diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 5b67a64..f5c5a80 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -20,7 +20,7 @@ jobs:
       matrix:
         version:
           - '1'
-          - '1.10'
+          - 'lts'
         os:
           - ubuntu-latest
           - macOS-latest
@@ -29,7 +29,7 @@ jobs:
           - x64
     steps:
       - uses: actions/checkout@v4
-      - uses: julia-actions/setup-julia@v1
+      - uses: julia-actions/setup-julia@v2
         with:
           version: ${{ matrix.version }}
           arch: ${{ matrix.arch }}
diff --git a/docs/src/gibbs_polar.md b/docs/src/gibbs_polar.md
index 56e48ca..d87a4d1 100644
--- a/docs/src/gibbs_polar.md
+++ b/docs/src/gibbs_polar.md
@@ -8,7 +8,6 @@ Unlike other slice sampling algorithms, it operates a Gibbs sampler over polar c
 Due to the involvement of polar coordinates, GPSS only works reliably on more than one dimension.
 However, unlike ESS, GPSS is applicable to any target distribution.
 
-
 ## Description
 For a $$d$$-dimensional target distribution $$\pi$$, GPSS utilizes the following augmented target distribution:
 ```math
@@ -34,26 +33,19 @@ The Gibbs steps on $$\theta$$ and $$r$$ are implemented through specialized shri
 
 The only tunable parameter of the algorithm is the size of the search interval (window) of the shrinkage sampler for the radius variable $$r$$.
 
+!!! warning 
+    A limitation of the current implementation of GPSS is that the acceptance rate exhibits a heavy tail. That is, occasionally, a single transition might take an excessive amount of time.
+
 !!! info
     The kernel corresponding to this sampler is defined on an **augmented state space** and cannot directly perform a transition on $$x$$.
     This also means that the corresponding kernel is not reversible with respect to $$x$$.
 	
 ## Interface
 
-!!! info
-    By the nature of polar coordinates, GPSS only works reliably for targets with dimension at least $$d \geq 2$$.
-
 ```@docs
 GibbsPolarSlice
 ```
 
-!!! warning
-    When initializing the chain (*e.g.* the `initial_params` keyword arguments in `AbstractMCMC.sample`), it is necessary to inialize from a point $$x_0$$ that has a sensible norm $$\lVert x_0 \rVert > 0$$, otherwise, the chain will start from a pathologic point in polar coordinates. This might even result in the sampler getting stuck in an infinite loop. (This can be prevented by setting `max_proposals`.) If $$\lVert x_0 \rVert \leq 10^{-5}$$, the current implementation will display a warning. 
-	
-!!! info
-	For Turing users: `Turing` might change `initial_params` to match the support of the posterior. This might lead to $$\lVert x_0 \rVert$$ being small, even though the vector you passed to`initial_params` has a sufficiently large norm. If this is suspected, simply try a different initialization value.
-
-
 ## Demonstration
 As illustrated in the original paper, GPSS shows good performance on heavy-tailed targets despite being a multivariate slice sampler.
 Consider a 10-dimensional Student-$$t$$ target with 1-degree of freedom (this corresponds to a multivariate Cauchy):
diff --git a/src/SliceSampling.jl b/src/SliceSampling.jl
index ad9f768..cb1c82e 100644
--- a/src/SliceSampling.jl
+++ b/src/SliceSampling.jl
@@ -20,6 +20,8 @@ export sample, MCMCThreads, MCMCDistributed, MCMCSerial
 # Interfaces
 abstract type AbstractSliceSampling <: AbstractMCMC.AbstractSampler end
 
+const DEFAULT_MAX_PROPOSALS = 10_000
+
 """
     struct Transition
 
@@ -52,10 +54,9 @@ Return the initial sample for the `model` using the random number generator `rng
 """
 function initial_sample(::Random.AbstractRNG, ::Any)
     error(
-        "`initial_sample` is not implemented but an initialization wasn't provided. " *
+        "`initial_sample` is not implemented but an initialization wasn't provided. ",
         "Consider supplying an initialization to `initial_params`."
     )
-    println("fuck!!!")
 end
 
 # If target is from `LogDensityProblemsAD`, unwrap target before calling `initial_sample`.
@@ -66,10 +67,16 @@ initial_sample(
 ) = initial_sample(rng, parent(wrap))
 
 function exceeded_max_prop(max_prop::Int)
-    error("Exceeded maximum number of proposal $(max_prop).\n", 
-          "Here are possible causes:\n",
-          "- The model might be broken or pathologic.\n",
-          "- There might be a bug in the sampler.")
