diff --git a/R/Prior.R b/R/Prior.R
index 253ac215..2e4c3d74 100755
--- a/R/Prior.R
+++ b/R/Prior.R
@@ -103,6 +103,15 @@ setValidity(
                 return(return_message)
             }
         }
+        if (length(object@limits) != 2) {
+            return("Limits must be a vector of length 2")
+        }
+        if (object@limits[1] >= object@limits[2]) {
+            return("Lower limit must be less than upper limit")
+        }
+        if (length(object@repr_model) != 1 || !is.character(object@repr_model)) {
+            return("Model representation must be length 1 string")
+        }
         return(TRUE)
     }
 )
@@ -113,6 +122,7 @@ setValidity(
 #' @export
 set_limits.Prior <- function(object, lower = -Inf, upper = Inf) {
     object@limits <- c(lower, upper)
+    validObject(object)
     return(object)
 }
 
@@ -127,10 +137,32 @@ as.character.Prior <- function(x, ...) {
 
     parameters_rounded <- lapply(x@parameters, round, 5)
 
-    do.call(
+    display_string <- do.call(
         glue::glue,
         append(x@display, parameters_rounded)
     )
+    display_limits <- render_stan_limits(x@limits)
+    if (display_limits != "" && display_string != "" && display_string != "<None>") {
+        display_string <- paste0(display_string, display_limits)
+    }
+    return(display_string)
+}
+
+
+#' Creates Stan Syntax for Truncated distributions
+#' @description
+#' This function creates the Stan syntax for truncated distributions
+#' @param limits (`numeric`)\cr the lower and upper limits for a truncated distribution
+#' @keywords internal
+#' @return (`character`)\cr the Stan syntax for truncated distributions
+render_stan_limits <- function(limits) {
+    l_bound <- if (limits[[1]] > -Inf) limits[[1]] else ""
+    u_bound <- if (limits[[2]] < Inf) limits[[2]] else ""
+    string <- ""
+    if (l_bound != "" || u_bound != "") {
+        string <- glue::glue(" T[{l_bound}, {u_bound}]", l_bound = l_bound, u_bound = u_bound)
+    }
+    return(string)
 }
 
