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Metric-based summary statistics such as mean and covariance have beenintroduced in neural spike train space. They can properly describe template andvariability in spike train data, but are often sensitive to outliers andexpensive to compute. Recent studies also examine outlier detection andclassification methods on point processes. These tools provide reasonable andefficient result, whereas the accuracy remains at a low level in certain cases.In this study, we propose to adopt a well-established notion of statisticaldepth to the spike train space. This framework can naturally define the medianin a set of spike trains, which provides a robust description of the 'center'or 'template' of the observations. It also provides a principled method toidentify 'outliers' in the data and classify data from different categories. Wesystematically compare the median with the state-of-the-art 'mean spike trains'in terms of robustness and efficiency. The performance of our novel outlierdetection and classification tools will be compared with previous methods. Theresult shows the median has superior description for 'template' than the mean.Moreover, the proposed outlier detection and classification perform moreaccurately than previous methods. The advantages and superiority are wellillustrated with simulations and real data.

Depth-Based Statistical Inferences in the Spike Train Space