The analysis of neural data from the brain, and in particular the hippocampus, which plays an active role in learning and memory, presents multiple statistical challenges. First of all, neurons communicate via stereotyped electrical impulses, or spikes, that are localized in time, and are most appropriately described by point processes. These spikes may be related to a multitude of continuous-valued or discrete biological and behavioral signals. Finally, new technologies allow simultaneous recording from hundreds of neurons. Establishing stochastic models relating thee signals requires principled statistical methods.

In this thesis, we establish a statistical modeling, estimation and hypothesis testing framework for hippocampal neural spiking data, based on point process theory. The fundamental component of this framework lies in the construction of a probability model based on the conditional intensity function (CIF), which uniquely characterizes a point process. We express the CIF as a function of biological and behavioral covariates that influence neural spiking. This allows us to compute likelihoods, fit models, and perform goodness-of-fit analyses. We develop a hypothesis-testing framework based on the fit models, and build sampling distributions for the test statistics. Finally, we develop adaptive estimation algorithms to reconstruct and predict behavior from spiking data.

We apply this framework to the analysis of spiking data from rat hippocampus, while the animal performed a spatial-navigation task on a T-shaped maze. We apply the point process estimation algorithm to reconstruct the animal's movement through the maze and predict future turn directions. We employ the hypothesis-testing framework to compare firing activity preceding different turn directions. Finally, we investigate the statistical relationship of spiking data to oscillatory neural rhythms. These analyses provide a deeper understanding of how the hippocampus maintains representations of spatial signals during memory related tasks.