The Ensemble Quadratic and Affine Invariant Markov chain Monte Carlo algorithms provide an efficient way to perform Bayesian inference in difficult parameter space geometries. The Ensemble Quadratic Monte Carlo algorithm was developed by Militzer (2023) <doi:10.3847/1538-4357/ace1f1>. The Ensemble Affine Invariant algorithm was developed by Goodman and Weare (2010) <doi:10.2140/camcos.2010565> and it was implemented in Python by Foreman-Mackey et al (2013) <doi:10.48550/arXiv.1202.3665>. The Quadratic Monte Carlo method was shown to perform better than the Affine Invariant method in the paper by Militzer (2023) <doi:10.3847/1538-4357/ace1f1> and the Quadratic Monte Carlo method is the default method used. The Chen-Shao Highest Posterior Density Estimation algorithm is used for obtaining credible intervals and the potential scale reduction factor diagnostic is used for checking the convergence of the chains.
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