Schematic comparison of the standard Gibbs sampler (top panels) and the joint sampler of Racine et al. (2016), bottom panels. The left and right columns show high and low signal-to-noise regimes, respectively. The Gibbs sampler performs poorly in the low signal-to-noise regime as it requires a large number of samples to explore the posterior distribution. The joint sampler in the lower panels performs well in both regimes as it allows the next sample to move diagonally in the {a, θ} parameter space.