diff --git a/NAMESPACE b/NAMESPACE
index 08ecab055..76f052cae 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -54,6 +54,7 @@ importFrom(checkmate,assert_numeric)
 importFrom(checkmate,assert_true)
 importFrom(cli,cli_abort)
 importFrom(cli,cli_inform)
+importFrom(cli,cli_warn)
 importFrom(dplyr,filter)
 importFrom(dplyr,mutate)
 importFrom(dplyr,select)
diff --git a/R/epidist-package.R b/R/epidist-package.R
index 293ed97f5..0859a1a6a 100644
--- a/R/epidist-package.R
+++ b/R/epidist-package.R
@@ -8,6 +8,6 @@
 #' @importFrom brms bf prior
 #' @importFrom checkmate assert_data_frame assert_names assert_integer
 #'   assert_true assert_factor assert_numeric
-#' @importFrom cli cli_abort cli_inform cli_abort
+#' @importFrom cli cli_abort cli_inform cli_abort cli_warn
 ## usethis namespace: end
 NULL
diff --git a/R/generics.R b/R/generics.R
index 851288518..cd5d70147 100644
--- a/R/generics.R
+++ b/R/generics.R
@@ -30,7 +30,7 @@ epidist_stancode <- function(data, ...) {
 #' Fit epidemiological delay distributions using a `brms` interface
 #'
 #' @inheritParams epidist_validate
-#' @param formula A formula object created using `brms::bf`. A formula must be
+#' @param formula A formula object created using [brms::bf()]. A formula must be
 #' provided for the distributional parameter `mu` common to all `brms` families.
 #' Optionally, formulas may also be provided for additional distributional
 #' parameters.
@@ -46,10 +46,10 @@ epidist_stancode <- function(data, ...) {
 #' @param backend Character string naming the package to use as the backend for
 #' fitting the Stan model. Options are `"rstan"` and `"cmdstanr"` (the default).
 #' This option is passed directly through to `fn`.
-#' @param fn The internal function to be called. By default this is `brms::brm`,
-#' which performs inference for the specified model. Other options
-#' `brms::make_stancode`, which returns the Stan code for the specified model,
-#' and `brms::make_standata` which returns the data passed to Stan. These
+#' @param fn The internal function to be called. By default this is
+#' [brms::brm()] which performs inference for the specified model. Other options
+#' [brms::make_stancode()], which returns the Stan code for the specified model,
+#' and [brms::make_standata()] which returns the data passed to Stan. These
 #' options may be useful for model debugging and extensions.
 #' @param ... Additional arguments for method.
 #' @family generics
diff --git a/R/prior.R b/R/prior.R
index c4ff2175b..839abae3b 100644
--- a/R/prior.R
+++ b/R/prior.R
@@ -7,12 +7,15 @@
 #' 2. Family specific prior distributions from [epidist_family_prior()]
 #' 3. User provided prior distributions
 #' Each element of this list overwrites previous elements, such that user
-#' provided prior distribution have the highest priority.
+#' provided prior distribution have the highest priority. At the third stage,
+#' if a prior distribution is provided which is not included in the model, then
+#' a warning will be shown. To prevent this warning, do not pass prior
+#' distributions for parameters which are not in the model.
 #'
-#' @param data ...
-#' @param family ...
-#' @param formula ...
-#' @param prior ...
+#' @param data A `data.frame` containing line list data
+#' @param family Output of a call to `brms::brmsfamily()`
+#' @param formula A formula object created using `brms::bf()`
+#' @param prior User provided prior distribution created using `brms::prior()`
 #' @rdname epidist_prior
 #' @family prior
 #' @export
@@ -23,7 +26,8 @@ epidist_prior <- function(data, family, formula, prior) {
   default <- brms::default_prior(formula, data = data)
   model <- epidist_model_prior(data, formula)
   family <-  epidist_family_prior(family, formula)
-  prior <- Reduce(.replace_prior, list(default, model, family, prior))
+  internal_prior <- Reduce(.replace_prior, list(default, model, family))
+  prior <- .replace_prior(internal_prior, prior, warn = TRUE)
   return(prior)
 }
 