 
@@ -157,12 +189,17 @@ setMethod(
 #' @family as.StanModule
 #' @export
 as.StanModule.Prior <- function(object, name, ...) {
+    trunctation <- if (object@repr_model != "") {
+        paste0(render_stan_limits(object@limits), ";")
+    } else {
+        ""
+    }
     string <- paste(
         "data {{",
         paste0("    ", object@repr_data, collapse = "\n"),
         "}}",
         "model {{",
-        paste0("    ", object@repr_model, collapse = "\n"),
+        paste0("    ", object@repr_model, trunctation),
         "}}",
         sep = "\n"
     )
@@ -233,7 +270,7 @@ prior_normal <- function(mu, sigma) {
     Prior(
         parameters = list(mu = mu, sigma = sigma),
         display = "normal(mu = {mu}, sigma = {sigma})",
-        repr_model = "{name} ~ normal(prior_mu_{name}, prior_sigma_{name});",
+        repr_model = "{name} ~ normal(prior_mu_{name}, prior_sigma_{name})",
         repr_data = c(
             "real prior_mu_{name};",
             "real<lower=0> prior_sigma_{name};"
@@ -257,7 +294,7 @@ prior_std_normal <- function() {
     Prior(
         parameters = list(),
         display = "std_normal()",
-        repr_model = "{name} ~ std_normal();",
+        repr_model = "{name} ~ std_normal()",
         repr_data = "",
         centre = 0,
         sample = \(n) local_rnorm(n),
@@ -276,7 +313,7 @@ prior_cauchy <- function(mu, sigma) {
     Prior(
         parameters = list(mu = mu, sigma = sigma),
         display = "cauchy(mu = {mu}, sigma = {sigma})",
-        repr_model = "{name} ~ cauchy(prior_mu_{name}, prior_sigma_{name});",
+        repr_model = "{name} ~ cauchy(prior_mu_{name}, prior_sigma_{name})",
         repr_data = c(
             "real prior_mu_{name};",
             "real<lower=0> prior_sigma_{name};"
@@ -301,7 +338,7 @@ prior_cauchy <- function(mu, sigma) {
 prior_gamma <- function(alpha, beta) {
     Prior(
         parameters = list(alpha = alpha, beta = beta),
-        repr_model = "{name} ~ gamma(prior_alpha_{name}, prior_beta_{name});",
+        repr_model = "{name} ~ gamma(prior_alpha_{name}, prior_beta_{name})",
         display = "gamma(alpha = {alpha}, beta = {beta})",
         repr_data = c(
             "real<lower=0> prior_alpha_{name};",
@@ -327,7 +364,7 @@ prior_lognormal <- function(mu, sigma) {
     Prior(
         parameters = list(mu = mu, sigma = sigma),
         display = "lognormal(mu = {mu}, sigma = {sigma})",
-        repr_model = "{name} ~ lognormal(prior_mu_{name}, prior_sigma_{name});",
+        repr_model = "{name} ~ lognormal(prior_mu_{name}, prior_sigma_{name})",
         repr_data = c(
             "real prior_mu_{name};",
             "real<lower=0> prior_sigma_{name};"
@@ -352,7 +389,7 @@ prior_beta <- function(a, b) {
     Prior(
         parameters = list(a = a, b = b),
         display = "beta(a = {a}, b = {b})",
-        repr_model = "{name} ~ beta(prior_a_{name}, prior_b_{name});",
+        repr_model = "{name} ~ beta(prior_a_{name}, prior_b_{name})",
         repr_data = c(
             "real<lower=0> prior_a_{name};",
             "real<lower=0> prior_b_{name};"
@@ -408,7 +445,7 @@ prior_uniform <- function(alpha, beta) {
     Prior(
         parameters = list(alpha = alpha, beta = beta),
         display = "uniform(alpha = {alpha}, beta = {beta})",
-        repr_model = "{name} ~ uniform(prior_alpha_{name}, prior_beta_{name});",
+        repr_model = "{name} ~ uniform(prior_alpha_{name}, prior_beta_{name})",
         repr_data = c(
             "real prior_alpha_{name};",
             "real prior_beta_{name};"
@@ -439,7 +476,7 @@ prior_student_t <- function(nu, mu, sigma) {
             sigma = sigma
         ),
         display = "student_t(nu = {nu}, mu = {mu}, sigma = {sigma})",
-        repr_model = "{name} ~ student_t(prior_nu_{name}, prior_mu_{name}, prior_sigma_{name});",
+        repr_model = "{name} ~ student_t(prior_nu_{name}, prior_mu_{name}, prior_sigma_{name})",
         repr_data = c(
             "real<lower=0> prior_nu_{name};",
             "real prior_mu_{name};",
@@ -471,7 +508,7 @@ prior_logistic <- function(mu, sigma) {
             sigma = sigma
         ),
         display = "logistic(mu = {mu}, sigma = {sigma})",
-        repr_model = "{name} ~ logistic(prior_mu_{name}, prior_sigma_{name});",
+        repr_model = "{name} ~ logistic(prior_mu_{name}, prior_sigma_{name})",
         repr_data = c(
             "real prior_mu_{name};",
             "real<lower=0> prior_sigma_{name};"
@@ -500,7 +537,7 @@ prior_loglogistic <- function(alpha, beta) {
             beta = beta
         ),
         display = "loglogistic(alpha = {alpha}, beta = {beta})",
-        repr_model = "{name} ~ loglogistic(prior_alpha_{name}, prior_beta_{name});",
+        repr_model = "{name} ~ loglogistic(prior_alpha_{name}, prior_beta_{name})",
         repr_data = c(
             "real<lower=0> prior_alpha_{name};",
             "real<lower=0> prior_beta_{name};"
@@ -531,7 +568,7 @@ prior_invgamma <- function(alpha, beta) {
             beta = beta
         ),
         display = "inv_gamma(alpha = {alpha}, beta = {beta})",
-        repr_model = "{name} ~ inv_gamma(prior_alpha_{name}, prior_beta_{name});",
+        repr_model = "{name} ~ inv_gamma(prior_alpha_{name}, prior_beta_{name})",
         repr_data = c(
             "real<lower=0> prior_alpha_{name};",
             "real<lower=0> prior_beta_{name};"
diff --git a/man/render_stan_limits.Rd b/man/render_stan_limits.Rd
new file mode 100644
index 00000000..5e0c885d
--- /dev/null
+++ b/man/render_stan_limits.Rd
@@ -0,0 +1,18 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/Prior.R
+\name{render_stan_limits}
+\alias{render_stan_limits}
+\title{Creates Stan Syntax for Truncated distributions}
+\usage{
+render_stan_limits(limits)
+}
+\arguments{
+\item{limits}{(\code{numeric})\cr the lower and upper limits for a truncated distribution}
+}
+\value{
+(\code{character})\cr the Stan syntax for truncated distributions
+}
+\description{
+This function creates the Stan syntax for truncated distributions
+}
+\keyword{internal}
diff --git a/tests/testthat/_snaps/JointModel.md b/tests/testthat/_snaps/JointModel.md
index 6c737856..4f663f7e 100644
--- a/tests/testthat/_snaps/JointModel.md
+++ b/tests/testthat/_snaps/JointModel.md
@@ -10,16 +10,16 @@
       
