**New sample size specific diagnostic threshold for Pareto**. The pre-2022 version of the PSIS paper recommended diagnostic thresholds of`k`

`k < 0.5 "good"`

,`0.5 <= k < 0.7 "ok"`

,`0.7 <= k < 1 "bad"`

,`k>=1 "very bad"`

. The 2022 revision of the PSIS paper now recommends`k < min(1 - 1/log10(S), 0.7) "good"`

,`min(1 - 1/log10(S), 0.7) <= k < 1 "bad"`

,`k > 1 "very bad"`

, where`S`

is the sample size. There is now one fewer diagnostic threshold (`"ok"`

has been removed), and the most important threshold now depends on the sample size`S`

. With sample sizes`100`

,`320`

,`1000`

,`2200`

,`10000`

the sample size specific part`1 - 1/log10(S)`

corresponds to thresholds of`0.5`

,`0.6`

,`0.67`

,`0.7`

,`0.75`

. Even if the sample size grows, the bias in the PSIS estimate dominates if`0.7 <= k < 1`

, and thus the diagnostic threshold for good is capped at`0.7`

(if`k > 1`

, the mean does not exist and bias is not a valid measure). The new recommended thresholds are based on more careful bias-variance analysis of PSIS based on truncated Pareto sums theory. For those who use the Stan default 4000 posterior draws, the`0.7`

threshold will be roughly the same, but there will be fewer warnings as there will be no diagnostic message for`0.5 <= k < 0.7`

. Those who use smaller sample sizes may see diagnostic messages with a threshold less than`0.7`

, and they can simply increase the sample size to about`2200`

to get the threshold to`0.7`

.**No more warnings if the**, and the default is now`r_eff`

argument is not provided`r_eff = 1`

. The summary print output showing MCSE and ESS now shows diagnostic information on the range of`r_eff`

. The change was made to reduce unnecessary warnings. The use of`r_eff`

does not change the expected value of`elpd_loo`

,`p_loo`

, and Pareto`k`

, and is needed only to estimate MCSE and ESS. Thus it is better to show the diagnostic information about`r_eff`

only when MCSE and ESS values are shown.

- Make Pareto
`k`

Inf if it is NA by @topipa in #224 - Fix bug in
`E_loo()`

when type is variance by @jgabry in #226 `E_loo()`

now allows`type="sd"`

by @jgabry in #226- update array syntax in vignettes by @jgabry in #229
- Fix unbalanced knitr backticks by @jgabry in #232
- include cc-by 4.0 license for documentation by @jgabry in #216
- Add order statistic warning by @yannmclatchie in #230
`pointwise()`

convenience function for extracting pointwise estimates by @jgabry in #241- use new
`k`

threshold by @avehtari in #235 - simplify
`mcse_elpd`

using log-normal approximation by @avehtari in #246 - show NA for
`n_eff/ESS`

if`k > k_threshold`

by @avehtari in #248 - improved
`E_loo()`

Pareto-k diagnostics by @avehtari in #247 - Doc improvement in
`loo_subsample.R`

by @avehtari in #238 - Fix typo and deprecations in LFO vignette by @jgabry in #244
- Register internal S3 methods by @jgabry in #239
- Avoid R cmd check NOTEs about some internal functions by @jgabry in #240
- fix R cmd check note due to importance_sampling roxygen template by @jgabry in #233
- fix R cmd check notes by @jgabry in #242

New

`loo_predictive_metric()`

function for computing estimates of leave-one-out predictive metrics: mean absolute error, mean squared error and root mean squared error for continuous predictions, and accuracy and balanced accuracy for binary classification. (#202, @LeeviLindgren)New functions

`crps()`

,`scrps()`

,`loo_crps()`

, and`loo_scrps()`

for computing the (scaled) continuously ranked probability score. (#203, @LeeviLindgren)New vignette “Mixture IS leave-one-out cross-validation for high-dimensional Bayesian models.” This is a demonstration of the mixture estimators proposed by Silva and Zanella (2022). (#210)

- Minor fix to model names displayed by
`loo_model_weights()`

to make them consistent with`loo_compare()`

. (#217)

- Fix R CMD check error on M1 Mac

New Frequently Asked Questions page on the package website. (#143)

Speed improvement from simplifying the normalization when fitting the generalized Pareto distribution. (#187, @sethaxen)

Added parallel likelihood computation to speedup

`loo_subsample()`

when using posterior approximations. (#171, @kdubovikov)Switch unit tests from Travis to GitHub Actions. (#164)

- Fixed a bug causing the normalizing constant of the PSIS (log) weights not to get updated when performing moment matching with
`save_psis = TRUE`

(#166, @fweber144).

