  In this paper, we explore various statistical techniques for anomaly
detection in conjunction with the popular Long Short-Term Memory (LSTM) deep
learning model for transportation networks. We obtain the prediction errors
from an LSTM model, and then apply three statistical models based on (i) the
Gaussian distribution, (ii) Extreme Value Theory (EVT), and (iii) the Tukey's
method. Using statistical tests and numerical studies, we find strong evidence
against the widely employed Gaussian distribution based detection rule on the
prediction errors. Next, motivated by fundamental results from Extreme Value
Theory, we propose a detection technique that does not assume any parent
distribution on the prediction errors. Through numerical experiments conducted
on several real-world traffic data sets, we show that the EVT-based detection
rule is superior to other detection rules, and is supported by statistical
evidence.
