*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/9780691151687.003.0005
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces the most important aspects of Bayesian statistical inference and techniques for performing such calculations in practice. It first reviews the basic steps in Bayesian ...
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This chapter introduces the most important aspects of Bayesian statistical inference and techniques for performing such calculations in practice. It first reviews the basic steps in Bayesian inference in early sections of the chapter, and then illustrates them with several examples in sections that follow. Numerical techniques for solving complex problems are next discussed, and the final section provides a summary of pros and cons for classical and Bayesian method. It argues that most users of Bayesian estimation methods are likely to use a mix of Bayesian and frequentist tools. The reverse is also true—frequentist data analysts, even if they stay formally within the frequentist framework, are often influenced by “Bayesian thinking,” referring to “priors” and “posteriors.” The most advisable position is to know both paradigms well, in order to make informed judgments about which tools to apply in which situations.Less

This chapter introduces the most important aspects of Bayesian statistical inference and techniques for performing such calculations in practice. It first reviews the basic steps in Bayesian inference in early sections of the chapter, and then illustrates them with several examples in sections that follow. Numerical techniques for solving complex problems are next discussed, and the final section provides a summary of pros and cons for classical and Bayesian method. It argues that most users of Bayesian estimation methods are likely to use a mix of Bayesian and frequentist tools. The reverse is also true—frequentist data analysts, even if they stay formally within the frequentist framework, are often influenced by “Bayesian thinking,” referring to “priors” and “posteriors.” The most advisable position is to know both paradigms well, in order to make informed judgments about which tools to apply in which situations.

*Odo Diekmann, Hans Heesterbeek, and Tom Britton*

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691155395
- eISBN:
- 9781400845620
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691155395.003.0015
- Subject:
- Biology, Disease Ecology / Epidemiology

Chapters 5, 13 and 14 presented methods for making inference about infectious diseases from available data. This is of course one of the main motivations for modeling: learning about important ...
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Chapters 5, 13 and 14 presented methods for making inference about infectious diseases from available data. This is of course one of the main motivations for modeling: learning about important features, such as R₀, the initial growth rate, potential outbreak sizes and what effect different control measures might have in the context of specific infections. The models considered in these chapters have all been simple enough to obtain more or less explicit estimates of just a few relevant parameters. In more complicated and parameter-rich models, and/or when analyzing large data sets, it is usually impossible to estimate key model parameters explicitly. In such situations there are (at least) two ways to proceed. One uses Bayesian statistical inference by means of Markov chain Monte Carlo methods (MCMC), and the other uses large scale simulations along with numerical optimization to fit parameters to data. This chapter mainly describes Bayesian inference using MCMC and only briefly some large simulation methods.Less

Chapters 5, 13 and 14 presented methods for making inference about infectious diseases from available data. This is of course one of the main motivations for modeling: learning about important features, such as R₀, the initial growth rate, potential outbreak sizes and what effect different control measures might have in the context of specific infections. The models considered in these chapters have all been simple enough to obtain more or less explicit estimates of just a few relevant parameters. In more complicated and parameter-rich models, and/or when analyzing large data sets, it is usually impossible to estimate key model parameters explicitly. In such situations there are (at least) two ways to proceed. One uses Bayesian statistical inference by means of Markov chain Monte Carlo methods (MCMC), and the other uses large scale simulations along with numerical optimization to fit parameters to data. This chapter mainly describes Bayesian inference using MCMC and only briefly some large simulation methods.

*Ziheng Yang*

- Published in print:
- 2014
- Published Online:
- August 2014
- ISBN:
- 9780199602605
- eISBN:
- 9780191782251
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199602605.003.0006
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies, Evolutionary Biology / Genetics

This chapter summarizes the Frequentist–Bayesian controversy in statistics, and introduces the basic theory of Bayesian statistical inference, such as the prior, posterior, and Bayes’ theorem. ...
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This chapter summarizes the Frequentist–Bayesian controversy in statistics, and introduces the basic theory of Bayesian statistical inference, such as the prior, posterior, and Bayes’ theorem. Classical methods for Bayesian computation, such as numerical integration, Laplacian expansion, Monte Carlo integration, and importance sampling, are illustrated using biological examples.Less

This chapter summarizes the Frequentist–Bayesian controversy in statistics, and introduces the basic theory of Bayesian statistical inference, such as the prior, posterior, and Bayes’ theorem. Classical methods for Bayesian computation, such as numerical integration, Laplacian expansion, Monte Carlo integration, and importance sampling, are illustrated using biological examples.