Skip to main content
SpringerLink
Log in

Perfect aggregation of Bayesian analysis on compositional data

  • Articles
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

Sufficiency is a widely used concept for reducing the dimensionality of a data set. Collecting data for a sufficient statistic is generally much easier and less expensive than collecting all of the available data. When the posterior distributions of a quantity of interest given the aggregate and disaggregate data are identical, perfect aggregation is said to hold, and in this case the aggregate data is a sufficient statistic for the quantity of interest. In this paper, the conditions for perfect aggregation are shown to depend on the functional form of the prior distribution. When the quantity of interest is the sum of some parameters in a vector having either a generalized Dirichlet or a Liouville distribution for analyzing compositional data, necessary and sufficient conditions for perfect aggregation are also established.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Azaiez MN (1993) Perfect Aggregation in Reliability Models with Bayesian Updating. Dissertation, University of Wisconsin-Madison.

  • Balachander S, Ghose S (2003) Reciprocal Spillover Effects: A Strategic Benefit of Brand Extensions. Journal of Marketing 67, 4–13.

    Article  Google Scholar 

  • Bier VM (1994) On the Concept of Perfect Aggregation in Bayesian Estimation. Reliability Engineering and System Safety 46, 271–281.

    Article  Google Scholar 

  • Castillo E, Hadi AS, Solares C (1997) Learning and Updating of Uncertainty in Dirichlet Models. Machine Learning 26, 43–63.

    Article  MATH  Google Scholar 

  • Chatfield C, Goodhardt G (1975) Results Concerning Brand Choice. Journal of Marketing Research 12, 110–113.

    Article  Google Scholar 

  • Connor RJ, Mosimann JE (1969) Concepts of Independence for Proportions with a Generalization of the Dirichlet Distribution. Journal of the American Statistical Association 64, 194–206.

    Article  MATH  MathSciNet  Google Scholar 

  • Fang KT, Kotz S, Ng KW (1990) Symmetric Multivariate and Related Distributions. Chapman and Hall, New York.

    MATH  Google Scholar 

  • Gupta AK, Nadarajah S (2004) Handbook of Beta Distribution and its Applications, Chapter 3. Marcel Dekker, New York.

    Google Scholar 

  • Ijiri Y (1971) Fundamental Queries in Aggregation Theory. Journal of the American Statistical Association 66, 766–782.

    Article  MATH  Google Scholar 

  • Lee PM (1989) Bayesian Statistics: An Introduction. Oxford University Press, London.

    MATH  Google Scholar 

  • Lochner RH (1975) A Generalized Dirichlet Distribution in Bayesian Life Testing. Journal of the Royal Statistical Society, Series B 37, 103–113.

    MATH  MathSciNet  Google Scholar 

  • Mosleh A, Bier VM (1992) On Decomposition and Aggregation Error in Estimation: Some Basic Principles and Examples. Risk Analysis 22, 203–214.

    Article  Google Scholar 

  • Simon H, Ando A (1961) Aggregation of Variables in Dynamic Systems. Econometrica 29, 111–113.

    Article  MATH  Google Scholar 

  • Sivazlian BD (1981) On a Multivariate Extension of the Gamma and Beta Distributions. SIAM Journal on Applied Mathematics 41, 205–209.

    Article  MATH  MathSciNet  Google Scholar 

  • Wilks SS (1962) Mathematical Statistics. John Wiley, New York.

    MATH  Google Scholar 

  • Wong TT (1998) Generalized Dirichlet Distribution in Bayesian Analysis. Applied Mathematics and Computation 97, 165–181.

    Article  MATH  MathSciNet  Google Scholar 

  • Zacks S (1971) The Theory of Statistical Inference. John Wiley & Sons, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Information Management, National Cheng Kung University 1, Ta-Sheuh Road, 701, Tainan City, Taiwan, ROC

    Tzu-Tsung Wong

Authors
  1. Tzu-Tsung Wong
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wong, TT. Perfect aggregation of Bayesian analysis on compositional data. Statistical Papers 48, 265–282 (2007). https://doi.org/10.1007/s00362-006-0330-y

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-006-0330-y

Keywords

Search

Navigation