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Recent design flows for photonic integrated circuits have been able to take advantage of mature capabilities available in electronic design automation such as schematic driven design and sophisticated circuit verification. Furthermore, new photonic integrated circuit simulators that can interface with electrical circuit simulators have been developed. As a result, photonic design flows are rapidly advancing in maturity. An area that still requires development is the statistical analysis of photonic circuits to be able to predict and improve yield, which is particularly challenging because photonic components tend to be large compared to the wavelength which makes them highly sensitive to phase errors. Furthermore, photonic devices tend to have long range spatial correlations in their parameters that cannot be ignored. In this paper, we present two approaches that enable Monte Carlo analysis of photonic integrated circuits, which include the treatment of spatial correlations, and we show how they can be used to predict the circuit yield. Example circuits include passive filters made from cascaded Mach-Zehnder interferometers and transceivers using active ring modulators.