diff --git a/turing/11-hierarchical_varying_intercept-cheese.jl b/turing/11-hierarchical_varying_intercept-cheese.jl
index 22c11ab..7c4b572 100644
--- a/turing/11-hierarchical_varying_intercept-cheese.jl
+++ b/turing/11-hierarchical_varying_intercept-cheese.jl
@@ -44,8 +44,8 @@ idx = cheese[:, :background_int]
 
     # prior for variance of random intercepts
     # usually requires thoughtful specification
-    τ ~ truncated(Cauchy(0, 2), 0, Inf) # group-level SDs intercepts
-    αⱼ ~ filldist(Normal(0, τ), n_gr)   # group-level intercepts
+    τ ~ truncated(Cauchy(0, 2); lower=0) # group-level SDs intercepts
+    αⱼ ~ filldist(Normal(0, τ), n_gr)    # group-level intercepts
 
     # likelihood
     y ~ MvNormal(α .+ αⱼ[idx] .+ X * β, σ^2 * I)
diff --git a/turing/11-hierarchical_varying_intercept-non_centered-cheese.jl b/turing/11-hierarchical_varying_intercept-non_centered-cheese.jl
index 833b8ff..5a8f8af 100644
--- a/turing/11-hierarchical_varying_intercept-non_centered-cheese.jl
+++ b/turing/11-hierarchical_varying_intercept-non_centered-cheese.jl
@@ -44,9 +44,9 @@ idx = cheese[:, :background_int]
 
     # prior for variance of random intercepts
     # usually requires thoughtful specification
-    τ ~ truncated(Cauchy(0, 2), 0, Inf) # group-level SDs intercepts
-    zⱼ ~ filldist(Normal(0, 1), n_gr)   # group-level non-centered intercepts
-    αⱼ = zⱼ .* τ                        # group-level intercepts
+    τ ~ truncated(Cauchy(0, 2); lower=0) # group-level SDs intercepts
+    zⱼ ~ filldist(Normal(0, 1), n_gr)    # group-level non-centered intercepts
+    αⱼ = zⱼ .* τ                         # group-level intercepts
 
     # likelihood
     y ~ MvNormal(α .+ αⱼ[idx] .+ X * β, σ^2 * I)
diff --git a/turing/12-hierarchical_varying_slope-cheese.jl b/turing/12-hierarchical_varying_slope-cheese.jl
index 83cd0ee..3736d9d 100644
--- a/turing/12-hierarchical_varying_slope-cheese.jl
+++ b/turing/12-hierarchical_varying_slope-cheese.jl
@@ -45,8 +45,8 @@ idx = cheese[:, :background_int]
 
     # prior for variance of random slopes
     # usually requires thoughtful specification
-    τ ~ filldist(truncated(Cauchy(0, 2), 0, Inf), n_gr)                             # group-level SDs slopes
-    βⱼ ~ arraydist([MvNormal(Diagonal(fill(τ[j], predictors).^2)) for j in 1:n_gr]) # group-level slopes
+    τ ~ filldist(truncated(Cauchy(0, 2); lower=0), n_gr)                             # group-level SDs slopes
+    βⱼ ~ arraydist([MvNormal(Diagonal(fill(τ[j], predictors).^2)) for j in 1:n_gr])  # group-level slopes
 
     # likelihood
     for i in 1:N
diff --git a/turing/12-hierarchical_varying_slope-non_centered-cheese.jl b/turing/12-hierarchical_varying_slope-non_centered-cheese.jl
index 78f3b93..2e12a85 100644
--- a/turing/12-hierarchical_varying_slope-non_centered-cheese.jl
+++ b/turing/12-hierarchical_varying_slope-non_centered-cheese.jl
@@ -44,9 +44,9 @@ idx = cheese[:, :background_int]
 
     # prior for variance of random slopes
     # usually requires thoughtful specification
-    τ ~ filldist(truncated(Cauchy(0, 2), 0, Inf), n_gr) # group-level SDs slopes
-    Zⱼ ~ filldist(Normal(0, 1), predictors, n_gr)       # group-level non-centered slopes
-    βⱼ = Zⱼ * τ                                         # group-level slopes
+    τ ~ filldist(truncated(Cauchy(0, 2); lower=0), n_gr) # group-level SDs slopes
+    Zⱼ ~ filldist(Normal(0, 1), predictors, n_gr)        # group-level non-centered slopes
+    βⱼ = Zⱼ * τ                                          # group-level slopes
 
     # likelihood
     y ~ MvNormal(α .+ X * β .+ X * βⱼ, σ^2 * I)
diff --git a/turing/13-hierarchical_varying_intercept_slope-cheese.jl b/turing/13-hierarchical_varying_intercept_slope-cheese.jl
index a668222..d69311f 100644
--- a/turing/13-hierarchical_varying_intercept_slope-cheese.jl
+++ b/turing/13-hierarchical_varying_intercept_slope-cheese.jl
@@ -45,8 +45,8 @@ idx = cheese[:, :background_int]
 
