From a2db12074c0a9fd037db560bdf70bb9c701009f5 Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Tue, 17 Mar 2026 19:58:14 +0100
Subject: [PATCH 01/13] set up documentation structure

---
 NAMESPACE           |  1 +
 R/loo_subsample.R   | 25 ++++++++++++++++++++++---
 man/srs_diff_est.Rd | 35 +++++++++++++++++++++++++++++++++++
 3 files changed, 58 insertions(+), 3 deletions(-)
 create mode 100644 man/srs_diff_est.Rd

diff --git a/NAMESPACE b/NAMESPACE
index 3405d737..05ffb3d1 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -154,6 +154,7 @@ export(psislw)
 export(relative_eff)
 export(scrps)
 export(sis)
+export(srs_diff_est)
 export(stacking_weights)
 export(tis)
 export(waic)
diff --git a/R/loo_subsample.R b/R/loo_subsample.R
index bcac4b17..1ba59ae9 100644
--- a/R/loo_subsample.R
+++ b/R/loo_subsample.R
@@ -1166,12 +1166,31 @@ loo_subsample_estimation_diff_srs <- function(x) {
   update_psis_loo_ss_estimates(x)
 }
 
-#' Difference estimation using SRS-WOR sampling (Magnusson et al., 2020)
-#' @noRd
+#' @title Difference estimation using SRS-WOR sampling
+#'
+#' @description This paragraph describes the function.
+#'
+#' @return A list with estimates. Function 9 of Magnusson et al. (2020).
+#'
+#' @details
+#' Implements Equations 7-9 of Magnusson et al. (2020).
+#'
+#'
 #' @param y_approx Approximated values of all observations.
 #' @param y The values observed.
 #' @param y_idx The index of `y` in `y_approx`.
-#' @return A list with estimates.
+#'
+#' @references
+#' Magnusson, M., Riis Andersen, M., Jonasson, J. and Vehtari, A. (2020).
+#' Leave-One-Out Cross-Validation for Model Comparison in Large Data.
+#' In _Proceedings of the 23rd International Conference on Artificial
+#' Intelligence and Statistics (AISTATS)_, PMLR 108:341-351.
+#'
+#' @seealso [loo_subsample()]
+#' @export
+#'
+#' @examples
+#' print(42)
 srs_diff_est <- function(y_approx, y, y_idx) {
   checkmate::assert_numeric(y_approx)
   checkmate::assert_numeric(y, max.len = length(y_approx))
diff --git a/man/srs_diff_est.Rd b/man/srs_diff_est.Rd
new file mode 100644
index 00000000..0fdc5ce7
--- /dev/null
+++ b/man/srs_diff_est.Rd
@@ -0,0 +1,35 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/loo_subsample.R
+\name{srs_diff_est}
+\alias{srs_diff_est}
+\title{Difference estimation using SRS-WOR sampling}
+\usage{
+srs_diff_est(y_approx, y, y_idx)
+}
+\arguments{
+\item{y_approx}{Approximated values of all observations.}
+
+\item{y}{The values observed.}
+
+\item{y_idx}{The index of \code{y} in \code{y_approx}.}
+}
+\value{
+A list with estimates.
+}
+\description{
+This paragraph describes the function.
+}
+\details{
+Implements Equations 7-9 of Magnusson et al. (2020).
+}
+\examples{
+print(42)
+}
+\references{
+Magnusson, M., Riis Andersen, M., Jonasson, J. and Vehtari, A. (2020).
+Leave-One-Out Cross-Validation for Model Comparison in Large Data.
+In \emph{Proceedings of the 23rd International Conference on Artificial
+Intelligence and Statistics (AISTATS)}, PMLR 108:341-351.
+}
+\code{\link[=loo_subsample]{loo_subsample()}}
+}

From 5fe5c340bcf3dc2019f84079f47322782772c012 Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Tue, 17 Mar 2026 20:01:34 +0100
Subject: [PATCH 02/13] srs_diff_est.Rd matches .R documentation

