Abstract: In data fusion, data owners seek to combine datasets with disjoint observations and distinct variables to estimate relationships among the variables. One approach is to concatenate the files, specify models relating the variables not jointly observed, and use the models to generate multiple imputations of the missing data. We show that the standard multiple imputation estimator of the sampling variance can have positive bias in such contexts. We present an approach for correcting this problem based on Bayesian finite population inference. We also present an approach for data fusion when some values are confidential and cannot be shared.