Tony O'Hagan (University of Sheffield) will give a SAMSI colloquium this Thursday afternoon. Tony is a renowned expert on Uncertainty Quantification. His talk will be aimed specifically at young researchers and postdocs. Everybody is welcome.
Tea and goodies will be served after the seminar concludes.
Maarten Arnst, (University of Southern California), will speak Thursday, September 29, 3:00-4:00, followed by tea.
Abstract
The modeling and simulation of complex coupled systems governed by multiple physical processes that may exist simultaneously across multiple scales and domains represent critical tools for addressing numerous science and engineering challenges. Models, by definition, are approximations of their target physical scenarios, and thus are prone to modeling errors; also, parametric uncertainties exist as a reflection of various limitations in experimental methods. The quantification of uncertainties thus constitutes a crucial requirement for predictive simulations of coupled systems to find useful applications in supporting scientific discovery and engineering.
We investigate in this work a computational framework for the efficient propagation of uncertainties through coupled models based on a general stochastic expansion methodology. We address the following two challenges that arise in extending stochastic expansion methods to coupled problems. The first challenge relates to the communication of information across physics, scale or domain interfaces. The process of condensing model predictions into physical parameters, solution patches, or other quantities to be communicated across interfaces often involves a compression of information, thus calling for probabilistic representations of exchanged information of reduced stochastic dimension. The second challenge is in the curse of dimensionality, in that the computational cost of expansion methods grows quickly with the stochastic dimension of the system, which can rapidly become large when uncertainties affect multiple model components.
We propose to systematically represent information by an adaptation of the Karhunen-Loeve decomposition as it is communicated across interfaces. Our adaptation permits the persistent segregation of uncertainty between components of the system, thus allowing for an efficient albeit accurate solution in a reduced dimensional space. We propose to take advantage of this dimension reduction by carrying out algorithmic operations (including the construction of orthogonal polynomials and cubature rules) in terms of the reduced stochastic degrees of freedom defined at the interfaces, thus mitigating the growth in stochastic dimension as uncertainties are exchanged.
The presentation will demonstrate the effectiveness of these techniques on a multiphysics prob- lem relevant to nuclear reactors. This problem consists of a coupled system of two second-order elliptic equations, which describes the stationary transport of neutrons in a reactor with a temperature feedback. We accommodate uncertainties in both the neutron-transport and heat-transfer equations, and solve for the solution of the fully coupled problem by an iteration procedure that only involves the successive solution of the model components in their reduced stochastic dimension.
Ruchi Choudhary ( University of Cambridge) will speak. The talk will be followed by tea and cookies.
Abstract: We quantify uncertainties in energy consumption of the built environment using Bayesian approaches and demonstrate examples of recent applications on individual buildings and for an entire population of buildings. We use the Kennedy O’ Hagan framework to calibrate energy models of representative buildings in a city, and argue that this approach is better suited than other existing protocols for evaluating retrofits of existing buildings. We consider alternative techniques, namely, Bayesian regression analysis and inverse methods to evaluate an entire set of buildings in a city. This work is driven by the need to quantify future energy demand of buildings in their urban context as a function of projected growth of buildings and populations, refurbishments, policies incentivizing energy efficiency measures, and changes in building operation.
Further extensions are proposed in three areas: (a) Using polynomial chaos for quantifying uncertainties in the case of PDE models of non-standard buildings or its components; (b) Weighted space filling design approaches to extend uncertainty quantification of particular buildings to whole populations of buildings in a district; and (c) Incorporating spatial parameters such as urban heat islands, noise pollution, and socio-economic conditions as covariates in urban scale energy analysis.
Susie Bayarri (University of Valencia) is our speaker. Tea and cookies will be served after the talk.
Abstract
Risk assessment of rare natural hazards is addressed. Assessment is approached through a combination of math/physics modeling, statistical modeling, and extreme-event probability computation. A computer model of the natural hazard is utilized to provide the needed extrapolation to unseen parts of the hazard space. Statistical modeling of the available data is needed to determine the initializing distribution for exercise of the computer model. In dealing with rare events, direct simulations involving the computer model are prohibitively expensive. Solution instead requires a combination of adaptive design of computer model approximations (emulators) and computation of the probability of rare events. The techniques are illustrated on a test-bed example involving volcanic pyroclastic flows.
Today's speaker is Devon Lin (Queen's University).
Abstract:
Pooling data from multiple sources is a growing trend in diverse fields. While meta-analysis of data from more than one source has attracted significant attention in statistics, little has been done so far on efficient data collection for multiple sources. To fill this gap, we propose an experimental design framework for multiple sources. In practice, multiple data sources are often analyzed by either modeling data from each source independently, referred to as the individual analysis, or integrating data from all the sources together, referred to as the integrated analysis. In this framework, we propose several approaches to constructing a new type of design, called a sliced orthogonal Latin hypercube design, suitable for these two types of analyses simultaneously. Simulations are provided to show the effectiveness of the constructed designs. This is joint work with Peter Qian, Jianfeng Yang and Dennis Lin.