         Survival:     
            Weibull-PH Survival Model with parameters:
-               sm_weibull_ph_lambda ~ gamma(alpha = 2, beta = 0.5)
-               sm_weibull_ph_gamma ~ gamma(alpha = 2, beta = 0.5)
+               sm_weibull_ph_lambda ~ gamma(alpha = 2, beta = 0.5) T[0, ]
+               sm_weibull_ph_gamma ~ gamma(alpha = 2, beta = 0.5) T[0, ]
                beta_os_cov ~ normal(mu = 0, sigma = 2)
            
         Longitudinal:     
            Random Slope Longitudinal Model with parameters:
                lm_rs_intercept ~ normal(mu = 30, sigma = 10)
                lm_rs_slope_mu ~ normal(mu = 1, sigma = 3)
-               lm_rs_slope_sigma ~ lognormal(mu = 0, sigma = 1.5)
-               lm_rs_sigma ~ lognormal(mu = 0, sigma = 1.5)
+               lm_rs_slope_sigma ~ lognormal(mu = 0, sigma = 1.5) T[0, ]
+               lm_rs_sigma ~ lognormal(mu = 0, sigma = 1.5) T[0, ]
                lm_rs_ind_rnd_slope ~ <None>
            
         Link:     
@@ -38,16 +38,16 @@
       
         Survival:     
            Weibull-PH Survival Model with parameters:
-               sm_weibull_ph_lambda ~ gamma(alpha = 2, beta = 0.5)
-               sm_weibull_ph_gamma ~ gamma(alpha = 2, beta = 0.5)
+               sm_weibull_ph_lambda ~ gamma(alpha = 2, beta = 0.5) T[0, ]
+               sm_weibull_ph_gamma ~ gamma(alpha = 2, beta = 0.5) T[0, ]
                beta_os_cov ~ normal(mu = 0, sigma = 2)
            
         Longitudinal:     
            Random Slope Longitudinal Model with parameters:
                lm_rs_intercept ~ normal(mu = 30, sigma = 10)
                lm_rs_slope_mu ~ normal(mu = 1, sigma = 3)
-               lm_rs_slope_sigma ~ lognormal(mu = 0, sigma = 1.5)
-               lm_rs_sigma ~ lognormal(mu = 0, sigma = 1.5)
+               lm_rs_slope_sigma ~ lognormal(mu = 0, sigma = 1.5) T[0, ]
+               lm_rs_sigma ~ lognormal(mu = 0, sigma = 1.5) T[0, ]
                lm_rs_ind_rnd_slope ~ <None>
            
         Link:     
@@ -66,8 +66,8 @@
       
         Survival:     
            Weibull-PH Survival Model with parameters:
-               sm_weibull_ph_lambda ~ gamma(alpha = 2, beta = 0.5)
-               sm_weibull_ph_gamma ~ gamma(alpha = 2, beta = 0.5)
+               sm_weibull_ph_lambda ~ gamma(alpha = 2, beta = 0.5) T[0, ]
+               sm_weibull_ph_gamma ~ gamma(alpha = 2, beta = 0.5) T[0, ]
                beta_os_cov ~ normal(mu = 0, sigma = 2)
            
