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in the SAR (IPCC 1996) and the TAR unequivocal attribution would require controlled
experimentation with our climate system. That, of course, is not possible, and thus from a
practical perspective, attribution of anthropogenic climate change is understood to mean (a)
detection as defined above, (b) demonstration that the detected change is consistent with a
combination of external forcing including anthropogenic changes in the composition of the
atmosphere and natural internal variability, and (c) that it is "not consistent with alternative,
physically-plausible explanations of recent climate change that exclude important elements of
the given combination of forcings" (IPCC 2001).
In this section we very briefly review the statistical methods that have been used in recent
detection and attribution work. Two statistical approaches have been used in recent studies.
Standard 'frequentist' methods (methods based on the relative frequency concept of probability)
continue to predominate, but there is increasing interest in the use of Bayesian methods of
statistical inference. One reason is that information from multiple lines of evidence can be
combined in the Bayesian framework. We will briefly review the optimal fingerprinting
technique in the following subsection. This will be followed by a short discussion on the
differences between the standard and Bayesian approaches to statistical inference that are
relevant to detection and attribution.
a. Optimal fingerprinting
Optimal fingerprinting is generalized multivariate regression that has been adapted for the
detection of climate change and the attribution of change to externally-forced climate change
signals (Hasselmann 1979, 1997; Allen and Tett 1999). The multiple regression model that is
used has the form y = Xa + u where vector y is a filtered version of the observed record, matrix
X contains the estimated response (signal) patterns to the external forcings that are under4
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Barnett, T.; Zwiers, F.; Hegerl, G.; Allen, M.; Crowley, T.; Gillett, N. et al. Detecting and Attributing External Influences on the Climate System: A Review of Recent Advances, article, January 26, 2005; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc1418795/m1/8/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.