Pareto smoothed importance sampling (PSIS)
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 (2019). For PSIS diagnostics see the pareto-k-diagnostic page.
psis(log_ratios, ...) ## S3 method for class 'array' psis(log_ratios, ..., r_eff = NULL, cores = getOption("mc.cores", 1)) ## S3 method for class 'matrix' psis(log_ratios, ..., r_eff = NULL, cores = getOption("mc.cores", 1)) ## Default S3 method: psis(log_ratios, ..., r_eff = NULL) is.psis(x) is.sis(x) is.tis(x)
log_ratios |
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. |
r_eff |
Vector of relative effective sample size estimates containing
one element per observation. The values provided should be the relative
effective sample sizes of |
cores |
The number of cores to use for parallelization. This defaults to
the option
|
x |
For |
The psis()
methods return an object of class "psis"
,
which is a named list with the following components:
log_weights
Vector or matrix of smoothed (and truncated) but unnormalized log
weights. To get normalized weights use the
weights()
method provided for objects of
class "psis"
.
diagnostics
A 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_log
Vector of precomputed values of colLogSumExps(log_weights)
that are
used internally by the weights
method to normalize the log weights.
tail_len
Vector of tail lengths used for fitting the generalized Pareto distribution.
r_eff
If specified, the user's r_eff
argument.
dims
Integer vector of length 2 containing S
(posterior sample size)
and N
(number of observations).
method
Method used for importance sampling, here 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.
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.
default
: A vector of length S (posterior sample size).
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
loo()
for approximate LOO-CV using PSIS.
pareto-k-diagnostic for PSIS diagnostics.
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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