         Longitudinal:
@@ -94,11 +94,11 @@
                lm_gsf_mu_ks ~ normal(mu = -0.69315, sigma = 1)
                lm_gsf_mu_kg ~ normal(mu = -1.20397, sigma = 1)
                lm_gsf_mu_phi ~ normal(mu = 0, sigma = 1)
-               lm_gsf_omega_bsld ~ lognormal(mu = -1.60944, sigma = 1)
-               lm_gsf_omega_ks ~ lognormal(mu = -1.60944, sigma = 1)
-               lm_gsf_omega_kg ~ lognormal(mu = -1.60944, sigma = 1)
-               lm_gsf_omega_phi ~ lognormal(mu = -1.60944, sigma = 1)
-               lm_gsf_sigma ~ lognormal(mu = -2.30259, sigma = 1)
+               lm_gsf_omega_bsld ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+               lm_gsf_omega_ks ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+               lm_gsf_omega_kg ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+               lm_gsf_omega_phi ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+               lm_gsf_sigma ~ lognormal(mu = -2.30259, sigma = 1) T[0, ]
                lm_gsf_eta_tilde_bsld ~ std_normal()
                lm_gsf_eta_tilde_ks ~ std_normal()
                lm_gsf_eta_tilde_kg ~ std_normal()
@@ -119,16 +119,16 @@
       
         Survival:     
            Weibull-PH Survival Model with parameters:
-               sm_weibull_ph_lambda ~ gamma(alpha = 2, beta = 0.5)
-               sm_weibull_ph_gamma ~ gamma(alpha = 2, beta = 0.5)
+               sm_weibull_ph_lambda ~ gamma(alpha = 2, beta = 0.5) T[0, ]
+               sm_weibull_ph_gamma ~ gamma(alpha = 2, beta = 0.5) T[0, ]
                beta_os_cov ~ normal(mu = 0, sigma = 2)
            
         Longitudinal:     
            Random Slope Longitudinal Model with parameters:
                lm_rs_intercept ~ normal(mu = 30, sigma = 10)
                lm_rs_slope_mu ~ normal(mu = 1, sigma = 3)
-               lm_rs_slope_sigma ~ lognormal(mu = 0, sigma = 1.5)
-               lm_rs_sigma ~ lognormal(mu = 0, sigma = 1.5)
+               lm_rs_slope_sigma ~ lognormal(mu = 0, sigma = 1.5) T[0, ]
+               lm_rs_sigma ~ lognormal(mu = 0, sigma = 1.5) T[0, ]
                lm_rs_ind_rnd_slope ~ <None>
            
