Encyclopedia of Social Network Analysis and Mining

Living Edition
| Editors: Reda Alhajj, Jon Rokne

Gibbs Sampling

  • Bruce E. Trumbo
  • Eric A. Suess
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7163-9_146-1


Gibbs Sampling

One of a number of computational methods collectively known as Markov chain Monte Carlo (MCMC) methods. In simulating a Markov chain, Gibbs sampling can be viewed as a special case of the Metropolis-Hastings algorithm. In statistical practice, the terminology Gibbs sampling most often refers to MCMC computations based on conditional distributions for the purpose of drawing inferences in multiparameter Bayesian models

Bayesian Inference

Consider the parameter θ of a probability model as a random variable with the prior density function p(θ). The choice of a prior distribution may be based on previous experience or personal opinion. Then Bayesian inference combines information in the observed data x with information provided by the prior distribution to obtain a posterior distribution p(θ|x). The parameter θ may be a vector.

The likelihood function p(x|θ) is defined (up to a constant multiple) as the joint density function of the data x, now viewed as a function...


Markov Chain Posterior Distribution Markov Chain Monte Carlo Prior Distribution Bayesian Inference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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  1. Box GEP, Tiao G (1973) Bayesian inference and statistical analysis. Addison-Wesley, ReadingMATHGoogle Scholar
  2. Chib S, Greenberg E (1994) Understanding the Metropolis-Hastings algorithm. Am Stat 49:327–335Google Scholar
  3. Cox DR, Miller HD (1965) The theory of stochastic processes. Wiley, New York, MATHMATHGoogle Scholar
  4. Davies OL (ed) (1957) Statistical methods in research and production, 3rd edn. Oliver and Boyd, Edinburgh, MATHMATHGoogle Scholar
  5. Diaconis P, Freedman D (1997) On Markov chains with continuous state spaces (Statistics Technical Report 501), University of California Berkeley Library. www.stat.berkeley.edu/tech-reports/501.pdf
  6. Donders FC (1868) Die Schnelligkeit psychischer Prozesse, Archiv für Anatomie und Physiologie und wissenschaftliche Medizin, pp. 657–681. English edition: Donders FC (1969) On the speed of mental processes, Attention and performance II (trans: Koster WG). North Holland, AmsterdamGoogle Scholar
  7. Gastwirth JL (1987) The statistical precision of medical screening procedures: applications to polygraph and AIDS antibody test data (including discussion). Stat Sci 2:213–238, MATHMathSciNetMathSciNetCrossRefMATHGoogle Scholar
  8. Gelfand AE, Smith AFM (1990) Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 85:398–409, MATHMathSciNetMathSciNetCrossRefMATHGoogle Scholar
  9. Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis, 2nd edn. Chapman & Hall/CRC, Boca Raton, MATHMATHGoogle Scholar
  10. Hastings C Jr (1955) Approximations for digital computers. Princeton University Press, Princeton, MATHCrossRefMATHGoogle Scholar
  11. Lee PM (2004) Bayesian statistics: an introduction, 3rd edn. Hodder Arnold, LondonMATHGoogle Scholar
  12. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Phys 21(6):1087–1092CrossRefGoogle Scholar
  13. Pagano M, Gauvreau K (2000) Principles of biostatistics, 2nd edn. Belmont, DuxburyMATHGoogle Scholar
  14. R Development Core Team (2012) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, www.R-project.org. ISBN 3-900051-07-0Google Scholar
  15. Robert CP, Casella G (2004) Monte Carlo statistical methods, 2nd edn. Springer, New York, MATHCrossRefMATHGoogle Scholar
  16. Snedecor GW, Cochran WG (1980) Statistical methods, 7th edn. Iowa State University Press, AhmmmmesGoogle Scholar
  17. Speigelhalter D, Thomas A, Best N, Lunn D (2011) BUGS: Bayesian inference using Gibbs sampling. MRC Biostatistics Unit, CambridgeGoogle Scholar
  18. Suess EA, Trumbo BE (2010) Introduction to probability simulation and Gibbs sampling with R. Springer, New YorkCrossRefGoogle Scholar
  19. Trumbo BE (2002) Learning statistics with real data. Duxbury Press, BelmontGoogle Scholar

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© Springer Science+Business Media LLC 2016

Authors and Affiliations

  1. 1.Department of Statistics and BiostatisticsCalifornia State University, East BayHaywardUSA