+    error("Exceeded maximum number of proposal $(max_prop), ",
+          "which indicates an acceptance rate less than $(1/max_prop*100)%. ", 
+          "A quick fix is to increase `max_prop`, ",
+          "but an acceptance rate that is too low often indicates that there is a problem. ",
+          "Here are some possible causes:\n",
+          "- The model might be broken or degenerate (most likely cause).\n",
+          "- The tunable parameters of the sampler are suboptimal.\n",
+          "- The initialization is pathologic. (try supplying a (different) `initial_params`)\n",
+          "- There might be a bug in the sampler. (if this is suspected, file an issue to `SliceSampling`)\n"
+          )
 end
 
 ## Univariate Slice Sampling Algorithms
diff --git a/src/multivariate/gibbspolar.jl b/src/multivariate/gibbspolar.jl
index 857e517..9600b03 100644
--- a/src/multivariate/gibbspolar.jl
+++ b/src/multivariate/gibbspolar.jl
@@ -9,14 +9,26 @@ Gibbsian polar slice sampling algorithm by P. Schär, M. Habeck, and D. Rudolf [
 
 # Keyword Arguments
 - `w::Real`: Initial window size for the radius shrinkage procedure
-- `max_proposals::Int`: Maximum number of proposals allowed until throwing an error (default: `typemax(Int)`).
+- `max_proposals::Int`: Maximum number of proposals allowed until throwing an error (default: `$(DEFAULT_MAX_PROPOSALS)`).
+
+!!! info
+    By the nature of polar coordinates, GPSS only works reliably for targets with dimension at least \$\$d \\geq 2\$\$.
+
+!!! info
+    The initial window size `w` must be set at least an order of magnitude larger than what is sensible for other slice samplers. Otherwise, a large number of rejections might be experienced.
+
+!!! warning
+    When initializing the chain (*e.g.* the `initial_params` keyword arguments in `AbstractMCMC.sample`), it is necessary to inialize from a point \$\$x_0\$\$ that has a sensible norm \$\$\\lVert x_0 \\rVert > 0\$\$, otherwise, the chain will start from a pathologic point in polar coordinates. This might even result in the sampler getting stuck in an infinite loop. (This can be prevented by setting `max_proposals`.) If \$\$\\lVert x_0 \\rVert \\leq 10^{-5}\$\$, the current implementation will display a warning. 
+	
+!!! info
+    For Turing users: `Turing` might change `initial_params` to match the support of the posterior. This might lead to \$\$\\lVert x_0 \\rVert\$\$ being small, even though the vector you passed to`initial_params` has a sufficiently large norm. If this is suspected, simply try a different initialization value.
 """
 struct GibbsPolarSlice{W <: Real} <: AbstractMultivariateSliceSampling
     w::W
     max_proposals::Int
 end
 
-GibbsPolarSlice(w::Real; max_proposals::Int = typemax(Int)) = GibbsPolarSlice(w, max_proposals)
+GibbsPolarSlice(w::Real; max_proposals::Int = DEFAULT_MAX_PROPOSALS) = GibbsPolarSlice(w, max_proposals)
 
 struct GibbsPolarSliceState{T <: Transition, R <: Real, D <: AbstractVector} 
     "Current [`Transition`](@ref)."
diff --git a/src/multivariate/latent.jl b/src/multivariate/latent.jl
index 0e93622..d3f7051 100644
--- a/src/multivariate/latent.jl
+++ b/src/multivariate/latent.jl
@@ -8,14 +8,14 @@ Latent slice sampling algorithm by Li and Walker[^LW2023].
 - `beta::Real`: Beta parameter of the Gamma distribution of the auxiliary variables.
 
 # Keyword Arguments
-- `max_proposals::Int`: Maximum number of proposals allowed until throwing an error (default: `typemax(Int)`).
+- `max_proposals::Int`: Maximum number of proposals allowed until throwing an error (default: `$(DEFAULT_MAX_PROPOSALS)`).