         Link:     
diff --git a/tests/testthat/_snaps/LongitudinalClaretBruno.md b/tests/testthat/_snaps/LongitudinalClaretBruno.md
index 079beb53..d0d3d7f9 100644
--- a/tests/testthat/_snaps/LongitudinalClaretBruno.md
+++ b/tests/testthat/_snaps/LongitudinalClaretBruno.md
@@ -10,11 +10,11 @@
           lm_clbr_mu_g ~ normal(mu = 0, sigma = 0.5)
           lm_clbr_mu_c ~ normal(mu = -0.91629, sigma = 0.5)
           lm_clbr_mu_p ~ normal(mu = 0.69315, sigma = 0.5)
-          lm_clbr_omega_b ~ lognormal(mu = -1.60944, sigma = 0.5)
-          lm_clbr_omega_g ~ lognormal(mu = -1.60944, sigma = 0.5)
-          lm_clbr_omega_c ~ lognormal(mu = -1.60944, sigma = 0.5)
-          lm_clbr_omega_p ~ lognormal(mu = -1.60944, sigma = 0.5)
-          lm_clbr_sigma ~ lognormal(mu = -2.30259, sigma = 0.5)
+          lm_clbr_omega_b ~ lognormal(mu = -1.60944, sigma = 0.5) T[0, ]
+          lm_clbr_omega_g ~ lognormal(mu = -1.60944, sigma = 0.5) T[0, ]
+          lm_clbr_omega_c ~ lognormal(mu = -1.60944, sigma = 0.5) T[0, ]
+          lm_clbr_omega_p ~ lognormal(mu = -1.60944, sigma = 0.5) T[0, ]
+          lm_clbr_sigma ~ lognormal(mu = -2.30259, sigma = 0.5) T[0, ]
           lm_clbr_eta_b ~ std_normal()
           lm_clbr_eta_g ~ std_normal()
           lm_clbr_eta_c ~ std_normal()
@@ -34,11 +34,11 @@
           lm_clbr_mu_g ~ gamma(alpha = 2, beta = 1)
           lm_clbr_mu_c ~ normal(mu = -0.91629, sigma = 0.5)
           lm_clbr_mu_p ~ normal(mu = 0.69315, sigma = 0.5)
-          lm_clbr_omega_b ~ lognormal(mu = -1.60944, sigma = 0.5)
-          lm_clbr_omega_g ~ lognormal(mu = -1.60944, sigma = 0.5)
-          lm_clbr_omega_c ~ lognormal(mu = -1.60944, sigma = 0.5)
-          lm_clbr_omega_p ~ lognormal(mu = -1.60944, sigma = 0.5)
-          lm_clbr_sigma ~ normal(mu = 0, sigma = 1)
+          lm_clbr_omega_b ~ lognormal(mu = -1.60944, sigma = 0.5) T[0, ]
+          lm_clbr_omega_g ~ lognormal(mu = -1.60944, sigma = 0.5) T[0, ]
+          lm_clbr_omega_c ~ lognormal(mu = -1.60944, sigma = 0.5) T[0, ]
+          lm_clbr_omega_p ~ lognormal(mu = -1.60944, sigma = 0.5) T[0, ]
+          lm_clbr_sigma ~ normal(mu = 0, sigma = 1) T[0, ]
           lm_clbr_eta_b ~ std_normal()
           lm_clbr_eta_g ~ std_normal()
           lm_clbr_eta_c ~ std_normal()
diff --git a/tests/testthat/_snaps/LongitudinalGSF.md b/tests/testthat/_snaps/LongitudinalGSF.md
index a02065f9..ed7c8b70 100644
--- a/tests/testthat/_snaps/LongitudinalGSF.md
+++ b/tests/testthat/_snaps/LongitudinalGSF.md
@@ -10,11 +10,11 @@
           lm_gsf_mu_ks ~ normal(mu = -0.69315, sigma = 1)
           lm_gsf_mu_kg ~ normal(mu = -1.20397, sigma = 1)
           lm_gsf_mu_phi ~ normal(mu = 0, sigma = 1)
-          lm_gsf_omega_bsld ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_gsf_omega_ks ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_gsf_omega_kg ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_gsf_omega_phi ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_gsf_sigma ~ lognormal(mu = -2.30259, sigma = 1)
+          lm_gsf_omega_bsld ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_gsf_omega_ks ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_gsf_omega_kg ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_gsf_omega_phi ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_gsf_sigma ~ lognormal(mu = -2.30259, sigma = 1) T[0, ]
           lm_gsf_eta_tilde_bsld ~ std_normal()
           lm_gsf_eta_tilde_ks ~ std_normal()
           lm_gsf_eta_tilde_kg ~ std_normal()
@@ -33,11 +33,11 @@
           lm_gsf_mu_ks ~ normal(mu = -0.69315, sigma = 1)
           lm_gsf_mu_kg ~ gamma(alpha = 2, beta = 1)
           lm_gsf_mu_phi ~ normal(mu = 0, sigma = 1)
-          lm_gsf_omega_bsld ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_gsf_omega_ks ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_gsf_omega_kg ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_gsf_omega_phi ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_gsf_sigma ~ normal(mu = 0, sigma = 1)
+          lm_gsf_omega_bsld ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_gsf_omega_ks ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_gsf_omega_kg ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_gsf_omega_phi ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_gsf_sigma ~ normal(mu = 0, sigma = 1) T[0, ]
           lm_gsf_eta_tilde_bsld ~ std_normal()
           lm_gsf_eta_tilde_ks ~ std_normal()
           lm_gsf_eta_tilde_kg ~ std_normal()
diff --git a/tests/testthat/_snaps/LongitudinalRandomSlope.md b/tests/testthat/_snaps/LongitudinalRandomSlope.md
index 997081e9..8694850f 100644
--- a/tests/testthat/_snaps/LongitudinalRandomSlope.md
+++ b/tests/testthat/_snaps/LongitudinalRandomSlope.md
@@ -8,8 +8,8 @@
       Random Slope Longitudinal Model with parameters:
           lm_rs_intercept ~ normal(mu = 30, sigma = 10)
           lm_rs_slope_mu ~ normal(mu = 1, sigma = 3)
-          lm_rs_slope_sigma ~ lognormal(mu = 0, sigma = 1.5)
-          lm_rs_sigma ~ lognormal(mu = 0, sigma = 1.5)
+          lm_rs_slope_sigma ~ lognormal(mu = 0, sigma = 1.5) T[0, ]
+          lm_rs_sigma ~ lognormal(mu = 0, sigma = 1.5) T[0, ]
           lm_rs_ind_rnd_slope ~ <None>
       
