Manuel Higueras1,2⇑, Pedro Puig2, Elizabeth A. Ainsbury1 and Kai Rothkamm11Centre for Radiation, Chemical and Environmental Hazards, Public Health England, Chilton, Oxfordshire OX11 0RQ, UK2Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona 08193, Spaine-mail: manuel.higueras-hernaezatphe.gov.ukAbstract Biological dosimetry based on chromosome aberration scoring in peripheral blood lymphocytes enables timely assessment of the ionizing radiation dose absorbed by an individual. Here, new Bayesian-type count data inverse regression methods are introduced for situations where responses are Poisson or two-parameter compound Poisson distributed. Our Poisson models are calculated in a closed form, by means of Hermite and negative binomial (NB) distributions. For compound Poisson responses, complete and simplified models are provided. The simplified models are also expressible in a closed form and involve the use of compound Hermite and compound NB distributions. Three examples of applications are given that demonstrate the usefulness of these methodologies in cytogenetic radiation biodosimetry and in radiotherapy. We provide R and SAS codes which reproduce these examples. Bayesian calibrationbiological dosimetryradiotherapycalibrative densitycompound Poisson distributionHermite distributionReceived August 1, 2014.Accepted December 4, 2014.textcopyright 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.