Caveats regarding MCMC and NS

PyORBIT is one of the few Exoplanetary codes that supports both Monte Carlo Markov Chain (MCMC) and Nested Sampling (NS), thus allowing a direct comparison of the two approaches over the same datasets and models. In my experience, when the model is appropriate, the two algorithms deliver the same results, i.e., the posteriors are perfectly superimposed. Although it does not guarantee your analysis’s correctness, it is indeed a useful check. It is essential to understand the different implementations of the two algorithms, as they affect how priors

Priors on parameters

In MCMC, a prior acts as a penalisation to the log-likelihood: the farther a parameter from the prior, the more negative (with the other parameters frozen) the log-likelihood will be. This is true for both sampler parameters and derived parameters. When using MCMC, it is possible to set a prior on a derived parameter. For example, it is possible to set a prior on the eccentricity when using the Eastman parametrisation, even if eccentricity is not a sampler parameter.

In NS, the prior is actually a reparametrisation of the unitary cube, in such a way that a uniform sampling of the unitary parameter will result into a distribution of the sampler parameter that follows the given prior. As a consequence, priors can be imposed only on sampler parameters. For example, you cannot use the Eastman parametrization and a prior on the eccentricity simultaneously.

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