---
 man/srs_diff_est.Rd | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/man/srs_diff_est.Rd b/man/srs_diff_est.Rd
index 0fdc5ce7..175c2356 100644
--- a/man/srs_diff_est.Rd
+++ b/man/srs_diff_est.Rd
@@ -14,7 +14,7 @@ srs_diff_est(y_approx, y, y_idx)
 \item{y_idx}{The index of \code{y} in \code{y_approx}.}
 }
 \value{
-A list with estimates.
+A list with estimates. Function 9 of Magnusson et al. (2020).
 }
 \description{
 This paragraph describes the function.
@@ -31,5 +31,6 @@ Leave-One-Out Cross-Validation for Model Comparison in Large Data.
 In \emph{Proceedings of the 23rd International Conference on Artificial
 Intelligence and Statistics (AISTATS)}, PMLR 108:341-351.
 }
+\seealso{
 \code{\link[=loo_subsample]{loo_subsample()}}
 }

From 6e8862d8f641d455ed29669382c70484472d9fac Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Sun, 22 Mar 2026 11:53:51 +0100
Subject: [PATCH 03/13] added documentation

as proposed by @avehtari in issue #333
---
 R/loo_subsample.R   | 27 +++++++++++++++++++--------
 man/srs_diff_est.Rd | 28 ++++++++++++++++++++++------
 2 files changed, 41 insertions(+), 14 deletions(-)

diff --git a/R/loo_subsample.R b/R/loo_subsample.R
index 1ba59ae9..48b95e1b 100644
--- a/R/loo_subsample.R
+++ b/R/loo_subsample.R
@@ -1166,19 +1166,30 @@ loo_subsample_estimation_diff_srs <- function(x) {
   update_psis_loo_ss_estimates(x)
 }
 
-#' @title Difference estimation using SRS-WOR sampling
+#' Difference estimator with simple random sampling without replacement.
 #'
-#' @description This paragraph describes the function.
+#' The difference estimator `srs_diff()` estimates
+#' the expectation $nE[y]$ when we have $n$ approximate values $\tilde{y}_i$,
+#' $i=1,\ldots,n$ and $m<n$ accurate values $y_j$, $j \in
+#' \mathcal{S}$, where $m$ is the subsample size and $\mathcal{S}$ is
+#' a simple random subsample without replacement.  The original
+#' approach is by Cochran (1977) and we follow the equations 7--9 by
+#' Magnusson et al. (2020).
 #'
 #' @return A list with estimates. Function 9 of Magnusson et al. (2020).
 #'
-#' @details
-#' Implements Equations 7-9 of Magnusson et al. (2020).
-#'
+#' @details Magnusson et al. (2020) Eq (9) first row second `+` should
+#'   be `-`. Supplementary material Eq (6) has this correct.
+#'   As `srs_diff_est()` in `loo` package is used for $nE[y]$, there is
+#'   a proportional difference of $1/n$ compared to the paper.
 #'
-#' @param y_approx Approximated values of all observations.
-#' @param y The values observed.
-#' @param y_idx The index of `y` in `y_approx`.
+#' @param y_approx (numeric) `n` approximated values.
+#' @param y (numeric) `m<n` subsampled values.
+#' @param y_idx (integerish) The index of `y` in `y_approx`.
+#' @return A named list containing numeric values:
+#' * `y_hat`: estimated mean of $y$ (Eq 7),
+#' * `v_y_hat`: variance of the mean estimate (Eq 8), and
+#' * `hat_v_y`: estimated variance of $y$ (Eq 9).
 #'
 #' @references
 #' Magnusson, M., Riis Andersen, M., Jonasson, J. and Vehtari, A. (2020).
diff --git a/man/srs_diff_est.Rd b/man/srs_diff_est.Rd
index 175c2356..1f6843d5 100644
--- a/man/srs_diff_est.Rd
+++ b/man/srs_diff_est.Rd
@@ -2,25 +2,41 @@
 % Please edit documentation in R/loo_subsample.R
 \name{srs_diff_est}
 \alias{srs_diff_est}
-\title{Difference estimation using SRS-WOR sampling}
+\title{Difference estimator with simple random sampling without replacement.}
 \usage{
 srs_diff_est(y_approx, y, y_idx)
 }
 \arguments{
-\item{y_approx}{Approximated values of all observations.}
+\item{y_approx}{(numeric) \code{n} approximated values.}
 
-\item{y}{The values observed.}
+\item{y}{(numeric) \code{m<n} subsampled values.}
 
