Fast Gibbs sampling for high-dimensional Bayesian inversion

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to explore and quantify its uncertainties. In applications where the inverse solution is subject to further analysis procedures, this can be a significant advantage. Alongside theoretical progress, various new computational techniques allow to sample very high dimensional posterior distributions: In [Lucka2012], a Markov chain Monte Carlo (MCMC) posterior sampler was developed for linear inverse problems with $\ell_1$-type priors. In this article, we extend this single component Gibbs-type sampler to a wide range of priors used in Bayesian inversion, such as general $\ell_p^q$ priors with additional hard constraints. Besides a fast computation of the conditional, single component densities in an explicit, parameterized form, a fast, robust and exact sampling from these one-dimensional densities is key to obtain an efficient algorithm. We demonstrate that a generalization of slice sampling can utilize their specific structure for this task and illustrate the performance of the resulting slice-within-Gibbs samplers by different computed examples. These new samplers allow us to perform sample-based Bayesian inference in high-dimensional scenarios with certain priors for the first time, including the inversion of computed tomography (CT) data with the popular isotropic total variation (TV) prior.Comment: submitted to "Inverse Problems

Dietary patterns and longitudinal change in body mass in European children: a follow-up study on the IDEFICS multicenter cohort

n/

Percentile reference values for anthropometric body composition indices in European children from the IDEFICS study

INTRODUCTION: To characterise the nutritional status in children with obesity or wasting conditions, European anthropometric reference values for body composition measures beyond the body mass index (BMI) are needed. Differentiated assessment of body composition in children has long been hampered by the lack of appropriate references. OBJECTIVES: The aim of our study is to provide percentiles for body composition indices in normal weight European children, based on the IDEFICS cohort (Identification and prevention of Dietary-and lifestyle-induced health Effects in Children and infantS). METHODS: Overall 18 745 2.0-10.9-year-old children from eight countries participated in the study. Children classified as overweight/obese or underweight according to IOTF (N = 5915) were excluded from the analysis. Anthropometric measurements (BMI (N = 12 830); triceps, subscapular, fat mass and fat mass index (N = 11 845-11 901); biceps, suprailiac skinfolds, sum of skinfolds calculated from skinfold thicknesses (N = 8129-8205), neck circumference (N = 12 241); waist circumference and waist-to-height ratio (N = 12 381)) were analysed stratified by sex and smoothed 1st, 3rd, 10th, 25th, 50th, 75th, 90th, 97th and 99th percentile curves were calculated using GAMLSS. RESULTS: Percentile values of the most important anthropometric measures related to the degree of adiposity are depicted for European girls and boys. Age-and sex-specific differences were investigated for all measures. As an example, the 50th and 99th percentile values of waist circumference ranged from 50.7-59.2 cm and from 51.3-58.7 cm in 4.5-to < 5.0-year-old girls and boys, respectively, to 60.6-74.5 cm in girls and to 59.9-76.7 cm in boys at the age of 10.5-10.9 years. CONCLUSION: The presented percentile curves may aid a differentiated assessment of total and abdominal adiposity in European children

Prevalence of overweight and obesity in European children below the age of 10

BACKGROUND: There is a lack of common surveillance systems providing comparable figures and temporal trends of the prevalence of overweight (OW), obesity and related risk factors among European preschool and school children. Comparability of available data is limited in terms of sampling design, methodological approaches and quality assurance. The IDEFICS (Identification and prevention of Dietary-and lifestyle-induced health Effects in Children and infantS) study provides one of the largest European data sets of young children based on state-of-the-art methodology. OBJECTIVE: To assess the European distribution of weight status according to different classification systems based on body mass index (BMI) in children (2.0-9.9 years). To describe the prevalence of weight categories by region, sex, age and socioeconomic position. DESIGN: Between 2007 and 2010, 18 745 children from eight European countries participated in an extensive, highly standardised protocol including, among other measures, anthropometric examinations and parental reports on socio-demographic characteristics. RESULTS: The combined prevalence of OW/obesity ranges from more than 40% in southern Europe to less than 10% in northern Europe. Overall, the prevalence of OW was higher in girls (21.1%) as compared with boys (18.6%). The prevalence of OW shows a negative gradient with social position, with some variation of the strength and consistency of this association across Europe. Overall, population groups with low income and/or lower education levels show the highest prevalence of obesity. The use of different reference systems to classify OW results in substantial differences in prevalence estimates and can even reverse the reported difference between boys and girls. CONCLUSIONS: There is a higher prevalence of obesity in populations from southern Europe and in population groups with lower education and income levels. Our data confirm the need to develop and reinforce European public health policies to prevent early obesity and to reduce these health inequalities and regional disparities