It is common in population screening surveys or in the investigation of new diagnostic tests to have results from one or more tests investigating the same condition or disease, none of which can be considered a gold standard. For example, two methods often used in population-based surveys for estimating the prevalence of a parasitic or other infection are stool examinations and serologic testing. However, it is known that results from stool examinations generally underestimate the prevalence, while serology generally results in overestimation. Using a Bayesian approach, simultaneous inferences about the population prevalence and the sensitivity, specificity, and positive and negative predictive values of each diagnostic test are possible. The methods presented here can be applied to each test separately or to two or more tests combined. Marginal posterior densities of all parameters are estimated using the Gibbs sampler. The techniques are applied to the estimation of the prevalence of Strongyloides infection and to the investigation of the diagnostic test properties of stool examinations and serologic testing, using data from a survey of all Cambodian refugees who arrived in Montreal, Canada, during an 8-month period.