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Statistical machine learning for efficient and reliable estimation in computationally intensive systems

  • Full or part time
  • Application Deadline
    Sunday, December 08, 2019
  • Competition Funded PhD Project (European/UK Students Only)
    Competition Funded PhD Project (European/UK Students Only)

Project Description

A computationally intensive Industrial process is sometimes considered and modelled as a black-box system, for which one can only observe/analyse system’ inputs and outputs but with very limited knowledge of its internal mechanism. Real-world applications such as climate forecasting in earth science, cancer modelling and simulation in biomedical diagnostics, wind tunnel simulation in aircraft manufacturing, and social network analysis in social science can all be classified as black-box systems. Practitioners often design complex computer-based models to emulate such systems to perform data analytic tasks, e.g., unknown parameter estimation, decision making, or risk management. The efforts of performing an accurate numerical analysis are often affected by issues such as complicated temporal correlation in noise, curse of dimensionality, and long algorithm runtime, etc.

However, for some complex models, the likelihood function can be analytically intractable or computationally expensive to be evaluated. Traditional solutions often employ deterministic estimation methods which can easily lead to deterministic suboptimal solutions. Efficient probabilistic solutions (with reliable parameter estimation and uncertainty quantification) are desirable, and of great interest to practitioners across various industrial sectors.

Statistical computational methods, such as Approximate Bayesian computation (ABC) [1], addresses this issue by broadening the model range and estimating posterior distribution by performing a series of carefully designed Monte Carlo simulations. Meanwhile, surrogate learning methods [2] bypass this problem by constructing surrogate models (or emulator) as the forward model within the Bayesian sampling framework.

The Ph.D. project aims to address the above challenge by using state-of-the-art statistical machine learning / deep learning techniques. This might involve development of novel algorithms and models for efficient parameter estimation in interdisciplinary applications; quantitative assessment of risk and uncertainty in such Artificial Intelligence assisted estimation system; and probabilistic model selection for strategic level decision making, etc.

The outcome of this project is expected to improve the efficiency and reliability of parameter estimation and decision-making process for complex industrial applications. The project will also contribute to the exploration of how AI affects the process of real-world interdisciplinary applications in both the risk assessment and policy-making aspects.


Applicants should hold, or expect to receive, a First Class or good Upper Second Class Honours degree in Statistics, Computer Science, Mathematics, Information Engineering, or a closely related discipline. A master level qualification would be an advantage. Good programming skills, or good statistical background is a plus. Prior knowledge in machine learning is desirable, but not required. Non-UK applicants must meet our English language entry requirement


Informal enquiries should be directed to Dr Xi Chen, email address .

Formal applications should be made via the University of Bath’s online application form:

Please ensure that you quote the supervisor’s name and project title in the ‘Your research interests’ section.

More information about applying for a PhD at Bath may be found here:

Anticipated start date: 28 September 2020.

Funding Notes

UK and EU candidates applying for this project will be considered for a University Research Studentship which will cover UK/EU tuition fees, a training support fee of £1,000 per annum and a tax-free maintenance allowance at the UKRI Doctoral Stipend rate (£15,009 in 2019-20) for a period of up to 3.5 years.


[1] Toni, T., Welch, D., Strelkowa, N., Ipsen, A. and Stumpf, M.P., 2008. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. Journal of the Royal Society Interface, 6(31), pp.187-202.

[2] Chen, X. and Hobson, M., 2019. Bayesian surrogate learning in dynamic simulator-based regression problems. arXiv preprint arXiv:1901.08898.

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