GRIMS — General R Interface for Markov Sampling
I have released a (very) preliminary version of my new MCMC software in R, which I’m calling GRIMS, for General R Interface for Markov Sampling. You can get it here.
This software differs from other more-or-less general MCMC packages in several respects, all but one of which make it, I think, a much better tool for serious MCMC applications. Here are some highlights:
- The distribution to be sampled is defined by an R function. This allows for full flexibility in defining models. For simple models, it is a bit clumsier than a BUGS specification, but one could address this by “compiling” a BUGS-like specification into such an R function (though I have no plans to write such a compiler myself).
- The Markov chain updates are also defined by R functions, which can easily be written by the user. Of course, some updates, such as random-walk Metropolis, are pre-defined.
- The interface between the R functions defining distributions and the R functions defining Markov chain updates converts between their different preferred representations of the state. A general-purpose update function (eg, Metropolis) is most naturally written to operate on a state that is a simple vector. But a function defining the posterior distribution for a Bayesian model is most naturally written to work with a state that is a list of vectors, with named elements for various types of parameters, hyperparameters, etc.
- The top-level function for running an MCMC simulation allows one to combine several different types of updates, which may each operate on only part of the state. This is often necessary for efficient MCMC sampling for a complex model.
- GRIMS supports incremental computation, in which the log probability density for a state is quickly recomputed after only a subset of the state variables change. This is a crucial capability for some sampling methods, such as Metropolis updates with proposals that change a single variable in the state. This support depends, of course, on the function that computes the log density being written to cache suitable intermediate quantities, and make use of them when possible.
- Updates that use the gradient of the log density are supported, provided the function defining the distribution is able to compute the gradient.
- The state can be supplemented with auxiliary “momentum” variables, allowing full use of sampling methods based on Hamiltonian dynamics.
- GRIMS has flexible facilities for specifying tuning parameters of update methods (eg, proposal standard deviations), and for collecting information (eg, acceptance rates) about how the update methods are operating.
There are other additional aspects of the design (or extensions to it that I envision) that are intended to support both complex applications and complex sampling methods, including methods like tempered transtions and ensemble MCMC in which a whole series of Markov chain updates are nested within a complex outer update (though nothing that elaborate is implemented yet). It’s not completely general, however. For example, with it’s present design, GRIMS can’t easily handle states of varying dimensionality.
So what’s the one undesirable respect in which GRIMS differs from other MCMC packages? Speed. Though I haven’t quantified this yet, GRIMS is likely to be rather slow, due to the overhead of implementing the nice things listed above in R. This is one of my motivations for speeding up R, though ironically, GRIMS has ended up making heavy use of some R operations, such as subscripting lists with strings using “[[…]]”, that I haven’t (yet) looked at speeding up.
We’ll have to see how fast or slow it ends up. In any case, speed isn’t essential to all uses of GRIMS. Since much of my research is on new MCMC methods, I want a better environment for quickly trying out new MCMC methods on a variety of applications. I also want these new MCMC methods, as well as new Bayesian models that use MCMC, to have implementations that are easily accessible to statisticians, for which an R function is a lot better than a C program.
If any readers want to try out this rather unpolished preliminary version of GRIMS (or just read the documentation), I’d be interested in your comments.
UPDATE: I’ve put up a new version that fixes some bugs, adds a Gibbs sampling / overrelaxation update for normals, and adds some tests. There may still be plenty of bugs remaining.