This book is about methodological aspects of uncertainty propagation in
data processing. Uncertainty propagation is an important problem: while
computer algorithms efficiently process data related to many aspects of
their lives, most of these algorithms implicitly assume that the numbers
they process are exact. In reality, these numbers come from
measurements, and measurements are never 100% exact. Because of this, it
makes no sense to translate 61 kg into pounds and get the result--as
computers do--with 13 digit accuracy.
In many cases--e.g., in celestial mechanics--the state of a system can
be described by a few numbers: the values of the corresponding physical
quantities. In such cases, for each of these quantities, we know (at
least) the upper bound on the measurement error. This bound is either
provided by the manufacturer of the measuring instrument--or is
estimated by the user who calibrates this instrument. However, in many
other cases, the description of the system is more complex than a few
numbers: we need a function to describe a physical field (e.g.,
electromagnetic field); we need a vector in Hilbert space to describe a
quantum state; we need a pseudo-Riemannian space to describe the
physical space-time, etc.
To describe and process uncertainty in all such cases, this book
proposes a general methodology--a methodology that includes intervals as
a particular case. The book is recommended to students and researchers
interested in challenging aspects of uncertainty analysis and to
practitioners who need to handle uncertainty in such unusual situations.
