Dear all,

I have an opening for a PhD studentship in belief functions theory, could you please make me aware of strong candidates with strong math skills interested in the job. Deadline (for now) is December 5th. Best,

Fabio

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(a)brookes.ac.uk Formal applications: follow the instructions here:

http://www.jobs.ac.uk/job/AFL096/phd-studentship/

and contact jheaton(a)brookes.ac.uk