoint linkage analysis via a new Markov chain Monte Carlo approach
    • George, A.W. Thompson, E.A. (2003). Discovering disease genes: multipoint linkage analysis via a new Markov chain Monte Carlo approach. Statist. Sci., 18, 515 531.
    • (2003) Statist. Sci. , vol.18 , pp. 515-531
    • George, A.W.1    Thompson, E.A.2
  • 34
    • 0000051109 scopus 로고
    • Constrained Monte Carlo maximum likelihood for dependent data (with discussion)
    • Geyer, C.J. Thompson, E.A. (1992). Constrained Monte Carlo maximum likelihood for dependent data (with discussion). J. Roy. Stat. Soc. B, 54, 657 699.
    • (1992) J. Roy. Stat. Soc. B , vol.54 , pp. 657-699
    • Geyer, C.J.1    Thompson, E.A.2
  • 35
    • 84950437936 scopus 로고
    • Annealing Markov chain Monte Carlo with applications to ancestral inference
    • Geyer, C.J. Thompson, E.A. (1995). Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Am. Stat. Assoc., 90, 909 920.
    • (1995) J. Am. Stat. Assoc. , vol.90 , pp. 909-920
    • Geyer, C.J.1    Thompson, E.A.2
  • 37
    • 0032733766 scopus 로고    scopus 로고
    • Assessing uncertainty in a stand growth model by Bayesian synthesis
    • Green, E.J., MacFarlane, H.T., Valentine, H.T. Strawderman, W.E. (1999). Assessing uncertainty in a stand growth model by Bayesian synthesis. For. Sci., 45, 528 538.
    • (1999) For. Sci. , vol.45 , pp. 528-538
    • Green, E.J.1    MacFarlane, H.T.2    Valentine, H.T.3    Strawderman, W.E.4
  • 38
    • 77956890234 scopus 로고
    • Monte Carlo sampling methods using Markov chains and their applications
    • Hastings, W.K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97 109.
    • (1970) Biometrika , vol.57 , pp. 97-109
    • Hastings, W.K.1
  • 39
    • 0032333314 scopus 로고    scopus 로고
    • A composite likelihood approach to binary data in space
    • Heagerty, P. Lele, S.R. (1998). A composite likelihood approach to binary data in space. J. Am. Stat. Assoc., 93, 1099 1111.
    • (1998) J. Am. Stat. Assoc. , vol.93 , pp. 1099-1111
    • Heagerty, P.1    Lele, S.R.2
  • 41
    • 0026643305 scopus 로고
    • Generalized linear models with random effects: Salamander mating revisited
    • Karim, M.R. Zeger, S.L. (1992). Generalized linear models with random effects: salamander mating revisited. Biometrics, 48, 631 644.
    • (1992) Biometrics , vol.48 , pp. 631-644
    • Karim, M.R.1    Zeger, S.L.2
  • 42
    • 26444479778 scopus 로고
    • Optimisation using simulated annealing
    • Kirkpatrick, S., Gelatt, C.D. Vecchi, M.P. (1983). Optimisation using simulated annealing. Science, 220, 671 680.
    • (1983) Science , vol.220 , pp. 671-680
    • Kirkpatrick, S.1    Gelatt, C.D.2    Vecchi, M.P.3
  • 43
    • 84950459387 scopus 로고
    • Non-Gaussian state-space modeling of nonstationary time series (with discussion)
    • Kitagawa, G. (1987). Non-Gaussian state-space modeling of nonstationary time series (with discussion). J. Am. Stat. Assoc., 82, 1032 1063.
    • (1987) J. Am. Stat. Assoc. , vol.82 , pp. 1032-1063
    • Kitagawa, G.1
  • 44
    • 33644839515 scopus 로고    scopus 로고
    • Sampling variability and estimates of density dependence: A composite-likelihood approach
    • Lele, S.R. (2006). Sampling variability and estimates of density dependence: a composite-likelihood approach. Ecology, 87, 189 202.
    • (2006) Ecology , vol.87 , pp. 189-202
    • Lele, S.R.1
  • 45
    • 0038477019 scopus 로고    scopus 로고
    • A hierarchical model for population change with application to Cerulean Warblers
    • Link, W.A. Sauer, J.R. (2002). A hierarchical model for population change with application to Cerulean Warblers. Ecology, 83, 2832 2840.
