Improving data analysis via better statistical infrastructure
Submitting InstitutionUniversity of Bath
Unit of AssessmentMathematical Sciences
Summary Impact TypeEconomic
Research Subject Area(s)
Mathematical Sciences: Applied Mathematics, Statistics
Summary of the impact
A generalized additive model (GAM) explores the extent to which a single
output variable of a complex system in a noisy environment can be
described by a sum of smooth functions of several input variables.
Bath research has substantially improved the estimation and formulation
of GAMs and hence
- driven the wide uptake, outside academia, of generalized additive
- increased the scope of applicability of these models.
This improved statistical infrastructure has resulted in improved data
analysis by practitioners in fields such as natural resource management,
energy load prediction, environmental impact assessment, climate policy,
epidemiology, finance and economics. In REF impact terms, such changes in
practice by practitioners leads ultimately to direct economic and societal
benefits, health benefits and policy changes. Below, these impacts are
illustrated via two specific examples: (1) use of the methods by the
energy company EDF for electricity load forecasting and (2) their use in
environmental management. The statistical methods are implemented in R
via the software package mgcv, largely written at Bath. As a `recommended'
R package mgcv has also contributed to the global growth of R,
which currently has an estimated 1.2M business users worldwide [A].
The underpinning research was undertaken by Simon Wood (Professor at Bath
since January 2006). The aim of the research programme is to make the use
of generalized additive models as reliable and routine as the use
of generalized linear models has long been, in order that these
flexible statistical models can routinely be used beyond academic
A generalized additive model is a regression model that relates a
univariate random response variable to one or more predictor variables. A
key feature is that the response depends on a sum of smooth functions of
the predictor variables. These functions must be estimated from the data.
The flexibility to specify models in terms of unknown functions is useful
in fields as diverse as fisheries science and finance, but the additional
flexibility comes at the cost of decreased numerical stability and the
need to estimate the degree of smoothness of the functions.
The primary contributions of the research programme undertaken at Bath
Reliable and efficient computational methods. The major problem
is simultaneously to estimate several smoothing parameters in a
computationally efficient and robust way [1, 2]. We have developed a
numerical scheme for this for which convergence is guaranteed, provided
that the GAM penalized likelihood has a well-defined optimum. Before the
development of this method, GAM estimation methods did not always
converge [B]. Before mgcv, the only software that estimated GAM
smoothing parameters had O(n3)
computational cost, limiting its usefulness. With mgcv the cost is about
Improved means of smoothing with respect to several variables.
Smooth interactions are best represented using tensor product smooth
constructions.  shows how this can be done in general, while
maintaining the important property of scale invariance (the results
should not depend on the units of measurement, for example). The
generality was important as it allowed, for the first time, the routine
construction of space-time smoothers for large datasets.  provides an
alternative general construction which has the advantage of being usable
as a component of any generalized linear mixed model, and also of being
quite natural when ANOVA decompositions of functions are of interest.
Moving to spatial smoothing,  uses the physical analogy of a
distorted soap film, and some PDE theory, to construct a novel method
for smoothing within finite geographic areas, without smoothing across
boundary features. The resulting smoothers have a form that allows their
full integration into GAMs.
A monograph on GAMs. This helps statisticians beyond HE to use
the methods .
High quality software implementing the methods. The Bath
written mgcv package  is supplied with the R statistical
programme as the default method for generalized additive modelling.
References to the research
References that best indicate the quality of the underpinning research
* S.N. Wood 2011 Fast stable restricted maximum likelihood and
marginal likelihood estimation of semiparametric generalized linear
models. J. Roy. Stat. Soc. B, 73(1), 3-36.
Details of the impact
The main contribution of the research is to provide numerical-statistical
methods that make the practical use of generalized additive models as
reliable and routine as the use of generalized linear models has long
been, ensuring wide uptake of the methods beyond academic research. The
quality of the methods produced by the research has been recognised by the
R core team's inclusion of the Bath produced software "mgcv" as one of
only a dozen recommended packages (out of thousands) supplied with all
versions of the R statistical computing environment.
R is an open source statistical package/environment that is widely used
both in academia and beyond [A]. While the wide academic uptake of R is
doubtless driven partly by the fact that it is free, this is less likely
as a primary driver of business uptake, where reliability and flexibility
are overriding concerns. mgcv and its underpinning research are part of
providing this reliability and flexibility.
Example 1. The electricity company EDF produces 22% of Europe's
electricity consumption, generating 652 TWh per year (at a wholesale price
of around £40 per MWh). It is the dominant electricity producer in France,
where it is also the monopoly distributor. French grid load varies between
30 and 80 GW, and with daily energy flows of around 1 Million MWh,
accurate load prediction is critical to the success of EDF as a company.
Moreover, as the dominant producer, substantial wider social benefits
accrue to client countries through the provision of a reliable electricity
Load prediction is particularly important for EDF because it generates
77% of its electricity from nuclear power plants, which cannot respond
rapidly to unforeseen demand. Under-prediction of load leads either to
supply failure, or to EDF having to buy in energy at premium prices.
Over-prediction leads to unnecessary production and business
inefficiencies. The cost to EDF of over-production by 1% for a single day
is around £0.5M [C].
EDF have developed methods for electricity grid load forecasting based on
the mgcv software and its underlying methods. EDF's use of GAMs has been
built directly on collaboration with Bath on large dataset and
autocorrelation issues [D]. The EDF work is, in particular, reliant on the
high degree of numerical reliability provided by the methods developed in
Bath [1, 2], on the ability to handle large datasets [D], and on the
handling of interaction terms .
