We use a Bayesian approach for estimating the models and estimating the number of people with health insurance. The estimated numbers of people are the posterior means conditioned on the CPS ASEC data, the Census 2000 data, the tax exemption data, the food stamp data, and the Medicaid/SCHIP data. The final estimate for a state demographic group by IPR category is a complex mixture of the direct CPS ASEC estimate for that group and the other data. Estimates with large sample sizes or very high insurance rates, and thus low variances, tend to be closer to the direct estimates.