Discrete probability distributions with probability mass function given by: . Modified power series distribution (MPSD) are more general distributions which arise when ? is a function of another (simple) parameter. In such a case we define the power parameter ? ( m ) and series function ? ( ? ) by: .Particular choices of the power parameter render power distributions that are analytic approximations to Maximum Entropy priors over finite domains.
Published in Chapter:
Uncovering Fine Structure in Gene Expression Profile by Maximum Entropy Modeling of cDNA Microarray Images and Kernel Density Methods
George Sakellaropoulos (University of Patras, Greece), Antonis Daskalakis (University of Patras, Greece), George Nikiforidis (University of Patras, Greece), and Christos Argyropoulos (University of Pittsburgh Medical Center, USA)
Copyright: © 2009
|Pages: 18
DOI: 10.4018/978-1-60566-076-9.ch012
Abstract
The presentation and interpretation of microarray-based genome-wide gene expression profiles as complex biological entities are considered to be problematic due to their featureless, dense nature. Furthermore microarray images are characterized by significant background noise, but the effects of the latter on the holistic interpretation of gene expression profiles remains under-explored. We hypothesize that a framework combining (a) Bayesian methodology for background adjustment in microarray images with (b) model-free modeling tools, may serve the dual purpose of data and model reduction, exposing hitherto hidden features of gene expression profiles. Within the proposed framework, microarray image restoration and noise adjustment is facilitated by a class of prior Maximum Entropy distributions. The resulting gene expression profiles are non-parametrically modeled by kernel density methods, which not only normalize the data, but facilitate the generation of reduced mathematical descriptions of biological variability as mixture models.