This PhD position is at the interface of computational statistics and Bayesian inference, motivated by applications ranging from ecology to engineering. The successful applicant will be supervised by Prof. Ruth King and Dr. Victor Elvira. Further collaborations may also develop as the project progresses.
Many problems across different scientific domains can be described through statistical models that describe the observed longitudinal data as a combination of an underlying (unobserved) latent process, and an associated observation process which area function of unknown model parameters. These models are often called state-space models (SSMs). In the simple linear and Gaussian SSM, the observed data likelihood is available in closed form via the Kalman filter. However, for more complex and often realistic models the likelihood is analytically intractable, and inference becomes more difficult and computationally intensive. Traditional approaches for fitting such models to data include the use of approximate likelihood approaches or Monte Carlo methods including Bayesian data augmentation schemes and/or importance Sampling (IS)-based algorithms.
In this project, we will develop novel Monte Carlo methods for Bayesian inference in complex systems (high-dimensional, large amount of data, non-linear non-Gaussian relations, with model misspecification, etc). We will depart from making simplifying linear and/or Gaussian approximations in the system and/or observation processes that allow us to adapt existing closed-form solutions (e.g. Kalman filtering), and design new Monte Carlo algorithms that are asymptotically exact. These new generation of algorithms will combine the efficiency of the closed-form solutions with the flexibility of specifying complex systems.
Candidate profile:
Essential:
– A Bachelor’s degree in Engineering, Statistics, Mathematics, Computer Science, Physics or similar
(a First Class or good Upper Second Class Honours degree, or the equivalent from an overseas
university);
– Programming ability in high-level scientific development language, e.g., R, Python, MATLAB;
– Experience in Bayesian inference and/or Monte Carlo methods;
– Strong verbal and written communication skills in English;
– High motivation, curiosity and proactivity.
Desirable:
– A Master’s degree in a relevant subject;
– Experience of working in a research environment and/or prior publications.
Application Procedure:
A formal application for this project can be made here: https://www.ed.ac.uk/studying/postgraduate/degrees/index.php?r=site/view&edition=2020&id=516
You are advised to contact the supervisor before applying, although this is not essential.
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