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See detailBayesian Design Space applied to Pharmaceutical Development
Lebrun, Pierre ULg

Doctoral thesis (2012)

Given the guidelines such as the Q8 document published by the International Conference on Harmonization (ICH), that describe the “Quality by Design” paradigm for the Pharmaceutical Development, the aim of ... [more ▼]

Given the guidelines such as the Q8 document published by the International Conference on Harmonization (ICH), that describe the “Quality by Design” paradigm for the Pharmaceutical Development, the aim of this work is to provide a complete methodology addressing this problematic. As a result, various Design Spaces were obtained for different analytical methods and a manufacturing process. In Q8, Design Space has been defined as the “the multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality” for the analytical outputs or processes involved in Pharmaceutical Development. Q8 is thus clearly devoted to optimization strategies and robustness studies. In the beginning of this work, it was noted that existing statistical methodolo- gies in optimization context were limited as the predictive framework is based on mean response predictions. In such situations, the data and model uncertainties are generally completely ignored. This often leads to increase the risks of taking wrong decision or obtaining unreliable manufactured product. The reasons why it happens are also unidentified. The “assurance of quality” is clearly not addressed in this case. To improve the predictive nature of statistical models, the Bayesian statistical framework was used to facilitate the identification of the predictive distribution of new outputs, using numerical simulations or mathematical derivations when possi- ble. By use of the improved models in a risk-based environment, separation analytical methods such as the high performance liquid chromatography were studied. First, optimal solutions of separation of several compounds in mixtures were identified. Second, the robustness of the methods was simultaneously assessed thanks to the risk-based Design Space identification. The usefulness of the methodology was also demonstrated in the optimization of the separation of subsets of relevant compounds, without additional experiments. The high guarantee of quality of the optimized methods allowed easing their use for their very purpose, i.e., the tracing of compounds and their quantification. Transfer of robust methods to high-end equipments was also simplified. In parallel, one sub-objective was the total automation of analytical method de- velopment and validation. Some data treatments including the Independent Com- ponent Analysis and clustering methodologies were found more than promising to provide accurate automated results. Next, the Design Space methodology was applied to a small-scale spray-dryer manufacturing process. It also allowed the expression of guarantees about the quality of the obtained powder. Finally, other predictive models including mixed-effects models were used for the validation of analytical and bio-analytical quantitative methods. [less ▲]

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See detailA Bayesian Design Space for analytical methods based on multivariate models and predictions
Lebrun, Pierre ULg; Boulanger, Bruno ULg; Debrus, Benjamin ULg et al

in Journal of Biopharmaceutical Statistics (2013), 23

The International Conference for Harmonization (ICH) has released regulatory guidelines for Pharmaceutical Development. In the document ICH Q8, The Design Space of a process is presented as the set of ... [more ▼]

The International Conference for Harmonization (ICH) has released regulatory guidelines for Pharmaceutical Development. In the document ICH Q8, The Design Space of a process is presented as the set of factor settings providing satisfactory results. However, ICH Q8 does not propose any practical methodology to define, derive and compute Design Space. In parallel, in the last decades, it has been observed that the diversity and the quality of analytical methods have evolved exponentially allowing substantial gains in selectivity and sensitivity. However, there is still a lack for a rationale towards the development of robust separation methods in a systematic way. Applying ICH Q8 to analytical methods provides a methodology for predicting a region of the space of factors in which results will be reliable. Combining design of experiments and Bayesian standard multivariate regression, an identified form of the predictive distribution of a new response vector has been identified and used, under non-informative as well as informative prior distributions of the parameters. From the responses and their predictive distribution, various critical quality attributes can be easily derived. This Bayesian framework was then extended to the multi-criteria setting to estimate the predictive probability that several critical quality attributes will be jointly achieved in the future use of an analytical method. An example based on a high-performance liquid chromatography (HPLC) method is given. For this example, a constrained sampling scheme was applied to ensure the modeled responses have desirable properties. [less ▲]

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See detailBayesian estimation of evoked and induced responses
Friston, Kark J.; Henson, Richard; Phillips, Christophe ULg et al

in Human Brain Mapping (2006), 27(9), 722-735

We describe an extension of our empirical Bayes approach to magnetoencephalography/electroencephalography (MEG/EEG) source reconstruction that covers both evoked and induced responses. The estimation ... [more ▼]

