Les modÃ¨les non linÃ©aires Ã effets mixtes - Isped

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Estimation of the Fisher Information matrix An estimate of the asymptotic covariance matrix of ̂θ g is the inverse of the observed Fisher Information matrix : −∂ 2 θ log g(y; ̂θ g ) Sminaire ”Statistique et Sant Publique”, Bordeaux - 8 novembre 2005, p.32
Estimation of the Fisher Information matrix An estimate of the asymptotic covariance matrix of ̂θ g is the inverse of the observed Fisher Information matrix : −∂ 2 θ log g(y; ̂θ g ) Louis’s missing information principle (1982) ∂θ 2 log g(y; θ) = E y;θ[∂θ 2 log f(y, φ; θ)] + Cov y;θ[∂ θ log f(y, φ; θ)] where Cov y;θ [∂ θ log f(y, φ; θ)] = E y;θ [ ( ∂ θ log f(y, φ; θ) )( ∂ θ log f(y, φ; θ) ) ′ ] − E y;θ [∂ θ log f(y, φ; θ)]E y;θ [∂ θ log f(y, φ; θ)] ′ and ∂ θ log g(y; θ) = E y;θ [∂ θ log f(y, φ; θ)] Sminaire ”Statistique et Sant Publique”, Bordeaux - 8 novembre 2005, p.32
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Les modèles non linéaires à effe
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A pharmacokinetics example : theoph
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One compartment model (oral adminis
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One compartment model (oral adminis
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Viral load decrease during anti-HIV
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Viral load decrease during anti-HIV
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Evolution of the weight of 560 cows
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Le modèle mixte On aimerait constr
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Les modèles à effets mixtes Smina
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The (nonlinear) mixed effects model
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Objectifs Estimation Estimer l’en
Page 29 and 30: Objectifs Estimation Estimer l’en
Page 31 and 32: Les modèles mixtes en plein boom .
Page 33 and 34: Le groupe de travail MONOLIX Groupe
Page 35 and 36: Le groupe de travail MONOLIX Groupe
Page 37 and 38: Le groupe de travail MONOLIX des th
Page 39 and 40: Le groupe de travail MONOLIX des th
Page 41 and 42: Les méthodes d’estimation exista
Page 43 and 44: Some existing methods 1. Methods ba
Page 49 and 50: The incomplete data model The compl
Page 51 and 52: The incomplete data model The compl
Page 53 and 54: The EM algorithm (Expectation-Maxim
Page 55 and 56: The EM algorithm (Expectation-Maxim
Page 57 and 58: Convergence of EM Dempster et al. (
Page 59 and 60: Convergence of EM Dempster et al. (
Page 61 and 62: The SAEM algorithm (Stochastic Appr
Page 63 and 64: The SAEM algorithm (Stochastic Appr
Page 65 and 66: Convergence of SAEM Delyon, Laviell
Page 71 and 72: A Simulated Annealing version of SA
Page 73 and 74: A Simulated Annealing version of SA
Page 75 and 76: Coupling SAEM and MCMC (Kuhn and La
Page 77 and 78: Coupling SAEM and MCMC (Kuhn and La
Page 79: Convergence of the algorithm (Kuhn
Page 83 and 84: Estimation of the Fisher Informatio
Page 85 and 86: Estimation of the likelihood Import
Page 87 and 88: Estimation of the likelihood Import
Page 89 and 90: Le logiciel MONOLIX Sminaire ”Sta
Page 91 and 92: Le logiciel MONOLIX A pharmacokinet
Page 93 and 94: Modèle défini par un système d
Page 95 and 96: Modèle mixte avec équation diffé
Page 97 and 98: Schéma numérique Utilisation d’
Page 99 and 100: Schéma numérique Utilisation d’
Page 101 and 102: Utilisation d’un modèle approch
Page 103 and 104: Quelques propriétés des algorithm
Page 105 and 106: Un schéma de linéarisation locale
Page 107 and 108: Model defined by ordinary different
Page 109 and 110: Exemple sur des données simulées
Page 111 and 112: Modèle défini par un système d
Page 113 and 114: Algorithme de Hastings-Metropolis A
Page 115 and 116: Application aux données de theophy
Page 117 and 118: Application aux données de theophy
Page 119 and 120: Conclusion Sminaire ”Statistique
Page 121 and 122: Conclusion Les modèles (non linéa
Page 123 and 124: Conclusion Les modèles (non linéa
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Les modÃ¨les non linÃ©aires Ã effets mixtes - Isped

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