     # prior for variance of random intercepts and slopes
     # usually requires thoughtful specification
-    τₐ ~ truncated(Cauchy(0, 2), 0, Inf)                                             # group-level SDs intercepts
-    τᵦ ~ filldist(truncated(Cauchy(0, 2), 0, Inf), n_gr)                             # group-level SDs slopes
+    τₐ ~ truncated(Cauchy(0, 2); lower=0)                                            # group-level SDs intercepts
+    τᵦ ~ filldist(truncated(Cauchy(0, 2); lower=0), n_gr)                            # group-level SDs slopes
     αⱼ ~ filldist(Normal(0, τₐ), n_gr)                                               # group-level intercepts
     βⱼ ~ arraydist([MvNormal(Diagonal(fill(τᵦ[j], predictors).^2)) for j in 1:n_gr]) # group-level slopes
 
diff --git a/turing/13-hierarchical_varying_intercept_slope-non_centered-cheese.jl b/turing/13-hierarchical_varying_intercept_slope-non_centered-cheese.jl
index 86562ec..438944f 100644
--- a/turing/13-hierarchical_varying_intercept_slope-non_centered-cheese.jl
+++ b/turing/13-hierarchical_varying_intercept_slope-non_centered-cheese.jl
@@ -44,12 +44,12 @@ idx = cheese[:, :background_int]
 
     # prior for variance of random intercepts and slopes
     # usually requires thoughtful specification
-    τₐ ~ truncated(Cauchy(0, 2), 0, Inf)                 # group-level SDs intercepts
-    τᵦ ~ filldist(truncated(Cauchy(0, 2), 0, Inf), n_gr) # group-level SDs slopes
-    zⱼ ~ filldist(Normal(0, 1), n_gr)                    # group-level non-centered intercepts
-    Zⱼ ~ filldist(Normal(0, 1), predictors, n_gr)        # group-level non-centered slopes
-    αⱼ = zⱼ .* τₐ                                        # group-level intercepts
-    βⱼ = Zⱼ * τᵦ                                         # group-level slopes
+    τₐ ~ truncated(Cauchy(0, 2); lower=0)                 # group-level SDs intercepts
+    τᵦ ~ filldist(truncated(Cauchy(0, 2); lower=0), n_gr) # group-level SDs slopes
+    zⱼ ~ filldist(Normal(0, 1), n_gr)                     # group-level non-centered intercepts
+    Zⱼ ~ filldist(Normal(0, 1), predictors, n_gr)         # group-level non-centered slopes
+    αⱼ = zⱼ .* τₐ                                         # group-level intercepts
+    βⱼ = Zⱼ * τᵦ                                          # group-level slopes
 
     # likelihood
     y ~ MvNormal(α .+ αⱼ[idx] .+ X * β .+ X * βⱼ, σ^2 * I)
diff --git a/turing/14-hierarchical_correlated_varying_intercept_slope-cheese.jl b/turing/14-hierarchical_correlated_varying_intercept_slope-cheese.jl
index 8cd9170..fb065be 100644
--- a/turing/14-hierarchical_correlated_varying_intercept_slope-cheese.jl
+++ b/turing/14-hierarchical_correlated_varying_intercept_slope-cheese.jl
@@ -52,9 +52,9 @@ idx = cheese[:, :background_int]
 
 #     # prior for variance of random intercepts and slopes
 #     # usually requires thoughtful specification
-#     τ ~ filldist(truncated(Cauchy(0, 2), 0, Inf), predictors) # group-level SDs
-#     γ ~ filldist(Normal(0, 5), predictors, n_gr)              # matrix of group coefficients
-#     Z ~ filldist(Normal(0, 1), predictors, n_gr)              # matrix of non-centered group coefficients
+#     τ ~ filldist(truncated(Cauchy(0, 2); lower=0), predictors) # group-level SDs
+#     γ ~ filldist(Normal(0, 5), predictors, n_gr)               # matrix of group coefficients
+#     Z ~ filldist(Normal(0, 1), predictors, n_gr)               # matrix of non-centered group coefficients
 
 #     # reconstruct β from Ω and τ
 #     β = γ + τ .* Ω.L * Z
@@ -85,12 +85,12 @@ using PDMats
 
     # prior for variance of random intercepts and slopes
     # usually requires thoughtful specification
-    τ ~ filldist(truncated(Cauchy(0, 2), 0, Inf), predictors) # group-level SDs
-    γ ~ filldist(Normal(0, 5), predictors, n_gr)              # matrix of group coefficients
-    Z ~ filldist(Normal(0, 1), predictors, n_gr)              # matrix of non-centered group coefficients
+    τ ~ filldist(truncated(Cauchy(0, 2); lower=0), predictors) # group-level SDs
+    γ ~ filldist(Normal(0, 5), predictors, n_gr)               # matrix of group coefficients
+    Z ~ filldist(Normal(0, 1), predictors, n_gr)               # matrix of non-centered group coefficients
 
     # reconstruct β from Ω and τ
-    Ω_L = LowerTriangular(collect(τ .* L_U'))                 # collect is necessary for ReverseDiff for some reason
+    Ω_L = LowerTriangular(collect(τ .* L_U'))                  # collect is necessary for ReverseDiff for some reason
     Ω = PDMat(Cholesky(Ω_L))
     β = γ + Ω * Z