We describe an extension of our empirical Bayes approach to magnetoencephalography/electroencephalography (MEG/EEG) source reconstruction that covers both evoked and induced responses. The estimation scheme is based on classical covariance component estimation using restricted maximum likelihood (ReML). We have focused previously on the estimation of spatial covariance components under simple assumptions about the temporal correlations. Here we extend the scheme using temporal basis functions to place constraints on the temporal form of the responses. We show how the same scheme can estimate evoked responses that are phase-locked to the stimulus and induced responses that are not. For a single trial the model is exactly the same, In the context of multiple trials, however, the inherent distinction between evoked and induced responses calls for different treatments of the underlying hierarchical multitrial model. We derive the respective models and show how they can be estimated efficiently using ReML. This enables the Bayesian estimation of evoked and induced changes in power or, more generally, the energy of wavelet coefficients. [less ▲]

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See detailBayesian estimation of the true prevalence, sensitivity and specificity of the Rose Bengal and indirect ELISA tests in the diagnosis of bovine brucellosis.
Sanogo, Moussa; Thys, Eric; Achi, Yaba L. et al

in Veterinary Journal (2013), 195

Serology is the most convenient method for detecting brucellosis but the efficient use of such tests in disease control requires evaluation of diagnostic performance and discriminative ability. The ... [more ▼]

Serology is the most convenient method for detecting brucellosis but the efficient use of such tests in disease control requires evaluation of diagnostic performance and discriminative ability. The objective of this study was to assess the performance of the Rose Bengal test (RBT) and an indirect ELISA (iELISA) in diagnosing brucellosis in 995 serum samples collected from cattle in the Ivory Coast between 2005 and 2009. A Bayesian approach was used to evaluate the two tests by estimating their sensitivities and specificities. The correlation-adjusted sensitivity of the iELISA was estimated to be 96.1% (credibility interval [CrI], 92.7-99.8), whereas that of the RBT was 54.9% (CrI, 23.5-95.1). High correlation-adjusted specificities were found for both tests (95.0%; [CrI, 91.1-99.6] for the iELISA and 97.7%; [CrI, 95.3-99.4] for the RBT, respectively). The true prevalence of brucellosis was estimated from the serum samples to be 4.6% (95%; [CrI, 0.6-9.5]). The level of agreement between the two tests was evaluated using indices of agreement (n=995). Good agreement was found for negative results (96.6%; confidence interval [CI], 95.7-97.4), a finding supported by an estimated significant correlation of 0.37 (95%; CI, 0.01-0.73) within the sera testing negative. Agreement was lower for sera testing positive (52.2% CI: 41.9-62.5). The findings highlight the importance of using these two tests in combination as part of any brucellosis control programme. [less ▲]

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See detailA Bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials
Laurent, Stéphane ULg; Legrand, Catherine

in ESAIM: Probability and Statistics = Probabilité et statistique : P & S (2011)

In many applications, we assume that two random observations x and y are generated according to independent Poisson distributions and we are interested in performing statistical inference on the ratio of ... [more ▼]

In many applications, we assume that two random observations x and y are generated according to independent Poisson distributions and we are interested in performing statistical inference on the ratio of the two incidence rates, called the relative risk in vaccine efficacy trials, in which context x and y are the numbers of cases in the vaccine and the control groups respectively. In this paper we start by defining a natural semi-conjugate family of prior distributions for this model, allowing straightforward computation of the posterior inference. Following theory on reference priors, we define the reference prior for the partial immunity model when the relative risk is the parameter of interest. We also define a family of reference priors with partial information on the incidence rate of the unvaccinated population while remaining uninformative about the relative risk . We notice that these priors belong to the semi-conjugate family. We then demonstrate using numerical examples that Bayesian credible intervals enjoy attractive frequentist properties when using reference priors, a typical property of reference priors. [less ▲]

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See detailBayesian hierarchical linear regression for the validation of analytical methods
Lebrun, Pierre ULg; Boulanger, Bruno ULg; Rozet, Eric ULg et al

Conference (2010, May)

Analytical quantitative methods are widely used to quantify analytes of interest, for instance in pharmaceutical formulations, linking an observed response to the concentration of one compound of the ... [more ▼]

