diff --git a/src/advancedHMC_MCMC.jl b/src/advancedHMC_MCMC.jl
index 18452df0c..98a8d5db2 100644
--- a/src/advancedHMC_MCMC.jl
+++ b/src/advancedHMC_MCMC.jl
@@ -104,6 +104,10 @@ function physloglikelihood(Tar::LogTargetDensity, θ)
     p = Tar.prob.p
     f = Tar.prob.f
 
+    allparams = Tar.priors
+    invparams = allparams[2:length(allparams)]
+    meaninv = [invparam[1] for invparam in invparams]
+
     autodiff = Tar.autodiff
     dt = Tar.physdt
     t = collect(Float64, Tar.prob.tspan[1]:dt:Tar.prob.tspan[2])
@@ -113,13 +117,17 @@ function physloglikelihood(Tar::LogTargetDensity, θ)
 
     # # this is a vector{vector{dx,dy}}(handle case single u(float passed))
     if length(out[:, 1]) == 1
+        # shifted by prior mean
+        ode_params = exp.(θ[((length(θ) - Tar.extraparams) + 1):length(θ)] + log.(meaninv))
         physsol = [f(out[:, i][1],
-                     θ[((length(θ) - Tar.extraparams) + 1):length(θ)],
+                     ode_params,
                      t[i])
                    for i in 1:length(out[1, :])]
     else
+        # shifted by prior mean
+        ode_params = exp.(θ[((length(θ) - Tar.extraparams) + 1):length(θ)] + log.(meaninv))
         physsol = [f(out[:, i],
-                     θ[((length(θ) - Tar.extraparams) + 1):length(θ)],
+                     ode_params,
                      t[i])
                    for i in 1:length(out[1, :])]
     end
@@ -132,9 +140,7 @@ function physloglikelihood(Tar::LogTargetDensity, θ)
     n = length(out[1, :])
     for i in 1:length(Tar.prob.u0)
         # can add phystd[i] for u[i]
-        physlogprob += logpdf(MvNormal(nnsol[i, :],
-                                       Diagonal(Tar.phystd[i]^2 .* ones(n))),
-                              physsol[i, :])
+        physlogprob += logpdf(MvNormal(nnsol[i, :], Tar.phystd[i]), physsol[i, :])
     end
     return physlogprob
 end
@@ -149,8 +155,7 @@ function L2LossData(Tar::LogTargetDensity, θ)
     for i in 1:length(Tar.prob.u0)
         # can add l2std[i] for u[i]
         # for u[i] ith vector must be added to dataset,nn[1,:] is the dx in lotka_volterra
-        L2logprob += logpdf(MvNormal(nn[i, :], Diagonal(Tar.l2std[i]^2 .* ones(n))),
-                            Tar.dataset[i])
+        L2logprob += logpdf(MvNormal(nn[i, :], Tar.l2std[i]), Tar.dataset[i])
     end
     return L2logprob
 end
@@ -158,27 +163,21 @@ end
 # priors for NN parameters + ODE constants
 function priorweights(Tar::LogTargetDensity, θ)
     allparams = Tar.priors
+    # ode parameters
     invparams = allparams[2:length(allparams)]
-    meaninv = [invparam[1] for invparam in invparams]
+    stdinv = [invparam[2] for invparam in invparams]
     # nn weights
     nnwparams = allparams[1]
-    varw = nnwparams[2]^2
+    stdw = nnwparams[2]
     prisw = nnwparams[1] .* ones(length(θ) - Tar.extraparams)
 
     if Tar.extraparams > 0
-        # ode parameters
-        invparams = allparams[2:length(allparams)]
-        varinv = [invparam[2]^2 for invparam in invparams]
-
-        return (logpdf(MvNormal(θ[((length(θ) - Tar.extraparams) + 1):length(θ)],
-                                Diagonal(varinv)), meaninv)
+        return (logpdf(MvNormal(zeros(Tar.extraparams), stdinv),
+                       θ[((length(θ) - Tar.extraparams) + 1):length(θ)])
                 +
-                logpdf(MvNormal(θ[1:(length(θ) - Tar.extraparams)],
-                                Diagonal(varw .*
-                                         ones(length(θ[1:(length(θ) - Tar.extraparams)])))),
-                       prisw))
+                logpdf(MvNormal(prisw, stdw), θ[1:(length(θ) - Tar.extraparams)]))
     else
-        return logpdf(MvNormal(θ, Diagonal(varw .* ones(length(θ)))), prisw)
+        return logpdf(MvNormal(prisw, stdw), θ)
     end
 end
 
@@ -240,7 +239,7 @@ function ahmc_bayesian_pinn_ode(prob::DiffEqBase.DEProblem, chain::Flux.Chain,
 
     # [i[1] for i in param]
     if length(param) > 0
-        append!(initial_θ, randn(length(param)))
+        append!(initial_θ, zeros(length(param)))
         append!(priors, param)
     end
     nparameters = length(initial_θ)
diff --git a/test/BPINN_Tests.jl b/test/BPINN_Tests.jl
index 240ef411a..ccfd7ceb0 100644
--- a/test/BPINN_Tests.jl
+++ b/test/BPINN_Tests.jl
@@ -211,4 +211,11 @@ fh_mcmc_chain, fhsamples, fhstats = ahmc_bayesian_pinn_ode(prob, chainfh, datase
                                                            autodiff = true, l2std = [0.05],
                                                            phystd = [0.05],
                                                            priorsNNw = (0.0, 3.0),
-                                                           param = [(2.3, 0.5), (4.3, 0.5)])
\ No newline at end of file
+                                                           param = [(2.3, 0.5), (4.3, 0.5)])
+fhsamples1[1000]
+fhsamples[1000]
+param = [(1.5, 0.5), (1.2, 0.5), (3.3, 0.5), (1.4, 0.5)]
+param = [(2.3, 0.5), (4.3, 0.5)]
+yuhj = log.([i[1] for i in param])
+exp.(fhsamples1[1000][17:18] + yuhj)
+exp.(fhsamples[1000][17:18] + yuhj)
\ No newline at end of file