Estimation algorithms available for rstanarm models
The modeling functions in the rstanarm package take an algorithm
argument that can be one of the following:
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. See sampling
(rstan) for more details. This is the slowest but most reliable of the
available estimation algorithms and it is the default and
recommended algorithm for statistical inference.
algorithm="meanfield")Uses mean-field variational inference to draw from an approximation 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.
algorithm="fullrank")Uses full-rank variational inference to draw from an approximation to the posterior distribution by finding the multivariate normal distribution in the unconstrained 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, fullrank variational inference is a more difficult optimization problem and the algorithm is more prone to non-convergence or convergence to a local optimum.
algorithm="optimizing")Finds the posterior mode using a C++ implementation of the LBGFS algorithm.
See optimizing for more details. 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.