Interval Length Analysis in Multi Layer Model

In this paper we present an hypothesis test of randomness based on the probability density function of the symmetrized Kulback-Leibler distance estimated, via a Monte Carlo simulation, by the distributions of the interval lengths detected using the Multi-Layer Model (MLM). The $MLM$ is based on the generation of several sub-samples of an input signal; in particular a set of optimal cut-set thresholds are applied to the data to detect signal properties. In this sense MLM is a general pattern detection method and it can be considered a preprocessing tool for pattern discovery. At the present the test has been evaluated on simulated signals which respect a particular tiled microarray approach used to reveal nucleosome positioning on Saccharomyces cerevisiae; this in order to control the accuracy of the proposed test of randomness. It has been also applied to real biological data. Results indicate that such statistical test may indicate the presence of structures in the signal with low signal to noise ratio.