The waic()
methods can be used to compute WAIC from the pointwise
log-likelihood. However, we recommend LOO-CV using PSIS (as implemented by
the loo()
function) because PSIS provides useful diagnostics as well as
effective sample size and Monte Carlo estimates.
waic(x, ...) # S3 method for array waic(x, ...) # S3 method for matrix waic(x, ...) # S3 method for `function` waic(x, ..., data = NULL, draws = NULL) is.waic(x)
x | A log-likelihood array, matrix, or function. The Methods (by class) section, below, has detailed descriptions of how to specify the inputs for each method. |
---|---|
draws, data, ... | For the function method only. See the Methods (by class) section below for details on these arguments. |
A named list (of class c("waic", "loo")
) with components:
estimates
A matrix with two columns ("Estimate"
, "SE"
) and three
rows ("elpd_waic"
, "p_waic"
, "waic"
). This contains
point estimates and standard errors of the expected log pointwise predictive
density (elpd_waic
), the effective number of parameters
(p_waic
) and the information criterion waic
(which is just
-2 * elpd_waic
, i.e., converted to deviance scale).
pointwise
A matrix with three columns (and number of rows equal to the number of
observations) containing the pointwise contributions of each of the above
measures (elpd_waic
, p_waic
, waic
).
array
: An \(I\) by \(C\) by \(N\) array, where \(I\)
is the number of MCMC iterations per chain, \(C\) is the number of
chains, and \(N\) is the number of data points.
matrix
: An \(S\) by \(N\) matrix, where \(S\) is the size
of the posterior sample (with all chains merged) and \(N\) is the number
of data points.
function
: A function f()
that takes arguments data_i
and draws
and returns a
vector containing the log-likelihood for a single observation i
evaluated
at each posterior draw. The function should be written such that, for each
observation i
in 1:N
, evaluating
f(data_i = data[i,, drop=FALSE], draws = draws)
results in a vector of length S
(size of posterior sample). The
log-likelihood function can also have additional arguments but data_i
and
draws
are required.
If using the function method then the arguments data
and draws
must also
be specified in the call to loo()
:
data
: A data frame or matrix containing the data (e.g.
observed outcome and predictors) needed to compute the pointwise
log-likelihood. For each observation i
, the i
th row of
data
will be passed to the data_i
argument of the
log-likelihood function.
draws
: An object containing the posterior draws for any
parameters needed to compute the pointwise log-likelihood. Unlike
data
, which is indexed by observation, for each observation the
entire object draws
will be passed to the draws
argument of
the log-likelihood function.
The ...
can be used if your log-likelihood function takes additional
arguments. These arguments are used like the draws
argument in that they
are recycled for each observation.
Watanabe, S. (2010). Asymptotic equivalence of Bayes cross validation and widely application information criterion in singular learning theory. Journal of Machine Learning Research 11, 3571-3594.
Vehtari, A., Gelman, A., and Gabry, J. (2017a). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing. 27(5), 1413--1432. doi:10.1007/s11222-016-9696-4 (journal version, preprint arXiv:1507.04544).
Vehtari, A., Simpson, D., Gelman, A., Yao, Y., and Gabry, J. (2019). Pareto smoothed importance sampling. preprint arXiv:1507.02646
The loo package vignettes and
Vehtari, Gelman, and Gabry (2017) and Vehtari, Simpson, Gelman, Yao,
and Gabry (2019) for more details on why we prefer loo()
to waic()
.
loo_compare()
for comparing models on approximate LOO-CV or WAIC.
#> [1] 500 2 32#> [1] 1000 32waic_arr <- waic(LLarr)#> Warning: #> 3 (9.4%) p_waic estimates greater than 0.4. We recommend trying loo instead.waic_mat <- waic(LLmat)#> Warning: #> 3 (9.4%) p_waic estimates greater than 0.4. We recommend trying loo instead.#> [1] TRUEif (FALSE) { log_lik1 <- extract_log_lik(stanfit1) log_lik2 <- extract_log_lik(stanfit2) (waic1 <- waic(log_lik1)) (waic2 <- waic(log_lik2)) print(compare(waic1, waic2), digits = 2) }