Skip to main content

Dependent Data Models

  • Chapter
  • First Online:
Statistical Modeling and Computation

Abstract

In the models considered so far the responses \(Y _{1},\ldots,Y _{n}\) have been assumed to be independent given the model parameters. Though convenient, this independence assumption is implausible in two common situations. First, in the case of time series—observations measured over time—the responses typically exhibit strong serial dependence. For example, high unemployment tends to last for a long period of time; given a high unemployment rate this period, one would expect that the unemployment rates in the next few periods would also be high.

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

Access this chapter

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

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). Dependent Data Models. In: Statistical Modeling and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8775-3_10

Download citation

Publish with us

Policies and ethics