Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop \emph{Optimal Concentration Inequalities} (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that uncertainties in input parameters, which propagate to output uncertainties in the classical sensitivity analysis paradigm, may fail to do so if the transfer functions (or probability distributions) are imperfectly known. We show how, for hierarchical structures, this phenomenon may lead to the non-propagation of uncertainties or information across scales. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact and on the seismic safety assessment of truss structures, suggesting the feasibility of the framework for important complex systems. The introduction of this paper provides both an overview of the paper and a self-contained mini-tutorial about basic concepts and issues of UQ.Comment: 90 pages. Accepted for publication in SIAM Review (Expository Research Papers). See SIAM Review for higher quality figure

Conversion of Vertical Banded Gastroplasty to Roux-en-Y Gastric Bypass Results in Restoration of the Positive Effect on Weight Loss and Co-morbidities: Evaluation of 101 Patients

BACKGROUND: Vertical banded gastroplasty (VBG) is a widely used restrictive procedure in bariatric surgery. However, the re-operation rate after this operation is high. In the case of VBG failure, a conversion to Roux-en-Y gastric bypass (RYGBP) is an option. A study was undertaken to evaluate the results of the conversion from VBG to RYGBP. METHODS: 101 patients had conversion from VBG to RYGBP. Patients were separated into 3 groups, based on the indication for conversion: weight regain (group 1), excessive weight loss (group 2) and severe eating difficulties (group 3). Data for the study were collected by retrospective analysis of prospectively recorded data. RESULTS: Weight regain (group 1) was the reason for conversion in 73.3% of patients. Staple-line disruption was the most important cause for the weight regain (74.3%). Excessive weight loss (group 2) affected 14% of patients and was caused by outlet stenosis in 78.6% of patients. The remaining 13% had severe eating difficulties as a result of outlet stenosis (46.1%), pouch dilatation (30.8%) and pouch diverticula (23.1%). Mean BMI before conversion to RYGBP was 40.5, 22.3 and 29.8 kg/m2 in group 1, 2 and 3, respectively. Minor or major direct postoperative complications were observed in 2.0% to 7.0%. Long-term complications were more frequent, and consisted mainly of anastomotic stenosis (22.7%) and incisional hernia (16.8%). Follow-up after conversion was achieved in all patients (100%), with a mean period of 38 +/- 29 months. BMI decreased from 40.5 to 30.1 kg/m2, increased from 22.3 to 25.3 kg/m2. and decreased slightly from 29.8 to 29.0 kg/m2 in group 1, 2 and 3, respectively. All patients in group 3 noticed an improvement in eating difficulties. CONCLUSION: Complications after conversion from failed VBG to RYGBP are substantial and need to be considered. However, the conversion itself is a successful operation in terms of effect on body weight and treating eating difficulties after VBG