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：关于大脑编码信息的问题需要统计框架来推断神经放电与世界特征之间的关系。网格细胞的里程碑式发现表明，神经元可通过规则重复的放电野来表征空间信息。然而，在现有的网格细胞活动统计模型中，协变量的影响可能被掩盖。这类模型采用离散化、聚合和平滑等方法，不仅计算效率低下，而且未能考虑物理世界的连续性本质。这些局限性促使我们开发基于似然的方法，用于在生物相关协变量条件下建模和估计网格细胞的放电活动。我们的方法采用带潜在高斯效应的泊松点过程来建模放电活动，能够处理持续存在的非均匀空间-方向模式及过度离散现象。推断过程采用完全贝叶斯方法，从而能够量化不确定性。将这些方法应用于实验数据后，我们提供了时间与局部头部方向对网格放电影响的证据。我们的方法为分析空间的神经表征提供了一个新颖且规范化的框架。