diff --git a/Project.toml b/Project.toml
index c7f265dda..2812a22b1 100644
--- a/Project.toml
+++ b/Project.toml
@@ -31,17 +31,17 @@ StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 
 [compat]
 AbstractGPs = "0.5.21"
-AbstractMCMC = "3.3, 4, 5"
-AdvancedMH = "0.6, 0.7, 0.8"
+AbstractMCMC = "5"
+AdvancedMH = "0.8"
 ChunkSplitters = "3.1.2"
 Conda = "1.7"
 Distributions = "0.24, 0.25"
 DocStringExtensions = "0.8, 0.9"
 EnsembleKalmanProcesses = "2"
-ForwardDiff = "0.10.38, 1"
+ForwardDiff = "1"
 GaussianProcesses = "0.12"
 KernelFunctions = "0.10.64"
-MCMCChains = "4.14, 5, 6, 7"
+MCMCChains = "7"
 Printf = "1"
 ProgressBars = "1"
 PyCall = "1.93"
diff --git a/src/MarkovChainMonteCarlo.jl b/src/MarkovChainMonteCarlo.jl
index c65655a6a..31d374040 100644
--- a/src/MarkovChainMonteCarlo.jl
+++ b/src/MarkovChainMonteCarlo.jl
@@ -379,9 +379,14 @@ function AbstractMCMC.step(
     new_params = AdvancedMH.propose(rng, sampler, model, current_state; stepsize = stepsize)
     # Calculate the log acceptance probability and the log density of the candidate.
     new_log_density = AdvancedMH.logdensity(model, new_params)
+
+    # Just to initialize: if you pass state, it just reads the old log_density (initialized as false). in this case, compute it by passing the actual parameter values
+    current_log_density =
+        isa(AdvancedMH.logdensity(model, current_state), Bool) ? AdvancedMH.logdensity(model, current_state.params) :
+        AdvancedMH.logdensity(model, current_state)
+
     log_α =
-        new_log_density - AdvancedMH.logdensity(model, current_state) +
-        AdvancedMH.logratio_proposal_density(sampler, current_state, new_params)
+        new_log_density - current_log_density + AdvancedMH.logratio_proposal_density(sampler, current_state, new_params)
 
     # Decide whether to return the previous params or the new one.
     new_state = if -Random.randexp(rng) < log_α
@@ -573,7 +578,7 @@ function MCMCWrapper(
     end
 
     sample_kwargs = (; # set defaults here
-        :init_params => deepcopy(init_params),
+        :initial_params => deepcopy(init_params),
         :param_names => param_names,
         :discard_initial => burnin,
         :chain_type => MCMCChains.Chains,
@@ -641,7 +646,7 @@ end
 
 function _find_mcmc_step_log(mcmc::MCMCWrapper)
     str_ = @sprintf "%d starting params:" 0
-    for p in zip(mcmc.sample_kwargs.param_names, mcmc.sample_kwargs.init_params)
+    for p in zip(mcmc.sample_kwargs.param_names, mcmc.sample_kwargs.initial_params)
         str_ *= @sprintf " %s: %.3g" p[1] p[2]
     end
     println(str_)