Preconditioned Crank Picture

Preconditioned Crank-Nicolson (pCN)


Aspect
Description
Acceptance Rate The optimal acceptance rate is based on the multivariate normality of the marginal posterior distributions, and ranges from 44% for one parameter to 23.4% for five or more parameters. The observed acceptance rate may be suitable in the interval [15%,50%].
Applications This is a widely applicable, general-purpose algorithm that is most useful with large-dimensional models.
Difficulty This algorithm is easy to use, having only one tuning parameter.
Final Algorithm? Yes.
Proposal Multivariate.

Preconditioned Crank-Nicolson (pCN) was introduced originally as the PIA algorithm in Beskos et al. (2008), and differs only slightly from Random-Walk Metropolis (RWM). The proposal is a first-order autoregressive process, rather than a centered random-walk. The pCN algorithm has an acceptance probability that is invariant to dimension, making pCN useful for large-dimensional models.

pCN has one algorithm specification, beta, which is the autoregressive parameter in (0,1).

As with RWM, the target acceptance rate is 23.4%. pCN seems to perform well only with an identity matrix as the proposal covariance matrix.

Since pcN is not adaptive, it is suitable as a final algorithm.

References

  • Beskos A, Roberts GO, Stuart AM, Voss J (2008). "MCMC Methods for Diffusion Bridges." Stoch. Dyn., 8, 319-350.

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