@@ -90,15 +94,7 @@ epidist_family_prior.default <- function(family, formula, ...) {
 #' @export
 epidist_family_prior.lognormal <- function(family, formula, ...) {
   prior <- prior("normal(1, 1)", class = "Intercept")
-  if ("sigma" %in% names(formula$pfix)) {
-    # Case with sigma fixed to a constant
-    sigma_prior <- NULL
-  } else {
-    # Case with a model on sigma
-    sigma_prior <- prior(
-      "normal(-0.7, 0.4)", class = "Intercept", dpar = "sigma"
-    )
-  }
+  sigma_prior <- prior("normal(-0.7, 0.4)", class = "Intercept", dpar = "sigma")
   prior <- prior + sigma_prior
   prior$source <- "family"
   prior[is.na(prior)] <- "" # This is because brms likes empty over NA
diff --git a/R/utils.R b/R/utils.R
index aa4ce62ee..39d5f28b0 100644
--- a/R/utils.R
+++ b/R/utils.R
@@ -45,37 +45,39 @@
 #' Replace `brms` prior distributions
 #'
 #' This function takes `old_prior` and replaces any prior distributions
-#' contained in it by the corresponding prior distribution in `new_prior`.
-#' If there is a prior distribution in `new_prior` with no match in `old_prior`
-#' then the function will error and give the name of the new prior distribution
-#' with no match.
+#' contained in it by the corresponding prior distribution in `prior`. If there
+#' is a prior distribution in `prior` with no match in `old_prior` then this
+#' function can optionally give a warning.
 #'
 #' @param old_prior One or more prior distributions in the class `brmsprior`
-#' @param new_prior One or more prior distributions in the class `brmsprior`
+#' @param prior One or more prior distributions in the class `brmsprior`
+#' @param warn If `TRUE` then a warning will be displayed if a `new_prior` is
+#' provided for which there is no matching `old_prior`. Defaults to `FALSE`
 #' @autoglobal
 #' @keywords internal
-.replace_prior <- function(old_prior, new_prior) {
-  if (is.null(new_prior)) {
+.replace_prior <- function(old_prior, prior, warn = FALSE) {
+  if (is.null(prior)) {
     return(old_prior)
   }
   cols <- c("class", "coef", "group", "resp", "dpar", "nlpar", "lb", "ub")
   prior <- dplyr::full_join(
-    old_prior, new_prior, by = cols, suffix = c("_old", "_new")
+    old_prior, prior, by = cols, suffix = c("_old", "_new")
   )
 
   if (any(is.na(prior$prior_old))) {
     missing_prior <- utils::capture.output(print(
       prior |>
         filter(is.na(.data$prior_old)) |>
-        select(
-          prior = prior_new, dplyr::all_of(cols), source = source_new
-        )
+        select(prior = prior_new, dplyr::all_of(cols), source = source_new)
     ))
-    msg <- c(
-      "i" = "No available prior to replace in old_prior found for:",
-      missing_prior
-    )
-    cli_abort(message = msg)
+    if (warn) {
+      msg <- c(
+        "!" = "One or more priors have no match in existing parameters:",
+        missing_prior,
+        "i" = "To remove this warning consider changing prior specification."
+      )
+      cli_warn(message = msg)
+    }
   }
 
   prior <- prior |>
diff --git a/man/dot-replace_prior.Rd b/man/dot-replace_prior.Rd
index 5abcb889a..3c70a95de 100644
--- a/man/dot-replace_prior.Rd
+++ b/man/dot-replace_prior.Rd
@@ -4,18 +4,20 @@
 \alias{.replace_prior}
 \title{Replace \code{brms} prior distributions}
 \usage{
-.replace_prior(old_prior, new_prior)
+.replace_prior(old_prior, prior, warn = FALSE)
 }
 \arguments{
 \item{old_prior}{One or more prior distributions in the class \code{brmsprior}}
 
-\item{new_prior}{One or more prior distributions in the class \code{brmsprior}}
+\item{prior}{One or more prior distributions in the class \code{brmsprior}}
+
+\item{warn}{If \code{TRUE} then a warning will be displayed if a \code{new_prior} is
+provided for which there is no matching \code{old_prior}. Defaults to \code{FALSE}}
 }
 \description{
 This function takes \code{old_prior} and replaces any prior distributions
-contained in it by the corresponding prior distribution in \code{new_prior}.
-If there is a prior distribution in \code{new_prior} with no match in \code{old_prior}
-then the function will error and give the name of the new prior distribution
-with no match.
+contained in it by the corresponding prior distribution in \code{prior}. If there
+is a prior distribution in \code{prior} with no match in \code{old_prior} then this
+function can optionally give a warning.
 }
 \keyword{internal}
diff --git a/man/epidist.Rd b/man/epidist.Rd
index 0620006ab..6ace0b497 100644
--- a/man/epidist.Rd
+++ b/man/epidist.Rd
@@ -9,7 +9,7 @@ epidist(data, formula, family, prior, backend, fn, ...)
 \arguments{
 \item{data}{A \code{data.frame} containing line list data.}
 