Tea and cookies will be served after the talk.
Abstract: Estimation theory techniques applied to problems of meteorology and oceanography are more commonly known in these circles as data assimilation. As in estimation theory, data assimilation techniques aim at combining model predictions and observations to determine the state of the atmosphere (or the ocean, or both) better than the estimate one would get from using either the model predictions or the observations alone. Data assimilation techniques are intrinsically statistical, and as such require representation of the model and observation error statistics. In practical applications, such as in weather prediction, these errors are only roughly known, and are commonly parametrized.
This presentation gives a brief overview of one classical technique used to parametrized prediction and observation errors; which follows directly from sequential estimation theory. Using similar ideas the presentation introduces a technique bases on the sequential fixed-lag smoother observation to estimate system (model) errors. The proposed procedure is recast into the language of variational assimilation, more suitable to practical weather prediction methodologies. The performance of the proposed estimation procedure is illustrated for simple dynamics. And finally, preliminary results from a complex, operational, data assimilation scheme are also presented.
Join us for tea and cookies after the talk.
Abstract: Monte Carlo estimation of small probabilities and expected values that are determined by rare events is difficult. The two most commonly applied methods are those based on change-of-measure arguments and known as importance sampling, and those which use branching processes and sometimes referred to as multi-level splitting. There are a number of heuristic guides to the design of schemes, and certainly successful applications have been reported. However, it is also known that these guides can suggest schemes that perform badly.
In this talk we first review both approaches and the sources of poor performance. When the probability of interest can be approximated via large deviations, there is a naturally related nonlinear partial differential equation (known as a Hamilton-Jacobi-Bellman equation). Schemes for both types of approximation can be associated with what are called importance functions. We will show that these schemes are in a certain sense stable if and only if the importance function is a subsolution to this equation, and characterize the performance of the scheme in terms of the value of the function at a certain point. If time permits, examples will be presented and more recent developments of the theory discussed.
Tea and cookies will be served after the talk.
Lasers are inherently noisy devices, and they introduce uncertainty into all applications based on them, from fiber-optic communications to frequency metrology. At the same time, industrial standards demand that this noise lead to failures, such as dropped bits or poorly resolved frequency measurements, with exceedingly low probability. The underlying stochastic models are nonlinear and high-dimensional, presenting a difficult challenge for the computation of failure probabilities. We discuss how importance sampling in combination with dynamical systems analysis of approximate reduced models can be used to resolve these probabilities with greatly improved efficiency over standard Monte Carlo techniques.
Join us for tea and cookies after the talk.
The fundamental task in climate variability research is to eke out structure from climate signals. Ideally we want a causal connection between a physical process and the structure of the signal. Sometimes we have to settle for a correlation between these. The challenge is that the data is often poorly constrained and/or sparse. Even though many data gathering campaigns are taking place or are being planned, the very high dimensional state space of the system makes the prospects of climate variability analysis from data alone impractical. Progress in the analysis is possible by the use of models and data. Data assimilation is one such strategy. In this talk we will describe the methodology, illustrate some of its challenges, and highlight some of the ways our group has proposed to improving the methodology.
Please join us for tea and cookies after the talk.
Random attractor is an important concept to describe long-term behavior of solutions for a given stochastic system. In this talk we will first provide sufficient conditions for the existence of a global compact random attractors for general dynamical systems in weighted space of infinite sequences. We then apply the result to show the existence of a unique global compact random attractor for first order, second order and partly dissipative stochastic lattice differential equations with random coupled coefficients and multiplicative/additive white noise in weighted spaces.
Bayesian statistics has become very popular in the past decades, especially after the widespread diffusion of MCMC methods. Sophisticated models and simulation techniques have been proposed to address problems in engineering, finance, genomics, biostatistics, etc. but the excitement for all those new opportunities has somehow driven away the attention from a basic aspect of the Bayesian approach: the choice of the prior distribution in practice. The talk will critically review the typical textbook prior distributions, before presenting the main ideas of the robust Bayesian approach (Rios Insua and Ruggeri, 2000), which was mainly developed because of the impractical possibility of eliciting a prior distribution corresponding to the effective knowledge of the expert. Bayesian robustness is interested in modelling the uncertainty in the prior specification, e.g. with a class of priors, and then quantifying the influence of such uncertainty on the quantity of interest, e.g. through its spanned range when the prior varies in the class. Uncertainty affects not only priors but model (likelihood) and loss function as well. Despite of the plethora of proposed methods, Bayesian robustness (as envisioned in the book edited by Rios Insua and Ruggeri) is not common practice of Bayesian analysis, probably because of its mostly mathematical nature which makes it quite impractical, especially in absence of user-friendly software. Nonetheless, there is a need to incorporate it in Bayesian analysis, as well as methods for practically eliciting priors from the experts. Stemming from the experience with engineers and, recently, with physicians, some ad hoc methods applied to get information from them and translate it into prior distributions will be presented.
