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.

翻译：大脑对信息的编码要求统计框架来推断神经元发射和世界特征之间的关系。Grid Cell 的重要发现证明了神经元可以通过定期重复的发射场来表示空间信息。然而，当前的 Grid Cell 模型可能掩盖了协变量的影响，这些模型通过离散化、聚合或平滑的方法来实施，这些方法计算效率低，也不能充分考虑物理世界的连续性。这些限制促使我们开发了基于似然的过程，用于在生物学上相关的协变量条件下建模和估计 Grid Cell 的发射活动。我们的方法使用带有潜在高斯效应的 Poisson 点过程来建模发射活动，这些效应可以容纳持久的不均匀空间定向模式和过离散化。我们以完全贝叶斯方法来进行推断，这使我们能够量化不确定性。通过将这些方法应用于实验数据，我们提供了时间和局部头向对 Grid 发射的影响的证据。我们的方法为分析空间的神经表示提供了一种新的和原则性的框架。