-\item{y_idx}{The index of \code{y} in \code{y_approx}.}
+\item{y_idx}{(integerish) The index of \code{y} in \code{y_approx}.}
 }
 \value{
 A list with estimates. Function 9 of Magnusson et al. (2020).
+
+A named list containing numeric values:
+\itemize{
+\item \code{y_hat}: estimated mean of $y$ (Eq 7),
+\item \code{v_y_hat}: variance of the mean estimate (Eq 8), and
+\item \code{hat_v_y}: estimated variance of $y$ (Eq 9).
+}
 }
 \description{
-This paragraph describes the function.
+The difference estimator \code{srs_diff()} estimates
+the expectation $nE\link[ggplot2:aes_position]{ggplot2::y}$ when we have $n$ approximate values $\tilde{y}_i$,
+$i=1,\ldots,n$ and $m<n$ accurate values $y_j$, $j \in
+\mathcal{S}$, where $m$ is the subsample size and $\mathcal{S}$ is
+a simple random subsample without replacement.  The original
+approach is by Cochran (1977) and we follow the equations 7--9 by
+Magnusson et al. (2020).
 }
 \details{
-Implements Equations 7-9 of Magnusson et al. (2020).
+Magnusson et al. (2020) Eq (9) first row second \code{+} should
+be \code{-}. Supplementary material Eq (6) has this correct.
+As \code{srs_diff_est()} in \code{loo} package is used for $nE\link[ggplot2:aes_position]{ggplot2::y}$, there is
+a proportional difference of $1/n$ compared to the paper.
 }
 \examples{
 print(42)

From bf6b2b3de415cac9a4f21b1f165b63bd685d8038 Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Sun, 22 Mar 2026 11:56:36 +0100
Subject: [PATCH 04/13] added @seealso at loo_subsample()

---
 R/loo_subsample.R    | 2 +-
 man/loo_subsample.Rd | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/R/loo_subsample.R b/R/loo_subsample.R
index 48b95e1b..9a1143d7 100644
--- a/R/loo_subsample.R
+++ b/R/loo_subsample.R
@@ -24,7 +24,7 @@
 #'   same length containing the posterior density and the approximation density
 #'   for the individual draws.
 #'
-#' @seealso [loo()], [psis()], [loo_compare()]
+#' @seealso [loo()], [psis()], [loo_compare()], [srs_diff_est()]
 #' @template loo-large-data-references
 #'
 #' @export loo_subsample loo_subsample.function
diff --git a/man/loo_subsample.Rd b/man/loo_subsample.Rd
index 6f381db6..5889be1e 100644
--- a/man/loo_subsample.Rd
+++ b/man/loo_subsample.Rd
@@ -196,5 +196,5 @@ In \emph{Proceedings of the 23rd International Conference on Artificial
 Intelligence and Statistics (AISTATS)}, PMLR 108:341-351.
 }
 \seealso{
-\code{\link[=loo]{loo()}}, \code{\link[=psis]{psis()}}, \code{\link[=loo_compare]{loo_compare()}}
+\code{\link[=loo]{loo()}}, \code{\link[=psis]{psis()}}, \code{\link[=loo_compare]{loo_compare()}}, \code{\link[=srs_diff_est]{srs_diff_est()}}
 }

From 6f485ac5165e4041dbac49358ceae68d7dccdf30 Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Sun, 22 Mar 2026 11:59:29 +0100
Subject: [PATCH 05/13] added reference Cochran (1977)

---
 R/loo_subsample.R   | 2 ++
 man/srs_diff_est.Rd | 2 ++
 2 files changed, 4 insertions(+)

diff --git a/R/loo_subsample.R b/R/loo_subsample.R
index 9a1143d7..60261e58 100644
--- a/R/loo_subsample.R
+++ b/R/loo_subsample.R
@@ -1197,6 +1197,8 @@ loo_subsample_estimation_diff_srs <- function(x) {
 #' In _Proceedings of the 23rd International Conference on Artificial
 #' Intelligence and Statistics (AISTATS)_, PMLR 108:341-351.
 #'
+#' Cochran, W. G. (1977). _Sampling Techniques, 3rd Edition_. John Wiley.
+#'
 #' @seealso [loo_subsample()]
 #' @export
 #'
diff --git a/man/srs_diff_est.Rd b/man/srs_diff_est.Rd
index 1f6843d5..a82b35e5 100644
--- a/man/srs_diff_est.Rd
+++ b/man/srs_diff_est.Rd
@@ -46,6 +46,8 @@ Magnusson, M., Riis Andersen, M., Jonasson, J. and Vehtari, A. (2020).
 Leave-One-Out Cross-Validation for Model Comparison in Large Data.
 In \emph{Proceedings of the 23rd International Conference on Artificial
 Intelligence and Statistics (AISTATS)}, PMLR 108:341-351.
+
+Cochran, W. G. (1977). \emph{Sampling Techniques, 3rd Edition}. John Wiley.
 }
 \seealso{
 \code{\link[=loo_subsample]{loo_subsample()}}

