A Fast and Simple Algorithm for Bayesian Adaptive Testing

Wim J. van der Linden*, Hao Ren

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)
6 Downloads (Pure)


The Bayesian way of accounting for the effects of error in the ability and item parameters in adaptive testing is through the joint posterior distribution of all parameters. An optimized Markov chain Monte Carlo algorithm for adaptive testing is presented, which samples this distribution in real time to score the examinee’s ability and optimally select the items. Thanks to extremely rapid convergence of the Markov chain and simple posterior calculations, the algorithm is ready for use in real-world adaptive testing with running times fully comparable with algorithms that fix all parameters at point estimates during testing.

Original languageEnglish
Pages (from-to)58-85
Number of pages28
JournalJournal of educational and behavioral statistics
Issue number1
Early online date10 Jul 2019
Publication statusPublished - 1 Feb 2020


  • UT-Hybrid-D
  • adaptive testing
  • Bayesian optimality
  • Gibbs sampler
  • item calibration
  • item response models
  • MCMC algorithm
  • ability estimation
  • n/a OA procedure


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