 """
 struct LatentSlice{B <: Real} <: AbstractMultivariateSliceSampling
     beta         ::B
     max_proposals::Int
 end
 
-function LatentSlice(beta::Real; max_proposals::Int = typemax(Int))
+function LatentSlice(beta::Real; max_proposals::Int = DEFAULT_MAX_PROPOSALS)
     @assert beta > 0 "Beta must be strictly positive"
     LatentSlice(beta, max_proposals)
 end
diff --git a/src/univariate/doublingout.jl b/src/univariate/doublingout.jl
index 1e6a8fc..3a9155e 100644
--- a/src/univariate/doublingout.jl
+++ b/src/univariate/doublingout.jl
@@ -9,7 +9,7 @@ Univariate slice sampling by automatically adapting the initial interval through
 
 # Keyword Arguments
 - `max_doubling_out`: Maximum number of "doubling outs" (default: 8).
-- `max_proposals::Int`: Maximum number of proposals allowed until throwing an error (default: `typemax(Int)`).
+- `max_proposals::Int`: Maximum number of proposals allowed until throwing an error (default: `$(DEFAULT_MAX_PROPOSALS)`).
 """
 struct SliceDoublingOut{W <: Real} <: AbstractUnivariateSliceSampling
     window          ::W
@@ -20,7 +20,7 @@ end
 function SliceDoublingOut(
     window          ::Real;
     max_doubling_out::Int = 8,
-    max_proposals   ::Int = typemax(Int),
+    max_proposals   ::Int = DEFAULT_MAX_PROPOSALS,
 )
     @assert window > 0
     SliceDoublingOut(window, max_doubling_out, max_proposals)
diff --git a/src/univariate/fixedinterval.jl b/src/univariate/fixedinterval.jl
index 4c075f6..b679ec3 100644
--- a/src/univariate/fixedinterval.jl
+++ b/src/univariate/fixedinterval.jl
@@ -8,7 +8,7 @@ Univariate slice sampling with a fixed initial interval (Scheme 2 by Neal[^N2003
 - `window::Real`: Proposal window.
 
 # Keyword Arguments
-- `max_proposals::Int`: Maximum number of proposals allowed until throwing an error (default: `typemax(Int)`).
+- `max_proposals::Int`: Maximum number of proposals allowed until throwing an error (default: `$(DEFAULT_MAX_PROPOSALS)`).
 """
 struct Slice{W <: Real} <: AbstractUnivariateSliceSampling
     window       ::W
@@ -17,7 +17,7 @@ end
 
 function Slice(
     window       ::Real;
-    max_proposals::Int = typemax(Int), 
+    max_proposals::Int = DEFAULT_MAX_PROPOSALS, 
 )
     @assert window > 0
     Slice(window, max_proposals)
diff --git a/src/univariate/steppingout.jl b/src/univariate/steppingout.jl
index 6ab9867..88d578e 100644
--- a/src/univariate/steppingout.jl
+++ b/src/univariate/steppingout.jl
@@ -9,7 +9,7 @@ Univariate slice sampling by automatically adapting the initial interval through
 
 # Keyword Arguments
 - `max_stepping_out::Int`: Maximum number of "stepping outs" (default: 32).
-- `max_proposals::Int`: Maximum number of proposals allowed until throwing an error (default: `typemax(Int)`).
+- `max_proposals::Int`: Maximum number of proposals allowed until throwing an error (default: `$(DEFAULT_MAX_PROPOSALS)`).
 """
 struct SliceSteppingOut{W <: Real} <: AbstractUnivariateSliceSampling
     window          ::W
@@ -20,7 +20,7 @@ end
 function SliceSteppingOut(
     window          ::Real;
     max_stepping_out::Int = 32,
-    max_proposals   ::Int = typemax(Int),
+    max_proposals   ::Int = DEFAULT_MAX_PROPOSALS,
 )
     @assert window > 0
     SliceSteppingOut(window, max_stepping_out, max_proposals)
diff --git a/test/multivariate.jl b/test/multivariate.jl
index d91233b..910fe63 100644
--- a/test/multivariate.jl
+++ b/test/multivariate.jl
@@ -78,7 +78,7 @@ end
         LatentSlice(5),
 
         # Gibbsian polar slice sampling
-        GibbsPolarSlice(10),
+        GibbsPolarSlice(100),
     ]
         @testset "initial_params" begin
             model  = MultiModel(1.0, 1.0, [0.0])
@@ -87,7 +87,7 @@ end
 
             θ0    = [1.0, 0.1]
             chain = sample(
-                model,
+                model′,
                 sampler,
                 10;
                 initial_params=θ0,