Skip to main content

Bayesian Inference

  • Chapter
  • First Online:
  • 8002 Accesses

Abstract

Bayesian statistics is a branch of statistics that is centered around Bayes’ formula (1.8), which is repeated in (8.1) below. To fully appreciate Bayesian inference, it is important to understand that the type of statistical reasoning here is somewhat different from that in classical statistics. In particular, model parameters are usually treated as random rather than fixed quantities.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Bishop, C. M. 2006. Pattern Recognition and Machine Learning. Springer-Verlag New York, Inc., Secaucus, NJ.

    MATH  Google Scholar 

  • Botev, Z. I., J. F. Grotowski, & D. P. Kroese 2010. Kernel density estimation via diffusion. Annals of Statistics, 38(5):2916–2957.

    Article  MathSciNet  MATH  Google Scholar 

  • Chib, S. 1995. Marginal Likelihood from the Gibbs Output. Journal of the American Statistical Association, 90:1313–1321.

    Article  MathSciNet  MATH  Google Scholar 

  • Chib, S., & I. Jeliazkov 2001. Marginal Likelihood from the Metropolis-Hastings Output. Journal of the American Statistical Association, 96:270–281.

    Article  MathSciNet  MATH  Google Scholar 

  • Fair, R. C. 1978. A Theory of Extramarital Affairs. Journal of Political Economy, 86:45–61.

    Article  Google Scholar 

  • Feller, W. 1970. An Introduction to Probability Theory and Its Applications, volume I. John Wiley & Sons, New York, second edition.

    Google Scholar 

  • Gelfand, A. E., S. Hills, A. Racine-Poon, & A. F. M. Smith 1990. Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling. Journal of American Statistical Association, 85:972–985.

    Article  Google Scholar 

  • Kim, S., N. Shepherd, & S. Chib 1998. Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models. Review of Economic Studies, 65(3):361–393.

    Article  MATH  Google Scholar 

  • Koop, G., D. J. Poirier, J. L., & Tobias 2007. Bayesian Econometric Methods. Cambridge University Press.

    Google Scholar 

  • Kroese, D. P., T. Taimre, & Z. I. Botev 2011. Handbook of Monte Carlo Methods. John Wiley & Sons, New York.

    Book  MATH  Google Scholar 

  • L’Ecuyer, P. 1999. Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators. Operations Research, 47(1):159 – 164.

    Article  MathSciNet  MATH  Google Scholar 

  • Marsaglia, G., & W. Tsang 2000. A Simple Method for Generating Gamma Variables. ACM Transactions on Mathematical Software, 26(3):363–372.

    Article  MathSciNet  Google Scholar 

  • McLachlan, G. J., & T. Krishnan 2008. The EM Algorithm and Extensions. John Wiley & Sons, Hoboken, NJ, second edition.

    Google Scholar 

  • Metropolis, M., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, & E. Teller 1953. Equations of state calculations by fast computing machines. J. of Chemical Physics, 21:1087–1092.

    Article  Google Scholar 

  • Verdinelli, I., & L. Wasserman 1995. Computing Bayes Factors Using a Generalization of the Savage-Dickey Density Ratio. Journal of the American Statistical Association, 90(430): 614–618.

    Article  MathSciNet  MATH  Google Scholar 

  • Williams, D. 1991. Probability with Martingales. Cambridge University Press, Cambridge.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 The Author(s)

About this chapter

Cite this chapter

Kroese, D.P., Chan, J.C.C. (2014). Bayesian Inference. In: Statistical Modeling and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8775-3_8

Download citation

Publish with us

Policies and ethics