An EDF representative [E] states that the Bath mgcv work "has had a
number of concrete and important impacts on our work at EDF... These are
commercially important for EDF, both in terms of complying with the
requirements of the national grid management bodies, and of matching
supply to demand in an economically and environmentally efficient
manner". He goes on to list several specific areas:
- "The methods encoded in mgcv are used to discover and investigate
new effects... A number of such effects have subsequently been
incorporated in the parametric models currently used for operational
- The methods have been successfully employed in pilot studies on EDF
subsidiary companies, and are currently being further developed for
operational forecasting purposes for these companies.
- The methods have been used operationally on the French national grid
as a tool to help operators when special meteorological events happen
(extreme absolute temperatures or rapid temperature variations, for
example). In these cases the GAM based models capture the electricity
grid load dynamics better than the current operational models, and are
used to correct the operational models.
- EDF uses the methods for forecasting of heat demand for cogeneration
plants where it achieves a 20% gain over the existing methods.
EDF leads some important research projects around [the methods].
Among them ... collaborations with IBM to implement GAM for massive
simulation and online forecasting." [E]
Example 2. The methods are widely used in fisheries where they
contribute to policy decisions about quota setting, as the following
examples illustrate. The enhanced reliability offered by the methods
allows CSIRO Tasmania to use GAMs to analyse and design their fisheries
independent survey programme, which helps to improve management of the
south east of Australian fisheries (estimated annual value AU$700M,
2005/6) [F]. Similarly, models based on  and  above have been used
as part of IFREMER's (French Research Institute for Exploration of the
Sea, wwz.ifremer.fr) input to quota setting for the Blue Ling Fishery [G].
The methods have also been used to develop models for catch per unit
effort standardization in deep sea fisheries which in turn inform the
policy and management advice of ICES (International Council for the
Exploration of the Sea), which is used by the EU for quota setting and
other management [H]. A separate use of the methods developed models for
fish stock indicator indices used by the EU for stock management
assessment [J]. To illustrate the breadth of extra academic impact within
fisheries, of the 689 publications citing Bath mgcv related papers on
Google Scholar from fisheries, 77% had at least one author with an address
outside higher education and on average each publication had 1.3 such
addresses [K]. The project has been sufficiently successful in making GAM
use statistically routine, that many fisheries uses result in no citation
[L]. It is the numerical reliability combined with sound smoothness
selection methods that has changed practice among many fisheries
statisticians involved in assessment so that they now use the Bath/mgcv
The success of the methods means that they have become part of the
`statistical infrastructure', and in combination with their availability
as free software, this complicates the process of gathering direct
evidence of extra-academic reach. However, indirect evidence is obtainable
[K]. By September 2013, there were over 3200 citations to Bath authored
mgcv related publications (i.e. to publications from 2006 onwards) on
Google Scholar. Approximately 55% of these have at least one author with a
non-academic address and the average number of non-academic author
addresses per paper is about 0.9. A substantial proportion of these were
government institutes charged with natural resource management (fisheries,
forestry, agriculture), but there were also private companies, health
charities and bodies, Government bodies (e.g. Deutsch Bundesbank) and
international bodies (e.g. WHO and UNESCO). Notable topics were fisheries
(689), air pollution (425), medicine (730) and energy (391). Further
evidence of the extra academic impact of the work is that SAS, the
major commercial provider of statistical software to industry are
currently implementing GAM functionality into their software, based on the
Bath work [M], while private statistics companies run courses in which
mgcv is a major component [N].
Sources to corroborate the impact
based on data from Revolution Analytics (http://www.revolutionanalytics.com/)
puts the number of R business users at >1.2M (c.f. ~1M academic).
However the figures are very uncertain. A Jan 2009 New York Times online
puts the user figure at 250,000 - 1M. Various other data are at: http://r4stats.com/articles/popularity/
[B] In 2002, problems with an earlier GAM function in S-plus, in the
context of air pollution modelling, were reported in the New York Times
provides EDF information.
[D] Wood, Goude and Shaw "Generalized Additive Models for Large
Datasets", accepted subject to minor corrections for Applied
Statistics (JRSSC). Describes collaboration with EDF on grid load
[E] Letter from EDF Research Engineer on the use of mgcv methods at EDF.
[F] Peel, Bravington, Kelly, Wood and Knuckey (2012) A Model-Based
Approach to Designing a Fishery-Independent Survey. Journal of
Agricultural, Biological and Environmental Statistics 18(1):1-21
describes application of GAM modelling in design of a fisheries survey for
[G] Email from scientist at IFREMER, describing use of Blue Ling work and
referring to official ICES blue ling assessment document (section 3.6 Data
analysis: space-time modelling).
[H] Email from same scientist at IFREMER describing CPUE work, with
[J] Email from another IFREMER scientist describing stock indicator work,
with supporting documents.
[K] Report on impact of mgcv project beyond the higher education
sector. University of Bath, internal report.
[L] Example: the FAO Tuna working group papers include a paper by Haritz
Arrizabalaga (2009) on "Estimation of Tuna fishing capacity from stock
assessment related information" (http://www.fao.org/docrep/012/i1212e/i1212e.pdf).
This makes considerable use of mgcv based GAMS, but you can only tell this
by looking up the citation to Retrepos, V.R. (2007) "Estimates of large
scale purse seine...", (FAO Fish. Proceedings 8:51-62), which also
contains no citation, but contains figures clearly plotted from mgcv,
making it clear that it is the basis of the GAM analysis.
[M] Email from SAS.
[N] For example http://www.highstat.com/.