I present some extensions of Bayesian methods to situations in which biases are of concern. First, a basic misclassification problem is illustrated using data from a study of sudden infant death syndrome. Bayesian analyses are then given. These analyses can be conducted directly, or by converting actual-data records to incomplete records and prior distributions to complete-data records, then applying missing-data techniques to the augmented data set. The analyses can easily incorporate any complete ('validation' or second-stage) data that might be available, as well as adjustments for confounding and selection bias. The approach illustrates how conventional analyses depend on implicit certainty that bias parameters are null and how these implausible assumptions can be replaced by plausible priors for bias parameters.