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PhD Studentship in Inference for distributed likelihoods

Value of award

100% of home tuition fees paid and annual living expenses of £15,609. We will consider covering the international fees for outstanding students and where possible.

Number of awards


Start date and duration

42 months from September 2021.

Application closing date

7 May 2021.


A problem arising in statistical inference is unifying distributed analyses and inferences on shared parameters from multiple sources, into a single coherent inference. This "unification problem" can arise explicitly due to the nature of a particular application (eg meta-analysis), or artificially as a consequence of the approach taken (eg distributed `big data'). Typically there is no closed form analytical approach to unifying inferences. We take a Monte Carlo approach: representing the distribution induced by the unified inferences using randomness. The "Monte Carlo Fusion" methodology introduced in [Dai et al., 2019], is one recent approach for doing this.

This project will look at extending this approach to practical applications. One particular on-going direction is in Statistical Cryptography. In the simplest setting we will have a number of trusted parties who wish to securely share their distributional information on a common parameter space and model, but would prefer not to reveal their individual level distributions. This is a problem recently considered by [Yildirim and Ermi s, 2019], which corrupts the likelihood with noise to construct a number of serially correlated draws from the distribution, and then considers the ramifications of this within the framework of differential privacy [Dwork et al., 2006]. However, it is possible to use other cryptographic techniques such as Homomorphic Secret Sharing (HSS) [Shamir, 1979] as an alternative to corrupting the likelihood within the Monte Carlo Fusion framework.

The direction of this project will depend on the student. It could be: developing the underpinning statistical theory and methodology; considering privacy in other settings (eg untrusted parties); developing and applying cryptographic techniques in statistical settings. It would be advantageous to have some aptitude for programming. It is strongly recommended to contact Murray Pollock for further information before application.


EPSRC / School of Mathematics, Statistics and Physics

Name of supervisor(s)

Murray Pollock (Alan Turing Institute / Newcastle University). Email:

Eligibility Criteria

This studentship is available to all candidates who have/expect a 2:1 honours degree in computing science, mathematics, physics, statistics or another strongly quantitative discipline, or an international equivalent.

If English is not your first language, you must have IELTS 6.5 overall (with a minimum of 5.5 in all sub-skills).

The award is available to home and international applicants.

How to apply

You must apply through the University’s online postgraduate application system.



Dr Murray Pollock (

Eligible Courses