Estimation algorithms

The modeling functions in the rstanarm package take an algorithm argument that can be one of the following:

Sampling

algorithm = "sampling"

Uses Markov Chain Monte Carlo (MCMC) — in particular, Hamiltonian Monte Carlo (HMC) with a tuned but diagonal mass matrix — to draw from the posterior distribution of the parameters. This is the slowest but most reliable of the available estimation algorithms and it is the default and recommended algorithm for statistical inference.

Mean-field

algorithm = "meanfield"

Uses mean-field variational inference to draw from an ap- proximation to the posterior distribution. In particular, this algorithm finds the set of independent normal distributions in the unconstrained space that — when transformed into the constrained space — most closely approximate the posterior distribution. Then it draws repeatedly from these independent normal distributions and transforms them into the constrained space. The entire process is much faster than HMC and yields independent draws but is not recommended for final statistical inference. It can be useful to narrow the set of candidate models in large problems, particularly when specifying QR=TRUE in stan_glm, stan_glmer, and stan_gamm4, but is only an approximation to the posterior distribution.

Full-rank

algorithm = "fullrank"

Uses full-rank variational inference to draw from an approximation to the posterior distribution by finding the multivariate normal distribution in the constrained space that — when transformed into the constrained space — most closely approximates the posterior distribution. Then it draws repeatedly from this multivariate normal distribution and transforms the draws into the constrained space. This process is slower than meanfield variational inference but is faster than HMC. Although still an approximation to the posterior distribution and thus not recommended for final statistical inference, the approximation is more realistic than that of mean-field variational inference because the parameters are not assumed to be independent in the unconstrained space. Nevertheless, full-rank variational inference is a more difficult optimization problem and the algorithm is more prone to non-convergence or convergence to a local optimum.

Optimizing

algorithm="optimizing"

Finds the posterior mode using a C++ implementation of the LBGFS algorithm. If there is no prior information, then this is equivalent to maximum likelihood, in which case there is no great reason to use the functions in the rstanarm package over the emulated functions in other packages. However, if priors are specified, then the estimates are penalized maximum likelihood estimates, which may have some redeeming value. Currently, optimization is only supported for stan_glm.