% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/loo_model_weights.R
\name{loo_model_weights}
\alias{loo_model_weights}
\alias{loo_model_weights.default}
\alias{stacking_weights}
\alias{pseudobma_weights}
\title{Model averaging/weighting via stacking or pseudo-BMA weighting}
\usage{
loo_model_weights(x, ...)

\method{loo_model_weights}{default}(
  x,
  ...,
  method = c("stacking", "pseudobma"),
  optim_method = "BFGS",
  optim_control = list(),
  BB = TRUE,
  BB_n = 1000,
  alpha = 1,
  r_eff_list = NULL,
  cores = getOption("mc.cores", 1)
)

stacking_weights(lpd_point, optim_method = "BFGS", optim_control = list())

pseudobma_weights(lpd_point, BB = TRUE, BB_n = 1000, alpha = 1)
}
\arguments{
\item{x}{A list of pointwise log-likelihood matrices or \code{"psis_loo"} objects
(objects returned by \code{\link[=loo]{loo()}}), one for each model. Each
matrix/object should have dimensions \eqn{S} by \eqn{N}, where \eqn{S} is
the size of the posterior sample (with all chains merged) and \eqn{N} is
the number of data points. If \code{x} is a list of log-likelihood matrices
then \code{\link[=loo]{loo()}} is called internally on each matrix. Currently the
\code{loo_model_weights()} function is not implemented to be used with
results from K-fold CV, but you can still obtain weights using K-fold CV
results by calling the \code{stacking_weights()} function directly.}

\item{...}{Unused, except for the generic to pass arguments to individual
methods.}

\item{method}{Either \code{"stacking"} (the default) or \code{"pseudobma"}, indicating which method
to use for obtaining the weights. \code{"stacking"} refers to stacking of
predictive distributions and  \code{"pseudobma"} refers to pseudo-BMA+ weighting
(or plain pseudo-BMA weighting if argument \code{BB} is \code{FALSE}).}

\item{optim_method}{If \code{method="stacking"}, a string passed to the \code{method}
argument of \code{\link[stats:constrOptim]{stats::constrOptim()}} to specify the optimization algorithm.
The default is \code{optim_method="BFGS"}, but other options are available (see
\code{\link[stats:optim]{stats::optim()}}).}

\item{optim_control}{If \code{method="stacking"}, a list of control parameters for
optimization passed to the \code{control} argument of \code{\link[stats:constrOptim]{stats::constrOptim()}}.}

\item{BB}{Logical used when \code{"method"}=\code{"pseudobma"}. If
\code{TRUE} (the default), the Bayesian bootstrap will be used to adjust
the pseudo-BMA weighting, which is called pseudo-BMA+ weighting. It helps
regularize the weight away from 0 and 1, so as to reduce the variance.}

\item{BB_n}{For pseudo-BMA+ weighting only, the number of samples to use for
the Bayesian bootstrap. The default is \code{BB_n=1000}.}

\item{alpha}{Positive scalar shape parameter in the Dirichlet distribution
used for the Bayesian bootstrap. The default is \code{alpha=1}, which
corresponds to a uniform distribution on the simplex space.}

\item{r_eff_list}{Optionally, a list of relative effective sample size
estimates for the likelihood \code{(exp(log_lik))} of each observation in
each model. See \code{\link[=psis]{psis()}} and  \code{\link[=relative_eff]{relative_eff()}} helper
function for computing \code{r_eff}. If \code{x} is a list of \code{"psis_loo"}
objects then \code{r_eff_list} is ignored.}

\item{cores}{The number of cores to use for parallelization. This defaults to
the option \code{mc.cores} which can be set for an entire R session by
\code{options(mc.cores = NUMBER)}. The old option \code{loo.cores} is now
deprecated but will be given precedence over \code{mc.cores} until
\code{loo.cores} is removed in a future release. \strong{As of version
2.0.0 the default is now 1 core if \code{mc.cores} is not set}, but we
recommend using as many (or close to as many) cores as possible.
\itemize{
\item Note for Windows 10 users: it is \strong{strongly}
\href{https://github.com/stan-dev/loo/issues/94}{recommended} to avoid using
the \code{.Rprofile} file to set \code{mc.cores} (using the \code{cores} argument or
setting \code{mc.cores} interactively or in a script is fine).
}}

\item{lpd_point}{If calling \code{stacking_weights()} or \code{pseudobma_weights()}
directly, a matrix of pointwise leave-one-out (or K-fold) log likelihoods
evaluated for different models. It should be a \eqn{N} by \eqn{K}  matrix
where \eqn{N} is sample size and \eqn{K} is the number of models. Each
column corresponds to one model. These values can be calculated
approximately using \code{\link[=loo]{loo()}} or by running exact leave-one-out or K-fold
cross-validation.}
}
\value{
A numeric vector containing one weight for each model.
}
\description{
Model averaging via stacking of predictive distributions, pseudo-BMA
weighting or pseudo-BMA+ weighting with the Bayesian bootstrap. See Yao et
al. (2018), Vehtari, Gelman, and Gabry (2017), and Vehtari, Simpson,
Gelman, Yao, and Gabry (2019) for background.
}
\details{
\code{loo_model_weights()} is a wrapper around the \code{stacking_weights()} and
\code{pseudobma_weights()} functions that implements stacking, pseudo-BMA, and
pseudo-BMA+ weighting for combining multiple predictive distributions. We can
use approximate or exact leave-one-out cross-validation (LOO-CV) or K-fold CV
to estimate the expected log predictive density (ELPD).

