The binding behavior of molecules in nuclei of living cells can be studied through the analysis of images from fluorescence recovery after photobleaching experiments. However, there is still a lack of methodology for the statistical evaluation of FRAP data, especially for the joint analysis of multiple dynamic images. We propose a hierarchical Bayesian nonlinear model with mixed-effect priors based on local compartment models in order to obtain joint parameter estimates for all nuclei as well as to account for the heterogeneity of the nuclei population. We apply our method to a series of FRAP experiments of DNA methyltransferase 1 tagged to green fluorescent protein expressed in a somatic mouse cell line and compare the results to the application of three different fixed-effects models to the same series of FRAP experiments. With the proposed model, we get estimates of the off-rates of the interactions of the molecules under study together with credible intervals, and additionally gain information about the variability between nuclei. The proposed model is superior to and more robust than the tested fixed-effects models. Therefore, it can be used for the joint analysis of data from FRAP experiments on various similar nuclei.