- Fixed issue reported by CRAN where one of the vignettes errored on an M1 Mac due to RStan’s dependency on V8.

Fixed a bug in

`relative_eff.function()`

that caused an error on Windows when using multiple cores. (#152)Fixed a potential numerical issue in

`loo_moment_match()`

with`split=TRUE`

. (#153)Fixed potential integer overflow with

`loo_moment_match()`

. (#155, @ecmerkle)Fixed

`relative_eff()`

when used with a`posterior::draws_array`

. (#161, @rok-cesnovar)

- New generic function
`elpd()`

(and methods for matrices and arrays) for computing expected log predictive density of new data or log predictive density of observed data. A new vignette demonstrates using this function when doing K-fold CV with rstan. (#159, @bnicenboim)

- Fixed a bug in
`loo_moment_match()`

that prevented`...`

arguments from being used correctly. (#149)

Added Topi Paananen and Paul Bürkner as coauthors.

New function

`loo_moment_match()`

(and new vignette), which can be used to update a`loo`

object when Pareto k estimates are large. (#130)The log weights provided by the importance sampling functions

`psis()`

,`tis()`

, and`sis()`

no longer have the largest log ratio subtracted from them when returned to the user. This should be less confusing for anyone using the`weights()`

method to make an importance sampler. (#112, #146)MCSE calculation is now deterministic (#116, #147)

Added Mans Magnusson as a coauthor.

New functions

`loo_subsample()`

and`loo_approximate_posterior()`

(and new vignette) for doing PSIS-LOO with large data. (#113)Added support for standard importance sampling and truncated importance sampling (functions

`sis()`

and`tis()`

). (#125)`compare()`

now throws a deprecation warning suggesting`loo_compare()`

. (#93)A smaller threshold is used when checking the uniqueness of tail values. (#124)

For WAIC, warnings are only thrown when running

`waic()`

and not when printing a`waic`

object. (#117, @mcol)Use markdown syntax in roxygen documentation wherever possible. (#108)

New function

`loo_compare()`

for model comparison that will eventually replace the existing`compare()`

function. (#93)New vignette on LOO for non-factorizable joint Gaussian models. (#75)

New vignette on “leave-future-out” cross-validation for time series models. (#90)

New glossary page (use

`help("loo-glossary")`

) with definitions of key terms. (#81)New

`se_diff`

column in model comparison results. (#78)Improved stability of

`psis()`

when`log_ratios`

are very small. (#74)Allow

`r_eff=NA`

to suppress warning when specifying`r_eff`

is not applicable (i.e., draws not from MCMC). (#72)Update effective sample size calculations to match RStan’s version. (#85)

Naming of k-fold helper functions now matches scikit-learn. (#96)

This is a major release with many changes. Whenever possible we have opted to deprecate rather than remove old functionality, but it is possible that old code that accesses elements inside loo objects by position rather than name may error.

New package documentation website http://mc-stan.org/loo/ with vignettes, function reference, news.

Updated existing vignette and added two new vignettes demonstrating how to use the package.

