diff --git a/Project.toml b/Project.toml
index 3c3935a9..ef8ac19a 100644
--- a/Project.toml
+++ b/Project.toml
@@ -27,7 +27,7 @@ UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
 [compat]
 Accessors = "0.1"
 Distributions = "0.25"
-DynamicPPL = "0.20, 0.21, 0.22, 0.23"
+DynamicPPL = "0.21, 0.22, 0.23, 0.24"
 Folds = "0.2"
 ForwardDiff = "0.10"
 IrrationalConstants = "0.1.1, 0.2"
@@ -46,7 +46,7 @@ SciMLBase = "1.8.1"
 Statistics = "1.6"
 StatsBase = "0.33, 0.34"
 Transducers = "0.4.5"
-Turing = "0.24, 0.25, 0.26"
+Turing = "0.24, 0.25, 0.26, 0.27"
 UnPack = "1"
 julia = "1.6"
 
diff --git a/docs/Project.toml b/docs/Project.toml
index 4a99bf83..890ad25a 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -15,7 +15,7 @@ TransformedLogDensities = "f9bc47f6-f3f8-4f3b-ab21-f8bc73906f26"
 Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
 
 [compat]
-AdvancedHMC = "0.4"
+AdvancedHMC = "0.4, 0.5"
 Documenter = "1"
 DynamicHMC = "3"
 ForwardDiff = "0.10"
@@ -26,4 +26,4 @@ StatsFuns = "0.9, 1"
 StatsPlots = "0.14, 0.15"
 TransformVariables = "0.6, 0.7, 0.8"
 TransformedLogDensities = "1"
-Turing = "0.24, 0.25, 0.26"
+Turing = "0.24, 0.25, 0.26, 0.27"
diff --git a/docs/src/examples/initializing-hmc.md b/docs/src/examples/initializing-hmc.md
index add0f0dd..2a0bbe70 100644
--- a/docs/src/examples/initializing-hmc.md
+++ b/docs/src/examples/initializing-hmc.md
@@ -172,11 +172,11 @@ metric = DiagEuclideanMetric(dim)
 hamiltonian = Hamiltonian(metric, ∇P)
 ϵ = find_good_stepsize(hamiltonian, init_params)
 integrator = Leapfrog(ϵ)
-proposal = AdvancedHMC.NUTS{MultinomialTS,GeneralisedNoUTurn}(integrator)
+kernel = HMCKernel(Trajectory{MultinomialTS}(integrator, GeneralisedNoUTurn()))
 adaptor = StepSizeAdaptor(0.8, integrator)
 samples_ahmc1, stats_ahmc1 = sample(
     hamiltonian,
-    proposal,
+    kernel,
     init_params,
     ndraws + nadapts,
     adaptor,
@@ -196,11 +196,11 @@ metric = DenseEuclideanMetric(Matrix(inv_metric))
 hamiltonian = Hamiltonian(metric, ∇P)
 ϵ = find_good_stepsize(hamiltonian, init_params)
 integrator = Leapfrog(ϵ)
-proposal = AdvancedHMC.NUTS{MultinomialTS,GeneralisedNoUTurn}(integrator)
+kernel = HMCKernel(Trajectory{MultinomialTS}(integrator, GeneralisedNoUTurn()))
 adaptor = StepSizeAdaptor(0.8, integrator)
 samples_ahmc2, stats_ahmc2 = sample(
     hamiltonian,
-    proposal,
+    kernel,
     init_params,
     ndraws + nadapts,
     adaptor,
@@ -220,11 +220,11 @@ metric = Pathfinder.RankUpdateEuclideanMetric(inv_metric)
 hamiltonian = Hamiltonian(metric, ∇P)
 ϵ = find_good_stepsize(hamiltonian, init_params)
 integrator = Leapfrog(ϵ)
-proposal = AdvancedHMC.NUTS{MultinomialTS,GeneralisedNoUTurn}(integrator)
+kernel = HMCKernel(Trajectory{MultinomialTS}(integrator, GeneralisedNoUTurn()))
 adaptor = StepSizeAdaptor(0.8, integrator)
 samples_ahmc3, stats_ahmc3 = sample(
     hamiltonian,
-    proposal,
+    kernel,
     init_params,
     ndraws + nadapts,
     adaptor,
diff --git a/docs/src/examples/turing.md b/docs/src/examples/turing.md
index 3bf3055a..66cf2a44 100644
--- a/docs/src/examples/turing.md
+++ b/docs/src/examples/turing.md
@@ -85,11 +85,11 @@ metric = Pathfinder.RankUpdateEuclideanMetric(inv_metric)
 hamiltonian = Hamiltonian(metric, ℓπ, ∂ℓπ∂θ)
 ϵ = find_good_stepsize(hamiltonian, init_params[1])
 integrator = Leapfrog(ϵ)
-proposal = AdvancedHMC.NUTS{MultinomialTS,GeneralisedNoUTurn}(integrator)
+kernel = HMCKernel(Trajectory{MultinomialTS}(integrator, GeneralisedNoUTurn()))
 adaptor = StepSizeAdaptor(0.8, integrator)
 samples, stats = sample(
     hamiltonian,
-    proposal,
+    kernel,
     init_params[1],
     ndraws + nadapts,
     adaptor,
diff --git a/test/integration/AdvancedHMC/Project.toml b/test/integration/AdvancedHMC/Project.toml
index 47c2aeee..fe958151 100644
--- a/test/integration/AdvancedHMC/Project.toml
+++ b/test/integration/AdvancedHMC/Project.toml
@@ -16,7 +16,7 @@ TransformVariables = "84d833dd-6860-57f9-a1a7-6da5db126cff"
 TransformedLogDensities = "f9bc47f6-f3f8-4f3b-ab21-f8bc73906f26"
 
