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Stake holders, regulatory administrations and public opinion feel
more and more concerned by environmental issues: soil, water and air
pollution, erosion or flooding hazards, sustainable agriculture and
development, etc. Often, those issues are sensible due to the complex
environmental, social and economical aspects that they involve. As experts,
we are thus asked to propose practical solutions. For this, we need
accurate knowledge about the relevant factors, and particularly about their
distribution in space and time. However, while sources of information
become each year more numerous and diversified, they rarely provide us with
data having at the same time the required level of spatial and attribute
accuracy.
In other fields, such as petroleum or mining engineering, most often
data are rather scarce. Indirect measurement devices are then frequently
used to overcome this lack of information, providing generally less
accurate measurements of the target variable. Some of them may even provide
qualitative results. As experts, we then have to deal with various
uncertainty sources while we are asked at the same time to produce accurate
results. Clearly, important technical and financial decisions may depend on
them.
An important challenge thus consists in combining at best all these
available data sources, in order to satisfy the highest possible accuracy
requirements.
The Bayesian Maximum Entropy (BME) approach appears to be a
potential candidate for achieving this task: it is especially designed for
managing simultaneously data of various nature and quality
("hard" and "soft" data, continuous or categorical). It
relies on a two-steps procedure that first involves an objective way of
obtaining a prior distribution in accordance with the general knowledge at
hand (the ME part), and a Bayesian conditionalization step that updates
this prior probability distribution function (pdf) with respect to the
specific data collected on the study site. At each prediction location, an
entire pdf is obtained, allowing subsequently the easy computation of
elaborate statistics chosen for their adequacy with respect to the
objectives of the study.
The BME approach thus appears as a kind of new unifying theory,
opening new perspectives for solving a set of particular issues within a
unique paradigm. Traditional kriging methods can even be derived as special
cases of it.
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The
course is intended as a large audience introduction to the concepts driving
the BME approach. The basic concepts will be illustrated through real case
studies using interactive software. The course will combine lecture
sessions and interactive practical sessions. Comparisons with traditional
geostatistical methods will be encouraged and open discussions are
expected. Each participant will receive at set of lecture notes. While BME
can be used in the space-time domain, this course will mainly focus on the
purely spatial component.
The
theoretical part of the course will include:
·
A quick
review of the fundamental concepts of geostatistics (random variable,
spatial correlation, spatial estimation and uncertainty assessment),
·
An
introduction to the fundamental concepts of the BME approach (information,
entropy, hard and soft data, Bayesian conditionalization, …)
·
A
detailed explanation of the various BME solutions for
continuous/categorical variables.
Those
concepts will be illustrated from several case studies that have been
conducted using the BMElib library of comprehensive computer programs (written in Matlab®).
The participants will be shown what are the benefit
of using this integrated toolbox for exploratory analysis of the data,
modeling of spatial variability, spatial analysis
and estimation, as well as graphical presentation of maps.
The
course will be given in English.
A
detailed program is available here.
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