-\item{formula}{A formula object created using \code{brms::bf}. A formula must be
+\item{formula}{A formula object created using \code{\link[brms:brmsformula]{brms::bf()}}. A formula must be
 provided for the distributional parameter \code{mu} common to all \code{brms} families.
 Optionally, formulas may also be provided for additional distributional
 parameters.}
@@ -29,10 +29,10 @@ for specifying prior distributions.}
 fitting the Stan model. Options are \code{"rstan"} and \code{"cmdstanr"} (the default).
 This option is passed directly through to \code{fn}.}
 
-\item{fn}{The internal function to be called. By default this is \code{brms::brm},
-which performs inference for the specified model. Other options
-\code{brms::make_stancode}, which returns the Stan code for the specified model,
-and \code{brms::make_standata} which returns the data passed to Stan. These
+\item{fn}{The internal function to be called. By default this is
+\code{\link[brms:brm]{brms::brm()}} which performs inference for the specified model. Other options
+\code{\link[brms:stancode]{brms::make_stancode()}}, which returns the Stan code for the specified model,
+and \code{\link[brms:standata]{brms::make_standata()}} which returns the data passed to Stan. These
 options may be useful for model debugging and extensions.}
 
 \item{...}{Additional arguments for method.}
diff --git a/man/epidist.default.Rd b/man/epidist.default.Rd
index 6a7f45ac4..6dac69030 100644
--- a/man/epidist.default.Rd
+++ b/man/epidist.default.Rd
@@ -17,7 +17,7 @@
 \arguments{
 \item{data}{A \code{data.frame} containing line list data.}
 
-\item{formula}{A formula object created using \code{brms::bf}. A formula must be
+\item{formula}{A formula object created using \code{\link[brms:brmsformula]{brms::bf()}}. A formula must be
 provided for the distributional parameter \code{mu} common to all \code{brms} families.
 Optionally, formulas may also be provided for additional distributional
 parameters.}
@@ -37,10 +37,10 @@ for specifying prior distributions.}
 fitting the Stan model. Options are \code{"rstan"} and \code{"cmdstanr"} (the default).
 This option is passed directly through to \code{fn}.}
 
-\item{fn}{The internal function to be called. By default this is \code{brms::brm},
-which performs inference for the specified model. Other options
-\code{brms::make_stancode}, which returns the Stan code for the specified model,
-and \code{brms::make_standata} which returns the data passed to Stan. These
+\item{fn}{The internal function to be called. By default this is
+\code{\link[brms:brm]{brms::brm()}} which performs inference for the specified model. Other options
+\code{\link[brms:stancode]{brms::make_stancode()}}, which returns the Stan code for the specified model,
+and \code{\link[brms:standata]{brms::make_standata()}} which returns the data passed to Stan. These
 options may be useful for model debugging and extensions.}
 
 \item{...}{Additional arguments for method.}
diff --git a/man/epidist_family_prior.Rd b/man/epidist_family_prior.Rd
index b58604220..72afd6056 100644
--- a/man/epidist_family_prior.Rd
+++ b/man/epidist_family_prior.Rd
@@ -7,7 +7,7 @@
 epidist_family_prior(family, ...)
 }
 \arguments{
-\item{family}{...}
+\item{family}{Output of a call to \code{brms::brmsfamily()}}
 
 \item{...}{...}
 }
diff --git a/man/epidist_family_prior.default.Rd b/man/epidist_family_prior.default.Rd
index 7fe8f7c19..ea58083af 100644
--- a/man/epidist_family_prior.default.Rd
+++ b/man/epidist_family_prior.default.Rd
@@ -7,9 +7,9 @@
 \method{epidist_family_prior}{default}(family, formula, ...)
 }
 \arguments{
-\item{family}{...}
+\item{family}{Output of a call to \code{brms::brmsfamily()}}
 
-\item{formula}{...}
+\item{formula}{A formula object created using \code{brms::bf()}}
 
 \item{...}{...}
 }
diff --git a/man/epidist_family_prior.lognormal.Rd b/man/epidist_family_prior.lognormal.Rd
index c31141538..827b2fc86 100644
--- a/man/epidist_family_prior.lognormal.Rd
+++ b/man/epidist_family_prior.lognormal.Rd
@@ -7,9 +7,9 @@
 \method{epidist_family_prior}{lognormal}(family, formula, ...)
 }
 \arguments{
-\item{family}{...}
+\item{family}{Output of a call to \code{brms::brmsfamily()}}
 
-\item{formula}{...}
+\item{formula}{A formula object created using \code{brms::bf()}}
 