Analytical quantitative methods are widely used to quantify analytes of interest, for instance in pharmaceutical formulations, linking an observed response to the concentration of one compound of the formulation. Current methodologies to validate these analytical methods are based on one-way ANOVA random effect model in order to estimate repeatability and intermediate precision variances. This model is then applied several times at different concentration levels over a range of concentrations where the method is intended to be used, assuming independency between the levels. In this way, the capacity of the method to be able to quantify accurately is assessed at various concentration levels, and the method is said to be fitted for purpose (or valid) at the concentration level(s) where it shows trueness and precision that are fully acceptable, i.e. within predefined acceptance limits. Problem of such approach is the amount of data required and the time needed to collect them, while small sample sizes (small number of series and of replicates per series) are often preferred and practiced by laboratories. A better use of the data could then be envisaged. In this presentation, we take into account the response-concentration relationship that exists by the use of a hierarchical linear regression model. Instead of fitting a model at each concentration level that is assessed, only one model is studied. We show how the Bayesian framework is well adapted to this task. Also, as a predictive tool, we naturally derive beta-expectation and beta-gamma content tolerance intervals by means of MCMC simulations. The Bayesian modeling can also include informative prior information whenever justified, leading to reliable decisions given the domain knowledge. [less ▲]

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See detailBayesian inference for transportation origin–destination matrices: the Poisson–inverse Gaussian and other Poisson mixtures
Perrakis, Konstantinos; Karlis, Dimitris; Cools, Mario ULg et al

in Journal of the Royal Statistical Society. Series A Statistics in Society (in press)

Transportation origin–destination analysis is investigated through the use of Poisson mixtures by introducing covariate-based models which incorporate different transport modelling phases and also allow ... [more ▼]

Transportation origin–destination analysis is investigated through the use of Poisson mixtures by introducing covariate-based models which incorporate different transport modelling phases and also allow for direct probabilistic inference on link traffic based on Bayesian predictions. Emphasis is placed on the Poisson–inverse Gaussian model as an alternative to the commonly used Poisson–gamma and Poisson–log-normal models. We present a first full Bayesian formulation and demonstrate that the Poisson–inverse Gaussian model is particularly suited for origin–destination analysis because of its desirable marginal and hierarchical properties. In addition, the integrated nested Laplace approximation is considered as an alternative to Markov chain Monte Carlo sampling and the two methodologies are compared under specific modelling assumptions. The case-study is based on 2001 Belgian census data and focuses on a large, sparsely distributed origin–destination matrix containing trip information for 308 Flemish municipalities. [less ▲]

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See detailBayesian inference of a dynamic vegetation model for grassland
Minet, Julien ULg; Laloy, Eric; Tychon, Bernard ULg et al

Conference (2014, April 02)

As a part of the MACSUR task L2.4, we probabilistically calibrated the CARAIB dynamic vegetation model by Markov chain Monte Carlo (MCMC) simulation with the DREAMZS sampler.. CARAIB is a mechanistic ... [more ▼]

As a part of the MACSUR task L2.4, we probabilistically calibrated the CARAIB dynamic vegetation model by Markov chain Monte Carlo (MCMC) simulation with the DREAMZS sampler.. CARAIB is a mechanistic model that calculates the carbon assimilation of the vegetation as a function of the soil and climatic conditions, and can thus be used for simulating grassland production under cutting or grazing management. Bayesian model inversion was performed at 4 grassland sites across Europe: Oensingen, CH; Grillenburg, DE; Laqueuille, FR and Monte-Bodone, IT. Four daily measured variables from these sites: the Gross Primary Productivity (GPP), Net Ecosystem Exchange (NEE), Evapotranspiration (ET) and Soil Water Content (SWC) were used to sample 10 parameters related to rooting depth, stomatal conductance, specific leaf area, carbon-nitrogen ratio and water stresses. The maximized likelihood function therefore involved four objectives, whereas the applied Bayesian framework allowed for assessing the so called parameter posterior probability density function (pdf), which quantifies model parameter uncertainty caused by measurement and model errors. Sampling trials were performed using merged data from all sites (all-sites-sampling) and for each site (site-specific sampling) separately. The derived posterior parameter pdfs from the all-sites sampling and site-specific sampling runs showed differences in relation with the specificities of each site. Analysis of these distributions also revealed model sensitivity to parameters conditioned on the measured data, as well as parameter correlations. [less ▲]

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See detailBayesian integration of external information into the single step approach for genomically enhanced prediction of breeding values
Vandenplas, Jérémie ULg; Misztal, Ignacy; Faux, Pierre ULg et al