    • (2002) Ecology , vol.83 , pp. 2832-2840
    • Link, W.A.1    Sauer, J.R.2
  • 46
    • 0036527211 scopus 로고    scopus 로고
    • Of bugs and birds: Markov chain Monte Carlo for hierarchical modeling in wildlife research
    • Link, W.A., Cam, E., Nichols, J.D. Cooch, E.G. (2002). Of bugs and birds: Markov chain Monte Carlo for hierarchical modeling in wildlife research. J. Wildlife Manage., 66, 277 291.
    • (2002) J. Wildlife Manage. , vol.66 , pp. 277-291
    • Link, W.A.1    Cam, E.2    Nichols, J.D.3    Cooch, E.G.4
  • 47
    • 32344432258 scopus 로고    scopus 로고
    • A hierarchical model for regional analysis of population change using Christmas Bird Count data, with application to the American Black Duck
    • Link, W.A., Sauer, J.R. Niven, D.K. (2006). A hierarchical model for regional analysis of population change using Christmas Bird Count data, with application to the American Black Duck. Condor, 108, 13 24.
    • (2006) Condor , vol.108 , pp. 13-24
    • Link, W.A.1    Sauer, J.R.2    Niven, D.K.3
  • 49
    • 0000336301 scopus 로고
    • Bifurcations and dynamic complexity in simple ecological models
    • May, R.M. Oster, G.F. (1976). Bifurcations and dynamic complexity in simple ecological models. Am. Nat., 110, 573 599.
    • (1976) Am. Nat. , vol.110 , pp. 573-599
    • May, R.M.1    Oster, G.F.2
  • 50
    • 0031479575 scopus 로고    scopus 로고
    • Maximum likelihood algorithms for generalized linear mixed models
    • McCulloch, C.E. (1997). Maximum likelihood algorithms for generalized linear mixed models. J. Am. Stat. Assoc., 92, 162 170.
    • (1997) J. Am. Stat. Assoc. , vol.92 , pp. 162-170
    • McCulloch, C.E.1
  • 52
    • 0032960742 scopus 로고    scopus 로고
    • Bayesian stock assessment using a state-space implementation of the delay difference model
    • Meyer, R. Millar, R.B. (1999a). Bayesian stock assessment using a state-space implementation of the delay difference model. Can. J. Fish. Aquat. Sci., 56, 37 52.
    • (1999) Can. J. Fish. Aquat. Sci. , vol.56 , pp. 37-52
    • Meyer, R.1    Millar, R.B.2
  • 53
    • 0033493957 scopus 로고    scopus 로고
    • BUGS in Bayesian stock assessments
    • Meyer, R. Millar, R.B. (1999b). BUGS in Bayesian stock assessments. Can. J. Fish. Aquat. Sci., 56, 1078 1087.
    • (1999) Can. J. Fish. Aquat. Sci. , vol.56 , pp. 1078-1087
    • Meyer, R.1    Millar, R.B.2
  • 54
    • 0034360571 scopus 로고    scopus 로고
    • Non-linear state space modeling of fisheries biomass dynamics using the Metropolis-Hastings within-Gibbs sampling
    • Millar, R.B. Meyer, R. (2000a). Non-linear state space modeling of fisheries biomass dynamics using the Metropolis-Hastings within-Gibbs sampling. Appl. Stat., 49, 327 342.
    • (2000) Appl. Stat. , vol.49 , pp. 327-342
    • Millar, R.B.1    Meyer, R.2
  • 55
    • 0034110745 scopus 로고    scopus 로고
    • Bayesian state-space modeling of age-structured data: Fitting a model is just the beginning
    • Millar, R.B. Meyer, R. (2000b). Bayesian state-space modeling of age-structured data: fitting a model is just the beginning. Can. J. Fish. Aquat. Sci., 57, 43 50.
    • (2000) Can. J. Fish. Aquat. Sci. , vol.57 , pp. 43-50
    • Millar, R.B.1    Meyer, R.2
  • 57
    • 0030389934 scopus 로고    scopus 로고
    • Predicting the outcome of competition using experimental data: Maximum likelihood and Bayesian approaches
    • Pascual, M.A. Kareiva, P. (1996). Predicting the outcome of competition using experimental data: maximum likelihood and Bayesian approaches. Ecology, 77, 337 349.
    • (1996) Ecology , vol.77 , pp. 337-349
    • Pascual, M.A.1    Kareiva, P.2
  • 58
    • 33847188754 scopus 로고    scopus 로고
    • The population biology of bacterial plasmids: A hidden Markov model approach
    • (in press).
