diff --git a/src/samplers/mcmc/mh_sampler.jl b/src/samplers/mcmc/mh_sampler.jl
index 811fc2c6f..ea9ad59e9 100644
--- a/src/samplers/mcmc/mh_sampler.jl
+++ b/src/samplers/mcmc/mh_sampler.jl
@@ -14,13 +14,13 @@ Fields:
 
 $(TYPEDFIELDS)
 """
-@with_kw struct RandomWalk{Q<:ContinuousUnivariateDistribution} <: MCMCProposal
+@with_kw struct RandomWalk{Q<:Union{AbstractMeasure,Distribution{<:Union{Univariate,Multivariate},Continuous}}} <: MCMCProposal
     proposaldist::Q = TDist(1.0)
 end
 
 export RandomWalk
 
-struct MHProposalState{Q<:ContinuousUnivariateDistribution} <: MCMCProposalState
+struct MHProposalState{Q<:BATMeasure} <: MCMCProposalState
     proposaldist::Q
 end
 export MHProposalState
@@ -44,6 +44,11 @@ bat_default(::Type{TransformedMCMC}, ::Val{:burnin}, proposal::RandomWalk, pretr
     MCMCMultiCycleBurnin(nsteps_per_cycle = max(div(nsteps, 10), 2500))
 
 
+function _get_sample_id(proposal::MHProposalState, id::Int32, cycle::Int32, stepno::Integer, sample_type::Integer)
+    return MCMCSampleID(id, cycle, stepno, sample_type), MCMCSampleID
+end
+
+
 function _create_proposal_state(
     proposal::RandomWalk, 
     target::BATMeasure, 
@@ -51,29 +56,54 @@ function _create_proposal_state(
     v_init::AbstractVector{<:Real}, 
     rng::AbstractRNG
 )
-    return MHProposalState(proposal.proposaldist)
+    n_dims = length(v_init)
+    mv_pdist = batmeasure(_full_random_walk_proposal(proposal.proposaldist, n_dims))
+    return MHProposalState(mv_pdist)
 end
 
 
-function _get_sample_id(proposal::MHProposalState, id::Int32, cycle::Int32, stepno::Integer, sample_type::Integer)
-    return MCMCSampleID(id, cycle, stepno, sample_type), MCMCSampleID
+function _full_random_walk_proposal(m::AbstractMeasure, n_dims::Integer)
+    x = testvalue(m)
+    @argcheck x isa AbstractVector{<:Real} && length(x) == n_dims
+    return m
+end
+
+function _full_random_walk_proposal(m::BATDistMeasure, n_dims::Integer)
+    d = convert(Distribution, m)
+    return batmeasure(_full_random_walk_proposal(d, n_dims))
 end
 
+function _full_random_walk_proposal(d::Distribution{Multivariate,Continuous}, n_dims::Integer)
+    @assert false
+    @argcheck length(d) == n_dims
+    return d
+end
 
-# Theoretical optimally proposal scale for random walk with gaussian proposal, according to
-# [Gelman et al., Ann. Appl. Probab. 7 (1) 110 - 120, 1997](https://doi.org/10.1214/aoap/1034625254)
-_optimal_proposal_scale(d::ContinuousUnivariateDistribution, n_dims::Integer) = 2.38 / sqrt(n_dims) / sqrt(var(d))
+function _full_random_walk_proposal(d::Normal, n_dims::Integer)
+    # Theoretical optimally proposal scale for random walk with gaussian proposal, according to
+    # [Gelman et al., Ann. Appl. Probab. 7 (1) 110 - 120, 1997](https://doi.org/10.1214/aoap/1034625254):
+    proposal_scale = 2.38 / sqrt(n_dims)
 
-# Determined experimentally for TDist
-const _tdist_corr_exp = [0.5, 0.2, 0.14, 0.085, 0.06, 0.045, 0.035, 0.02, 0.015, 0.015]
-function _optimal_proposal_scale(d::TDist, n_dims::Integer)
-    ν_int = round(Int, d.ν)
-    k = ν_int > 10 ? zero(eltype(_tdist_corr_exp)) : _tdist_corr_exp[ν_int]
-    2.38 / sqrt(n_dims) / n_dims^k
+    @argcheck mean(d) ≈ 0 
+    σ² = var(d)
+    Σ = ScalMat(n_dims, proposal_scale^2 * σ²)
+    return MvNormal(Σ)
 end
 
+function _full_random_walk_proposal(d::TDist, n_dims::Integer)
+    # Theoretically optimal proposal scale for gaussian seems to work quite well for
+    # t-distribution proposals with any degrees of freedom as well:
+    proposal_scale = 2.38 / sqrt(n_dims)
+
+    ν = dof(d)
+    Σ = ScalMat(n_dims, proposal_scale^2)
+    return Distributions.IsoTDist(ν, Σ)
+end
+
+
 const MHChainState = MCMCChainState{<:BATMeasure, <:RNGPartition, <:Function, <:MHProposalState} 
 
+
 function mcmc_propose!!(mc_state::MHChainState)
     @unpack target, proposal, f_transform, context = mc_state
     rng = get_rng(context)
@@ -85,11 +115,9 @@ function mcmc_propose!!(mc_state::MHChainState)
 
     z_current, logd_z_current = sample_z_current.v, sample_z_current.logd
     T = eltype(z_current)
-    n_dims = size(z_current, 1)
-
-    proposal_scale = T(_optimal_proposal_scale(pdist, n_dims))
 
-    z_proposed = z_current + proposal_scale .* T.(rand(rng, pdist, n_dims)) #TODO: check if proposal is symmetric? otherwise need additional factor?
+    # ToDo: Use gen-context:
+    z_proposed = z_current + T.(rand(rng, pdist))
     x_proposed, ladj = with_logabsdet_jacobian(f_transform, z_proposed)
     logd_x_proposed = BAT.checked_logdensityof(target, x_proposed)
     logd_z_proposed = logd_x_proposed + ladj
@@ -99,12 +127,9 @@ function mcmc_propose!!(mc_state::MHChainState)
     mc_state.samples[proposed_x_idx] = DensitySample(x_proposed, logd_x_proposed, 0, _get_sample_id(proposal, mc_state.info.id, mc_state.info.cycle, mc_state.stepno, PROPOSED_SAMPLE)[1], nothing)
     mc_state.sample_z[2] = DensitySample(z_proposed, logd_z_proposed, 0, _get_sample_id(proposal, mc_state.info.id, mc_state.info.cycle, mc_state.stepno, PROPOSED_SAMPLE)[1], nothing)
 
-    # TODO: MD, should we check for symmetriy of proposal distribution?
+    # TODO: check if proposal is symmetric - otherwise need Hastings correction:
     p_accept = clamp(exp(logd_z_proposed - logd_z_current), 0, 1)
-
-    
     @assert p_accept >= 0
-
     accepted = rand(rng) <= p_accept
 
     return mc_state, accepted, p_accept