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/9780231153676.003.0005
- Subject:
- Economics and Finance, Development, Growth, and Environmental
The Bayesian paradigm provides an elegant framework for resolving problems of uncertainty by permitting one to treat all unknown parameters as random variables and thus impose prior probability ...
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The Bayesian paradigm provides an elegant framework for resolving problems of uncertainty by permitting one to treat all unknown parameters as random variables and thus impose prior probability distributions over them. This chapter begins by showing how this approach allows one to make explicit statements about the probability distributions of future observations, and then argues in favor of a “fundamentalist” (or “literalist”) Bayesian approach to generating prior probability distributions. Next, it introduces the expected-utility principle in a Bayesian context and explains how it leads to a very natural system for making decisions in the presence of uncertainty. Finally, it shows how the Bayesian decision framework is sufficiently powerful to address problems of extreme (Knightian) uncertainty.Less
The Bayesian paradigm provides an elegant framework for resolving problems of uncertainty by permitting one to treat all unknown parameters as random variables and thus impose prior probability distributions over them. This chapter begins by showing how this approach allows one to make explicit statements about the probability distributions of future observations, and then argues in favor of a “fundamentalist” (or “literalist”) Bayesian approach to generating prior probability distributions. Next, it introduces the expected-utility principle in a Bayesian context and explains how it leads to a very natural system for making decisions in the presence of uncertainty. Finally, it shows how the Bayesian decision framework is sufficiently powerful to address problems of extreme (Knightian) uncertainty.
