Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Symbols
- Acronyms
- 1 An introduction to empirical modeling
- 2 Probability theory: a modeling framework
- 3 The notion of a probability model
- 4 The notion of a random sample
- 5 Probabilistic concepts and real data
- 6 The notion of a non-random sample
- 7 Regression and related notions
- 8 Stochastic processes
- 9 Limit theorems
- 10 From probability theory to statistical inference*
- 11 An introduction to statistical inference
- 12 Estimation I: Properties of estimators
- 13 Estimation II: Methods of estimation
- 14 Hypothesis testing
- 15 Misspecification testing
- References
- Index
2 - Probability theory: a modeling framework
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Symbols
- Acronyms
- 1 An introduction to empirical modeling
- 2 Probability theory: a modeling framework
- 3 The notion of a probability model
- 4 The notion of a random sample
- 5 Probabilistic concepts and real data
- 6 The notion of a non-random sample
- 7 Regression and related notions
- 8 Stochastic processes
- 9 Limit theorems
- 10 From probability theory to statistical inference*
- 11 An introduction to statistical inference
- 12 Estimation I: Properties of estimators
- 13 Estimation II: Methods of estimation
- 14 Hypothesis testing
- 15 Misspecification testing
- References
- Index
Summary
Introduction
Primary aim
The primary objective of this and the next several chapters is to introduce probability theory not as part of pure mathematics but as a mathematical framework for modeling certain observable phenomena which we call stochastic: phenomena that exhibit chance regularity (see chapter 1). Center stage in this modeling framework is given to the notion of a statistical model. This concept is particularly crucial in modeling observational (non-experimental) data. The approach adopted in this book is that the mathematical concepts underlying the notion of a statistical model are motivated by formalizing a generic simple stochastic phenomenon we call a random experiment. An example of such a phenomenon is that of “counting the number of calls arriving in a telephone exchange, over a certain period of time.” The formalization (mathematization) of this generic stochastic phenomenon will motivate the basic constituent elements that underlie the notion of a statistical model and provide the foundation for a broader framework in the context of which empirical modeling takes place.
Why do we care?
The first question we need to consider before we set out on the long journey to explore the theory of probability as a modeling framework is:
Why do we care about probability theory?
The answer in a nutshell is that it provides both the foundation and the frame of reference for data modeling and statistical inference.
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- Chapter
- Information
- Probability Theory and Statistical InferenceEconometric Modeling with Observational Data, pp. 31 - 76Publisher: Cambridge University PressPrint publication year: 1999
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