From the above derivation, we know the probability distribution of time delay parameter given the lens mode. To draw a prior from this, we could do an numerical integration on probability distribution and get Cumulative Distribution Functions. We then inverse this cumulative distribution function and applies it on a uniform distribution. The method is called transformation method as described in Statistics, Data Mining, and Machine Learning in Astronomy (Ivezi´c, Z., et al.)
From the above derivation, we know the probability distribution of time delay parameter given the lens mode. To draw a prior from this, we could do an numerical integration on probability distribution and get Cumulative Distribution Functions. We then inverse this cumulative distribution function and applies it on a uniform distribution. The method is called transformation method as described in Statistics, Data Mining, and Machine Learning in Astronomy (Ivezi´c, Z., et al.)