New function

`psis()`

replaces`psislw()`

(now deprecated). This version implements the improvements to the PSIS algorithm described in the latest version of https://arxiv.org/abs/1507.02646. Additional diagnostic information is now also provided, including PSIS effective sample sizes.New

`weights()`

method for extracting smoothed weights from a`psis`

object. Arguments`log`

and`normalize`

control whether the weights are returned on the log scale and whether they are normalized.Updated the interface for the

`loo()`

methods to integrate nicely with the new PSIS algorithm. Methods for log-likelihood arrays, matrices, and functions are provided. Several arguments have changed, particularly for the`loo.function`

method. The documentation at`help("loo")`

has been updated to describe the new behavior.The structure of the objects returned by the

`loo()`

function has also changed slightly, as described in the**Value**section at`help("loo", package = "loo")`

.New function

`loo_model_weights()`

computes weights for model averaging as described in https://arxiv.org/abs/1704.02030. Implemented methods include stacking of predictive distributions, pseudo-BMA weighting or pseudo-BMA+ weighting with the Bayesian bootstrap.Setting

`options(loo.cores=...)`

is now deprecated in favor of`options(mc.cores=...)`

. For now, if both the`loo.cores`

and`mc.cores`

options have been set, preference will be given to`loo.cores`

until it is removed in a future release. (thanks to @cfhammill)New functions

`example_loglik_array()`

and`example_loglik_matrix()`

that provide objects to use in examples and tests.When comparing more than two models with

`compare()`

, the first column of the output is now the`elpd`

difference from the model in the first row.New helper functions for splitting observations for K-fold CV:

`kfold_split_random()`

,`kfold_split_balanced()`

,`kfold_split_stratified()`

. Additional helper functions for implementing K-fold CV will be included in future releases.

- Introduce the
`E_loo()`

function for computing weighted expectations (means, variances, quantiles).

`pareto_k_table()`

and`pareto_k_ids()`

convenience functions for quickly identifying problematic observations- pareto k values now grouped into
`(-Inf, 0.5]`

,`(0.5, 0.7]`

,`(0.7, 1]`

,`(1, Inf)`

(didn’t used to include 0.7) - warning messages are now issued by
`psislw()`

instead of`print.loo`

`print.loo()`

shows a table of pareto k estimates (if any k > 0.7)- Add argument to
`compare()`

to allow loo objects to be provided in a list rather than in`'...'`

- Update references to point to published paper

- GitHub repository moved from @jgabry to @stan-dev
- Better error messages from
`extract_log_lik()`

- Fix example code in vignette (thanks to GitHub user @krz)

- Add warnings if any p_waic estimates are greather than 0.4
- Improve line coverage of tests to 100%
- Update references in documentation
- Remove model weights from
`compare()`

. In previous versions of**loo**model weights were also reported by`compare()`

. We have removed the weights because they were based only on the point estimate of the elpd values ignoring the uncertainty. We are currently working on something similar to these weights that also accounts for uncertainty, which will be included in future versions of**loo**.

This update makes it easier for other package authors using **loo** to write tests that involve running the `loo`

function. It also includes minor bug fixes and additional unit tests. Highlights:

- Don’t call functions from
**parallel**package if`cores=1`

. - Return entire vector/matrix of smoothed weights rather than a summary statistic when
`psislw`

function is called in an interactive session. - Test coverage > 80%

This update provides several important improvements, most notably an alternative method for specifying the pointwise log-likelihood that reduces memory usage and allows for **loo** to be used with larger datasets. This update also makes it easier to to incorporate **loo**’s functionality into other packages.

- Add Ben Goodrich as contributor
- S3 generics and
`matrix`

and`function`

methods for both`loo()`

and`waic()`

. The matrix method provide the same functionality as in previous versions of**loo**(taking a log-likelihood matrix as the input). The function method allows the user to provide a function for computing the log-likelihood from the data and posterior draws (which are also provided by the user). The function method is less memory intensive and should make it possible to use**loo**for models fit to larger amounts of data than before. - Separate
`plot`

and`print`

methods.`plot`

also provides`label_points`

argument, which, if`TRUE`

, will label any Pareto`k`

points greater than 1/2 by the index number of the corresponding observation. The plot method also now warns about`Inf`

/`NA`

/`NaN`

values of`k`

that are not shown in the plot. `compare`

now returns model weights and accepts more than two inputs.- Allow setting number of cores using
`options(loo.cores = NUMBER)`

.

- Updates names in package to reflect name changes in the accompanying paper.

- Better handling of special cases
- Deprecates
`loo_and_waic`

function in favor of separate functions`loo`

and`waic`

- Deprecates
`loo_and_waic_diff`

. Use`compare`

instead.

- Initial release