Conference (2012, July 17)

An assumption to compute unbiased estimated breeding values (EBV) is that all information, i.e. genomic, pedigree and phenotypic information, has to be considered simultaneously. However, current ... [more ▼]

An assumption to compute unbiased estimated breeding values (EBV) is that all information, i.e. genomic, pedigree and phenotypic information, has to be considered simultaneously. However, current developments of genomic selection will bias evaluations because only records related to selected animals will be available. The single step genomic evaluation (ssGBLUP) could reduce pre-selection bias by the combination of genomic, pedigree and phenotypic information which are internal for the ssGBLUP. But, in opposition to multi-step methods, external information, i.e. information from outside ssGBLUP, like EBV and associated reliabilities from Multiple Across Country Evaluation which represent a priori known phenotypic information, are not yet integrated into the ssGBLUP. To avoid multi-step methods, the aim of the study was to assess the potential of a Bayesian procedure to integrate a priori known external information into a ssGBLUP by considering simplifications of computational burden, a correct propagation of external information and no multiple considerations of contributions due to relationships. To test the procedure, 2 dairy cattle populations (referenced by “internal” and “external”) were simulated as well as milk production for the first lactation of each female in both populations. Internal females were randomly mated with internal and 50 external males. Genotypes of 3000 single-nucleotide polymorphisms for the 50 males were simulated. A ssGBLUP was applied as the internal evaluation. The external evaluation was based on phenotypic and pedigree external information. External information integrated into the ssGBLUP consisted to external EBV and associated reliabilities of the 50 males. Results showed that rank correlations among Bayesian EBV and EBV based on the joint use of external and internal data and genomic information were higher than 0.99 for the 50 males and internal animals. The respective correlations for the internal evaluation were equal to 0.50 and 0.90. Thereby, the Bayesian procedure can integrate external information into ssGBLUP. [less ▲]

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See detailBayesian integration of external information into the single step approach for genomically enhanced prediction of breeding values
Vandenplas, Jérémie ULg; Misztal, Ignacy; Faux, Pierre ULg et al

in Journal of Dairy Science (2012), 95(Supplement 2),

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See detailBayesian inversion for induced responses
Mattout, Jérémie; Phillips, Christophe ULg; Daunizeau, Jean et al

in Friston, Karl; Ashburner, John; Kiebel, Stefan (Eds.) et al Statistical Parametric Mapping: the analysis of functional brain images (2007)

The book Statistical Parametric Mapping: The Analysis of Functional Brain Images (2007) provides the background and methodology for the analysis of all types of brain imaging data, from functional ... [more ▼]

The book Statistical Parametric Mapping: The Analysis of Functional Brain Images (2007) provides the background and methodology for the analysis of all types of brain imaging data, from functional magnetic resonance imaging to magnetoencephalography. Critically, "Statistical Parametric Mapping" provides a widely accepted conceptual framework which allows treatment of all these different modalities. The book takes the reader from the basic concepts underlying the analysis of neuroimaging data to cutting edge approaches that would be difficult to find in any other source. The material is presented in an incremental way so that the reader can understand the precedents for each new development. This book will be particularly useful to neuroscientists engaged in any form of brain mapping; who have to contend with the real-world problems of data analysis and understanding the techniques they are using. It is primarily a scientific treatment and a didactic introduction to the analysis of brain imaging data. It can be used as both a textbook for students and scientists starting to use the techniques, as well as a reference for practicing neuroscientists. [less ▲]

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See detailBayesian inversion of EEG models
Mattout, Jérémie; Phillips, Christophe ULg; Daunizeau, Jean et al

in Friston, Karl; Ashburner, John; Kiebel, Stefan (Eds.) et al Statistical Parametric Mapping: the analysis of functional brain images (2007)

The book Statistical Parametric Mapping: The Analysis of Functional Brain Images (2007) provides the background and methodology for the analysis of all types of brain imaging data, from functional ... [more ▼]

