Dr Arthur Guillaumin

Profile

I am a lecturer in Mathematical Data Science at Queen Mary University of London. I studied in France my masters, after which I pursued a PhD under the supervision of Pr Sofia C. Olhede and Dr Adam M. Sykulski, at the Department of Statistical Science of University College London. I then held a postdoctoral position for two years with the same supervisors, following which I moved to a postdoctoral position at New York University under the supervision of Pr Laure Zanna.

Research

Research Interests:

From a methodological aspect, my main research interest is to develop new parametric models for spatio-temporal data that can represent the complexity of real-world phenomena. At the same time, I am interested in developing estimation methods for these models that offer a trade-off between computational and statistical efficiency.

I am also interested in Deep Learning, in particular when it is used to infer the parameters of a distribution rather than a point prediction.

From an application point of view, being a data scientist means being able to apply new methods to a variety of fascinating fields and being able to collaborate with real scientists! I collaborate with oceanographers, geoscientists, and neuroscientists. I plan to pursue new collaborations in astronomy (in particular for the discovery of exoplanets and spectral analysis of their atmosphere).

For an example of some recent work, please take a look here.

Dissemination

I currently have a PhD project for interested students:

Big environmental data combined with modern data science offer a key opportunity to better understand our environment and address climate change. Yet environmental data poses specific challenges due to spatio-temporal dependence: 1. Modelling. Most models of spatio-temporal dependence are homogenous, which in general is not an accurate description of real-world phenomena. 2. Estimation. More complex parametric models of covariance are often not amenable to estimation via exact likelihood due to computational inefficiency and lack of robustness to model misspecification.  

In this project, you will develop new parametric covariance models and estimation methods for the analysis of Sea Surface Height (SSH). The surface height of the oceans is monitored by passing satellites on a global scale. The modelling of SSH is vital to a better understanding of the global climate and to making more accurate interpolation via kriging [1]. 

Firstly, your research will focus on estimating the parameters of a spatial covariance model of Sea Surface Height. You will pursue recent developments in quasi-likelihood estimation [2, 3, 4, 5, 6] for spatio-temporal data to propose a parametric estimation method that is both computationally and statistically efficient. The idea behind quasi-likelihood estimation is to maximize a computationally efficient approximation to the exact likelihood. 

Secondly, you will develop more advanced parametric models of covariance that can incorporate some additional physical phenomena that drive SSH. Possible directions for this part of the project range from relaxing the assumption of spatial homogeneity [7], to modelling temporal dependence and seasonal patterns [8]. These methodological developments can also have an impact in other application areas such as econometrics. 

This project will be in collaboration with C. Wortham and J. Early, NorthWest Research Associates, Seattle, USA, who have been granted funding by the NASA to develop mapping software for SSH. 

References 

1. Stein, M. L. (1999). Interpolation of Spatial Data: Some Theory for Kriging. 1st ed., Springer Series in Statistics, Springer. 
2. Sykulski A. M., Olhede S. C., Guillaumin A. P., Lilly J. M., Early J. J (2019). The Debiased Whittle Likelihood. Biometrika 106(2), 251–266. 
3. Guillaumin A. P., Sykulski A. M., Olhede S. C., Simmons F. V. (2022). The Debiased Spatial Whittle Likelihood. Journal of the Royal Statistical Society: Series B (under review). 
4. Guinness J. (2018). Permutation and Grouping Methods for Sharpening Gaussian Process Approximations. Technometrics 1706, 1-15. 
5. Guinness J, Fuentes M. (2017). Circulant Embedding of Approximate Covariances for Inference from Gaussian Data on Large Lattices. Journal of Computational and Graphical Statistics 26(1), 88-97.  
6. Fuentes M. (2007). Approximate likelihood for large irregularly spaced spatial data. Journal of the American Statistical Association 102(477), 321-331. 
7. Matsuda, Y., Yajima, Y. (2018). Locally stationary spatio-temporal processes. Japanese Journal of Statistics and Data Science 1, 41–57. 
8. Napolitano A. (2016). Cyclostationarity: New trends and applications. Signal Processing 120, 385-408.