Quantifying Sustainability - Green Finance and Sustainability - page 75

Breiman states - Statistics starts with data ;
improved methods can illustrate latent phenom-
ena and uncover alternative metrics in extant
data [Breiman 2001]. This statistical duality, the
hysteretic iteration of statistical theory and data
application, is especially instrumental in emerging
fields where functional and causal representations
are sparse.
Social indexes, in particular environmental
indexes, seek to describe as well as predict
phenomena that are often poorly measured and
ill-defined. An index is a metric, often at adminis-
trative levels, used to characterize a latent quality.
Gross Domestic Product (GDP) and of the
Dow Jones indexes are common economic indices;
Pacific Decadal Oscillation (PDO) and El Nino
([Francis 1998], [Gershunov1998]), climato-
logical indices; the National Threat Level could
also be called an index. Example environmental
indices are the Natural Disaster Hotspots report
[CHRR-World Bank 2005]; the Human and Eco-
systems Wellbeing Indexes - (HWI) and (EWI)
[Prescott-Allen 2001]; and the United Nations
Human Development Index - (HDI) [UNDP 2006].
A goal for these environmental indices is the
extraction of salient, perhaps latent, characteristics
that describe or predict the elusive and undefined
sustainability concept. A fortiori , the identification
of as yet unmeasured information can illustrate the
appropriate experimental design and thus guide
future measurement (See Fuentes et al. [2007]
for a creative example using Bernardo's [1979]
fundamental comment on information maximiza-
tion as a criteria).
Independent Component Analysis (ICA) - and
the special case Principal Component Analysis
(PCA) - extract uncorrelated and statistically in-
dependent components - or bases - of multivariate
data. In ICA the model is explicit - the observed
data are mixed independent sources; in PCA, im-
plicitly, the data are mixed multivariate Gaussian.
These component analysis procedures are used
to reduce dimension - by yielding a lower order
basis - and to parse or elucidate latent factors.

Environmental data are often non-Gaussian,
and frequently - characteristically - extreme value
[Meyers and Ganipati 2006]. Researchers apply
an array of approaches: from spatial-temporal
processes [Stein 2007], to stochastic optimization
[Tsai and Chen 2004], and hierarchical models
[Lin, Gelman, Price,and Krantz 1999]. Environ-
mental statisticians rely upon a suite of statistical
methodologies as the underlying processes are
complex (as in transport phenomena), multiple
(as in wastewater treatment), or latent (as in ecol-
ogy). Environmental statisticians face particular
challenges in modeling environmental processes;
these are typically 'out-of-control' and require
more sophisticated assumptions.
While the concept of sustainability has been
widely embraced, it has been defined only vaguely
and has proven difficult to measure with any con-
sensus. There is a critical need for sustainability
indicators; environmental statisticians have a
stake in making the broad concept of sustain-
ability operational. Researchers can justify an
increased focus by providing specific measures
- which decision makers can use and the public
can judge - of progress or failure.
In this chapter we illustrate the 2002 En-
vironmental Sustainability Index and exploit
its dependency structure using a new version
of ICA - Copula Based Component Analysis
(CICA) - to extract a reduced component set as
the determinants of environmental sustainability.
This approach is designed to highlight important
information, suggest some focal metrics, and
discredit others.
A unifying definition for an index , in the con-
text of this paper: a function that maps disparate
multivariate data onto a scalar at administrative
units. An index should be:

1. Transparent : The methodology use to
construct the index should be clear and
unambiguous. Assumptions and decisions
that affect index values (`scoring') should
be well stated.