The book Statistical Parametric Mapping: The Analysis of Functional Brain Images (2007) provides the background and methodology for the analysis of all types of brain imaging data, from functional magnetic resonance imaging to magnetoencephalography. Critically, "Statistical Parametric Mapping" provides a widely accepted conceptual framework which allows treatment of all these different modalities. The book takes the reader from the basic concepts underlying the analysis of neuroimaging data to cutting edge approaches that would be difficult to find in any other source. The material is presented in an incremental way so that the reader can understand the precedents for each new development. This book will be particularly useful to neuroscientists engaged in any form of brain mapping; who have to contend with the real-world problems of data analysis and understanding the techniques they are using. It is primarily a scientific treatment and a didactic introduction to the analysis of brain imaging data. It can be used as both a textbook for students and scientists starting to use the techniques, as well as a reference for practicing neuroscientists. [less ▲]

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See detailBayesian methods for predicting and modelling winter wheat biomass
Mansouri, Majdi ULg; Dumont, Benjamin ULg; Destain, Marie-France ULg

Poster (2014, February)

The objectives of this paper are threefold. The first objective is to propose to use an Improved Particle Filtering (IPF) based on minimizing Kullback-Leibler divergence for crop models' predictions. The ... [more ▼]

The objectives of this paper are threefold. The first objective is to propose to use an Improved Particle Filtering (IPF) based on minimizing Kullback-Leibler divergence for crop models' predictions. The performances of the proposed technique are compared with those of the conventional Particle Filtering (PF) for improving nonlinear crop model predictions. The main novelty of this task is to develop a Bayesian algorithm for nonlinear and non-Gaussian state and parameter estimation with better proposal distribution. The second objective is to investigate the effects of practical challenges on the performances of state estimation algorithms PF and IPF. Such practical challenges include (i) the effect of measurement noise on the estimation performances and (ii) the number of states and parameters to be estimated. The third objective is to use the state estimation techniques PF and IPF for updating prediction of nonlinear crop model in order to predict winter wheat biomass. PF and IPF are applied at a dynamic crop model with the aim to predict a state variable, namely the winter wheat biomass, and to estimate several model parameters. Furthermore, the effect of measurement noise (e.g., different signal-to-noise ratios) on the performances of PF and IPF is investigated. The results of the comparative studies show that the IPF provides a significant improvement over the PF because, unlike the PF which depends on the choice of sampling distribution used to estimate the posterior distribution, the IPF yields an optimum choice of the sampling distribution, which also accounts for the observed data. [less ▲]

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See detailBayesian methods for predicting LAI and soil moisture
Mansouri, Majdi ULg; Dumont, Benjamin ULg; Destain, Marie-France ULg

in Proceedings of the 11th International Conference on Precision Agriculture (2012)

The prediction errors of crop models are often important due to uncertainties in the estimates of initial values of the states, in parameters, and in equations. The measurements needed to run the model ... [more ▼]

The prediction errors of crop models are often important due to uncertainties in the estimates of initial values of the states, in parameters, and in equations. The measurements needed to run the model are sometimes not numerous or known with some uncertainty. In this paper, two Bayesian filtering methods were used to update the state variable values predicted by MiniSTICS model. The chosen state variates were the LAI (Leaf Area Index) of a wheat crop (Triticum aestivum L.) and the corresponding moisture content of two soil layers (0-20 cm and 30-50 cm). These state variates were estimated simultaneously with several parameters. The assessed filtering methods were the centralized Particle Filtering (PF) and the Variational Bayesian Filtering (VF). The former is known to be sensitive to the number of particles while the latter yields an optimal choice of the sampling distribution over the state variable by minimizing the Kullback-Leibler divergence. In fact, variational calculus leads to a simple Gaussian sampling distribution whose parameters (estimated iteratively) depends on the observed data. On basis of a case study, the VF method was found more efficient than the PF method. Indeed, with the VF, the Root Mean Square Error (RMSE) of the three estimated states was smaller and the convergence of the all parameters was ensured. [less ▲]

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See detailBayesian methods for predicting LAI and soil water content
Mansouri, Majdi ULg; Dumont, Benjamin ULg; Leemans, Vincent ULg et al

in Precision Agriculture (2014), 15(2), 184-201

LAI of winter wheat (Triticum aestivum L.) and soil water content of the topsoil (200 mm) and of the subsoil (500 mm) were considered as state variables of a dynamic soil-crop system. This system was ... [more ▼]

