  Questions about information encoded by the brain demand statistical
frameworks for inferring relationships between neural firing and features of
the world. The landmark discovery of grid cells demonstrates that neurons can
represent spatial information through regularly repeating firing fields.
However, the influence of covariates may be masked in current statistical
models of grid cell activity, which by employing approaches such as
discretizing, aggregating and smoothing, are computationally inefficient and do
not account for the continuous nature of the physical world. These limitations
motivated us to develop likelihood-based procedures for modelling and
estimating the firing activity of grid cells conditionally on biologically
relevant covariates. Our approach models firing activity using Poisson point
processes with latent Gaussian effects, which accommodate persistent
inhomogeneous spatial-directional patterns and overdispersion. Inference is
performed in a fully Bayesian manner, which allows us to quantify uncertainty.
Applying these methods to experimental data, we provide evidence for temporal
and local head direction effects on grid firing. Our approaches offer a novel
and principled framework for analysis of neural representations of space.