 
@@ -24,8 +24,8 @@
       Random Slope Longitudinal Model with parameters:
           lm_rs_intercept ~ normal(mu = 0, sigma = 1)
           lm_rs_slope_mu ~ normal(mu = 1, sigma = 3)
-          lm_rs_slope_sigma ~ lognormal(mu = 0, sigma = 1.5)
-          lm_rs_sigma ~ gamma(alpha = 2, beta = 1)
+          lm_rs_slope_sigma ~ lognormal(mu = 0, sigma = 1.5) T[0, ]
+          lm_rs_sigma ~ gamma(alpha = 2, beta = 1) T[0, ]
           lm_rs_ind_rnd_slope ~ <None>
       
 
diff --git a/tests/testthat/_snaps/LongitudinalSteinFojo.md b/tests/testthat/_snaps/LongitudinalSteinFojo.md
index 1acd86a3..4ccd6682 100644
--- a/tests/testthat/_snaps/LongitudinalSteinFojo.md
+++ b/tests/testthat/_snaps/LongitudinalSteinFojo.md
@@ -9,10 +9,10 @@
           lm_sf_mu_bsld ~ normal(mu = 4.09434, sigma = 1)
           lm_sf_mu_ks ~ normal(mu = -0.69315, sigma = 1)
           lm_sf_mu_kg ~ normal(mu = -1.20397, sigma = 1)
-          lm_sf_omega_bsld ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_sf_omega_ks ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_sf_omega_kg ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_sf_sigma ~ lognormal(mu = -2.30259, sigma = 1)
+          lm_sf_omega_bsld ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_sf_omega_ks ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_sf_omega_kg ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_sf_sigma ~ lognormal(mu = -2.30259, sigma = 1) T[0, ]
           lm_sf_eta_tilde_bsld ~ std_normal()
           lm_sf_eta_tilde_ks ~ std_normal()
           lm_sf_eta_tilde_kg ~ std_normal()
@@ -29,10 +29,10 @@
           lm_sf_mu_bsld ~ normal(mu = 4.09434, sigma = 1)
           lm_sf_mu_ks ~ normal(mu = -0.69315, sigma = 1)
           lm_sf_mu_kg ~ gamma(alpha = 2, beta = 1)
-          lm_sf_omega_bsld ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_sf_omega_ks ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_sf_omega_kg ~ lognormal(mu = -1.60944, sigma = 1)
-          lm_sf_sigma ~ normal(mu = 0, sigma = 1)
+          lm_sf_omega_bsld ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_sf_omega_ks ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_sf_omega_kg ~ lognormal(mu = -1.60944, sigma = 1) T[0, ]
+          lm_sf_sigma ~ normal(mu = 0, sigma = 1) T[0, ]
           lm_sf_eta_tilde_bsld ~ std_normal()
           lm_sf_eta_tilde_ks ~ std_normal()
           lm_sf_eta_tilde_kg ~ std_normal()
diff --git a/tests/testthat/_snaps/SurvivalGamma.md b/tests/testthat/_snaps/SurvivalGamma.md
index 2cb71967..ca86ce0b 100644
--- a/tests/testthat/_snaps/SurvivalGamma.md
+++ b/tests/testthat/_snaps/SurvivalGamma.md
@@ -6,8 +6,8 @@
     Output
       
       Gamma Survival Model with parameters:
-          sm_gamma_k ~ gamma(alpha = 2, beta = 0.5)
-          sm_gamma_theta ~ gamma(alpha = 2, beta = 0.5)
+          sm_gamma_k ~ gamma(alpha = 2, beta = 0.5) T[0, ]
+          sm_gamma_theta ~ gamma(alpha = 2, beta = 0.5) T[0, ]
           beta_os_cov ~ normal(mu = 0, sigma = 2)
       
