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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 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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See detailBayesian penalized smoothing approaches in models specified using affine differential equations with unknown error distributions
Jaeger, Jonathan ULg; Lambert, Philippe ULg

E-print/Working paper (2012)

A full Bayesian approach based on ODE-penalized B-splines and penalized Gaussian mixture is proposed to jointly estimate ODE-parameters, state function and error distribution from the observation of some ... [more ▼]

A full Bayesian approach based on ODE-penalized B-splines and penalized Gaussian mixture is proposed to jointly estimate ODE-parameters, state function and error distribution from the observation of some state functions involved in systems of affine differential equations. Simulations inspired by pharmacokinetic studies show that the proposed method provides comparable results to the method based on the standard ODE-penalized B-spline approach (i.e. with the Gaussian error distribution assumption) and outperforms the standard ODE-penalized B-splines when the distribution is not Gaussian. This methodology is illustrated on the Theophylline dataset. [less ▲]

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See detailA Bayesian person fit evaluation for polytomous response data
Béland, Sébastien; Hoijtink, Herbert; Raîche, Gilles et al

Conference (2011, July 19)

Studies about Person-fit are generally produced under a frequentist approach. For example, Meijer & Sijtsma (2001) discussed many parametric and non-parametric indexes in their review on this topic ... [more ▼]

Studies about Person-fit are generally produced under a frequentist approach. For example, Meijer & Sijtsma (2001) discussed many parametric and non-parametric indexes in their review on this topic. However, it exists also few papers about the investigation of person-fit in a Bayesian context (e.g. Glas & Meijer, 2003; Van Der Linden & Guo, 2008). In this talk, we present a new method based on the evaluation of informative hypotheses using the Bayes factor. This approach is non-parametric in nature and can be applied to a large variety of situations and many types of data. Here, we focus on the use of Bayesian person-fit methods that can be used with polytomous response data. This presentation is divided in two sections. First, we present the technical aspects of this approach by discussing some hypotheses of interest, the nature of the prior and the nature of the posterior. Second, we present results from a real data matrix. The first analysis shows that Bayesian person-fit evaluation is efficient and can be easily applied to small data matrices. [less ▲]

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See detailA BAYESIAN PROBABILITY CRITERION TO ASSESS ANALYTICAL RESULTS RELIABILITY
Rozet, Eric ULg; Lebrun, Pierre ULg; Boulanger, B et al

Conference (2013, May 21)

In pharmaceutical and biomedical industries, quantitative analytical methods such as HPLC play a key role. Indeed, the analytical results obtained from them are used to make crucial decisions such as the ... [more ▼]

In pharmaceutical and biomedical industries, quantitative analytical methods such as HPLC play a key role. Indeed, the analytical results obtained from them are used to make crucial decisions such as the release of batches of drugs, the evaluation of safety and efficacy of new drug candidates or the monitoring of patients health. Prior to their routine use, analytical methods are submitted to a stringent validation study [1] where they have to demonstrate that they are fit for their final purpose, i.e. providing accurate results: where is the analytical result, is the theoretical unknown true concentration of analyte in the sample analyzed and a regulatory acceptance limit. Typically this demonstration is made by either providing point estimates of systematic error (bias) and random error (variance) or sometimes by providing interval estimates of these statistical parameters at several well defined concentration levels of the target analyte [2]. They are then compared to maximum acceptable levels. More recently, tolerance intervals approaches have been proposed that are evaluated in a similar way at these key concentration levels [3]. However none of these decision approaches allow knowing the probability to obtain accurate results over the whole concentration range of interest: is a vector of parameters and Pmin is a minimum reliability probability. Frequentist approximations have been proposed to estimate this probability but only at the concentration levels experimentally tested [4,5]. In this work, a linear hierarchical Bayesian approach is proposed. It takes into account the potential random characteristic of the slope and intercept observed from one analytical run to the other, but it also integrates the possible covariance between the parameters. Additionally, heteroscedasticity of the residual variance over the concentration range investigated is taken into account. A situation regularly observed in practice. Finally a reliability profile for the whole concentration range studied is obtained using MCMC sampling. This profile provides the probability (Prel) to obtain accurate results over the full concentration range investigated. This profile is then compared to a minimum reliability probability (Pmin) that will define the valid concentration range of the analytical method. The usefulness of this approach is illustrated through the validation of a bioanalytical method and also compared with one concentration level at a time frequentist approaches [4,5]. [1] International Conference on Harmonization (ICH) of Technical Requirements for registration of Pharmaceuticals for Human Use Topic Q2 (R1): Validation of Analytical Procedures: Text and Methodology, Geneva, 2005. [2] A. Bouabidi and al., J. Chromatogr. A, 1217 (2010) 3180. [3] Ph. Hubert and al., J. Pharm. Biomed. Anal., 36 (2004) 579. [4] W. Dewé and al., Chemometr. Intell. Lab. Syst. 85 (2007) 262. [5] B. Govaerts and al., Qual. Reliab. Engng. Int. 24 (2008) 667. [less ▲]

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See detailBayesian proportional hazards model with time varying regression coefficients: a penalized Poisson regression approach
Lambert, Philippe ULg; Eilers, Paul H.C.

in Statistics in Medicine (2005), 24

One can fruitfully approach survival problems without covariates in an actuarial way. In narrow time bins, the number of people at risk is counted together with the number of events. The relationship ... [more ▼]

One can fruitfully approach survival problems without covariates in an actuarial way. In narrow time bins, the number of people at risk is counted together with the number of events. The relationship between time and probability of an event can then be estimated with a parametric or semi-parametric model. The number of events observed in each bin is described using a Poisson distribution with the log mean speci ed using a exible penalized B-splines model with a large number of equidistant knots. Regression on pertinent covariates can easily be performed using the same log-linear model, leading to the classical proportional hazard model. We propose to extend that model by allowing the regression coe cients to vary in a smooth way with time. Penalized B-splines models will be proposed for each of these coe cients. We show how the regression parameters and the penalty weights can be estimated e ciently using Bayesian inference tools based on the Metropolis-adjusted Langevin algorithm. [less ▲]

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See detailBazooka est-il soluble dans l'art contemporain ?
Dejasse, Erwin ULg

in 9e Art : Les Cahiers du Musée de la Bande Dessinée (2006), 12

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