LAI of winter wheat (Triticum aestivum L.) and soil water content of the topsoil (200 mm) and of the subsoil (500 mm) were considered as state variables of a dynamic soil-crop system. This system was assumed to progress according to a Bayesian probabilistic state space model, in which real values of LAI and soil water content were daily introduced in order to correct the model trajectory and reach better future evolution. The chosen crop model was mini STICS which can reduce the computing and execution times while ensuring the robustness of data processing and estimation. To predict simultaneously state variables and model parameters in this non-linear environment, three techniques were used: Extended Kalman Filtering (EKF), Particle Filtering (PF), and Variational Filtering (VF). The significantly improved performance of the VF method when compared to EKF and PF is demonstrated. The variational filter has a low computational complexity and the convergence speed of states and parameters estimation can be adjusted independently. Detailed case studies demonstrated that the root mean square error (RMSE) of the three estimated states (LAI and soil water content of two soil layers) was smaller and that the convergence of all considered parameters was ensured when using VF. Assimilating measurements in a crop model allows accurate prediction of LAI and soil water content at a local scale. As these biophysical properties are key parameters in the crop-plant system characterization, the system has the potential to be used in precision farming to aid farmers and decision makers in developing strategies for site-specific management of inputs, such as fertilizers and water irrigation. [less ▲]

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See detailBayesian model screening for the identification of nonlinear mechanical structures
Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg; Hemez, F. M.

in Journal of Vibration and Acoustics-Transactions of the Asme (2003), 125(3), 389-397

The development of techniques for identification and updating of nonlinear mechanical structures has received increasing attention in recent years. In practical situations, there is not necessarily a ... [more ▼]

The development of techniques for identification and updating of nonlinear mechanical structures has received increasing attention in recent years. In practical situations, there is not necessarily a priori knowledge about the nonlinearity. This suggests the need for strategies that allow inference of useful information from the data. The present study proposes an algorithm based on a Bayesian inference approach for giving insight into the form of the nonlinearity. A family of parametric models is defined to represent the nonlinear response of a system and the selection algorithm estimates the likelihood that each member of the family is appropriate. The (unknown) probability density function of the family of models is explored using a simple variant of the Markov Chain Monte Carlo sampling technique. This technique offers the advantage that the nature of the underlying statistical distribution need not be assumed a priori. Enough samples are drawn to guarantee that the empirical distribution approximates the true but unknown distribution to the desired level of accuracy. It provides an indication of which models are the most appropriate to represent the nonlinearity and their respective goodness-of-fit to the data. The methodology is illustrated using two examples, one of which comes from experimental data. [less ▲]

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See detailBayesian ODE-penalized B-spline model with Gaussian mixture as error distribution
Jaeger, Jonathan ULg; Lambert, Philippe ULg

Scientific conference (2012, July 18)

In the standard Bayesian ODE-penalized B-spline approach, it is assumed that the error distribution is homogeneous Gaussian. But, in many applications, the normal assumption for the error distribution is ... [more ▼]

In the standard Bayesian ODE-penalized B-spline approach, it is assumed that the error distribution is homogeneous Gaussian. But, in many applications, the normal assumption for the error distribution is not a realistic choice. The goal of this paper is to extend the standard Bayesian ODE-penalized B-spline approach to settings where the error term distribution can be described using a mixture of normals. [less ▲]

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See detailBayesian P-spline estimation in hierarchical models specified by systems of affine differential equations
Jaeger, Jonathan ULg; Lambert, Philippe ULg

in Statistical Modelling : An International Journal (2013), 13

Ordinary differential equations (ODEs) are widely used to model physical, chemical and biological processes. Current methods for parameter estimation can be computationally intensive and/or not suitable ... [more ▼]

Ordinary differential equations (ODEs) are widely used to model physical, chemical and biological processes. Current methods for parameter estimation can be computationally intensive and/or not suitable for inference and prediction. Frequentist approaches based on ODE-penalized smoothing techniques have recently solved part of these drawbacks. A full Bayesian approach based on ODE-penalized B-splines is proposed to jointly estimate ODE parameters and state functions from affine systems of differential equations. Simulations inspired by pharmacokinetic studies show that the proposed method provides comparable results to methods based on explicit solution of the ODEs and outperforms the frequentist ODE-penalized smoothing approach. The basic model is extended to a hierarchical one in order to study cases where several subjects are involved. This Bayesian hierarchical approach is illustrated on real data for the study of perfusion ratio after a femoral artery occlusion. Model selection is feasible through the analysis of the posterior distributions of the ODE adhesion parameters and is illustrated on a real pharmacokinetic dataset. [less ▲]

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