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We investigate a modern statistical approach to a classic deterministic demographic estimation technique. When vital event registration is missing or inadequate, it is possible to approximate a population's total fertility rate (TFR) from information about its distribution by age and sex. For example, if under-five child mortality is low then TFR is often close to seven times the child/woman ratio (CWR), the number of 0-4 year olds per 15-49-year-old woman. We analyse the formal relationship between CWR and TFR to identify sources of uncertainty in indirect estimates. We construct a Bayesian model for the statistical distribution of TFR conditional on the population's age-sex structure, in which unknown demographic quantities in the standard approximation are parameters with prior distributions. We apply the model in two case studies: to a small indigenous population in the Amazon region of Brazil that has extremely high fertility rates, and to the set of 159 counties in the US state of Georgia. A statistical approach yields important insights into the sources of error in indirect estimation, and their relative magnitudes. [ABSTRACT FROM AUTHOR]