diff --git a/NAMESPACE b/NAMESPACE
index da305ab6c..12f70286a 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -1,5 +1,8 @@
 # Generated by roxygen2: do not edit by hand
 
+S3method(add_natural_scale_mean_sd,default)
+S3method(add_natural_scale_mean_sd,latent_gamma)
+S3method(add_natural_scale_mean_sd,latent_lognormal)
 S3method(as_latent_individual,data.frame)
 S3method(epidist,default)
 S3method(epidist_family,default)
diff --git a/R/globals.R b/R/globals.R
index f961f4e21..e9c8256d3 100644
--- a/R/globals.R
+++ b/R/globals.R
@@ -5,9 +5,6 @@ utils::globalVariables(c(
   "max_treedepth", # <epidist_diagnostics>
   "per_at_max_treedepth", # <epidist_diagnostics>
   "samples", # <epidist_diagnostics>
-  "meanlog", # <add_natural_scale_mean_sd>
-  "sdlog", # <add_natural_scale_mean_sd>
-  "sd", # <add_natural_scale_mean_sd>
   "sdlog", # <extract_lognormal_draws>
   "sdlog_log", # <extract_lognormal_draws>
   "meanlog", # <extract_lognormal_draws>
@@ -72,6 +69,13 @@ utils::globalVariables(c(
   "ptime_daily", # <plot_mean_posterior_pred>
   "n", # <plot_mean_posterior_pred>
   "obs_horizon", # <plot_mean_posterior_pred>
+  "mu", # <add_natural_scale_mean_sd.latent_lognormal>
+  "sigma", # <add_natural_scale_mean_sd.latent_lognormal>
+  "sd", # <add_natural_scale_mean_sd.latent_lognormal>
+  "sigma", # <add_natural_scale_mean_sd.latent_gamma>
+  "sd", # <add_natural_scale_mean_sd.latent_gamma>
+  "mu", # <add_natural_scale_mean_sd.latent_gamma>
+  "shape", # <add_natural_scale_mean_sd.latent_gamma>
   "time", # <linelist_to_counts>
   "primary", # <linelist_to_cases>
   "secondary", # <linelist_to_cases>
diff --git a/R/postprocess.R b/R/postprocess.R
index 58df198f0..700506115 100644
--- a/R/postprocess.R
+++ b/R/postprocess.R
@@ -13,6 +13,7 @@ add_natural_scale_mean_sd <- function(data, ...) {
 #' @inheritParams add_natural_scale_mean_sd
 #' @param ... Additional arguments for method.
 #' @family postprocess
+#' @method add_natural_scale_mean_sd default
 #' @export
 add_natural_scale_mean_sd.default <- function(data, ...) {
   cli::cli_inform(
@@ -31,6 +32,7 @@ add_natural_scale_mean_sd.default <- function(data, ...) {
 #' @inheritParams add_natural_scale_mean_sd
 #' @param ... Additional arguments for method.
 #' @family postprocess
+#' @method add_natural_scale_mean_sd latent_lognormal
 #' @autoglobal
 #' @export
 add_natural_scale_mean_sd.latent_lognormal <- function(data, ...) {
@@ -47,6 +49,7 @@ add_natural_scale_mean_sd.latent_lognormal <- function(data, ...) {
 #' @inheritParams add_natural_scale_mean_sd
 #' @param ... Additional arguments for method.
 #' @family postprocess
+#' @method add_natural_scale_mean_sd latent_gamma
 #' @autoglobal
 #' @export
 add_natural_scale_mean_sd.latent_gamma <- function(data, ...) {
diff --git a/man/add_natural_scale_mean_sd.Rd b/man/add_natural_scale_mean_sd.Rd
index d0754226d..5983c4bdf 100644
--- a/man/add_natural_scale_mean_sd.Rd
+++ b/man/add_natural_scale_mean_sd.Rd
@@ -1,19 +1,24 @@
 % Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/fitting-and-postprocessing.R
+% Please edit documentation in R/postprocess.R
 \name{add_natural_scale_mean_sd}
 \alias{add_natural_scale_mean_sd}
-\title{Add natural scale summary parameters for a lognormal distribution}
+\title{Add natural scale parameters}
 \usage{
-add_natural_scale_mean_sd(dt)
+add_natural_scale_mean_sd(data, ...)
