Dealing with Uncertainties: A Guide to Error Analysis

249 Pages·2009·2.09 MB·English

by  Manfred Drosg (auth.)

Dealing with Uncertainties
Second, Enlarged Edition
Manfred Drosg
Dealing with Uncertainties
A Guide to Error Analysis
Second, Enlarged Edition
Prof.Dr.ManfredDrosg
UniversitätWien
FakultätfürPhysik
Strudlhofgasse4
A-1090Wien,Austria
[email protected]
ISBN978-3-642-01383-6 e-ISBN978-3-642-01384-3
DOI10.1007/978-3-642-01384-3
SpringerDordrechtHeidelbergLondonNewYork
LibraryofCongressControlNumber:2009933277
(cid:2)cSpringer-VerlagBerlinHeidelberg2007,2009
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I dedicate this book to my American friends;
in particular to those I met in New Mexico,
and to Peter Weinzierl,
who patronized me by arranging for me,
with the magnificent support
of R.F. Taschek, former P-Division leader of LANL,
to become the first foreign postdoctoral fellow in said division.

Preface
Aninnovativeapproachtouncertaintiesbasedontheeasilyunderstoodround-
ing uncertainty is introduced in this edition facilitating the understanding of
the nature of a (scientific) uncertainty; in particular it is clear from the very
beginning that measurements are not the cause of the phenomenon uncer-
tainty. At the same time this choice provides an excellent example for the
importance of the shape of the uncertainty distribution. Several recent devel-
opments have centered on the determination of such shapes because of their
importance in finding confidence levels. Thus, more attention is paid to the
shape of uncertainty distributions throughout this edition.
In recent years the term uncertainty has become generally accepted and
the controversial term error appears to be finally outdated. Consequently, a
criticalreviewofthetextwasnecessarytofullycomplywiththisdevelopment.
Stressing the usually disregarded distinction between measurement and
experimental uncertainty made it necessary to deal to some extent with the
modeluncertainty.Someadditionalthoughtsoncountinguncertaintiesshould
make it easier for the reader to deal with this interesting subject. Added
emphasis on linear regression of transformed data should be welcomed by
some readers.
Asubstantialincreaseofthenumberoffiguresshouldbehelpfulinunder-
standingsomeofthepointsmoreeasily.Theabundanceofpracticalexamples
and problems was praised by many readers. Consequently, I added more of
them. They reflect mypersonal experiences inthis field. Because ofthis plen-
itude I can encourage readers to skip Examples or Problems if these are too
alien to their knowledge. There should be others that are better suited.
SeveralreadershavepointedoutmistakeswhichIcorrectedinthisedition.
I am very thankful to them and am encouraging new readers to follow suite
([email protected]).Veryvaluableinput wasreceivedfrom
Dr. Robert C. Haight, Los Alamos National Laboratory. I am indebted to
him. My very good colleague Prof. Gerhard Winkler was again available for
discussions that helped this project a lot. I thank him sincerely.
Vienna, March 2009 Manfred Drosg

Preface to the First Edition
For many people uncertainty as it occurs in the scientific context is still a
matter of speculation and frustration. One of the reasons is that there are
several ways of approaching this subject, depending upon the starting point.
The theoretical part has been well established over centuries. However, the
application of this knowledge on empirical data, freshly produced (e.g., by
an experiment) or when evaluating data, can often present a problem. In
some cases this is triggered by the word “error” that is an alternative term
for uncertainty. For many the word error means something that is wrong.
However,aswillbeshown,anuncertaintyisjustonecharacteristicofscientific
dataanddoesnotindicatethatthesedataarewrong.Toavoidanyassociation
with something being wrong, the term error is avoided in this book whenever
possible, and the term uncertainty is used instead. This appears to be in
agreement with the general tendency in modern science.
The philosopher Sir Karl Popper made it clear that any scientific truth
is uncertain. Usually, uncertainty is mentally associated only with measured
data for which an “error analysis” is mandatory, as many know. This makes
peoplethinkthatuncertaintyhasonlytodowithmeasurements.However,all
scientific truths, even predictions of theories and of computer models, should
beassigneduncertainties.Whereastheuncertaintyofmeasureddataisrather
easy to determine, it is too difficult, if not impossible, to establish reliable
uncertainties for theoretical data of either origin.
Thus, this book deals mainly with uncertainties of empirical data, even
if much of it is applicable in a more general way. In particular, I want to
promote a deeper understanding of the phenomenon of uncertainty and to
removeatleasttwomajorhurdlesenroute.Oneistoemphasizetheexistence
of internal uncertainties. Usually only external uncertainties are considered
because they are the direct result of the theoretical approach. The former
are the result of a deductive approach to uncertainties, whereas the latter are
obtained inductively. The other hurdle is the so-called systematic error. The
conflicting nomenclature of this term is cause of many misunderstandings. It
is used both for correlated (or systematic) uncertainties and for systematic
X Preface to the First Edition
deviations of data. The latter just means that these data are wrong, that is,
thattheyshouldhavebeencorrectedforthatdeviation.Thereareevenbooks
in which both meanings are intermingled!
Not using the term error will make such misconceptions less likely. So I
speak of uncorrelated uncertainty instead of random error, and of correlated
uncertainty (and of systematic deviation, respectively) instead of systematic
error.Inaddition,itwillbeshownthatthesetwotypesofuncertaintiesareof
the same nature. Thus, a remark taken from a more recent book like “there
is no evidence that you cannot treat random and systematic errors the same
way” is self-evident.
Myfirstinterestinthesubjectofthisbookgoesbackto1969,whenNelson
(Bill)JarmieatLosAlamosNationalLaboratory,USA,whowasapioneerin
accurate measurements of cross sections, introduced me to various subtleties
inthis field.Iamindebted to himformanyinsights. Notsurprisingly, quitea
few examples deal with nuclear physics. In this field (and in electronics) I am
most experienced and, even more important, uncertainties of data based on
radioactive decay can easily be determined both deductively and inductively.
The essence of this book is found already in work sheets that I prepared
for undergraduate students in an advanced practical physics course when it
became clear that nothing like it was available in either German or English
books. This lack is the reason for not including a reference list.
Students and colleagues have contributed by asking the right questions,
my colleague Prof. Gerhard Winkler by way of enlightening discussions and
very valuable suggestions, and M.M. Steurer, MS, by reporting a couple of
mistakes. My sincere thanks to all of them.
I sincerely urge my readers to contact me at [email protected]
whenever they can report a mistake or want to suggest some additional topic
to be included in this book. Any such corrections or additions I will post at
http://homepage.univie.ac.at/Manfred.Drosg/uncertaintybook.htm.
Vienna, September 2006 Manfred Drosg