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Transit timing variations (TTVs) are a valuable tool to determine the massesand orbits of transiting planets in multi-planet systems. TTVs can be readilymodeled given knowledge of the interacting planets' orbital configurations andplanet-star mass ratios, but such models are highly nonlinear and difficult toinvert. Markov chain Monte Carlo (MCMC) methods are often used to explore theposterior distribution for model parameters, but, due to the high correlationsbetween parameters, nonlinearity, and potential multi-modality in theposterior, many samplers perform very inefficiently. Therefore, we assess theperformance of several MCMC samplers that use varying degrees of geometricinformation about the target distribution. We generate synthetic datasets frommultiple models, including the TTVFaster model and a simple sinusoidal model,and test the efficiencies of various MCMC samplers. We find that samplingefficiency can be greatly improved for all models by sampling from a parameterspace transformed using an estimate of the covariance and means of the targetdistribution. No one sampler performs the best for all datasets, but severalsamplers, such as Differential Evolution Monte Carlo and Geometric adaptiveMonte Carlo, have consistently efficient performance. For datasets with nearGaussian posteriors, Hamiltonian Monte Carlo samplers with 2 or 3 leapfrogsteps obtained the highest efficiencies. Based on differences in effectivesample sizes per time, we show that the right choice of sampler can improvesampling efficiencies by several orders of magnitude.

The Efficiency of Geometric Samplers for Exoplanet Transit Timing Variation Models