Intended audience and distinguishing features

This is a textbook intended for an introductory course in probability theory and statistical inference, written for students who have had at least a semester course in calculus. The additional mathematics needed are coalesced into the discussion to make it self contained, paying particular attention to the intuitive understanding of the mathematical concepts. No prerequisites in probability and statistical inference are required but some familiarity with descriptive statistics will be of value.

The primary objective of this book is to lay the foundations and assemble the over arching framework for the empirical modeling of observational (non-experimental) data. This framework, known as probabilistic reduction, is formulated with a view to accommodating the peculiarities of observational (as opposed to experimental) data in a unifying and logically coherent way. It differs from traditional textbooks in so far as it emphasizes concepts, ideas, notions, and procedures which are appropriate for modeling observational data.

The primary intended audience of this book includes interested undergraduate and graduate students of econometrics as well as practicing econometricians who have been trained in the traditional textbook approach. Special consideration has been given to the needs of those using the textbook for self-study. This text can also be used by students of other disciplines, such as biology, sociology, education, psychology, and climatology, where the analysis of observational data is of interest.

The traditional statistical literature over the last 50 years or so, has focused, almost exclusively, on procedures and methods appropriate for the analysis of experimental type (experimental and sample survey) data.