José M. Bernardo · 2009
Scientific Reporting. Mathematical statistics uses two major paradigms, conventional (or frequentist), and Bayesian. Bayesian methods provide a complete paradigm for both statistical inference and decision making under uncertainty. Bayesian methods may be derived from an axiomatic system, and hence provide a general, coherent methodology. Bayesian methods contain as particular cases many of the more often used frequentist procedures, solve many of the difficulties faced by conventional statistical methods, and extend the applicability of statistical methods. In particular, Bayesian methods make it possible to incorporate scientific hypothesis in the analysis (by means of the prior distribution) and may be applied to problems whose structure is too complex for conventional methods to be able to handle. The Bayesian paradigm is based on an interpretation of probability as a rational, conditional measure of uncertainty, which closely matches the sense of the word ‘probability ’ in ordinary language. Statistical inference about a quantity of interest is described as the modification of the uncertainty about its value in the light of evidence, and Bayes ’ theorem precisely specifies how this modification should be made. The special situation, often met in scientific reporting and public decision making, where the only acceptable information is that which may be deduced from available documented data, is addressed by objective Bayesian methods, as a particular case. 1.
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Alexander LoPilato, Mo Wang · Oxford Bibliographies Online Datasets · 2016
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Janet L. Peacock, Philip J. Peacock · 2020
Abstract This chapter describes the Bayesian approach to statistical analysis in contrast to the frequentist approach. It discusses how clinicians often use a Bayesian approach in interpreting clinical findings and forming management plans. It describes how Bayesian methods work including a description of prior and posterior distributions. The chapter outlines the role and choice of prior distributions and how they are combined with the data collected to provide an updated estimate of the unknown quantity being studied. It includes examples of the use of Bayesian methods in medicine, and discusses the pros and cons of the Bayesian approach compared to the frequentist approach. Finally, guidance is given on how to read and interpret Bayesian analyses in the medical literature.
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Petr Novák · Digital Repository (National Repository of Grey Literature) · 2007
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Muhammad Ali Imran, Michail Tsagris, Farrukh Jamal et al. · Elsevier eBooks · 2026
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SpringerReference · 2011
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F. J. Anscombe · The American Statistician · 1961
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Donald L. Meyer · Review of Educational Research · 1966
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2024
Citation: 'Bayesian statistics' in the IUPAC Compendium of Chemical Terminology, 5th ed.; International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.11411 • License: The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International for individual terms. Requests for commercial usage of the compendium should be directed to IUPAC.
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Lawrence D. Phillips · Encyclopedia of Statistics in Behavioral Science · 2005
Abstract Bayesian statistics is based on the interpretation of a probability as a degree of belief held by an individual about some hypothesis, event, or uncertain quantity. These ‘prior’ degrees of belief are revised in light of new information by the application of Bayes's theorem, a simple consequence of the addition and multiplication laws of probability, thereby resulting in a ‘posterior’ probability distribution. Bayesian statistical inferences are based on this posterior distribution, usually in the form of probability statements about the hypotheses, events, or uncertain quantities of interest, sometimes giving different inferences from classical statistical methods even though they are both based on the same data.
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José M. Bernardo · The New Palgrave Dictionary of Economics · 2008
Bayesian statistics is a comprehensive approach to both statistical inference and decision analysis which derives from the fact that, for rational behaviour, all uncertainties in a problem must necessarily be described by probability distributions.
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Robert Johansson · Apress eBooks · 2024
This chapter explores an alternative interpretation of statistics—Bayesian statistics—and the methods associated with this interpretation. In contrast to the frequentist statistics used in Chapter 13 and Chapter 14 , Bayesian statistics treats probability as a degree of belief rather than as a measure of the proportions of observed outcomes. This different point of view gives rise to distinct statistical methods we can use in problem-solving. While it is generally true that statistical problems can, in principle, be solved using either frequentist or Bayesian statistics, practical differences make these two approaches to statistics suitable for different types of problems.