 
@@ -19,8 +19,8 @@
     Output
       
       Gamma Survival Model with parameters:
-          sm_gamma_k ~ gamma(alpha = 3, beta = 4)
-          sm_gamma_theta ~ cauchy(mu = 0, sigma = 1)
+          sm_gamma_k ~ gamma(alpha = 3, beta = 4) T[0, ]
+          sm_gamma_theta ~ cauchy(mu = 0, sigma = 1) T[0, ]
           beta_os_cov ~ normal(mu = 0, sigma = 2)
       
 
diff --git a/tests/testthat/_snaps/SurvivalWeibullPH.md b/tests/testthat/_snaps/SurvivalWeibullPH.md
index 326b229e..97e832c3 100644
--- a/tests/testthat/_snaps/SurvivalWeibullPH.md
+++ b/tests/testthat/_snaps/SurvivalWeibullPH.md
@@ -6,8 +6,8 @@
     Output
       
       Weibull-PH Survival Model with parameters:
-          sm_weibull_ph_lambda ~ gamma(alpha = 2, beta = 0.5)
-          sm_weibull_ph_gamma ~ gamma(alpha = 2, beta = 0.5)
+          sm_weibull_ph_lambda ~ gamma(alpha = 2, beta = 0.5) T[0, ]
+          sm_weibull_ph_gamma ~ gamma(alpha = 2, beta = 0.5) T[0, ]
           beta_os_cov ~ normal(mu = 0, sigma = 2)
       
 
@@ -19,8 +19,8 @@
     Output
       
       Weibull-PH Survival Model with parameters:
-          sm_weibull_ph_lambda ~ gamma(alpha = 2, beta = 0.5)
-          sm_weibull_ph_gamma ~ cauchy(mu = 0, sigma = 1)
+          sm_weibull_ph_lambda ~ gamma(alpha = 2, beta = 0.5) T[0, ]
+          sm_weibull_ph_gamma ~ cauchy(mu = 0, sigma = 1) T[0, ]
           beta_os_cov ~ gamma(alpha = 3, beta = 4)
       
 
diff --git a/tests/testthat/test-Prior.R b/tests/testthat/test-Prior.R
index 7f9238bb..aae5ab05 100644
--- a/tests/testthat/test-Prior.R
+++ b/tests/testthat/test-Prior.R
@@ -199,6 +199,11 @@ test_that("Limits work as expected", {
     expect_true(all(ivs > 0))
     expect_true(all(ivs < 1))
 
+    expect_equal(
+        as.StanModule(x, name = "bob")@model,
+        "    bob ~ normal(prior_mu_bob, prior_sigma_bob) T[0, 1];"
+    )
+
 
     x <- prior_cauchy(-200, 150)
     x <- set_limits(x, lower = 0)
@@ -207,12 +212,20 @@ test_that("Limits work as expected", {
         initialValues(x)
     )
     expect_true(all(ivs > 0))
+    expect_equal(
+        as.StanModule(x, name = "tim")@model,
+        "    tim ~ cauchy(prior_mu_tim, prior_sigma_tim) T[0, ];"
+    )
 
 
     ## Put an impossible constraint on the distribution
     x <- prior_lognormal(0, 1)
     x <- set_limits(x, upper = 0)
     expect_error(initialValues(x), regex = "Unable to generate")
+    expect_equal(
+        as.StanModule(x, name = "phil")@model,
+        "    phil ~ lognormal(prior_mu_phil, prior_sigma_phil) T[, 0];"
+    )
 })
 
 
diff --git a/tests/testthat/test-stan_functions.R b/tests/testthat/test-stan_functions.R
index 786fd2ef..64b64898 100644
--- a/tests/testthat/test-stan_functions.R
+++ b/tests/testthat/test-stan_functions.R
@@ -22,6 +22,7 @@ run_stan_function <- function(stan_data, fun_files, dir, basename) {
             )
         )
     )
+
     # Completely silence call to STAN as we aren't fitting a real model
     devnull <- capture.output({
         suppressMessages({
@@ -38,6 +39,7 @@ run_stan_function <- function(stan_data, fun_files, dir, basename) {
         })
     })
     return(fit)
+    mod$stan_file()
 }