# Probability Theory and Statistical Inference: Econometric Modeling with Observational Data

# Probability Theory and Statistical Inference: Econometric Modeling with Observational Data

## Synopsis

## Excerpt

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 selfcontained, 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 overarching 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 **experimentaltype** (experimental and sample survey) **data**. the traditional modeling framework has been that of the *experimental design* tradition, as molded by Fisher (1935) (and formulated by the sample survey literature of the 1940s and 1950s), and the "curve fitting" perspective of the *least-squares* tradition. Both of these traditions presume a modeling framework in the context of which the observed data are interpreted as a realization of an observable phenomenon which can be realistically viewed as a *nearly isolated* (by divine or human intervention) system; see Spanos (1995b). This book purports to redress (somewhat) the balance by expounding a modeling framework appropriate for observational data. This modeling framework can be viewed in the spirit of the . . .