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Questions about information encoded by the brain demand statisticalframeworks for inferring relationships between neural firing and features ofthe world. The landmark discovery of grid cells demonstrates that neurons canrepresent spatial information through regularly repeating firing fields.However, the influence of covariates may be masked in current statisticalmodels of grid cell activity, which by employing approaches such asdiscretizing, aggregating and smoothing, are computationally inefficient and donot account for the continuous nature of the physical world. These limitationsmotivated us to develop likelihood-based procedures for modelling andestimating the firing activity of grid cells conditionally on biologicallyrelevant covariates. Our approach models firing activity using Poisson pointprocesses with latent Gaussian effects, which accommodate persistentinhomogeneous spatial-directional patterns and overdispersion. Inference isperformed in a fully Bayesian manner, which allows us to quantify uncertainty.Applying these methods to experimental data, we provide evidence for temporaland local head direction effects on grid firing. Our approaches offer a noveland principled framework for analysis of neural representations of space.

Bayesian inference of grid cell firing patterns using Poisson point process models with latent oscillatory Gaussian random fields