  Physical parameters are often constrained from the data likelihoods using
sampling methods. Changing some parameters can be much more computationally
expensive (`slow') than changing other parameters (`fast parameters'). I
describe a method for decorrelating fast and slow parameters so that parameter
sampling in the full space becomes almost as efficient as sampling in the slow
subspace when the covariance is well known and the distributions are simple.
This gives a large reduction in computational cost when there are many fast
parameters. The method can also be combined with a fast 'dragging' method
proposed by Neal (2005) that can be more robust and efficient when parameters
cannot be fully decorrelated a priori or have more complicated dependencies. I
illustrate these methods for the case of cosmological parameter estimation
using data likelihoods from the Planck satellite observations with dozens of
fast nuisance parameters, and demonstrate a speed up by a factor of five or
more. In more complicated cases, especially where the fast subspace is very
fast but complex or highly correlated, the fast-slow sampling methods can in
principle give arbitrarily large performance gains. The new samplers are
implemented in the latest version of the publicly available CosmoMC code.
