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Society for Industrial and Applied Mathematics

The newest journal from the Society for Industrial and Applied Mathematics, *SIAM/ASA Journal on Uncertainty Quantification* (*JUQ*), launched today with its first seven papers publishing online to Volume 1.

Offered jointly by SIAM and the American Statistical Association, the journal publishes research articles presenting significant mathematical, statistical, algorithmic, and application advances in uncertainty quantification, and is dedicated to nurturing synergistic interactions between these and related areas.

Under the leadership of Senior Editor Max Gunzburger, Editors-in-Chief James Berger and Donald Estep and more than 35 others comprising the editorial board, the journal will feature continuous electronic publication at SIAM Journals Online with complimentary access in 2013.

If the first few research articles are any indication—covering the analysis and quantification of uncertainty in areas as far-reaching as finance, disaster preparedness and porous media flows— the journal promises great depth and breadth of coverage in uncertainty quantification research.

Below is an overview of some of the interesting topics you will read about in *JUQ*'s maiden volume:

In a paper titled "Mean Exit Times and the Multilevel Monte Carlo Method" Desmond Higham, Xuerong Mao, Mikolaj Roj, Qingshuo Song, and George Yin propose a method to reduce the computational complexity of a simple and widely used algorithm, Euler/Monte Carlo simulation for a mean exit time. The multilevel algorithm proposed in the paper improves the expected computational complexity by an order of magnitude, in terms of required accuracy. The analysis is illustrated with numerical results.

In "Variance Components and Generalized Sobol' Indices," author Art Owen describes Sobol' indices, which are used to determine and quantify the importance of variables used in modeling and simulation. Computer simulations are so pervasive in engineering applications that the performance of anything from an airplane to a power dam is usually investigated computationally, in addition to laboratory experiments. Such simulated models depend on several input variables that describe product dimensions and composition, manufacturing processes, and so on and so forth. Sobol' indices have been developed to quantify the importance of such variables. Owen's article introduces readers to generalized Sobol' indices, relates them to well-known ideas in experimental design, and compares methods to estimate them.

In the paper, "Formulating Natural Hazard Policies under Uncertainty," Jerome and Seth Stein present a general stochastic model to minimize expected damage from natural disasters. Uncertainty issues are important in the assessment of risks posed by natural hazards and in developing strategies to alleviate their consequences. Using the 2011 earthquake in Japan as an example, the authors describe a model that estimates the balance between the costs and benefits of mitigation, and can help answer questions regarding the kinds of strategies to employ against such rare events, and whether to rebuild defenses in their aftermath. The model selects an optimum strategy by minimizing the expected present value of damage, the costs of mitigation, and risk premium, which reflects the variance of the hazard. Such a model can help shape natural hazard policy in a variety of situations.

"A Nonstationary Space-Time Gaussian Process Model for Partially Converged Simulations" by Victor Picheny and David Ginsbourger proposes fitting a Gaussian process model to partially converged simulation data for computational efficiency. A solution for alleviating computational costs in numerically-expensive experiments involves using partially converged simulations instead of exact solutions. Computational time is gained at the expense of precision in the response. In this work, Gaussian processes are used to approximate the simulator response in the joint space of design parameters and computational time. When applied to a computational fluid dynamics test case, the method shows significant improvement in prediction compared to a classical kriging model.

In a paper titled "Reduced Basis Methods for Parameterized Partial Differential Equations with Stochastic Influences Using the Karhunen-Loève Expansion," authors Bernard Haasdonk, Karsten Urban, and Bernhard Wieland consider parametric partial differential equations (PPDEs) with stochastic influences that are used to model various problems in science and engineering. PPDEs are particularly useful in the case of measurements that are uncertain or unknown, such as, in porous media flows, financial models, and inverse problems. Many of these problems also depend on deterministic parameters in addition to uncertainties; hence the use of parameterized PDEs. This paper explores situations where the PPDE has to be evaluated under different scenarios for various instances of the deterministic parameter as well as the stochastic influences.

In the paper, "A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation," K. Singh, A. Sandu, M. Jardak, K. W. Bowman, and M. Lee use computationally feasible approaches to assess the information content of observations in the context of a data assimilation framework. Data assimilation can help improve estimates of a physical system's state by dynamically combining imperfect model results with sparse and noisy observations of reality. However, since not all observations used in data assimilation are equally valuable, it is important to characterize the usefulness of different data points in order to analyze the effectiveness of the assimilation system. Using a four-dimensional variational (4D-Var) data assimilation framework, the authors use metrics from information theory to assess the information content of observations: specifically, by quantifying the contribution of these observations to decreasing uncertainty in the system state.

In "A Posteriori Estimates for Backward SDEs," Christian Bender and Jessica Steiner propose a method for approximation of backward stochastic differential equations (BSDEs). BSDEs, which have traditionally had applications in stochastic control, have recently been found to be of great value in mathematical finance. Motivated by these applications, many numerical algorithms have been developed for BSDEs in recent years. However, solving BSDEs is a very challenging task. The paper proposes an approximation to the solution of a BSDE, precomputed by some numerical algorithm.

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Access the full text of the abovementioned research articles at http://epubs.siam.org/journal/S*JUQ*A3.

Authors are encouraged to submit their uncertainty quantification work for consideration for publication at http://juq.siam.org.

Information on the Editorial Policy, review procedures, and members of the board, is available here.

**About SIAM**

The Society for Industrial and Applied Mathematics (SIAM), headquartered in Philadelphia, Pennsylvania, is an international society of over 14,000 individual members, including applied and computational mathematicians and computer scientists, as well as other scientists and engineers. Members from 85 countries are researchers, educators, students, and practitioners in industry, government, laboratories, and academia. The Society, which also includes nearly 500 academic and corporate institutional members, serves and advances the disciplines of applied mathematics and computational science by publishing a variety of books and prestigious peer-reviewed research journals, by conducting conferences, and by hosting activity groups in various areas of mathematics. SIAM provides many opportunities for students including regional sections and student chapters. Further information is available at http://www.siam.org.

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