 \item{...}{...}
 }
diff --git a/man/epidist_model_prior.Rd b/man/epidist_model_prior.Rd
index 20f68fb60..36f3a35d5 100644
--- a/man/epidist_model_prior.Rd
+++ b/man/epidist_model_prior.Rd
@@ -7,7 +7,7 @@
 epidist_model_prior(data, ...)
 }
 \arguments{
-\item{data}{...}
+\item{data}{A \code{data.frame} containing line list data}
 
 \item{...}{...}
 }
diff --git a/man/epidist_model_prior.default.Rd b/man/epidist_model_prior.default.Rd
index d506cf252..f9de37fa6 100644
--- a/man/epidist_model_prior.default.Rd
+++ b/man/epidist_model_prior.default.Rd
@@ -7,9 +7,9 @@
 \method{epidist_model_prior}{default}(data, formula, ...)
 }
 \arguments{
-\item{data}{...}
+\item{data}{A \code{data.frame} containing line list data}
 
-\item{formula}{...}
+\item{formula}{A formula object created using \code{brms::bf()}}
 
 \item{...}{...}
 }
diff --git a/man/epidist_prior.Rd b/man/epidist_prior.Rd
index 8d64b4089..2454db586 100644
--- a/man/epidist_prior.Rd
+++ b/man/epidist_prior.Rd
@@ -8,13 +8,13 @@ family specific priors, and user provided priors}
 epidist_prior(data, family, formula, prior)
 }
 \arguments{
-\item{data}{...}
+\item{data}{A \code{data.frame} containing line list data}
 
-\item{family}{...}
+\item{family}{Output of a call to \code{brms::brmsfamily()}}
 
-\item{formula}{...}
+\item{formula}{A formula object created using \code{brms::bf()}}
 
-\item{prior}{...}
+\item{prior}{User provided prior distribution created using \code{brms::prior()}}
 }
 \description{
 This function obtains the \code{brms} default prior distributions for a particular
@@ -24,7 +24,10 @@ model, then replaces these prior distributions using:
 \item Family specific prior distributions from \code{\link[=epidist_family_prior]{epidist_family_prior()}}
 \item User provided prior distributions
 Each element of this list overwrites previous elements, such that user
-provided prior distribution have the highest priority.
+provided prior distribution have the highest priority. At the third stage,
+if a prior distribution is provided which is not included in the model, then
+a warning will be shown. To prevent this warning, do not pass prior
+distributions for parameters which are not in the model.
 }
 }
 \seealso{
diff --git a/tests/testthat/test-int-latent_individual.R b/tests/testthat/test-int-latent_individual.R
index e33ccbd4a..c3758999f 100644
--- a/tests/testthat/test-int-latent_individual.R
+++ b/tests/testthat/test-int-latent_individual.R
@@ -81,7 +81,7 @@ test_that("epidist.epidist_latent_individual fits and the MCMC converges in the
   expect_convergence(fit)
 })
 
-test_that("epidist.epidist_latent_individual fit and the MCMC converges when setting sigma = 1 (a constant)", { # nolint: line_length_linter.
+test_that("epidist.epidist_latent_individual fits, the MCMC converges, and the draws of sigma are indeed a constant, when setting sigma = 1 (a constant)", { # nolint: line_length_linter.
   # Note: this test is stochastic. See note at the top of this script
   skip_on_cran()
   set.seed(1)
@@ -95,6 +95,8 @@ test_that("epidist.epidist_latent_individual fit and the MCMC converges when set
   expect_s3_class(fit_constant, "brmsfit")
   expect_s3_class(fit_constant, "epidist_fit")
   expect_convergence(fit_constant)
+  sigma <- rstan::extract(fit_constant$fit, pars = "sigma")$sigma
+  expect_true(all(sigma == 1))
 })
 
 test_that("epidist.epidist_latent_individual Stan code has no syntax errors and compiles with lognormal family as a string", { # nolint: line_length_linter.
diff --git a/tests/testthat/test-utils.R b/tests/testthat/test-utils.R
index c39a3c38b..0f931dc9a 100644
--- a/tests/testthat/test-utils.R
+++ b/tests/testthat/test-utils.R
@@ -23,7 +23,7 @@ test_that(".replace_prior errors when passed a new prior without a match in old_
   new_prior <- brms::prior("normal(0, 5)", class = "Intercept") +
     brms::prior("normal(0, 5)", class = "Intercept", dpar = "sigma") +
     brms::prior("normal(0, 5)", class = "Intercept", dpar = "shape")
-  expect_error(.replace_prior(old_prior, new_prior))
+  expect_warning(.replace_prior(old_prior, new_prior, warn = TRUE))
 })
 
 test_that(".add_dpar_info works as expected for the lognormal and gamma families", { # nolint: line_length_linter.