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 paretokdiagnostic page.
psis(log_ratios, ...) # S3 method for array psis(log_ratios, ..., r_eff = NULL, cores = getOption("mc.cores", 1)) # S3 method for matrix psis(log_ratios, ..., r_eff = NULL, cores = getOption("mc.cores", 1)) # S3 method for default 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 PSISLOO these are negative loglikelihood 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 paretokdiagnostic
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 leaveoneout crossvalidation and WAIC. Statistics and Computing. 27(5), 14131432. doi:10.1007/s1122201696964 (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 LOOCV using PSIS.
paretokdiagnostic 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)#> List of 2 #> $ log_weights: num [1:1000, 1:32] 2.37 2.12 2.24 2.41 2.25 ... #> $ diagnostics:List of 2 #> ..$ pareto_k: num [1:32] 0.0447 0.0593 0.0696 0.052 0.1159 ... #> ..$ n_eff : num [1:32] 901 923 929 896 895 ... #>  attr(*, "norm_const_log")= num [1:32] 9.28 9.04 9.25 9.09 9 ... #>  attr(*, "tail_len")= num [1:32] 99 98 97 100 100 102 99 100 103 98 ... #>  attr(*, "r_eff")= num [1:32] 0.933 0.939 0.968 0.913 0.911 ... #>  attr(*, "dims")= int [1:2] 1000 32 #>  attr(*, "method")= chr "psis" #>  attr(*, "class")= chr [1:3] "psis" "importance_sampling" "list"plot(psis_result)# extract smoothed weights lw < weights(psis_result) # default args are log=TRUE, normalize=TRUE ulw < weights(psis_result, normalize=FALSE) # unnormalized logweights w < weights(psis_result, log=FALSE) # normalized weights (not logweights) uw < weights(psis_result, log=FALSE, normalize = FALSE) # unnormalized weights