From 67275cf92ae6cbb103e72ec0379326617787762c Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Sun, 22 Mar 2026 12:01:20 +0100
Subject: [PATCH 06/13] removed oudated @return duplicate

---
 R/loo_subsample.R | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/R/loo_subsample.R b/R/loo_subsample.R
index 60261e58..788e4bb2 100644
--- a/R/loo_subsample.R
+++ b/R/loo_subsample.R
@@ -1176,8 +1176,6 @@ loo_subsample_estimation_diff_srs <- function(x) {
 #' approach is by Cochran (1977) and we follow the equations 7--9 by
 #' Magnusson et al. (2020).
 #'
-#' @return A list with estimates. Function 9 of Magnusson et al. (2020).
-#'
 #' @details Magnusson et al. (2020) Eq (9) first row second `+` should
 #'   be `-`. Supplementary material Eq (6) has this correct.
 #'   As `srs_diff_est()` in `loo` package is used for $nE[y]$, there is
@@ -1186,6 +1184,7 @@ loo_subsample_estimation_diff_srs <- function(x) {
 #' @param y_approx (numeric) `n` approximated values.
 #' @param y (numeric) `m<n` subsampled values.
 #' @param y_idx (integerish) The index of `y` in `y_approx`.
+#'
 #' @return A named list containing numeric values:
 #' * `y_hat`: estimated mean of $y$ (Eq 7),
 #' * `v_y_hat`: variance of the mean estimate (Eq 8), and

From caa9ef6b18099258bd7111c43c741eef2b2abbf6 Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Sun, 22 Mar 2026 12:14:14 +0100
Subject: [PATCH 07/13] corrected .R formulas to render in .Rd

---
 R/loo_subsample.R   | 18 +++++++++---------
 man/srs_diff_est.Rd | 20 +++++++++-----------
 2 files changed, 18 insertions(+), 20 deletions(-)

