  Simulation Based Calibration (SBC) is applied to analyse two commonly used,
competing Markov chain Monte Carlo algorithms for estimating the posterior
distribution of a stochastic volatility model. In particular, the bespoke
'off-set mixture approximation' algorithm proposed by Kim, Shephard, and Chib
(1998) is explored together with a Hamiltonian Monte Carlo algorithm
implemented through Stan. The SBC analysis involves a simulation study to
assess whether each sampling algorithm has the capacity to produce valid
inference for the correctly specified model, while also characterising
statistical efficiency through the effective sample size. Results show that
Stan's No-U-Turn sampler, an implementation of Hamiltonian Monte Carlo,
produces a well-calibrated posterior estimate while the celebrated off-set
mixture approach is less efficient and poorly calibrated, though model
parameterisation also plays a role. Limitations and restrictions of generality
are discussed.
