Niko Brummer's home page

Aliases to this page:

Fully Bayesian stuff

  • Here is a very simple, but practical, fully Bayesian, generative, multiclass pattern classifier: derivation, MATLAB implementation.
  • Some (in-progress) notes analysing various aspects of the problem of forensic likelihood-ratio calibration, with the aim of working towards more Bayesian solutions:
    • Integrating out model parameters in generative and discriminative classifiers. [PDF].
    • What is the ‘relevant population’ in Bayesian forensic inference?
    • Tutorial for Bayesian forensic likelihood ratio. Available:
    • Fully Bayesian Score Calibration assuming Gaussian Distributions. [PDF]
  • See also 'Bayesian PLDA' below.
  • "Fully Bayesian Forensic LR: Extending the paradigm shift", presentation at the NFI, Netherlands, October 2011. [pdf
  • Niko Brummer and Albert Swart, 'Bayesian calibration for forensic evidence reporting', submitted Interspeech 2014. Avaliable:

Text-dependent speaker verification

The terminology in this field can be confusing. Here is a proposal of how to term the various possible outcomes when verifying combinations of speakers and phrases:


This is the successor to the FoCal Toolkit. The BOSARIS Toolkit provides MATLAB code for calibrating, fusing and evaluating scores from (automatic) binary classifiers. It was developed
to provide solutions for automatic speaker recognition, but we envision that much of the code will have wider applicability for other biometric and/or forensics problems, where the calibration of likelihood-ratios is of interest.

Selected Papers




Book chapter

Invited Talks

  • "Calibration of Binary (Speaker Recognition) and Multiclass (Language Recognition) Statictical Pattern Recognizers", at ATVS UAM, 2008. [slides].  
  • "Calibration of Likelihood-Ratios in Automatic Speaker Recognition: Applicability to other Forensic Technologies", presented at BBfor2 Workshop, IDIAP, Martigny, December 2011. [pdf]
  • "The Role of Proper Scoring Rules in Training and Evaluating Probabilistic Speaker and Language Recognizers", Odyssey 2012, 25-28 June, Singapore. See abstract and details at: Presentation is here. Video here.
  • "Binary and Multiclass Calibration in Speaker and Language Recognition", ASRU 2013, Olomouc. Slides: Video:
  • "Bayesian Calibration for Forensic Speaker Recognition", HLT Winter School, CSIR, Pretoria, July 2014. PDF Slides.
  • "Bayesian Calibration for Forensic Evidence Reporting", Keynote, ICFIS 2014, Leiden, Netherlands,  August 2014. Slides [PDF]:



Odyssey conferences

Details and links to archived proceedings of the Odyssey Speaker and Language Recognition Workshop series is available at:

The last Odyssey was in Joensuu, Finland, June 2014: For online talks and proceedings, see:

The next Odyssey will be in Bilbao, Spain, June 2016.