diff --git a/R/loo_subsample.R b/R/loo_subsample.R
index 788e4bb2..1805cd36 100644
--- a/R/loo_subsample.R
+++ b/R/loo_subsample.R
@@ -1169,26 +1169,26 @@ loo_subsample_estimation_diff_srs <- function(x) {
 #' Difference estimator with simple random sampling without replacement.
 #'
 #' The difference estimator `srs_diff()` estimates
-#' the expectation $nE[y]$ when we have $n$ approximate values $\tilde{y}_i$,
-#' $i=1,\ldots,n$ and $m<n$ accurate values $y_j$, $j \in
-#' \mathcal{S}$, where $m$ is the subsample size and $\mathcal{S}$ is
+#' the expectation \eqn{n E[y]} when we have \eqn{n} approximate values \eqn{\tilde{y}_i},
+#' \eqn{i = 1, \ldots, n} and \eqn{m < n} accurate values \eqn{y_j}, \eqn{j \in \mathcal{S}},
+#' where \eqn{m} is the subsample size and \eqn{\mathcal{S}} is
 #' a simple random subsample without replacement.  The original
 #' approach is by Cochran (1977) and we follow the equations 7--9 by
 #' Magnusson et al. (2020).
 #'
-#' @details Magnusson et al. (2020) Eq (9) first row second `+` should
-#'   be `-`. Supplementary material Eq (6) has this correct.
-#'   As `srs_diff_est()` in `loo` package is used for $nE[y]$, there is
-#'   a proportional difference of $1/n$ compared to the paper.
+#' @details In Magnusson et al. (2020) Eq (9) first row, the second `+` should
+#'   be a `-`; Supplementary Material Eq (6) has this correct.
+#'   As `srs_diff_est()` in the `loo` package is used for \eqn{n E[y]}, there is
+#'   a proportional difference of \eqn{1/n} compared to the paper.
 #'
 #' @param y_approx (numeric) `n` approximated values.
 #' @param y (numeric) `m<n` subsampled values.
 #' @param y_idx (integerish) The index of `y` in `y_approx`.
 #'
 #' @return A named list containing numeric values:
-#' * `y_hat`: estimated mean of $y$ (Eq 7),
+#' * `y_hat`: estimated mean of \eqn{y} (Eq 7),
 #' * `v_y_hat`: variance of the mean estimate (Eq 8), and
-#' * `hat_v_y`: estimated variance of $y$ (Eq 9).
+#' * `hat_v_y`: estimated variance of \eqn{y} (Eq 9).
 #'
 #' @references
 #' Magnusson, M., Riis Andersen, M., Jonasson, J. and Vehtari, A. (2020).
diff --git a/man/srs_diff_est.Rd b/man/srs_diff_est.Rd
index a82b35e5..274a7e0e 100644
--- a/man/srs_diff_est.Rd
+++ b/man/srs_diff_est.Rd
@@ -14,29 +14,27 @@ srs_diff_est(y_approx, y, y_idx)
 \item{y_idx}{(integerish) The index of \code{y} in \code{y_approx}.}
 }
 \value{
-A list with estimates. Function 9 of Magnusson et al. (2020).
-
 A named list containing numeric values:
 \itemize{
-\item \code{y_hat}: estimated mean of $y$ (Eq 7),
+\item \code{y_hat}: estimated mean of \eqn{y} (Eq 7),
 \item \code{v_y_hat}: variance of the mean estimate (Eq 8), and
-\item \code{hat_v_y}: estimated variance of $y$ (Eq 9).
+\item \code{hat_v_y}: estimated variance of \eqn{y} (Eq 9).
 }
 }
 \description{
 The difference estimator \code{srs_diff()} estimates
-the expectation $nE\link[ggplot2:aes_position]{ggplot2::y}$ when we have $n$ approximate values $\tilde{y}_i$,
-$i=1,\ldots,n$ and $m<n$ accurate values $y_j$, $j \in
-\mathcal{S}$, where $m$ is the subsample size and $\mathcal{S}$ is
+the expectation \eqn{n E[y]} when we have \eqn{n} approximate values \eqn{\tilde{y}_i},
+\eqn{i = 1, \ldots, n} and \eqn{m < n} accurate values \eqn{y_j}, \eqn{j \in \mathcal{S}},
+where \eqn{m} is the subsample size and \eqn{\mathcal{S}} is
 a simple random subsample without replacement.  The original
 approach is by Cochran (1977) and we follow the equations 7--9 by
 Magnusson et al. (2020).
 }
 \details{
-Magnusson et al. (2020) Eq (9) first row second \code{+} should
-be \code{-}. Supplementary material Eq (6) has this correct.
-As \code{srs_diff_est()} in \code{loo} package is used for $nE\link[ggplot2:aes_position]{ggplot2::y}$, there is
-a proportional difference of $1/n$ compared to the paper.
+In Magnusson et al. (2020) Eq (9) first row, the second \code{+} should
+be a \code{-}; Supplementary Material Eq (6) has this correct.
+As \code{srs_diff_est()} in the \code{loo} package is used for \eqn{n E[y]}, there is
+a proportional difference of \eqn{1/n} compared to the paper.
 }
 \examples{
 print(42)

From ddf1d873a1eaea2dac57f27fb9182dde59c465ed Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Sun, 22 Mar 2026 12:15:25 +0100
Subject: [PATCH 08/13] removed example placeholder

---
 R/loo_subsample.R | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/R/loo_subsample.R b/R/loo_subsample.R
index 1805cd36..24e042a9 100644
--- a/R/loo_subsample.R
+++ b/R/loo_subsample.R
@@ -1200,9 +1200,6 @@ loo_subsample_estimation_diff_srs <- function(x) {
 #'
 #' @seealso [loo_subsample()]
 #' @export
-#'
-#' @examples
-#' print(42)
 srs_diff_est <- function(y_approx, y, y_idx) {
   checkmate::assert_numeric(y_approx)
   checkmate::assert_numeric(y, max.len = length(y_approx))

From 9699240759b8bcb5fcbbfb241e13a322e13efc04 Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Sun, 22 Mar 2026 12:17:03 +0100
Subject: [PATCH 09/13] updated .Rd to match .R

---
 man/srs_diff_est.Rd | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/man/srs_diff_est.Rd b/man/srs_diff_est.Rd
index 274a7e0e..6f49e9c5 100644
--- a/man/srs_diff_est.Rd
+++ b/man/srs_diff_est.Rd
@@ -36,9 +36,6 @@ be a \code{-}; Supplementary Material Eq (6) has this correct.
 As \code{srs_diff_est()} in the \code{loo} package is used for \eqn{n E[y]}, there is
 a proportional difference of \eqn{1/n} compared to the paper.
 }
-\examples{
-print(42)
-}
 \references{
 Magnusson, M., Riis Andersen, M., Jonasson, J. and Vehtari, A. (2020).
 Leave-One-Out Cross-Validation for Model Comparison in Large Data.

