This thesis, presented to The University of Manchester in 2012 by Dr. Linda Walsh, is in fulfilment of the requirements for the degree of Doctor of Science (DSc) and is entitled "Quantifications of the detrimental health effects of ionising radiation." A body of work and ensuing publications covering 2000-2012 are presented, predominantly concerning studies of various cohorts of people exposed to ionising radiation. The major areas cover epidemiological and statistical studies on the Life span study (LSS) cohort of Japanese survivors of the World War II atomic-bomb attacks on Hiroshima and Nagasaki and the mortality follow-up of German uranium miners. Following the presentation of a very brief history of the effects of radiation exposure on humans, the background and context of the advances achieved by the candidate are described. The LSS provides the most studied cohort and a range of topics from cancer risks related to neutron and γ-ray doses, organ specific doses, and carcinogenesis have been explored covering about half of the candidate's publications. The cohort of German "Wismut" uranium miners exposed to radon and other potential carcinogens, which is the largest one of its kind, has enabled the development of epidemiological models for lung and extra-pulmonary cancers. The third distinct topic relates to analyses of data on cellular radiation damage relevant to the evaluation of both diagnostic radiation characteristics and the effects on cancer patients. Other studies have considered the incidence of malignant diseases in humans injected with radium-224 and development of epidemiological models for thyroid cancer risk in areas affected by the 1986 Chernobyl accident. Fundamental contributions have been published in the application of mathematical methods for data analysis. The candidate has succeeded in going beyond the traditional statistical methods in radiation epidemiology by introduction of numerical techniques deriving from the field of information science and novel to the field. These methods, such as techniques for model selection and mitigation of strongly correlated quantities, have been presented as general tools and have demonstrated powerful results, such as in applications to data from LSS. The impact and relevance for public health of the epidemiological results is indicated by their frequent citation in recent reports by international bodies such as by the International Commission on Radiological Protection, the United Nations Scientific Committee on the Effects of Atomic Radiation, the World Health Organization (WHO) and WHO-International Agency for Research on Cancer.Several topics, from among this broad coverage of radiation epidemiological themes, the development of novel statistical techniques and their application, are highlighted. Work on distinguishing the effect of neutrons and γ-rays in the Japanese LSS data has led to progress on quantifying their relative biological effectiveness with important consequences for the health effects of modern radiation diagnostics. A technique for combining risks from several risk models, called multi-model inference, has been shown to ease the dilemma of selecting between models with very different consequences, with particular relevance for major issues of public health concern connected with radiation exposure. The Wismut cohort has revealed for the first time the response characteristics of a significant effect of working underground on prostate cancer incidence, suggesting a relation with lack of exposure to light which remains unexplained.