BAYESIAN ANALYSIS

BAYESIAN ANALYSIS

30 Jun 2000 | Harrison B. Prosper
Bayesian analysis is a framework for scientific inference that emphasizes the use of probability to quantify uncertainty. The paper discusses the philosophical and practical implications of Bayesian methods in physics, contrasting them with frequentist approaches. It begins with an introduction to the debate between Bayesian and frequentist inference, highlighting the subjective nature of Bayesian probability and the challenges of defining prior probabilities. The author argues that while frequentist methods are often seen as objective, they rely on ensembles that do not objectively exist, whereas Bayesian methods, though subjective, provide a more coherent framework for incorporating uncertainty and updating beliefs based on data. The paper then presents two examples to illustrate Bayesian methods. The first is a simple "toy" model that highlights the challenges of assigning prior probabilities and the importance of coherence in Bayesian reasoning. The second example involves the measurement of solar neutrino survival probability, where Bayesian analysis is used to infer the survival probability from experimental data. This example demonstrates how Bayesian methods can provide a coherent and intuitive framework for dealing with uncertainty in complex scientific problems. The author concludes that Bayesian methods are not only suitable for scientific use but are essential for maximizing the use of data. While frequentist methods have their place, Bayesian methods offer a more flexible and coherent approach to inference, particularly in situations where prior knowledge is important. The paper emphasizes that Bayesian methods are not inherently subjective but are a natural way to incorporate uncertainty and update beliefs in light of new evidence. The author argues that Bayesian methods are more aligned with the way physicists think and are therefore a valuable tool for scientific inference.Bayesian analysis is a framework for scientific inference that emphasizes the use of probability to quantify uncertainty. The paper discusses the philosophical and practical implications of Bayesian methods in physics, contrasting them with frequentist approaches. It begins with an introduction to the debate between Bayesian and frequentist inference, highlighting the subjective nature of Bayesian probability and the challenges of defining prior probabilities. The author argues that while frequentist methods are often seen as objective, they rely on ensembles that do not objectively exist, whereas Bayesian methods, though subjective, provide a more coherent framework for incorporating uncertainty and updating beliefs based on data. The paper then presents two examples to illustrate Bayesian methods. The first is a simple "toy" model that highlights the challenges of assigning prior probabilities and the importance of coherence in Bayesian reasoning. The second example involves the measurement of solar neutrino survival probability, where Bayesian analysis is used to infer the survival probability from experimental data. This example demonstrates how Bayesian methods can provide a coherent and intuitive framework for dealing with uncertainty in complex scientific problems. The author concludes that Bayesian methods are not only suitable for scientific use but are essential for maximizing the use of data. While frequentist methods have their place, Bayesian methods offer a more flexible and coherent approach to inference, particularly in situations where prior knowledge is important. The paper emphasizes that Bayesian methods are not inherently subjective but are a natural way to incorporate uncertainty and update beliefs in light of new evidence. The author argues that Bayesian methods are more aligned with the way physicists think and are therefore a valuable tool for scientific inference.
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