Applications are invited for several PhD funding opportunities based
in the department of Statistics of Athens University of Economics and
Business (AUEB) in Greece, to commence in September 2012. The research theme of
these grants is based on the project "Likelihood methods for jump
diffusions and related Markov processes" that was recently funded in
the "ARISTEIA" national funding program. The research team that will
act as supervisors consists of Petros Dellaportas (AUEB), Omiros
Papaspiliopoulos (Universitat Pompeu Fabra, Barcelona, Spain), Aleksandar
Mijiatovic (Imperial College, UK), and Gareth Roberts (Univesity of
Warwick, UK).
Candidates should have an MSc degree in statistics, mathematics,
computer science or related subjects. Successful candidates will enroll
as full-time PhD students in AUEB but will be expected to make several academic
visits to other members of the research team.
Detailed cv's naming two academic Referees should be sent to Petros Dellaportas
([log in to unmask]) by 15/6/2012.
A summary of the research project is given below:
This project is about the development of novel methodology, theory and
software for the statistical estimation of a very large family of stochastic models
which are widely used in Science. Two different but related descriptions of the family
of mathematical models of interest are as solutions to stochastic
differential equations driven by Brownian noise and jumps, and as Feller processes.
Our target is the identification of such dynamics from observations using likelihood
methods. Statistical inference for such processes is well-recognized as a very challenging
problem due to the continuous-time non-linear nature of the models, and the discrete-time
available data. Specifically, the required likelihood functions are typically intractable for
discrete-time data. This project will attack this problem from two directions. First, by developing
state-of-the-art Markov chain Monte Carlo computational methods for
Bayesian inference for these models. Second, by developing tailored approximate likelihood methods
for Feller processes by constructing a sequence of approximating but
numerically tractable Feller processes. The project aspires to address a broad and ambitious
research agenda which includes the underlying probability theory, the computational statistics methodology
and the computer implementation.
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