The NuZZ: Numerical ZigZag Sampling for General Models
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We present the Numerical ZigZag (NuZZ) algorithm, a Piecewise Deterministic MCMC algorithm that is applicable to general statistical models, without the need for bounds on the gradient of the log posterior. This allows us to investigate: (i) how the ZigZag process behaves on some test problems with common challenging features; (ii) the performance of NuZZ compared to other numerical approaches to the ZigZag; (iii) the error between the target and sampled distributions as a function of computational effort for different MCMC algorithms including the NuZZ. Through a series of test problems we compare the mixing of the ZigZag process against other common methods. We present numerical evidence and an analytical argument that the Wasserstein distance between the target distribution and the invariant distribution of the NuZZ process is expected to exhibit asymptotically linearly dependence on the tolerances of both the numerical integration and root finding schemes used. Notably we present a real-life example which demonstrates that NuZZ can outperform not only the super-efficient version of the ZigZag process with thinning, but also well-established methods such as Hamiltonian Monte Carlo.
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