We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Statistics for Spatial Data.

Social Network Analysis

2019 ACC/AHA Guideline on the Primary Prevention of Cardiovascular Disease: Executive Summary: A Report of the American College of Cardiology/American Heart Association Task Force on Clinical Practice Guidelines

Solar Engineering Of Thermal Processes

http://journal-sfds.fr/article/download/57/48

Modèles réduits à partir d’expériences numériques

The maternal protein diet during the perinatal period can program the health of adult offspring. This study in rats evaluated the effects of protein quantity and quality in the maternal diet during gestation and lactation on weight and adiposity in female offspring. Six groups of dams were fed a high-protein (HP; 47% protein) or normal-protein (NP; 19% protein) isocaloric diet during gestation (G) using either cow's milk (M), pea (P) or turkey (T) proteins. During lactation, all dams received the NP diet (protein source unchanged). From postnatal day (PND) 28 until PND70, female pups (n=8) from the dam milk groups were exposed to either an NP milk diet (NPMW) or to dietary self-selection (DSS). All other pups were only exposed to DSS. The DSS design was a choice between five food cups containing HPM, HPP, HPT, carbohydrates or lipids. The weights and food intakes of the animals were recorded throughout the study, and samples from offspring were collected on PND70. During the lactation and postweaning periods, body weight was lower in the pea and turkey groups (NPG and HPG) versus the milk group (P<.0001). DSS groups increased their total energy and fat intakes compared to the NPMW group (P<.0001). In all HPG groups, total adipose tissue was increased (P=.03) associated with higher fasting plasma leptin (P<.05). These results suggest that the maternal protein source impacted offspring body weight and that protein excess during gestation, irrespective of its source, increased the risk of adiposity development in female adult offspring.

/pdf/perinatal-exposure-of-rats-to-a-maternal-diet-with-varying-474h8dxths.pdf

Perinatal exposure of rats to a maternal diet with varying protein quantity and quality affects the risk of overweight in female adult offspring

/pdf/bayesian-calibration-of-a-numerical-code-for-prediction-28mgc94w31.pdf

Bayesian calibration of a numerical code for prediction

Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The standard statistical approach is mixed-effects model, with regression functions that are now highly-developed to describe precisely the biological processes (solutions of multi-dimensional ordinary differential equations or of partial differential equation). When there is no analytical solution, a classical estimation approach relies on the coupling of a stochastic version of the EM algorithm (SAEM) with a MCMC algorithm. This procedure needs many evaluations of the regression function which is clearly prohibitive when a time-consuming solver is used for computing it. In this work a meta-model relying on a Gaussian process emulator is proposed to replace this regression function. The new source of uncertainty due to this approximation can be incorporated in the model which leads to what is called a mixed meta-model. A control on the distance between the maximum likelihood estimates in this mixed meta-model and the maximum likelihood estimates obtained with the exact mixed model is guaranteed. Eventually, numerical simulations are performed to illustrate the efficiency of this approach.

Parametric estimation of complex mixed models based on meta-model approach

When computer codes are used for modeling complex physical systems, their unknown parameters are tuned by calibration techniques. A discrepancy function may be added to the computer code in order to capture its discrepancy with the real physical process. By considering the validation question of a computer code as a Bayesian selection model problem, Damblin et al. (2016) have highlighted a possible confounding effect in certain configurations between the code discrepancy and a linear computer code by using a Bayesian testing procedure based on the intrinsic Bayes factor. In this paper, we investigate the issue of code error identifiability by applying another Bayesian model selection technique which has been recently developed by Kamary et al. (2014). By embedding the competing models within an encompassing mixture model, Kamary et al. (2014)'s method allows each observation to belong to a different mixing component, providing a more flexible inference, while remaining competitive in terms of computational cost with the intrinsic Bayesian approach. By using the technique of sharing parameters mentioned in Kamary et al. (2014), an improper non-informative prior can be used for some computer code parameters and we demonstrate that the resulting posterior distribution is proper. We then check the sensitivity of our posterior estimates to the choice of the parameter prior distributions. We illustrate that the value of the correlation length of the discrepancy Gaussian process prior impacts the Bayesian inference of the mixture model parameters and that the model discrepancy can be identified by applying the Kamary et al. (2014) method when the correlation length is not too small. Eventually, the proposed method is applied on a hydraulic code in an industrial context.

Pierre Barbillon

Papers

Modèles réduits à partir d’expériences numériques

Perinatal exposure of rats to a maternal diet with varying protein quantity and quality affects the risk of overweight in female adult offspring

Bayesian calibration of a numerical code for prediction

Parametric estimation of complex mixed models based on meta-model approach

Computer code validation via mixture model estimation