From c0a5447cc0f7f9f842804ed67fdeaadcc687e74b Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Sun, 22 Mar 2026 12:23:51 +0100
Subject: [PATCH 10/13] Update NEWS.md

---
 NEWS.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/NEWS.md b/NEWS.md
index 6f182376..30903c38 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -17,6 +17,7 @@
 * Added contribution section. by @VisruthSK in #286
 * Update LOO uncertainty paper to use BA doi by @avehtari in #311
 * Update documentation for `E_loo()` function by @avehtari in #312
+* Export `srs_diff_est()` function by @vinniott in #340
 
 
 # loo 2.8.0

From 94fb75799a419fabcb6cbfbeee54e45388579cc6 Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Sun, 26 Apr 2026 11:00:39 +0200
Subject: [PATCH 11/13] added @examples placeholder

---
 R/loo_subsample.R   | 5 +++++
 man/srs_diff_est.Rd | 5 +++++
 2 files changed, 10 insertions(+)

diff --git a/R/loo_subsample.R b/R/loo_subsample.R
index 24e042a9..0cb30f20 100644
--- a/R/loo_subsample.R
+++ b/R/loo_subsample.R
@@ -1199,6 +1199,11 @@ loo_subsample_estimation_diff_srs <- function(x) {
 #' Cochran, W. G. (1977). _Sampling Techniques, 3rd Edition_. John Wiley.
 #'
 #' @seealso [loo_subsample()]
+#'
+#' @examples
+#' print("Hello, World!")
+#'
+#'
 #' @export
 srs_diff_est <- function(y_approx, y, y_idx) {
   checkmate::assert_numeric(y_approx)
diff --git a/man/srs_diff_est.Rd b/man/srs_diff_est.Rd
index 6f49e9c5..9dded25f 100644
--- a/man/srs_diff_est.Rd
+++ b/man/srs_diff_est.Rd
@@ -35,6 +35,11 @@ In Magnusson et al. (2020) Eq (9) first row, the second \code{+} should
 be a \code{-}; Supplementary Material Eq (6) has this correct.
 As \code{srs_diff_est()} in the \code{loo} package is used for \eqn{n E[y]}, there is
 a proportional difference of \eqn{1/n} compared to the paper.
+}
+\examples{
+print("Hello, World!")
+
+
 }
 \references{
 Magnusson, M., Riis Andersen, M., Jonasson, J. and Vehtari, A. (2020).

From 535f464f6105e1a359a1dad647774a75aa4560d4 Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Sun, 26 Apr 2026 11:29:30 +0200
Subject: [PATCH 12/13] added generation of wine example

---
 R/loo_subsample.R   | 29 ++++++++++++++++++++++++++++-
 man/srs_diff_est.Rd | 30 +++++++++++++++++++++++++++++-
 2 files changed, 57 insertions(+), 2 deletions(-)

