In this paper, we present a sequence classifier for detecting host intrusions from long process system call sequences . The proposed classifier (called SC2.2) is a naïve Bayes classifier that builds class conditional probabilities from Markov modeling of system call sequences. We describe the proposed classifier, and then provide experimental results o n the widely used University of New Mexico ’s system call trace data sets. The r esults of our proposed classifier are benchmarked against leading classifiers, namely naive Bayes multinomial, C4.5 decision tree , RIPPER, support vector machine , and logistic regression. A key feature of the proposed classifier is its ability to handle efficiently arbitrarily long sequences , and zero transitional probabilities in the modeled Markov chain, by using a ―test, backtrack, scale and remultiply‖ technique, and using the m-estimate of conditional probabilities . Furthermore, it capitalizes on IEEE standard for floating-point arithmetic error specification to return classification confidence. Results show that the proposed classifier yields a better performance than standard classifiers on most datasets used.