Robust Bayesian analysis of loss reserving data using scale mixtures distributions

S. T.Boris Choy, Jennifer S.K. Chan, Udi E. Makov

Research output: Contribution to journalArticlepeer-review


It is vital for insurance companies to have appropriate levels of loss reserving to pay outstanding claims and related settlement costs. With many uncertainties and time lags inherently involved in the claims settlement process, loss reserving therefore must be based on estimates. Existing models and methods cannot cope with irregular and extreme claims and hence do not offer an accurate prediction of loss reserving. This paper extends the conventional normal error distribution in loss reserving modeling to a range of heavy-tailed distributions which are expressed by certain scale mixtures forms. This extension enables robust analysis and, in addition, allows an efficient implementation of Bayesian analysis via Markov chain Monte Carlo simulations. Various models for the mean of the sampling distributions, including the log-Analysis of Variance (ANOVA), log-Analysis of Covariance (ANCOVA) and state space models, are considered and the straightforward implementation of scale mixtures distributions is demonstrated using OpenBUGS.

Original languageEnglish
Pages (from-to)396-411
Number of pages16
JournalJournal of Applied Statistics
Issue number3
StatePublished - 17 Feb 2016

Bibliographical note

Publisher Copyright:
© 2015 Taylor & Francis.


  • Gibbs sampler
  • OpenBUGS
  • heavy-tailed distributions
  • loss reserving model
  • robustness
  • scale mixtures of normal
  • scale mixtures of uniform

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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