The stacking method (\code{method="stacking"}), which is the default for
\code{loo_model_weights()}, combines all models by maximizing the leave-one-out
predictive density of the combination distribution. That is, it finds the
optimal linear combining weights for maximizing the leave-one-out log score.

The pseudo-BMA method (\code{method="pseudobma"}) finds the relative weights
proportional to the ELPD of each model. However, when
\code{method="pseudobma"}, the default is to also use the Bayesian bootstrap
(\code{BB=TRUE}), which corresponds to the pseudo-BMA+ method. The Bayesian
bootstrap  takes into account the uncertainty of finite data points and
regularizes the weights away from the extremes of 0 and 1.

In general, we recommend stacking for averaging predictive distributions,
while pseudo-BMA+ can serve as a computationally easier alternative.
}
\examples{
\dontrun{
### Demonstrating usage after fitting models with RStan
library(rstan)

# generate fake data from N(0,1).
N <- 100
y <- rnorm(N, 0, 1)

# Suppose we have three models: N(-1, sigma), N(0.5, sigma) and N(0.6,sigma).
stan_code <- "
  data {
    int N;
    vector[N] y;
    real mu_fixed;
  }
  parameters {
    real<lower=0> sigma;
  }
  model {
    sigma ~ exponential(1);
    y ~ normal(mu_fixed, sigma);
  }
  generated quantities {
    vector[N] log_lik;
    for (n in 1:N) log_lik[n] = normal_lpdf(y[n]| mu_fixed, sigma);
  }"

mod <- stan_model(model_code = stan_code)
fit1 <- sampling(mod, data=list(N=N, y=y, mu_fixed=-1))
fit2 <- sampling(mod, data=list(N=N, y=y, mu_fixed=0.5))
fit3 <- sampling(mod, data=list(N=N, y=y, mu_fixed=0.6))
model_list <- list(fit1, fit2, fit3)
log_lik_list <- lapply(model_list, extract_log_lik)

# optional but recommended
r_eff_list <- lapply(model_list, function(x) {
  ll_array <- extract_log_lik(x, merge_chains = FALSE)
  relative_eff(exp(ll_array))
})

# stacking method:
wts1 <- loo_model_weights(
  log_lik_list,
  method = "stacking",
  r_eff_list = r_eff_list,
  optim_control = list(reltol=1e-10)
)
print(wts1)

# can also pass a list of psis_loo objects to avoid recomputing loo
loo_list <- lapply(1:length(log_lik_list), function(j) {
  loo(log_lik_list[[j]], r_eff = r_eff_list[[j]])
})

wts2 <- loo_model_weights(
  loo_list,
  method = "stacking",
  optim_control = list(reltol=1e-10)
)
all.equal(wts1, wts2)


# pseudo-BMA+ method:
set.seed(1414)
loo_model_weights(loo_list, method = "pseudobma")

# pseudo-BMA method (set BB = FALSE):
loo_model_weights(loo_list, method = "pseudobma", BB = FALSE)

# calling stacking_weights or pseudobma_weights directly
lpd1 <- loo(log_lik_list[[1]], r_eff = r_eff_list[[1]])$pointwise[,1]
lpd2 <- loo(log_lik_list[[2]], r_eff = r_eff_list[[2]])$pointwise[,1]
lpd3 <- loo(log_lik_list[[3]], r_eff = r_eff_list[[3]])$pointwise[,1]
stacking_weights(cbind(lpd1, lpd2, lpd3))
pseudobma_weights(cbind(lpd1, lpd2, lpd3))
pseudobma_weights(cbind(lpd1, lpd2, lpd3), BB = FALSE)
}

}
\references{
Vehtari, A., Gelman, A., and Gabry, J. (2017a). Practical Bayesian model
evaluation using leave-one-out cross-validation and WAIC.
\emph{Statistics and Computing}. 27(5), 1413--1432. doi:10.1007/s11222-016-9696-4
(\href{https://link.springer.com/article/10.1007/s11222-016-9696-4}{journal version},
\href{https://arxiv.org/abs/1507.04544}{preprint arXiv:1507.04544}).

Vehtari, A., Simpson, D., Gelman, A., Yao, Y., and Gabry, J. (2019).
Pareto smoothed importance sampling.
\href{https://arxiv.org/abs/1507.02646}{preprint arXiv:1507.02646}

Yao, Y., Vehtari, A., Simpson, D., and Gelman, A. (2018) Using
stacking to average Bayesian predictive distributions.
\emph{Bayesian Analysis}, advance publication,  doi:10.1214/17-BA1091.
(\href{https://projecteuclid.org/euclid.ba/1516093227}{online}).
}
\seealso{
\itemize{
\item The \strong{loo} package \href{https://mc-stan.org/loo/articles/}{vignettes}, particularly
\href{https://mc-stan.org/loo/articles/loo2-weights.html}{Bayesian Stacking and Pseudo-BMA weights using the \strong{loo} package}.
\item \code{\link[=loo]{loo()}} for details on leave-one-out ELPD estimation.
\item \code{\link[=constrOptim]{constrOptim()}} for the choice of optimization methods and control-parameters.
\item \code{\link[=relative_eff]{relative_eff()}} for computing \code{r_eff}.
}
}
