5. Credible Intervals

  1. Franco Taroni1,
  2. Silvia Bozza2,
  3. Alex Biedermann1,
  4. Paolo Garbolino3 and
  5. Colin Aitken4

Published Online: 9 APR 2010

DOI: 10.1002/9780470665084.ch5

Data Analysis in Forensic Science: A Bayesian Decision Perspective

Data Analysis in Forensic Science: A Bayesian Decision Perspective

How to Cite

Taroni, F., Bozza, S., Biedermann, A., Garbolino, P. and Aitken, C. (2010) Credible Intervals, in Data Analysis in Forensic Science: A Bayesian Decision Perspective, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470665084.ch5

Author Information

  1. 1

    School of Criminal Justice, University of Lausanne, Switzerland

  2. 2

    Department of Statistics, University Ca' Foscari, Venice, Italy

  3. 3

    Faculty of Arts and Design, IUAV University, Venice, Italy

  4. 4

    School of Mathematics, University of Edinburgh, UK

Publication History

  1. Published Online: 9 APR 2010
  2. Published Print: 9 APR 2010

ISBN Information

Print ISBN: 9780470998359

Online ISBN: 9780470665084

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Keywords:

  • confidence interval;
  • credible probability;
  • decision-theoretic evaluation;
  • inferential statistics;
  • interval estimation;
  • predictive distribution

Summary

Interval estimation represents common approach to statistical inference. Credible probability reflects the information contained in the posterior distribution and allows the scientist to assert that the region contains the parameter with a given probability. If the set is not disjoint it is called a credible interval. The highest posterior density (HPD) interval consists of the values of the parameter for which the posterior density is highest. This chapter considers the predictive approach. It involves a predictive distribution for the quantity of handled drugs based on independent prior distributions for both the mean and the variance. The chapter outlines that an optimal interval should meet two conditions: it should have a high credible probability and be of the shortest size. If both of these requirements are met by a loss function, then the optimal interval estimator can be found using a decision approach.

Controlled Vocabulary Terms

confidence interval; inferential statistics; interval estimation; posterior predictive distribution; probability