In today's fast paced computing world security is a main concern. Intrusion detection systems are an important component of defensive measures protecting computer systems and networks from abuse. This paper will examine various intrusion detection systems. The task of intrusion detection is to monitor usage of a system and detect and malicious activity, therefore, the architecture is a key component when studying intrusion detection systems. This thesis will also analyze various neural networks for statistical anomaly intrusion detection systems. The thesis will focus on the Hierarchical Intrusion Detection system (HIDE) architecture. The HIDE system detects network based attack as anomalies using statistical preprocessing and neural network classification. The thesis will conclude with studies conducted on the HIDE architecture. The studies conducted on the HIDE architecture indicate how the hierarchical multi-tier anomaly intrusion detection system is an effective one.