diff --git a/R/loo_subsample.R b/R/loo_subsample.R
index 0cb30f20..8473bb07 100644
--- a/R/loo_subsample.R
+++ b/R/loo_subsample.R
@@ -1198,10 +1198,37 @@ loo_subsample_estimation_diff_srs <- function(x) {
 #'
 #' Cochran, W. G. (1977). _Sampling Techniques, 3rd Edition_. John Wiley.
 #'
+#' Cortez, P., Cerdeira, A.L., Almeida, F., Matos, T., & Reis, J. (2009).
+#' Modeling wine preferences by data mining from physicochemical properties.
+#' _Decis. Support Syst._, _47_, 547-553.
+#'
 #' @seealso [loo_subsample()]
 #'
 #' @examples
-#' print("Hello, World!")
+#' ### This example predicts wine quality (data from Cortez et al., 2009).
+#' ## First, commented out code shows to generate a loglik_matrix.
+#' ## Second, running code illustrates how to use srs_diff_est().
+#' # library(dplyr)
+#' # library(brms)
+#' # options(brms.backend = "cmdstanr")
+#' # options(mc.cores = 4)
+#' # library(loo)
+#' #
+#' # wine <- read.delim(root("winequality-red", "winequality-red.csv"), sep = ";") |>
+#' #   distinct()
+#' #
+#' # wine_scaled <- as.data.frame(scale(wine))
+#' #
+#' # fitos <- brm(ordered(quality) ~ .,
+#' #              family = cumulative("logit"),
+#' #              prior = prior(R2D2(mean_R2 = 1/3, prec_R2 = 3)),
+#' #              data = wine_scaled,
+#' #              seed = 1,
+#' #              silent = 2,
+#' #              refresh = 0)
+#' #
+#' # wine_loglik_matrix <- log_lik(fitos)
+#' wine_loglik_matrix <- example_wine_loglik_matrix()  # Installed with loo to save time of fitting model shown above
 #'
 #'
 #' @export
diff --git a/man/srs_diff_est.Rd b/man/srs_diff_est.Rd
index 9dded25f..c481d095 100644
--- a/man/srs_diff_est.Rd
+++ b/man/srs_diff_est.Rd
@@ -37,7 +37,31 @@ As \code{srs_diff_est()} in the \code{loo} package is used for \eqn{n E[y]}, the
 a proportional difference of \eqn{1/n} compared to the paper.
 }
 \examples{
-print("Hello, World!")
+### This example predicts wine quality (data from Cortez et al., 2009).
+## The following, commented out code shows how you to fit the model
+## to generate the wine_log_lik_matrix.
+## The matrix is part of loo as wine_log_lik_matrix()
+# library(dplyr)
+# library(brms)
+# options(brms.backend = "cmdstanr")
+# options(mc.cores = 4)
+# library(loo)
+#
+# wine <- read.delim(root("winequality-red", "winequality-red.csv"), sep = ";") |>
+#   distinct()
+#
+# wine_scaled <- as.data.frame(scale(wine))
+#
+# fitos <- brm(ordered(quality) ~ .,
+#              family = cumulative("logit"),
+#              prior = prior(R2D2(mean_R2 = 1/3, prec_R2 = 3)),
+#              data = wine_scaled,
+#              seed = 1,
+#              silent = 2,
+#              refresh = 0)
+#
+# wine_log_lik_matrix <- log_lik(fitos)
+wine_log_lik_matrix <- "hi"
 
 
 }
@@ -48,6 +72,10 @@ In \emph{Proceedings of the 23rd International Conference on Artificial
 Intelligence and Statistics (AISTATS)}, PMLR 108:341-351.
 
 Cochran, W. G. (1977). \emph{Sampling Techniques, 3rd Edition}. John Wiley.
+
+Cortez, P., Cerdeira, A.L., Almeida, F., Matos, T., & Reis, J. (2009).
+Modeling wine preferences by data mining from physicochemical properties.
+\emph{Decis. Support Syst.}, \emph{47}, 547-553.
 }
 \seealso{
 \code{\link[=loo_subsample]{loo_subsample()}}

From 30cc34e539c36d6a6f0df682016936a95657510e Mon Sep 17 00:00:00 2001
From: vinniott <vinni.ott@posteo.de>
Date: Sun, 10 May 2026 15:39:00 +0200
Subject: [PATCH 13/13] added full example

---
 NEWS.md             |  2 +-
 R/loo_subsample.R   | 28 ++++++++++++++++++++++------
 man/srs_diff_est.Rd | 29 ++++++++++++++++++++++-------
 3 files changed, 45 insertions(+), 14 deletions(-)

diff --git a/NEWS.md b/NEWS.md
index 30903c38..8ebccfd6 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -17,7 +17,7 @@
 * Added contribution section. by @VisruthSK in #286
 * Update LOO uncertainty paper to use BA doi by @avehtari in #311
 * Update documentation for `E_loo()` function by @avehtari in #312
-* Export `srs_diff_est()` function by @vinniott in #340
+* Export `srs_diff_est()` function by @vinniott and @avehtari in #340
 
