[robotics-worldwide] PhD Studentship in Belief Theory - Oxford Brookes University - EXTENDED TO JANUARY 15 2013
Fabio Cuzzolin
fabio.cuzzolin at brookes.ac.uk
Thu Dec 13 06:06:44 PST 2012
The Department of Computing and Communications Technologies at Oxford
Brookes University is pleased to announce that it is able to offer a
Doctoral Bursary to a new PhD student in for full time study
commencing in January 2013. The successful applicant will have course
fees waived and will be awarded a bursary of £10,000 per annum for
three years (with no inflation increase).
The PhD project will be focus on decision making and estimation. These
are central problems in most applied sciences, as both people and
machines need to make inferences about the state of the external
world, and take appropriate actions.
Traditionally, the (uncertain) state of the world is assumed to be
described by a probability distribution over a set of alternative,
disjoint hypotheses.
Sometimes, however, as in the case of extremely rare events (e.g., a
volcanic eruption), few statistics are available to drive the
estimation. Part of the data can be missing. Furthermore, under the
law of large numbers, probability distributions are the outcome of an
infinite process of evidence accumulation, drawn from an infinite
series of samples: in all practical cases, instead, the available
evidence only provides some sort of constraint on the unknown
probabilities governing the process. All these issues have led to the
recognition of the need for a coherent mathematical theory of
uncertainty.
Shafer’s theory of belief functions, in particular, allows us to
express partial belief by providing lower and upper bounds to
probability values. It is appealing because it addresses all the above
mentioned issues; its rationale is neat and simple; it is a
straightforward generalization of probability theory; it does not
require abandoning the notion of event. The widespread influence of
uncertainty at different levels explains why belief functions are
being increasingly applied to fields as diverse as robotics, fault
analysis, decision making, sensor fusion, machine vision, and many
more.
Mathematically, a belief function is a random set, i.e. a probability
distribution on the power set (the collection of all subsets).
Equivalent alternative interpretations can be given in terms of
compatibility relations, inner measures, and sum functions. However,
the necessary mathematical tools for prediction and estimation in this
framework have only partially been developed yet, due to their
inherent complexity: this is the case, in particular, for the
generalization of the classical total probability theorem to belief
functions.
The aim of this studentship is to study the mathematical properties of
belief functions, and give a contribution towards the development of
crucial tools such as the total belief theorem.
Informal requests: fabio.cuzzolin at brookes.ac.uk
Formal applications: contact jheaton at brookes.ac.uk
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