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Janet L. Peacock, Philip J. Peacock · Oxford University Press eBooks · 2010
Bayesian statistics <italic>478</italic> How Bayesian methods work <italic>480</italic> Prior distributions <italic>482</italic> Likelihood; posterior distributions <italic>484</italic> Summarizing and presenting results <italic>486</italic> Using Bayesian analyses in medicine <italic>488</italic> Software for Bayesian statistics <italic>492</italic> Reading Bayesian analyses in papers <italic>494</italic> Bayesian methods: a summary <italic>496</italic> In this chapter we describe the Bayesian approach to statistical analysis in contrast to the frequentist approach. We describe how Bayesian methods work including a description of prior and posterior distributions. We outline the role and choice of prior distributions and how they are combined with the data collected to provide an updated estimate of the unknown quantity being studied. We include examples of the use of Bayesian methods in medicine, and discuss the pros and cons of the Bayesian approach compared with the frequentist approach Finally, we give guidance on how to read and interpret Bayesian analyses in the medical literature....
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Encyclopedia of Measurement and Statistics · 2007
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Richard Kay · 2014
This chapter outlines the Bayesian approach and sets down how Bayesian methods can be applied in the analysis of data. It discusses implications for trial design and looks at an application of these methods within a regulatory context. The statistical methods used to make inferences within the frequentist framework are p-values and confidence intervals. The p-value is the probability associated with observed difference when the null hypothesis is true. The chapter considers a specific example and contrast the frequentist and Bayesian approaches to the analysis of data and the associated interpretations.
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National Cancer Institute · Definitions · 2020
Ope n Pe e r Re v ie w on Qe ios
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Richard Kay · 2023
This chapter outlines the Bayesian approach and contrasts it with the frequentist way of thinking. It explains how Bayesian methods can be applied in the analysis of data and discusses implications for trial design. The chapter discusses the application of these methods within a regulatory context. The Bayesian approach also allows the incorporation of beliefs about parameters based on knowledge and information from outside the clinical trial under consideration. The Bayesian analysis combines the observed data with the prior beliefs to produce posterior beliefs in the form of a second probability distribution, the posterior distribution . The chapter explains a specific example and contrast the frequentist and Bayesian approaches to the analysis of data and the associated interpretations. In some cases, prior distributions are based entirely on data, perhaps from a previous trial or some other alternative source external to the trial.
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Thomas J. Faulkenberry · 2025
Bayesian Statistics: The Basics provides a comprehensive yet accessible introduction to Bayesian statistics, specifically tailored for any researcher with an interest in statistical methods. It covers the theoretical foundations of Bayesian inference, contrasting it with classical statistical methods like null hypothesis significance testing. The book emphasizes key concepts such as prior and posterior distributions, Bayes’ theorem, and the Bayes factor, making them understandable even for readers with minimal mathematical backgrounds. Methodologically, the book offers practical, step-by-step guides on how to conduct Bayesian analyses using the free software package JASP. Each chapter focuses on applying Bayesian methods to common research designs with real-world data. Readers will benefit from the clear examples, visualizations, and JASP screenshots that ensure the learning experience is interactive and easy to follow. Full of practical content, the book emphasizes the advantages of Bayesian model comparison over traditional approaches, especially in quantifying evidence for competing hypotheses. Readers will also learn how to perform sensitivity analyses to assess the impact of different prior assumptions on their results. By the end of the book, readers will get both the theoretical understanding and practical skills to implement Bayesian methods in their own research, making it an invaluable resource for both novice and experienced researchers studying Bayesian statistics.
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Joseph V. Casillas · The Encyclopedia of Applied Linguistics · 2025
Abstract Over the past two decades, advances in computational power have facilitated the use of complex statistical modeling in academic research. As a result, sophisticated analytic strategies, such as multilevel modeling and structural equation modeling, are becoming commonplace, and computationally costly procedures, like Bayesian data analysis, have moved to the forefront. In particular, the use of Bayesian methods is gaining ground in the field of applied linguistics. The present overview provides a brief introduction to Bayesian data analysis, covering both why and how one might decide to use Bayesian estimation for statistical modeling, along with some of the commonly referenced advantages and disadvantages of this approach. This primer serves as a starting point for any linguist interested in beginning the journey of understanding and implementing Bayesian methods.
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M. Goldstein, J. M. Bernardo · Journal of the Royal Statistical Society Series A (General) · 1984
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