Book contents
- Frontmatter
- Contents
- Preface
- PART I INTRODUCTION
- 1 The meaning of ‘probability’
- 2 Basic definitions for frequentist statistics and Bayesian inference
- 3 Bayesian inference
- 4 Combinatorics
- 5 Random walks
- 6 Limit theorems
- 7 Continuous distributions
- 8 The central limit theorem
- 9 Poisson processes and waiting times
- PART II ASSIGNING PROBABILITIES
- PART III PARAMETER ESTIMATION
- PART IV TESTING HYPOTHESES
- PART V REAL-WORLD APPLICATIONS
- PART VI PROBABILISTIC NUMERICAL TECHNIQUES
- Appendix A Mathematical compendium
- Appendix B Selected proofs and derivations
- Appendix C Symbols and notation
- References
- Index
1 - The meaning of ‘probability’
from PART I - INTRODUCTION
Published online by Cambridge University Press: 05 July 2014
- Frontmatter
- Contents
- Preface
- PART I INTRODUCTION
- 1 The meaning of ‘probability’
- 2 Basic definitions for frequentist statistics and Bayesian inference
- 3 Bayesian inference
- 4 Combinatorics
- 5 Random walks
- 6 Limit theorems
- 7 Continuous distributions
- 8 The central limit theorem
- 9 Poisson processes and waiting times
- PART II ASSIGNING PROBABILITIES
- PART III PARAMETER ESTIMATION
- PART IV TESTING HYPOTHESES
- PART V REAL-WORLD APPLICATIONS
- PART VI PROBABILISTIC NUMERICAL TECHNIQUES
- Appendix A Mathematical compendium
- Appendix B Selected proofs and derivations
- Appendix C Symbols and notation
- References
- Index
Summary
Probability theory has a long, eventful, and still not fully settled history. As pointed out in [63]: ‘For all human history, people have invented methods for coming to terms with the seemingly unpredictable vicissitudes of existence … Oracles, amulets, and incantations belonged to the indispensable techniques for interpreting and influencing the fate of communities and individuals alike … In the place of superstition there was to be calculation — a project aiming at nothing less than the rationalization of fortune. From that moment on, there was no more talk of fortune but instead of this atrophied cousin: chance.’
The only consistent mathematical way to handle chance, or rather probability, is provided by the rules of (Bayesian) probability theory. But what does the notion ‘probability’ really mean? Although it might appear, at flrst sight, as obvious, it actually has different connotations and definitions, which will be discussed in the following sections.
For the sake of a smooth introduction to probability theory, we will forego a closer definition of some technical terms, as long as their colloquial meaning suffices for understanding the concepts. A precise definition of these terms will be given in a later section.
Classical definition of ‘probability’
The first quantitative definition of the term ‘probability’ appears in the work of Blaise Pascal (1623–1662) and Pierre de Fermat (1601–1665). Antoine Gombauld Chevalier de Mere, Sieur de Baussay (1607–1685) pointed out to them that ‘…mathematics does not apply to real life’.
- Type
- Chapter
- Information
- Bayesian Probability TheoryApplications in the Physical Sciences, pp. 3 - 14Publisher: Cambridge University PressPrint publication year: 2014