A hierarchical Bayesian approach for parameter estimation in HIV models

Banks, Harvey Thomas; Grove, Sarah L.; Hu, Shuhua

doi:10.1088/0266-5611/21/6/001

Cited by 17 publications

(16 citation statements)

References 47 publications

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“…The methods developed for ordinary differential equations have been extended to ordinary differential equations with time delays (Horbelt et al, 2002). Deterministic models have also been parameterized in a Bayesian framework using Bayesian hierarchical models (Putter et al, 2002;Banks et al, 2005;Huang et al, 2006). Simulated annealing, which attempts to avoid getting trapped in local minima, is another well known optimization algorithm that has been found successful in various applications (Kirkpatrick et al, 1983;Mendes & Kell, 1998).…”

Section: Introductionmentioning

confidence: 99%

Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Toni

Welch

Strelkowa

et al. 2008

J. R. Soc. Interface.

1,318

1,660

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Approximate Bayesian computation (ABC) methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper, we discuss and apply an ABC method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC provides information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well-known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.

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Section: Introductionmentioning

confidence: 99%

Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Toni

Welch

Strelkowa

et al. 2008

J. R. Soc. Interface.

1,318

1,660

View full text Add to dashboard Cite

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“…We note here that the problem we outlined above is different from those, for example, in pharmacokinetics studies and HIV studies, where one desires to estimate both individualspecific parameters θ (such as clearance rate of the virus and infection rate in HIV studies) and their associated probability distribution function P 0 from blood samples taken serially in time from individuals in the population (e.g., see [11,19]). This is because in this case the data f j is dependent on θ instead of P 0 ; that is, one has individual longitudinal data instead of aggregate longitudinal data (i.e., data collected by sampling from the population at large).…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Properties of Probability Measure Estimators in a Nonparametric Model

Banks¹,

Catenacci²,

Hu³

2015

SIAM/ASA J. Uncertainty Quantification

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We consider probability measure estimation in a nonparametric model using a leastsquares approach under the Prohorov metric framework. We summarize the computational methods and their convergence results that were developed by our group over the past two decades. New results are presented on the bias and the variance due to the approximation and the pointwise asymptotic normality of the approximated probability measure estimator. We propose use of model selection criterion to balance the bias and the variance, and compare the pointwise confidence band constructed using the asymptotic normality results with that obtained by Monte Carlo simulations.

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“…As noted in Wu (2005) in the framework of the HIV dynamics models and more generally in Davidian and Giltinian (1995) and Pinheiro and Bates (2000), a major improvement for the practical identifiability is to take advantage of the whole available information, in particular the between-subject variation: the parameters may vary from one subject to another while being considered as realisations from the same distribution (Putter et al, 2002, Banks et al, 2005Huang and Wu, 2006;Huang et al, 2006;Bortz and Nelson, 2006;Guedj et al, 2007). Such models are in the framework of Non-Linear Mixed Effect models (NLME).…”

Section: Introduction: Generalmentioning

confidence: 99%

Practical Identifiability of HIV Dynamics Models

2007

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We study the practical identifiability of parameters, i.e the accuracy of the estimation that can be hoped, in a model of HIV dynamics based on a system of non-linear Ordinary Differential Equations (ODE). This depends on the available information such as the schedule of the measurements, the observed components, and the measurement precision. The number of patients is another way to increase it by introducing an appropriate statistical "population" framework. The impact of each improvement of the experimental condition is not known in advance but it can be evaluated via the Fisher Information Matrix (FIM). If the non-linearity of the biological model, as well as the complex statistical framework makes computation of the FIM challenging, we show that the particular structure of these models enables to compute it as precisely as wanted. In the HIV model, measuring HIV viral load and total CD4+ count were not enough to achieve identifiability of all the parameters involved. However, we show that an appropriate statistical approach together with the availability of additional markers such as * email: jg1@isped.u-bordeaux2.fr 1The original publication is available at www.springerlink.com HAL author manuscript inserm-00204273, version 1 HAL author manuscript Bulletin of Mathematical Biology 2007;69(8):2493-513 infected cells or activated cells should considerably improve the identifiability and thus the usefulness of dynamical models of HIV.

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A hierarchical Bayesian approach for parameter estimation in HIV models

Cited by 17 publications

References 47 publications

Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Asymptotic Properties of Probability Measure Estimators in a Nonparametric Model

Practical Identifiability of HIV Dynamics Models

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