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

Critical seismic load inputs for simple inelastic structures

The modelling of earthquake loads as design inputs for inelastic single-degree-of-freedom structures is considered. The earthquake load is modelled as a deterministic time history which is expressed in terms of a Fourier series that is modulated by an enveloping function. Subsequently, the coefficients of the series representation, and, the parameters of the envelope function are determined such that the structure inelastic deformation is maximized subject to a set of predefined constraints. These constraints include bounds on the total energy of the earthquake signal, peak values on ground acceleration, velocity and displacement and upper and lower bounds on the Fourier spectra of the ground acceleration. Additional mathematical limits on the envelope parameters are also considered. The quantification of these constraints is obtained based on numerical analysis of a set of past recorded ground motions at the site under consideration or other sites with similar soil conditions. The structure force?displacement relation is taken to possess an elastic?plastic behavior. The resulting nonlinear optimization problem is tackled by using the sequential quadratic optimization method. The study, also, examines influences of the structure yield strength and damping ratio on the derived earthquake load and the associated structure response. Issues related to the time-variation of various energy forms dissipated by the inelastic system are also explored. The proposed formulation is demonstrated with reference to the inelastic response analysis of a frame structure driven by a single component of earthquake load

Discussion of ‘A new approach of selecting real input ground motions for seismic design: The most unfavourable real seismic design ground motions’ by C-H Zhai and L-L Xie

This discussion consists of two parts. The first part raises a few comments and questions on the method presented in the above paper. The second part proposes a measure for identifying resonant accelerograms in a set of earthquake records without the need for pre-processing of the records or inclusion of the structure dynamic analysis

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

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

Parenteral Nutrition‐Associated Liver Complications in Children

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90071/1/phco.22.3.188.33553.pd