
Chapter 1
Introduction
The terms uncertai nty quantification and u ncertainty propagation have
become so widely used as to almost have little meaning unless they are further
explained. Here we focus primarily on two basic types of problems:
1. Modeling and inverse problems where one assumes that a precis e math-
ematical model without modeling error is available. This is a standard
assumption underlying a large segment of what is taught in many mod-
ern statistics courses w ith a frequentist philosophy. More precisely, a
mathematical model is given by a dynamical s ystem
dx
dt
(t) = g(t, x(t), q) (1.1)
x(t
0
) = x
0
(1.2)
with o bservation process
f (t; θ) =