The tracking-by-detection strategy is the backbone of many methods for tracking living cells in time-lapse microscopy. An object detector is first applied to the input images, and the resulting detection candidates are then linked by a data association module. The performance of such methods strongly depends on the quality of the detector because detection errors propagate to the linking step. To tackle this issue, we propose a joint model for segmentation, detection and tracking. The model is defined implicitly as limiting distribution of a Markov chain Monte Carlo algorithm and contains a temporal feedback, which allows to dynamically alter detector parameters using hints given by neighboring frames and, in this way, correct detection errors. The proposed method can integrate any detector and is therefore not restricted to a specific domain. The parameters of the model are learned using an objective based on empirical risk minimization. We use our method to conduct large-scale experiments for confluent cultures of endothelial cells and evaluate its performance in the ISBI Cell Tracking Challenge, where it consistently scored among the best three methods.