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Statistical modelling of grid-cell firing using log-Gaussian Cox processes through the SPDE approach

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  • Full or part time
    Dr Ioannis Papastathopoulos
    Prof Finn Lindgren
  • Application Deadline
    No more applications being accepted
  • Competition Funded PhD Project (European/UK Students Only)
    Competition Funded PhD Project (European/UK Students Only)

Project Description

One of the most important unsolved problems in science today is to understand the codes that neurons in our brains use to communicate with one another and, collectively, to generate phenomena such as perception and cognition. Currently, approaches to this problem are limited by our ability to analyze neural codes. Grid cells (Hafting et al. 2005) are nerve cells in the entorhinal cortex that represent the location of an animal in its environment and, in combination with place cells, form a coordinate system that allows spatial navigation and learning of maps of the world (Moser et al. 2017). There are many open problems in this area that are related to accurate identification of covariate effects on the patterns of grid-cell firing and include an opportunity to develop new statistical methodology for point processes. This project will look at developing novel methods for the statistical modelling of neural firing based on the class of log-Gaussian Cox processes. The methods will be based on the SPDE (Lindgren et al. 2011, Simpson et al. 2016) approach to Gaussian Fields and will facilitate spatial, temporal and directional covariate effects on the intensity of grid-cell point patterns. This methodology will provide a key basis for understanding and quantifying the grid-field and more importantly for investigating how additional information can be multiplexed within the grid representation.

Entry requirements:
Essential:
• A Bachelor’s degree in Computer Science, Engineering, Statistics, Mathematics, Physics or similar (a First Class or good Upper Second Class Honours degree, or the equivalent from an overseas university);
• Experience in statistics, probability and data analysis;
• Programming ability in high-level scientific development language, e.g. Python, R, Matlab;
• Strong verbal and written communication skills in English.

Desirable:
• Mathematical maturity with emphasis on estimation and inference;
• Expertise in Bayesian methods;
• A Master’s degree with prior publications in statistics.

Funding Notes

This project is funded by a scholarship which fully covers the cost of tuition fees and provides an annual stipend. This scholarship is only open to UK and EU students.

You are advised to contact the supervisor before applying, although this is not essential.

References

Hafting, T., Fyhn, M., Molden, S., Moser, M.-B. & Moser, E. I. (2005), ‘Microstructure of a spatial map in the entorhinal cortex’, Nature 436(7052), 801.
Lindgren, F., Rue, H. & Lindström, J. (2011), ‘An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach (with discussion)’, J. Roy. Statist. Soc., B 73(4), 423–498.
Moser, E. I., Moser, M.-B. & McNaughton, B. L. (2017), ‘Spatial representation in the hippocampal formation: a history’, Nature Neuroscience 20(11), 1448–1464.
Simpson, D., Illian, J. B., Lindgren, F., Sø rbye, S. H. & Rue, H. (2016), ‘Going off grid: computationally efficient inference for log-Gaussian Cox processes’, Biometrika 103(1), 49–70



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