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Start Over Author "Donnet, Sophie" Topic bayesian analysis
4 results on '"Donnet, Sophie"'

1. Bayesian Inference for Partially Observed Branching Processes

Author

Donnet, Sophie, Rousseau, Judith, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Centre de Recherche en Économie et Statistique (CREST), and Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI)-École polytechnique (X)-École Nationale de la Statistique et de l'Administration Économique (ENSAE Paris)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[STAT.AP]Statistics [stat]/Applications [stat.AP], Counting Process, Computer Science::Information Retrieval, Bayesian analysis, Branching process, Latent variables
Abstract

Poisson processes are used in various application fields applications (public health biology, reliability and so on). In their homogeneous version, the intensity process is a deterministic constant. In their inhomogeneous version, it depends on time. To allow for an endogenous evolution of the intensity process we consider multiplicative intensity processes. Inference methods have been developed when the trajectories are fully observed. We deal with the case of a partially observed process. As a motivating example, consider the analysis of an electrical network through time. This network is composed of cables and accessories (joints). When a cable fails, the cable is replaced by a new cable connected to the network by two new accessories. When an accessory fails, the same kind of reparation is done leading to the addition of only one accessory. The failure rate depends on the stochastically evolving number of accessories. We only observe the times events; the initial number of accessories and the cause of the incident (cable or accessory) are only partially observed. The aim is to estimate the different failure rates or to make predictions. The inference is strongly influenced by the initial number of accessories, which is typically an unknown quantity. We deduce a sensible prior on the initial number of accessories using the probabilistic properties of the process . We illustrate the performances of our methodology on a large simulation study.

Published
2013

2. Bayesian Analysis of Growth Curves Using Mixed Models Defined by Stochastic Differential Equations.

Author

Donnet, Sophie, Foulley, Jean-Louis, and Samson, Adeline

Subjects
*BAYESIAN analysis, *EULER'S numbers, *DISTRIBUTION (Probability theory), *STOCHASTIC analysis, *STOCHASTIC differential equations, *BIOMETRY
Abstract

Growth curve data consist of repeated measurements of a continuous growth process over time in a population of individuals. These data are classically analyzed by nonlinear mixed models. However, the standard growth functions used in this context prescribe monotone increasing growth and can fail to model unexpected changes in growth rates. We propose to model these variations using stochastic differential equations (SDEs) that are deduced from the standard deterministic growth function by adding random variations to the growth dynamics. A Bayesian inference of the parameters of these SDE mixed models is developed. In the case when the SDE has an explicit solution, we describe an easily implemented Gibbs algorithm. When the conditional distribution of the diffusion process has no explicit form, we propose to approximate it using the Euler–Maruyama scheme. Finally, we suggest validating the SDE approach via criteria based on the predictive posterior distribution. We illustrate the efficiency of our method using the Gompertz function to model data on chicken growth, the modeling being improved by the SDE approach. [ABSTRACT FROM AUTHOR]

Published
2010
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3. Estimation of parameters in incomplete data models defined by dynamical systems

Author

Donnet, Sophie and Samson, Adeline

Subjects
*MISSING data (Statistics), *ESTIMATION theory, *BAYESIAN analysis, *PROBABILITY theory, *STOCHASTIC approximation, *DIFFERENTIAL equations, *NUMERICAL integration
Abstract

Abstract: Parametric incomplete data models defined by ordinary differential equations (ODEs) are widely used in biostatistics to describe biological processes accurately. Their parameters are estimated on approximate models, whose regression functions are evaluated by a numerical integration method. Accurate and efficient estimations of these parameters are critical issues. This paper proposes parameter estimation methods involving either a stochastic approximation EM algorithm (SAEM) in the maximum likelihood estimation, or a Gibbs sampler in the Bayesian approach. Both algorithms involve the simulation of non-observed data with conditional distributions using Hastings–Metropolis (H–M) algorithms. A modified H–M algorithm, including an original local linearization scheme to solve the ODEs, is proposed to reduce the computational time significantly. The convergence on the approximate model of all these algorithms is proved. The errors induced by the numerical solving method on the conditional distribution, the likelihood and the posterior distribution are bounded. The Bayesian and maximum likelihood estimation methods are illustrated on a simulated pharmacokinetic nonlinear mixed-effects model defined by an ODE. Simulation results illustrate the ability of these algorithms to provide accurate estimates. [Copyright &y& Elsevier]

Published
2007
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4. Bayesian inference for partially observed multiplicative intensity processes

Author

Judith Rousseau, Sophie Donnet, Mathématiques et Informatique Appliquées (MIA-Paris), AgroParisTech-Institut National de la Recherche Agronomique (INRA), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Institut National de la Recherche Agronomique (INRA)-AgroParisTech, Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), and DONNET, SOPHIE

Subjects
Statistics and Probability, Méthodologie, Inference, Bayesian Analysis, counting process, latent variable, multiplicative intensity process, Bayesian inference, 01 natural sciences, 62M09, law.invention, 010104 statistics & probability, law, 62N01, Econometrics, 0101 mathematics, Mathematics, Branching process, latent variables, Counting process, Computer Science::Information Retrieval, Applied Mathematics, Probabilistic logic, Methodology, Failure rate, Electrical network, 62P30, 62F15, Constant (mathematics), Algorithm, [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract

Poisson processes are used in various application fields applications (public health biology, reliability and so on). In their homogeneous version, the intensity process is a deterministic constant. In their inhomogeneous version, it depends on time. To allow for an endogenous evolution of the intensity process we consider multiplicative intensity processes. Inference methods have been developed when the trajectories are fully observed. We deal with the case of a partially observed process. As a motivating example, consider the analysis of an electrical network through time. This network is composed of cables and accessories (joints). When a cable fails, the cable is replaced by a new cable connected to the network by two new accessories. When an accessory fails, the same kind of reparation is done leading to the addition of only one accessory. The failure rate depends on the stochastically evolving number of accessories. We only observe the times events; the initial number of accessories and the cause of the incident (cable or accessory) are only partially observed. The aim is to estimate the different failure rates or to make predictions. The inference is strongly influenced by the initial number of accessories, which is typically an unknown quantity. We deduce a sensible prior on the initial number of accessories using the probabilistic properties of the process . We illustrate the performances of our methodology on a large simulation study.

Published
2016

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