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, Gelman and Gabry (2017b). For PSIS diagnostics see the pareto-k-diagnostic 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)

# S3 method for psis
weights(object, ..., log = TRUE, normalize = TRUE)

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 `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 will be over-optimistic. See the `relative_eff`

helper function for computing `r_eff`

.

cores

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.**

object

For the `weights`

method, an object
returned by `psis`

(a list with class `"psis"`

).

log

For the `weights`

method, should the weights be returned on
the log scale? Defaults to `TRUE`

.

normalize

For the `weights`

method, should the weights be
normalized? Defaults to `TRUE`

.

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).

The `weights`

method returns an object with the same dimensions
as the `log_weights`

component of the `"psis"`

object. The
`normalize`

and `log`

arguments control whether the returned
weights are normalized and whether or not to return them on the log scale.

`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.
(published
version, arXiv preprint).

Vehtari, A., Gelman, A., and Gabry, J. (2017b). Pareto smoothed importance sampling. arXiv preprint: http://arxiv.org/abs/1507.02646/

`loo`

for approximate LOO-CV using PSIS.`pareto-k-diagnostic`

for PSIS diagnostics.

```
# NOT RUN {
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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