Biological dosimeters are useful for epidemiologic risk assessment in populations exposed to catastrophic nuclear events and as a means of validating physical dosimetry in radiation workers. Application requires knowledge of the magnitude of uncertainty in the biological dose estimates and an understanding of potential statistical pitfalls arising from their use. This paper describes the statistical aspects of biological dosimetry in general and presents a detailed analysis in the specific case of dosimetry for risk assessment using stable chromosome aberration frequency. Biological dose estimates may be obtained from a dose-response curve, but negative estimates can result and adjustment must be made for regression bias due to imprecise estimation when the estimates are used in regression analyses. Posterior-mean estimates, derived as the mean of the distribution of true doses compatible with a given value of the biological endpoint, have several desirable properties: they are nonnegative, less sensitive to extreme skewness in the true dose distribution, and implicitly adjusted to avoid regression bias. The methods necessitate approximating the true-dose distribution in the population in which biological dosimetry is being applied, which calls for careful consideration of this distribution through other information. An important question addressed here is to what extent the methods are robust to misspecification of this distribution, because in many applications of biological dosimetry it cannot be characterized well. The findings suggest that dosimetry based solely on stable chromosome aberration frequency may be useful for population-based risk assessment.