*Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray*

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691151687
- eISBN:
- 9781400848911
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691151687.003.0004
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces the main concepts of statistical inference, or drawing conclusions from data. There are three main types of inference: point estimation, confidence estimation, and hypothesis ...
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This chapter introduces the main concepts of statistical inference, or drawing conclusions from data. There are three main types of inference: point estimation, confidence estimation, and hypothesis testing. There are two major statistical paradigms which address the statistical inference questions: the classical, or frequentist paradigm, and the Bayesian paradigm. While most of statistics and machine learning is based on the classical paradigm, Bayesian techniques are being embraced by the statistical and scientific communities at an ever-increasing pace. The chapter begins with a short comparison of classical and Bayesian paradigms, and then discusses the three main types of statistical inference from the classical point of view.Less

This chapter introduces the main concepts of statistical inference, or drawing conclusions from data. There are three main types of inference: point estimation, confidence estimation, and hypothesis testing. There are two major statistical paradigms which address the statistical inference questions: the classical, or frequentist paradigm, and the Bayesian paradigm. While most of statistics and machine learning is based on the classical paradigm, Bayesian techniques are being embraced by the statistical and scientific communities at an ever-increasing pace. The chapter begins with a short comparison of classical and Bayesian paradigms, and then discusses the three main types of statistical inference from the classical point of view.

*Michael R. Powers*

- Published in print:
- 2014
- Published Online:
- November 2015
- ISBN:
- 9780231153676
- eISBN:
- 9780231527057
- Item type:
- chapter

- Publisher:
- Columbia University Press
- DOI:
- 10.7312/columbia/9780231153676.003.0004
- Subject:
- Economics and Finance, Development, Growth, and Environmental

This chapter explores a number of concepts and methods employed in the frequency/classical approach, called frequentism. To present the standard frequentist paradigm, it begins by defining the ...
More

This chapter explores a number of concepts and methods employed in the frequency/classical approach, called frequentism. To present the standard frequentist paradigm, it begins by defining the concept of a random sample, and then summarizes how such samples are used to construct both point and interval estimates. Next, it introduces three important asymptotic results—the law of large numbers, the central limit theorem, and the generalized central limit theorem—followed by a discussion of the practical validity of the independence assumption underlying random samples. Finally, it considers in some detail the method of hypothesis testing, whose framework follows much the same logic as both the U.S. criminal justice system and the scientific method as it is generally understood.Less

This chapter explores a number of concepts and methods employed in the frequency/classical approach, called frequentism. To present the standard frequentist paradigm, it begins by defining the concept of a random sample, and then summarizes how such samples are used to construct both point and interval estimates. Next, it introduces three important asymptotic results—the law of large numbers, the central limit theorem, and the generalized central limit theorem—followed by a discussion of the practical validity of the independence assumption underlying random samples. Finally, it considers in some detail the method of hypothesis testing, whose framework follows much the same logic as both the U.S. criminal justice system and the scientific method as it is generally understood.