
Preconditioned Crank-Nicolson (pCN)
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.



