Stochastic promoter switching between transcriptionally active (ON) and inactive (OFF) states is a major source of noise in gene expression. It is often implicitly assumed that transitions between promoter states are memoryless, i.e. promoters spend an exponentially distributed time interval in each of the two states. However, increasing evidence suggests that promoter ON/OFF times can be non-exponential, hinting at more complex transcriptional regulatory architectures. Given the essential role of gene expression in all cellular functions, efficient computational techniques for characterizing promoter architectures are critically needed.