Flow chart depicting the iterative block sampling approach of the BORG inference framework. As can be seen, the BORG algorithm first infers three-dimensional initial and evolved density fields from quasar spectra using assumed astrophysical parameters of the FGPA model. Then, using realizations of the evolved density field, the algorithm updates these astrophysical parameters and a new iteration of the process begins. Iterating this procedure results in a valid Markov Monte Carlo chain that correctly explores the joint posterior distribution of the three-dimensional matter distribution and astrophysical properties underlying Ly-α forest observations.