Implementation of Pareto smoothed importance sampling (PSIS), a method for stabilizing importance ratios. The version of PSIS implemented here corresponds to the algorithm presented in Vehtari, Simpson, Gelman, Yao, and Gabry (2022). For PSIS diagnostics see the pareto-k-diagnostic page.
psis(log_ratios, ...)# S3 method for array
psis(log_ratios, ..., r_eff = 1, cores = getOption("mc.cores", 1))
# S3 method for matrix
psis(log_ratios, ..., r_eff = 1, cores = getOption("mc.cores", 1))
# S3 method for default
psis(log_ratios, ..., r_eff = 1)
is.psis(x)
is.sis(x)
is.tis(x)
The psis() methods return an object of class "psis",
which is a named list with the following components:
log_weightsVector or matrix of smoothed (and truncated) but unnormalized log
weights. To get normalized weights use the
weights() method provided for objects of
class "psis".
diagnosticsA named list containing two vectors:
pareto_k: Estimates of the shape parameter \(k\) of the
generalized Pareto distribution. See the pareto-k-diagnostic
page for details.
n_eff: PSIS effective sample size estimates.
Objects of class "psis" also have the following attributes:
norm_const_logVector of precomputed values of colLogSumExps(log_weights) that are
used internally by the weights method to normalize the log weights.
tail_lenVector of tail lengths used for fitting the generalized Pareto distribution.
r_effIf specified, the user's r_eff argument.
dimsInteger vector of length 2 containing S (posterior sample size)
and N (number of observations).
methodMethod used for importance sampling, here psis.
An array, matrix, or vector of importance ratios on the log scale (for PSIS-LOO these are negative log-likelihood values). See the Methods (by class) section below for a detailed description of how to specify the inputs for each method.
Arguments passed on to the various methods.
Vector of relative effective sample size estimates containing
one element per observation. The values provided should be the relative
effective sample sizes of 1/exp(log_ratios) (i.e., 1/ratios).
This is related to the relative efficiency of estimating the normalizing
term in self-normalizing importance sampling. If r_eff is not
provided then the reported PSIS effective sample sizes and Monte Carlo
error estimates can be over-optimistic. If the posterior draws are (near)
independent then r_eff=1 can be used. r_eff has to be a scalar (same
value is used for all observations) or a vector with length equal to the
number of observations. The default value is 1. See the relative_eff()
helper function for computing r_eff.
The number of cores to use for parallelization. This defaults to
the option mc.cores which can be set for an entire R session by
options(mc.cores = NUMBER). The old option loo.cores is now
deprecated but will be given precedence over mc.cores until
loo.cores is removed in a future release. As of version
2.0.0 the default is now 1 core if mc.cores is not set, but we
recommend using as many (or close to as many) cores as possible.
Note for Windows 10 users: it is strongly
recommended to avoid using
the .Rprofile file to set mc.cores (using the cores argument or
setting mc.cores interactively or in a script is fine).
For is.psis(), an object to check.
psis(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.
psis(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.
psis(default): A vector of length \(S\) (posterior sample size).
Vehtari, A., Gelman, A., and Gabry, J. (2017). 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. (2022). Pareto smoothed importance sampling. preprint arXiv:1507.02646
log_ratios <- -1 * example_loglik_array()
r_eff <- relative_eff(exp(-log_ratios))
psis_result <- psis(log_ratios, r_eff = r_eff)
str(psis_result)
plot(psis_result)
# extract smoothed weights
lw <- weights(psis_result) # default args are log=TRUE, normalize=TRUE
ulw <- weights(psis_result, normalize=FALSE) # unnormalized log-weights
w <- weights(psis_result, log=FALSE) # normalized weights (not log-weights)
uw <- weights(psis_result, log=FALSE, normalize = FALSE) # unnormalized weights
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