    • Ponciano, J.M., De Gelder, L. Top, E.M. (2007). The population biology of bacterial plasmids: a hidden Markov model approach. Genetics (in press).
    • (2007) Genetics
    • Ponciano, J.M.1    De Gelder, L.2    Top, E.M.3
  • 60
    • 33748324384 scopus 로고    scopus 로고
    • R Core Development Team (. R Foundation for Statistical Computing, Vienna, Austria.
    • R Core Development Team (2006). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
    • (2006) R: A Language and Environment for Statistical Computing.
  • 61
    • 0036846065 scopus 로고    scopus 로고
    • Bayesian melding of a forest ecosystem model with correlated inputs
    • Radtke, P.J., Burk, T.E. Bolstad, P.V. (2002). Bayesian melding of a forest ecosystem model with correlated inputs. For. Sci., 48, 701 711.
    • (2002) For. Sci. , vol.48 , pp. 701-711
    • Radtke, P.J.1    Burk, T.E.2    Bolstad, P.V.3
  • 62
    • 0036881803 scopus 로고    scopus 로고
    • Hierarchical Bayesian analysis of capture-mark-capture data
    • Rivot, E. Prévost, E. (2002). Hierarchical Bayesian analysis of capture-mark-capture data. Can. J. Fish. Aquat. Sci., 59, 1768 1784.
    • (2002) Can. J. Fish. Aquat. Sci. , vol.59 , pp. 1768-1784
    • Rivot, E.1    Prévost, E.2
  • 63
    • 21344493244 scopus 로고
    • Prior feedback: Bayesian tools for maximum likelihood estimation
    • Robert, C.P. (1993). Prior feedback: Bayesian tools for maximum likelihood estimation. J. Comput. Stat., 8, 279 294.
    • (1993) J. Comput. Stat. , vol.8 , pp. 279-294
    • Robert, C.P.1
  • 65
    • 0041724127 scopus 로고    scopus 로고
    • Reparameterization strategies for hidden Markov models and Bayesian approches to maximum likelihood estimation
    • Robert, C.P. Titterington, D.M. (1998). Reparameterization strategies for hidden Markov models and Bayesian approches to maximum likelihood estimation. Stat. Comput., 8, 145 158.
    • (1998) Stat. Comput. , vol.8 , pp. 145-158
    • Robert, C.P.1    Titterington, D.M.2
  • 66
    • 0037633165 scopus 로고    scopus 로고
    • Hierarchical modeling of population stability and species group attributes using Markov chain Monte Carlo methods
    • Sauer, J.R. Link, W.A. (2002). Hierarchical modeling of population stability and species group attributes using Markov chain Monte Carlo methods. Ecology, 83, 1743 1751.
    • (2002) Ecology , vol.83 , pp. 1743-1751
    • Sauer, J.R.1    Link, W.A.2
  • 67
    • 33747839964 scopus 로고    scopus 로고
    • Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models
    • Skaug, H.G. Fournier, D.A. (2006). Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models. Comput. Stat. Data An., 51, 699 709.
    • (2006) Comput. Stat. Data An. , vol.51 , pp. 699-709
    • Skaug, H.G.1    Fournier, D.A.2
  • 72
    • 7544251105 scopus 로고    scopus 로고
    • A hierarchical spatial model of avian abundance with application to Cerulean Warblers
    • Thogmartin, W.E., Sauer, J.R. Knutson, M.G. (2004). A hierarchical spatial model of avian abundance with application to Cerulean Warblers. Ecol. Appl., 14, 1766 1779.
    • (2004) Ecol. Appl. , vol.14 , pp. 1766-1779
    • Thogmartin, W.E.1    Sauer, J.R.2    Knutson, M.G.3
  • 73
    • 0001905135 scopus 로고
    • On the asymptotic behaviour of posterior distributions
    • Walker, A.M. (1969). On the asymptotic behaviour of posterior distributions. J. Roy. Stat. Soc. B, 31, 80 88.
    • (1969) J. Roy. Stat. Soc. B , vol.31 , pp. 80-88
    • Walker, A.M.1
  • 74
    • 0041985115 scopus 로고    scopus 로고
    • Hierarchical Bayesian models for predicting the spread of ecological processes
    • Wikle, C.K. (2003). Hierarchical Bayesian models for predicting the spread of ecological processes. Ecology, 84, 1382 1394.
    • (2003) Ecology , vol.84 , pp. 1382-1394
    • Wikle, C.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.