 }
 \arguments{
-\item{dt}{...}
+\item{data}{A dataframe of distributional parameters}
+
+\item{...}{Additional arguments for method.}
 }
 \description{
-Add natural scale summary parameters for a lognormal distribution
+Add natural scale parameters
 }
 \seealso{
 Other postprocess: 
+\code{\link{add_natural_scale_mean_sd.default}()},
+\code{\link{add_natural_scale_mean_sd.latent_gamma}()},
+\code{\link{add_natural_scale_mean_sd.latent_lognormal}()},
 \code{\link{draws_to_long}()},
 \code{\link{extract_lognormal_draws}()},
 \code{\link{make_relative_to_truth}()},
diff --git a/man/add_natural_scale_mean_sd.default.Rd b/man/add_natural_scale_mean_sd.default.Rd
new file mode 100644
index 000000000..1e64690bd
--- /dev/null
+++ b/man/add_natural_scale_mean_sd.default.Rd
@@ -0,0 +1,28 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/postprocess.R
+\name{add_natural_scale_mean_sd.default}
+\alias{add_natural_scale_mean_sd.default}
+\title{Default method for add natural scale parameters}
+\usage{
+\method{add_natural_scale_mean_sd}{default}(data, ...)
+}
+\arguments{
+\item{data}{A dataframe of distributional parameters}
+
+\item{...}{Additional arguments for method.}
+}
+\description{
+Default method for add natural scale parameters
+}
+\seealso{
+Other postprocess: 
+\code{\link{add_natural_scale_mean_sd}()},
+\code{\link{add_natural_scale_mean_sd.latent_gamma}()},
+\code{\link{add_natural_scale_mean_sd.latent_lognormal}()},
+\code{\link{draws_to_long}()},
+\code{\link{extract_lognormal_draws}()},
+\code{\link{make_relative_to_truth}()},
+\code{\link{summarise_draws}()},
+\code{\link{summarise_variable}()}
+}
+\concept{postprocess}
diff --git a/man/add_natural_scale_mean_sd.latent_gamma.Rd b/man/add_natural_scale_mean_sd.latent_gamma.Rd
new file mode 100644
index 000000000..fee000953
--- /dev/null
+++ b/man/add_natural_scale_mean_sd.latent_gamma.Rd
@@ -0,0 +1,28 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/postprocess.R
+\name{add_natural_scale_mean_sd.latent_gamma}
+\alias{add_natural_scale_mean_sd.latent_gamma}
+\title{Add natural scale parameters for a latent gamma model}
+\usage{
+\method{add_natural_scale_mean_sd}{latent_gamma}(data, ...)
+}
+\arguments{
+\item{data}{A dataframe of distributional parameters}
+
+\item{...}{Additional arguments for method.}
+}
+\description{
+Again, \code{mu} and \code{shape} here are the distributional parameters of \code{brms}.
+}
+\seealso{
+Other postprocess: 
+\code{\link{add_natural_scale_mean_sd}()},
+\code{\link{add_natural_scale_mean_sd.default}()},
+\code{\link{add_natural_scale_mean_sd.latent_lognormal}()},
+\code{\link{draws_to_long}()},
+\code{\link{extract_lognormal_draws}()},
+\code{\link{make_relative_to_truth}()},
+\code{\link{summarise_draws}()},
+\code{\link{summarise_variable}()}
+}
+\concept{postprocess}
diff --git a/man/add_natural_scale_mean_sd.latent_lognormal.Rd b/man/add_natural_scale_mean_sd.latent_lognormal.Rd
new file mode 100644
index 000000000..ab9d2c247
--- /dev/null
+++ b/man/add_natural_scale_mean_sd.latent_lognormal.Rd
@@ -0,0 +1,29 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/postprocess.R
+\name{add_natural_scale_mean_sd.latent_lognormal}
+\alias{add_natural_scale_mean_sd.latent_lognormal}
+\title{Add natural scale parameters for a latent lognormal model}
+\usage{
+\method{add_natural_scale_mean_sd}{latent_lognormal}(data, ...)
+}
+\arguments{
+\item{data}{A dataframe of distributional parameters}
+
+\item{...}{Additional arguments for method.}
+}
+\description{
+Note that the input parameters here are \code{mu} and \code{sigma}, corresponding to
+the distributional parameters used by \code{brms} for the \code{lognormal} family.
