RESEARCH FIELDComputer science › ProgrammingEngineeringMathematics › Probability theory
RESEARCHER PROFILEFirst Stage Researcher (R1)
APPLICATION DEADLINE24/03/2017 23:00 - Europe/Brussels
LOCATIONBelgium › Ghent
TYPE OF CONTRACTTemporary
HOURS PER WEEK40
EU RESEARCH FRAMEWORK PROGRAMMEH2020 / Marie Skłodowska-Curie Actions
MARIE CURIE GRANT AGREEMENT NUMBER722734
PhD Position on Imprecise (Hidden) Markov Chains within the UTOPIAE H2020 training and research network
We have a vacancy for a 3-year PhD research position at Ghent University on the topic of Imprecise (Hidden) Markov Chains within the UTOPIAE training and research network.
A Markov chain is a popular probabilistic model, successful at describing the uncertain time evolution of various systems. It can be in any one of several states, and moves between them as time progresses. At each time and in each state, it is uncertain which state it will move to next, and this uncertainty is modelled using so-called transition probabilities, assumed to depend only on the current state.
It turns out to be quite simple to make predictions about the future behaviour of a Markov chain, and this makes it a popular tool in various applied domains, including engineering (filtering, control, queueing), artificial intelligence (text and speech recognition), mathematical finance and bio-informatics. However, in order to make these predictions reliable, perfect knowledge of the parameters of the Markov chain is required, and such knowledge is seldom available. Furthermore, the so-called Markov-assumption, which prescribes that transition probabilities depend only on the current state, is often unrealistic in practice.
An efficient way of dealing with these two problems is to allow for partially specified parameters, using the theory of imprecise probabilities, while at the same time dropping the Markov assumption and replacing it with a more realistic alternative. In the recent past, this idea has led to the successful development of so-called imprecise Markov chains.
This project is concerned with imprecise hidden Markov chains, which are imprecise Markov chains of which the state evolution can only be observed indirectly through noisy measurements.
This project has four main objectives
1) To study the mathematical properties of imprecise hidden Markov chains, both in continuous and discrete time, and to exploit the obtained results to design efficient inference algorithms for them. Typical inference problems that will be considered will consist in using noisy observations to make predictions about the future behaviour of the system, where `behaviour’ may refer to the state-evolution itself, but also to the time it will take for the system to reach a given state, or the time the system will remain in a given state.
2) To develop efficient and reliable methods for estimating the parameters of imprecise hidden Markov chains from data, expert knowledge, or a combination of both. Since the system itself cannot be observed directly, this is clearly a challenging task. Initial ideas can take inspiration from existing precise-probabilistic methods such as the expectation-maximisation algorithm. However, given the more general imprecise-probabilistic context that we consider, new methods will surely need to be developed as well.
3) To implement the obtained inference algorithms and estimation methods, thereby creating a piece of software that (a) can construct imprecise hidden Markov chains from data and/or expert knowledge and (b) can efficiently compute various types of inferences for them.
4) To apply the proposed methodology and software to a tracking problem in aerospace transportation, in close collaboration with the project partners that will host the applicant during his or her secondments (these will be Strathclyde and Durham University; see below for more information)
The applicant must not hold a PhD at the time of the start of the contract and have less than four years of experience in research. Furthermore, at the time of recruitment by the host organisation, the applicant must not have resided or carried out their main activity (work, studies, etc.) in Belgium for more than 12 months in the 3 years immediately prior to the recruitment. Additional information can be found at the website utopiae.eu.
Instructions for applicants can be found on the UTOPIAE website (utopiae.eu), which directs all interested applicants to submit a CV, a cover letter and two letters of reference. Each applicant can apply for a maximum of 2 posts within the UTOPIAE network, and must indicate their order of preference. All applications should be sent to email@example.com.
In the context of the planned secondments, the applicant will also be temporarily based in the following two institutions:
- Strathclyde University, Glasgow, Scotland, UK, for 3 months, to test the proposed inference algorithms on multisensory tracking and vehicle tracking with FSS.
- Durham University, Durham, England, UK, for 3 months, to work on evolvable optimisation under uncertainty.
Web site for additional job details
REQUIRED EDUCATION LEVELEngineering: Master Degree or equivalentComputer science: Master Degree or equivalentMathematics: Master Degree or equivalent
REQUIRED LANGUAGESENGLISH: Excellent
The candidate should have a research background in probabilistic modelling and be able to demonstrate experience with programming. The candidate should also be confident and enthusiastic about the project and must be able to work both independently and as part of a team.
The ideal candidate can demonstrate previous experience with stochastic processes, imprecise probability methods, software development or algorithm design and has scientific publications.
EURAXESS offer ID: 182119