Quantitatively understanding the stochastic dynamics of gene expression requires measurements at the level of single cells. A common approach to follow the expression of genes in single cells and in real time is to make use of fluorescent reporter proteins and to record the cells' fluorescence by microscopy. However, this provides only an indirect readout of the biological processes that are of interest such as the regulation mechanisms at the promoter. A possible way to uncover the unobservable biological processes is to infer the hidden dynamics from the available data through the use of mechanistic models of gene expression. The goal of this project is to develop methods for state estimation and parameter inference for such models and to test these methods on real data.

In early development, regulation of transcription results in precisely positioned and highly reproducible expression patterns that specify cellular identities. How transcription, a fundamentally noisy