 
 # loo 2.8.0
diff --git a/R/loo_subsample.R b/R/loo_subsample.R
index 8473bb07..a5c44141 100644
--- a/R/loo_subsample.R
+++ b/R/loo_subsample.R
@@ -1206,8 +1206,9 @@ loo_subsample_estimation_diff_srs <- function(x) {
 #'
 #' @examples
 #' ### This example predicts wine quality (data from Cortez et al., 2009).
-#' ## First, commented out code shows to generate a loglik_matrix.
-#' ## Second, running code illustrates how to use srs_diff_est().
+#' ## The code is commented out for easier installation of the package
+#' ## because brm() takes two or three seconds to fit.
+#' ## A log_lik_matrix is generated from a fit, then it is used for srs_diff_est().
 #' # library(dplyr)
 #' # library(brms)
 #' # options(brms.backend = "cmdstanr")
@@ -1227,10 +1228,25 @@ loo_subsample_estimation_diff_srs <- function(x) {
 #' #              silent = 2,
 #' #              refresh = 0)
 #' #
-#' # wine_loglik_matrix <- log_lik(fitos)
-#' wine_loglik_matrix <- example_wine_loglik_matrix()  # Installed with loo to save time of fitting model shown above
-#'
-#'
+#' # log_lik_matrix <- log_lik(fitos)
+#' #
+#' # N <- nrow(wine_scaled)
+#' # Nsub <- 100
+#' #
+#' # # posterior log-score
+#' # lpd <- elpd(log_lik_matrix)
+#' # sum(lpd$pointwise[,"elpd"])
+#' # # Use PSIS-LOO for subsample of Nsub randomly selected observations
+#' # set.seed(1)
+#' # idx <- sample(1:N, Nsub)
+#' # elpd_loo_sub <- loo(log_lik_matrix[,idx])
+#' # sum(elpd_loo_sub$pointwise[,"elpd_loo"]) / Nsub * N
+#' #
+#' # # Use difference estimator to combine fast result and subsampled accurate result
+#' # loo:::srs_diff_est(lpd$pointwise[,"elpd"], elpd_loo_sub$pointwise[,"elpd_loo"], idx)
+#' #
+#' # # Comparison to using PSIS-LOO for all observations
+#' # loo(log_lik_matrix)
 #' @export
 srs_diff_est <- function(y_approx, y, y_idx) {
   checkmate::assert_numeric(y_approx)
diff --git a/man/srs_diff_est.Rd b/man/srs_diff_est.Rd
index c481d095..72f8faf5 100644
--- a/man/srs_diff_est.Rd
+++ b/man/srs_diff_est.Rd
@@ -38,9 +38,9 @@ a proportional difference of \eqn{1/n} compared to the paper.
 }
 \examples{
 ### This example predicts wine quality (data from Cortez et al., 2009).
-## The following, commented out code shows how you to fit the model
-## to generate the wine_log_lik_matrix.
-## The matrix is part of loo as wine_log_lik_matrix()
+## The code is commented out for easier installation of the package
+## because brm() takes two or three seconds to fit.
+## A log_lik_matrix is generated from a fit, then it is used for srs_diff_est().
 # library(dplyr)
 # library(brms)
 # options(brms.backend = "cmdstanr")
@@ -60,10 +60,25 @@ a proportional difference of \eqn{1/n} compared to the paper.
 #              silent = 2,
 #              refresh = 0)
 #
-# wine_log_lik_matrix <- log_lik(fitos)
-wine_log_lik_matrix <- "hi"
-
-
+# log_lik_matrix <- log_lik(fitos)
+#
+# N <- nrow(wine_scaled)
+# Nsub <- 100
+#
+# # posterior log-score
+# lpd <- elpd(log_lik_matrix)
+# sum(lpd$pointwise[,"elpd"])
+# # Use PSIS-LOO for subsample of Nsub randomly selected observations
+# set.seed(1)
+# idx <- sample(1:N, Nsub)
+# elpd_loo_sub <- loo(log_lik_matrix[,idx])
+# sum(elpd_loo_sub$pointwise[,"elpd_loo"]) / Nsub * N
+#
+# # Use difference estimator to combine fast result and subsampled accurate result
+# loo:::srs_diff_est(lpd$pointwise[,"elpd"], elpd_loo_sub$pointwise[,"elpd_loo"], idx)
+#
+# # Comparison to using PSIS-LOO for all observations
+# loo(log_lik_matrix)
 }
 \references{
 Magnusson, M., Riis Andersen, M., Jonasson, J. and Vehtari, A. (2020).