Signal Detection for Medical Scientists: Likelihood Ratio Based Test-Based Methodology presents the data mining techniques with focus on likelihood ratio test (LRT) based methods for signal detection. It emphasizes computational aspect of LRT methodology and is pertinent for first-time researchers and graduate students venturing into this interesting field. The book is written as a reference book for professionals in pharmaceutical industry, manufactures of medical devices, and regulatory agencies. The book deals with the signal detection in drug/device evaluation, which is important in the post-market evaluation of medical products, and in the pre-market signal detection during clinical trials for monitoring procedures. It should also appeal to academic researchers, and faculty members in mathematics, statistics, biostatistics, data science, pharmacology, engineering, epidemiology, and public health. Therefore, this book is well suited for both research and teaching. Key Features: Includes a balanced discussion of art of data structure, issues in signal detection, statistical methods and analytics, and implementation of the methods. Provides a comprehensive summary of the LRT methods for signal detection including the basic theory and extensions for varying datasets that may be large post-market data or pre-market clinical trial data. Contains details of scientific background, statistical methods, and associated algorithms that a reader can quickly master the materials and apply methods in the book on one's own problems

This book presents recent results on nonlinear parabolic-hyperbolic coupled systems such as the compressible Navier-Stokes equations, and liquid crystal system. It summarizes recently published research by the authors and their collaborators, but also includes new and unpublished material. All models under consideration are built on compressible equations and liquid crystal systems. This type of partial differential equations arises not only in many fields of mathematics, but also in other branches of science such as physics, fluid dynamics and material science.