+}
+\seealso{
+Other postprocess: 
+\code{\link{add_natural_scale_mean_sd}()},
+\code{\link{add_natural_scale_mean_sd.default}()},
+\code{\link{add_natural_scale_mean_sd.latent_gamma}()},
+\code{\link{draws_to_long}()},
+\code{\link{extract_lognormal_draws}()},
+\code{\link{make_relative_to_truth}()},
+\code{\link{summarise_draws}()},
+\code{\link{summarise_variable}()}
+}
+\concept{postprocess}
diff --git a/man/draws_to_long.Rd b/man/draws_to_long.Rd
index f4b346ef9..61653792d 100644
--- a/man/draws_to_long.Rd
+++ b/man/draws_to_long.Rd
@@ -15,6 +15,9 @@ Convert posterior lognormal samples to long format
 \seealso{
 Other postprocess: 
 \code{\link{add_natural_scale_mean_sd}()},
+\code{\link{add_natural_scale_mean_sd.default}()},
+\code{\link{add_natural_scale_mean_sd.latent_gamma}()},
+\code{\link{add_natural_scale_mean_sd.latent_lognormal}()},
 \code{\link{extract_lognormal_draws}()},
 \code{\link{make_relative_to_truth}()},
 \code{\link{summarise_draws}()},
diff --git a/man/extract_lognormal_draws.Rd b/man/extract_lognormal_draws.Rd
index d7270f874..bfa0fc37a 100644
--- a/man/extract_lognormal_draws.Rd
+++ b/man/extract_lognormal_draws.Rd
@@ -19,6 +19,9 @@ Extract posterior samples for a lognormal brms model
 \seealso{
 Other postprocess: 
 \code{\link{add_natural_scale_mean_sd}()},
+\code{\link{add_natural_scale_mean_sd.default}()},
+\code{\link{add_natural_scale_mean_sd.latent_gamma}()},
+\code{\link{add_natural_scale_mean_sd.latent_lognormal}()},
 \code{\link{draws_to_long}()},
 \code{\link{make_relative_to_truth}()},
 \code{\link{summarise_draws}()},
diff --git a/man/make_relative_to_truth.Rd b/man/make_relative_to_truth.Rd
index 97cd56564..e31ca744c 100644
--- a/man/make_relative_to_truth.Rd
+++ b/man/make_relative_to_truth.Rd
@@ -19,6 +19,9 @@ Make posterior lognormal samples relative to true values
 \seealso{
 Other postprocess: 
 \code{\link{add_natural_scale_mean_sd}()},
+\code{\link{add_natural_scale_mean_sd.default}()},
+\code{\link{add_natural_scale_mean_sd.latent_gamma}()},
+\code{\link{add_natural_scale_mean_sd.latent_lognormal}()},
 \code{\link{draws_to_long}()},
 \code{\link{extract_lognormal_draws}()},
 \code{\link{summarise_draws}()},
diff --git a/man/summarise_draws.Rd b/man/summarise_draws.Rd
index d8d0b29a9..3ec4afb15 100644
--- a/man/summarise_draws.Rd
+++ b/man/summarise_draws.Rd
@@ -21,6 +21,9 @@ Summarise posterior draws
 \seealso{
 Other postprocess: 
 \code{\link{add_natural_scale_mean_sd}()},
+\code{\link{add_natural_scale_mean_sd.default}()},
+\code{\link{add_natural_scale_mean_sd.latent_gamma}()},
+\code{\link{add_natural_scale_mean_sd.latent_lognormal}()},
 \code{\link{draws_to_long}()},
 \code{\link{extract_lognormal_draws}()},
 \code{\link{make_relative_to_truth}()},
diff --git a/man/summarise_variable.Rd b/man/summarise_variable.Rd
index c7a2dc30f..245c8a867 100644
--- a/man/summarise_variable.Rd
+++ b/man/summarise_variable.Rd
@@ -21,6 +21,9 @@ Summarise a variable
 \seealso{
 Other postprocess: 
 \code{\link{add_natural_scale_mean_sd}()},
+\code{\link{add_natural_scale_mean_sd.default}()},
+\code{\link{add_natural_scale_mean_sd.latent_gamma}()},
+\code{\link{add_natural_scale_mean_sd.latent_lognormal}()},
 \code{\link{draws_to_long}()},
 \code{\link{extract_lognormal_draws}()},
 \code{\link{make_relative_to_truth}()},
diff --git a/tests/testthat/test-unit-postprocess.R b/tests/testthat/test-unit-postprocess.R
index a01a67532..0ed2d481b 100644
--- a/tests/testthat/test-unit-postprocess.R
+++ b/tests/testthat/test-unit-postprocess.R
@@ -16,10 +16,12 @@ brms::posterior_predict(fit)
 linpred_mu <- brms::posterior_linpred(fit, transform = TRUE, dpar = "mu")
 linpred_sigma <- brms::posterior_linpred(fit, transform = TRUE, dpar = "sigma")
 
-linpred_mu_melt <- reshape2::melt(linpred_mu, varnames = c("aaa", "bbb"), value.name = "mu")
-linpred_sigma_melt <- reshape2::melt(linpred_sigma, varnames = c("aaa", "bbb"), value.name = "sigma")
+linpred_mu_melt <- reshape2::melt(linpred_mu, varnames = c("draw", "index"), value.name = "mu")
+linpred_sigma_melt <- reshape2::melt(linpred_sigma, varnames = c("draw", "index"), value.name = "sigma")
 
 linpred_melt <- dplyr::left_join(linpred_mu_melt, linpred_sigma_melt)
+class(linpred_melt) <- c(class(linpred_melt), "latent_lognormal")
+add_natural_scale_mean_sd(data.table::as.data.table(linpred_melt))
 
 pp <- brms::prepare_predictions(fit)
 pp$dpars$mu$fe$b