Introduction

This introductory chapter gives an overview of the key concepts discussed in the subsequent chapters of this book. The objective of statistical inference is to draw conclusions about the study population following the sampling of observations. The book presents HGLMs, a class of statistical models that allow flexible modeling of data from a wide range of applications and we describe the theory for their inferences. Further it presents the methods of statistical testing based on HGLMs and prediction problems which can be tackled by this class. It also describes extensions of classical HGLMs in various ways with a focus on dispersion modeling. The book covers statistical models and likelihood-based inferences for various problems. GLMs have been widely used in practice, based on classical likelihood theory. In close connection to the development of the h-likelihood, terminology has been used where a number of different likelihoods have been referred to.