 [compat]
-AdvancedHMC = "0.4"
+AdvancedHMC = "0.4, 0.5"
 Distributions = "0.25"
 ForwardDiff = "0.10"
 LogDensityProblems = "1, 2"
diff --git a/test/integration/AdvancedHMC/runtests.jl b/test/integration/AdvancedHMC/runtests.jl
index 6e713c55..8f1bcd0e 100644
--- a/test/integration/AdvancedHMC/runtests.jl
+++ b/test/integration/AdvancedHMC/runtests.jl
@@ -13,7 +13,7 @@ using AdvancedHMC,
     TransformVariables
 using TransformedLogDensities: TransformedLogDensity
 
-Random.seed!(0)
+Random.seed!(2)
 
 struct RegressionProblem{X,Y}
     x::X
@@ -53,7 +53,7 @@ function compare_estimates(xs1, xs2, α=0.05)
     p = α / 2
     m1, s1 = mean_and_mcse(xs1)
     m2, s2 = mean_and_mcse(xs2)
-    zs = @. (m1 - m2) / sqrt(s1^2 + s2^2)
+    zs = @. (m1 - m2) / hypot(s1, s2)
     @test all(norminvcdf(p) .< zs .< norminvccdf(p))
 end
 
@@ -106,7 +106,7 @@ end
     end
 
     @testset "sample" begin
-        ndraws = 1_000
+        ndraws = 10_000
         nadapts = 500
         nparams = 5
         x = 0:0.01:1
@@ -122,15 +122,15 @@ end
         hamiltonian = Hamiltonian(metric, ∇P)
         ϵ = find_good_stepsize(hamiltonian, θ₀)
         integrator = Leapfrog(ϵ)
-        proposal = NUTS{MultinomialTS,GeneralisedNoUTurn}(integrator)
+        kernel = HMCKernel(Trajectory{MultinomialTS}(integrator, GeneralisedNoUTurn()))
         adaptor = StanHMCAdaptor(
             MassMatrixAdaptor(metric), StepSizeAdaptor(0.8, integrator)
         )
         samples1, stats1 = sample(
             hamiltonian,
-            proposal,
+            kernel,
             θ₀,
-            ndraws,
+            ndraws + nadapts,
             adaptor,
             nadapts;
             drop_warmup=true,
@@ -144,13 +144,13 @@ end
             hamiltonian = Hamiltonian(metric, ∇P)
             ϵ = find_good_stepsize(hamiltonian, θ₀)
             integrator = Leapfrog(ϵ)
-            proposal = NUTS{MultinomialTS,GeneralisedNoUTurn}(integrator)
+            kernel = HMCKernel(Trajectory{MultinomialTS}(integrator, GeneralisedNoUTurn()))
             adaptor = StepSizeAdaptor(0.8, integrator)
             samples2, stats2 = sample(
                 hamiltonian,
-                proposal,
+                kernel,
                 result_pf.draws[:, 1],
-                ndraws,
+                ndraws + nadapts,
                 adaptor,
                 nadapts;
                 drop_warmup=true,
@@ -164,13 +164,13 @@ end
             hamiltonian = Hamiltonian(metric, ∇P)
