# What is Uncertainty Quantiﬁcation anyway?

For me Paul Constantine is a celebrity. His primer of stochastic methods was the best document that helped me while digging into the world of stochastic and uncertainty quantification.

Early this month Paul Constantine, Postdoctoral researcher at Stanford University, posted a blog post on his lecture on uncertainty quantification.

Loved the varied quotes defining uncertainty quantification. Here are few of those definitions.

Combining computational models, physical observations, and possibly expert judgment to make inferences about a physical system.

(David Higdon – Los Alamos National Labs)

Uncertainty quantiﬁcation attempts to express the known unknowns.

(Bill Oberkampf – Sandia National Labs)

UQ is about providing bounds on our knowledge of system behavior and on conﬁdence in our predictions.

(Omar Knio – Johns Hopkins University)

UQ is the difference between success and failure.

(Gianluca Iaccarino – Stanford University)

UQ is quantiﬁcation of the effect of uncertainty. It sounds boring indeed but I don’t see anything else to it.

(Dongbin Xiu – Purdue University)

Man – that’s a hard question!!

(Tim Trucano – Sandia National Labs)

UQ is engineers discovering statistics.

(Overheard at the UQ summer school)

I guess “uncertainty” means a lack of certainty or knowledge; i.e. ignorance. This is one deﬁnition that suggests that subjective probability may be a reasonable way to think of uncertainty wherein randomness refers to a lack of knowledge. Quantiﬁcation, of course, means to quantify, to observe and assign a measure. I like the Wikipedia deﬁnition: an act of measuring that maps human observations and experiences into a set of numbers. I would weaken that a little: human observations include those made by humans using instruments. Thus, Uncertainty Quantiﬁcation is precisely the quantiﬁcation of one’s lack of knowledge concerning (in science and engineering) a physical reality.

(J. Tinsley Oden – University of Texas)

Paul goes on to talk about why we need UQ? To read the rest, click the link below.

View all posts by Paul Constantine here