| We are in an era of information revolution where it is hard to find a manufacturing or service enterprise that isn't collecting large amounts of data about their day to day operations and the complexity of such databases is increasing at an unprecedented rate. In this thesis, I have been interested in building statistical modeling and inference tools for various complex data-sets and utilize these tools to quickly detect deterioration in the system from which the data is collected. In this thesis we present various statistical monitoring methods for such complex data types. They are discussed below:;(i) Monitoring multivariate count data and multi-stream binary data: We develop a statistical monitoring method for multiple binary data stream that should accommodate for over-dispersion in the data. In statistical monitoring of multivariate count data, we study a model that accounts not only for over-dispersion but also for correlation among various variables.;(ii) Maximum entropy density estimation methods for statistical monitoring: Information theoretic measures like Shannon's entropy are a measure of uncertainty in data, which can be viewed as inverse of information content in the data. We develop a statistical monitoring scheme that is based on fitting the density function that is least committal, i.e. the maximum entropy density function.;Also, in many applications involving categorical data, a degradation in the system from which the data is collected is reflected by an increase in entropy of the data. We formulate the problem of estimating the maximum entropy distribution from a test categorical data sample and developed statistical monitoring methods based on it.;(iii) Extracting nonlinear invariant measures from time series data: Recently data driven methods are being adopted in developing technologies when it is hard to understand the underlying process from first principles. In order to analyze the data we extracted various non-linear measures such as sample entropy, correlation dimension and Lyapunov's exponent from the signal. These non-linear metrics are based on principles of information theory and non-linear dynamics. They condense the rich information content of the complex signals. |