             ϵ = find_good_stepsize(hamiltonian, θ₀)
             integrator = Leapfrog(ϵ)
-            proposal = NUTS{MultinomialTS,GeneralisedNoUTurn}(integrator)
+            kernel = HMCKernel(Trajectory{MultinomialTS}(integrator, GeneralisedNoUTurn()))
             adaptor = StepSizeAdaptor(0.8, integrator)
             samples3, stats3 = sample(
                 hamiltonian,
-                proposal,
+                kernel,
                 result_pf.draws[:, 1],
-                ndraws,
+                ndraws + nadapts,
                 adaptor,
                 nadapts;
                 drop_warmup=true,
@@ -184,13 +184,13 @@ end
             hamiltonian = Hamiltonian(metric, ∇P)
             ϵ = find_good_stepsize(hamiltonian, θ₀)
             integrator = Leapfrog(ϵ)
-            proposal = NUTS{MultinomialTS,GeneralisedNoUTurn}(integrator)
+            kernel = HMCKernel(Trajectory{MultinomialTS}(integrator, GeneralisedNoUTurn()))
             adaptor = StepSizeAdaptor(0.8, integrator)
             samples4, stats4 = sample(
                 hamiltonian,
-                proposal,
+                kernel,
                 result_pf.draws[:, 1],
-                ndraws,
+                ndraws + nadapts,
                 adaptor,
                 nadapts;
                 drop_warmup=true,
diff --git a/test/integration/DynamicHMC/runtests.jl b/test/integration/DynamicHMC/runtests.jl
index 71f7ce97..3bce8fe0 100644
--- a/test/integration/DynamicHMC/runtests.jl
+++ b/test/integration/DynamicHMC/runtests.jl
@@ -47,7 +47,7 @@ function compare_estimates(xs1, xs2, α=0.05)
     p = α / 2
     m1, s1 = mean_and_mcse(xs1)
     m2, s2 = mean_and_mcse(xs2)
-    zs = @. (m1 - m2) / sqrt(s1^2 + s2^2)
+    zs = @. (m1 - m2) / hypot(s1, s2)
     @test all(norminvcdf(p) .< zs .< norminvccdf(p))
 end
 
@@ -76,7 +76,7 @@ end
     end
 
     @testset "DynamicHMC.mcmc_with_warmup" begin
-        ndraws = 1_000
+        ndraws = 10_000
         x = 0:0.01:1
         y = sin.(x) .+ randn.() .* 0.2 .+ x
         X = [x x .^ 2 x .^ 3]
diff --git a/test/integration/Turing/Project.toml b/test/integration/Turing/Project.toml
index 1b41377e..669f8981 100644
--- a/test/integration/Turing/Project.toml
+++ b/test/integration/Turing/Project.toml
@@ -6,5 +6,5 @@ Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
 
 [compat]
 Pathfinder = "0.5, 0.6, 0.7"
-Turing = "0.24, 0.25, 0.26"
+Turing = "0.24, 0.25, 0.26, 0.27"
 julia = "1.6"