### Introduction to Uncertainty Quantification Now Available as e-Book and Hardcover

A 350-page introduction to the key mathematical ideas underlying uncertainty quantification, designed as a course text or self-study for finalist undergraduates, master\'s students, or beginning doctoral students.

T. J. Sullivan. *Introduction to Uncertainty Quantification*, volume 63 of *Texts in Applied Mathematics*.
Springer, 2015.
ISBN 978-3-319-23394-9 (hardcover) 978-3-319-23395-6 (e-book) doi:10.1007/978-3-319-23395-6

**Update, 11 March 2016.** A list of errata can now be found here.

Published on Tuesday 22 December 2015 at 11:00 UTC #publication #i2uq

### Bayesian Brittleness in SIAM Review

The 2015 Q4 issue of *SIAM Review* will carry an article by Houman Owhadi, Clint Scovel, and myself on the brittle dependency of Bayesian posteriors as a function of the prior.
This is an abbreviated presentation of results given in full earlier this year in *Elec. J. Stat.*
The PDF is available for free under the terms of the Creative Commons 4.0 licence.

H. Owhadi, C. Scovel & T. J. Sullivan. “On the Brittleness of Bayesian Inference” *SIAM Review* **57**(4):566–582, 2015. doi:10.1137/130938633

Published on Friday 6 November 2015 at 12:00 UTC #publication #siam-review

### Bayesian Brittleness in Elec. J. Stat.

The *Electronic Journal of Statistics* has published an article by Houman Owhadi, Clint Scovel, and myself on the brittle dependency of Bayesian posteriors as a function of the prior.

H. Owhadi, C. Scovel & T. J. Sullivan. “Brittleness of Bayesian inference under finite information in a continuous world” *Electronic Journal of Statistics* **9**:1–79, 2015. doi:10.1214/15-EJS989

Published on Tuesday 3 February 2015 at 10:00 UTC #publication

### UQ for Legacy Data from Lipschitz Functions in M2AN

*Mathematical Modelling and Numerical Analysis* has just published a paper by Mike McKerns, Dominic Meyer, Florian Theil, Houman Owhadi and Michael Ortiz and myself on optimal UQ for legacy data observations of Lipschitz functions.

In this paper, we address both mathematically and numerically the challenge of giving optimal bounds on quantities of interest of the form \(\mathbb{P}_{X \sim \mu}[f(X) \geq t]\), where the probability distribution \(\mu\) of \(X\) is only partially known through some of its moments, and the forward model \(f\) is partially known through some pointwise observations and smoothness information.

T. J. Sullivan, M. McKerns, D. Meyer, F. Theil, H. Owhadi & M. Ortiz. “Optimal uncertainty quantification for legacy data observations of Lipschitz functions.” *ESAIM. Mathematical Modelling and Numerical Analysis* **47**(6):1657–1689, 2013. doi:10.1051/m2an/2013083

Published on Friday 30 August 2013 at 18:00 UTC #publication

### Optimal Uncertainty Quantification in SIAM Review

The 2013 Q2 issue of *SIAM Review* will carry an article by Houman Owhadi, Clint Scovel, Mike McKerns, Michael Ortiz and myself on the optimization approaches to uncertainty quantification in the presence of infinite-dimensional epistemic uncertainties about the probability measures and response functions of interest.

We present both a mathematical framework for the reduction of such infinite-dimensional problems to finite-dimensional effective feasible sets, and apply the methods to practical examples arising in hypervelocity impact and seismic safety certification.

H. Owhadi, C. Scovel, T. J. Sullivan, M. McKerns & M. Ortiz. “Optimal Uncertainty Quantification.” *SIAM Review* **55**(2):271–345, 2013. doi:10.1137/10080782X

Published on Monday 10 June 2013 at 20:00 UTC #publication #siam-review