Researchers in medicine and the social sciences attempt to identify and document causal relationships. Those not fortunate enough to be able to design and implement randomized control trials must resort to observational studies. To preserve the ability to make causal inferences outside the experimental realm, researchers attempt to post-process observational data to draw meaningful insights and conclusions. Finding the subset of data that most closely resembles experimental data is a challenging, complex problem. However, the rise in computational power and discrete optimization algorithmic advances suggests an operations research solution as an alternative to methods currently being employed.
Joint work with Alexander G. Nikolaev (University at Buffalo), Wendy K. Tam Cho, Jason J. Sauppe(University of Illinois at Urbana-Champaign), Edward C. Sewell (Southern Illinois University Edwardsville)
Biography
Sheldon H. Jacobson is a Professor and Director of the Simulation and Optimization Laboratory at the University of Illinois. He has a broad set of basic and applied research interests, including problems related to optimal decision-making, national security, and public health. His research has been disseminated in numerous archival journals, including Operations Research, Mathematical Programming, SIAM Journal on Control and Optimization, IIE Transactions, INFORMS Journal on Computing, Transportation Science, Journal of the American Medical Informatics Association, and Vaccine. He has been recognized with several national awards, including the Aviation Security Research Award (2002), a Best Paper Award in IIE Transactions Focused Issue on Operations Engineering (2003), a Guggenheim Fellowship (2003), the Outstanding IIE Publication Award (2009), the IIE Award for Technical Innovation in Industrial Engineering (2010), and an IIE Fellow (2011). His research has been supported by grants from the National Science Foundation and the Air Force Office of Scientific Research. He currently serves as the Focused Issue Editor for Operations Engineering and Analysis for IIE Transactions.
Noncompliance is often present in randomized experiment and needs to be adjusted for making valid causal inferences. Principal stratification is a framework to deal with such complication. Due to the latent nature of compliance principal strata, model-based analysis usually involves weakly identified models and identification of causal effects relies on untestable structural assumptions, such as exclusion restriction. Information on multiple outcomes is routinely collected in intervention studies, but is rarely used to improve model identification. This article develops a Bayesian approach to exploit multivariate outcomes to sharpen inferences for weakly identified models. Simulation studies are performed to illustrate the potential gains in identifiability of jointly modeling more than one outcome. This approach can be used to assess robustness with respect to deviations from structural identifying assumptions. The method is applied to evaluate the causal effect of a job training program on trainees' depression.
Joint work with Fan Li and Fabrizia Mealli.
The talk will be followed by tea & cookies.
Empirical likelihood methods have been popular in interval estimation and hypothesis test, which require no ad hoc way to obtain critical values. However it is known that the computation of empirical likelihood methods becomes a serious issue when the number of constraints is not small. In this talk, we propose some novel empirical likelihood tests for testing high dimensional means and some structures of a high dimensional covariance matrix.
Tea and cookies will be served after the talk.
We construct and analyze sparse tensorized space-time Galerkin discretizations for boundary integral equations resulting from the boundary reduction of nonstationary diffusion equations with either Dirichlet or Neumann boundary conditions. The ap- proach is based on biorthogonal multilevel subspace decompositions and a weighted sparse tensor product construction. We compare the convergence behavior of the proposed method to the standard full tensor product discretizations. In particular, we show for the problem of nonstationary heat conduction in a bounded two- or three-dimensional spatial domain that low order sparse space-time Galerkin schemes are competitive with high order full tensor product discretizations in terms of the asymptotic convergence rate of the Galerkin error in the energy norms, under lower regularity requirements on the solution.
The suggested sparse space-time Galerkin BEM can be applied as a building block for solution of nonstationary heat equations with random data.
The knowledge and information on cancer is continuously accumulated as the advances in cancer research. How to appropriately incorporate them in data analysis to obtain more meaningful results presents a challenge to the statistical society. In this talk, we are concentrated in Glioblastoma, a most common and aggressive brain cancer. The objective is to identify genes that are related to Glioblastoma with incorporating the information on genetic pathways. The problem is formulated as a linearly constrained lasso problem. In general we have a lasso-type problem with linear equality and inequality constraints. We develop a solution path algorithm to fit this model efficiently, and also work out some asymptotic properties to understand its advantages. The method is proven to be efficient and flexible as demonstrated in simulation studies and real data analysis.
We consider the problem of approximating the probability distribution for a quantity of interest computed from the solution of an elliptic problem with a randomly perturbed diffusion coefficient. We model the uncertainty using a piecewise representation that is suited to situations in which there is limited experimental data and to a common technique in multiscale modeling. By applying nonoverlapping domain decomposition and the Neumann series to the finite element method, we derive a method to compute an approximate distribution in which the cost grows very mildly with the number of samples. We briefly discuss the convergence and then describe an a posteriori error estimate for the computed distribution that takes into account all sources of deterministic and stochastic errors. Finally, we use the estimate to derive an adaptive method for achieving a desired accuracy in the computed distribution by an efficient division of computational resources.
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