From ca6b8484720ef2b1753bde681a6d63feb00193eb Mon Sep 17 00:00:00 2001
From: Aki Vehtari <Aki.Vehtari@aalto.fi>
Date: Thu, 15 Feb 2024 19:21:02 +0200
Subject: [PATCH 1/2] simplify mcse_elpd using log-normal approximation

---
 R/loo.R                                       |  26 +++++++++---------
 tests/testthat/reference-results/loo.rds      | Bin 2079 -> 2090 bytes
 tests/testthat/reference-results/mcse_loo.rds | Bin 47 -> 55 bytes
 .../reference-results/moment_match_loo_1.rds  | Bin 1739 -> 1748 bytes
 .../reference-results/moment_match_loo_2.rds  | Bin 1739 -> 1748 bytes
 .../reference-results/moment_match_loo_3.rds  | Bin 1738 -> 1748 bytes
 .../moment_match_var_and_cov.rds              | Bin 1922 -> 1933 bytes
 7 files changed, 13 insertions(+), 13 deletions(-)

diff --git a/R/loo.R b/R/loo.R
index a321ff08..3c242c45 100644
--- a/R/loo.R
+++ b/R/loo.R
@@ -484,31 +484,31 @@ importance_sampling_loo_object <- function(pointwise, diagnostics, dims,
 #' @param ll Log-likelihood matrix.
 #' @param E_elpd elpd_loo column of pointwise matrix.
 #' @param psis_object Object returned by [psis()].
-#' @param n_samples Number of draws to take from `Normal(E[epd_i], SD[epd_i])`.
+#' @param n_samples Deprecated
 #' @return Vector of standard error estimates.
 #'
-mcse_elpd <- function(ll, lw, E_elpd, r_eff, n_samples = 1000) {
+mcse_elpd <- function(ll, lw, E_elpd, r_eff, n_samples = NULL) {
   lik <- exp(ll)
   w2 <- exp(lw)^2
   E_epd <- exp(E_elpd)
-  # zn is approximate ordered statistics of unit normal distribution with offset
-  # recommended by Blom (1958)
-  S <- n_samples
-  c <- 3/8
-  r <- 1:n_samples
-  zn <- qnorm((r - c) / (S - 2 * c + 1))
+  if (length(r_eff)==1 && !is.null(ncol(ll))) {
+    r_eff <- rep(r_eff, ncol(ll))
+  }
   var_elpd <-
     vapply(
       seq_len(ncol(w2)),
       FUN.VALUE = numeric(1),
       FUN = function(i) {
-        var_epd_i <- sum(w2[, i] * (lik[, i] - E_epd[i]) ^ 2)
-        sd_epd_i <- sqrt(var_epd_i)
-        z <- E_epd[i] + sd_epd_i * zn
-        var(log(z[z > 0]))
+        # Variance in linear scale
+        # Equation (6) in Vehtari et al. (2022)
+        var_epd_i <- sum(w2[, i] * (lik[, i] - E_epd[i]) ^ 2) / r_eff[i]
+        # Compute variance in log scale by match the variance of a
+        # log-normal approximation
+        # https://en.wikipedia.org/wiki/Log-normal_distribution#Arithmetic_moments
+        log(1 + var_epd_i/E_epd[i]^2)
       }
     )
-  sqrt(var_elpd / r_eff)
+  sqrt(var_elpd)
 }
 
 
diff --git a/tests/testthat/reference-results/loo.rds b/tests/testthat/reference-results/loo.rds
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diff --git a/tests/testthat/reference-results/mcse_loo.rds b/tests/testthat/reference-results/mcse_loo.rds
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diff --git a/tests/testthat/reference-results/moment_match_loo_1.rds b/tests/testthat/reference-results/moment_match_loo_1.rds
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From 473e1071122a72acdeae7c72df02e8a4f45e94c8 Mon Sep 17 00:00:00 2001
From: jgabry <jgabry@gmail.com>
Date: Thu, 15 Feb 2024 14:12:56 -0700
Subject: [PATCH 2/2] use saveRDS(..., version = 2) to maintain compatibility
 with R < 3.5

---
 R/loo.R                                       |   4 ++--
 tests/testthat/reference-results/loo.rds      | Bin 2090 -> 2081 bytes
 tests/testthat/reference-results/mcse_loo.rds | Bin 55 -> 47 bytes
 .../reference-results/moment_match_loo_1.rds  | Bin 1748 -> 1741 bytes
 .../reference-results/moment_match_loo_2.rds  | Bin 1748 -> 1740 bytes
 .../reference-results/moment_match_loo_3.rds  | Bin 1748 -> 1740 bytes
 .../moment_match_var_and_cov.rds              | Bin 1933 -> 1924 bytes
 7 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/R/loo.R b/R/loo.R
index 3c242c45..b8899ff6 100644
--- a/R/loo.R
+++ b/R/loo.R
@@ -491,7 +491,7 @@ mcse_elpd <- function(ll, lw, E_elpd, r_eff, n_samples = NULL) {
   lik <- exp(ll)
   w2 <- exp(lw)^2
   E_epd <- exp(E_elpd)
-  if (length(r_eff)==1 && !is.null(ncol(ll))) {
+  if (length(r_eff) == 1 && !is.null(ncol(ll))) {
     r_eff <- rep(r_eff, ncol(ll))
   }
   var_elpd <-
@@ -505,7 +505,7 @@ mcse_elpd <- function(ll, lw, E_elpd, r_eff, n_samples = NULL) {
         # Compute variance in log scale by match the variance of a
         # log-normal approximation
         # https://en.wikipedia.org/wiki/Log-normal_distribution#Arithmetic_moments
-        log(1 + var_epd_i/E_epd[i]^2)
+        log(1 + var_epd_i / E_epd[i]^2)
       }
     )
   sqrt(var_elpd)
diff --git a/tests/testthat/reference-results/loo.rds b/tests/testthat/reference-results/loo.rds
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diff --git a/tests/testthat/reference-results/mcse_loo.rds b/tests/testthat/reference-results/mcse_loo.rds
index 964e3ad01e110376e119a3cd73363cf976a38eee..20de2a2943454f982cf349b97e5640ae029ed7a3 100644
GIT binary patch
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diff --git a/tests/testthat/reference-results/moment_match_loo_1.rds b/tests/testthat/reference-results/moment_match_loo_1.rds
index 8b75e1349a8ce7216de87ccfd39cd55b1ba9e91b..a6e8d9b5bd87de9bdefb37b10bab03dc70a828ef 100644
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diff --git a/tests/testthat/reference-results/moment_match_loo_2.rds b/tests/testthat/reference-results/moment_match_loo_2.rds
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diff --git a/tests/testthat/reference-results/moment_match_loo_3.rds b/tests/testthat/reference-results/moment_match_loo_3.rds
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diff --git a/tests/testthat/reference-results/moment_match_var_and_cov.rds b/tests/testthat/reference-results/moment_match_var_and_cov.rds
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GIT binary patch
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