Converting variance-covariance matrix to LKJCholesky prior in Bayesian estimation

Sooyoung.Lee · April 27, 2023, 9:41pm

Hello, I am trying to perform Bayesian estimation.
Then, I would like to use an informative prior distribution for the variance-covariance matrix based on LKJCholesky.
However, I have been failed so far.

I would like to know what is the problem,
how to convert my variance-covariance matrix (Ω_1 and Ω_2) to LKJCholesky prior,
and how to adjust the amount of correlation based on this prior.

Here is the variance-covariance matrix:

Ω_1 =[0.114 0.080
       0.080 0.081]
Ω_2 =[0.047 -0.013
       -0.013 0.0056]

Here is the model:

model_ = @model begin
  @metadata begin
      desc        = "two compartment model with first-order absorption and Tlag"
    end

  @param begin
      "Clearance (L/hr)"
      tvcl_other   ~ LogNormal(log(7.97), 0.1)
      tvcl_GF      ~ LogNormal(log(8.52), 0.1)
      "Volume of Central Compartment (L)"
      tvvc         ~ LogNormal(log(122.7), 0.1)
      "Intercompartmental Clearance (L/hr)"
      tvq          ~ LogNormal(log(10.1), 0.1)
      "Volume of Peripheral Compartment (L)"
      tvvp         ~ LogNormal(log(97.91), 0.1)
      "Absorption Rate Constant (hr⁻¹)"
      tvka         ~ LogNormal(log(2.15), 0.1)
      "Lagtime (hr)"
      tvlag        ~ LogNormal(log(0.22), 0.1)
      "LBM exponent"
      LBM_exp      ~ LogNormal(log(0.92), 0.1)
      "BSV"
      C_1       ~ LKJCholesky(2, 1.0)
      Ω_1      ~ Constrained(
        MvNormal(zeros(2), Diagonal([0.114, 0.081]));
        lower=zeros(2),
        upper=fill(Inf, 2),
        init=ones(2)
      )
      C_2       ~ LKJCholesky(2, 1.0)
      Ω_2      ~ Constrained(
        MvNormal(zeros(2), Diagonal([0.047, 0.0056]));
        lower=zeros(2),
        upper=fill(Inf, 2),
        init=ones(2)
      )
      "BOV"
      ω²η       ~ InverseGamma(154.40134051923962, 154.30201062815695)
      "Proportional RUV"
      σ²_prop   ∈ RealDomain(lower=0.0001, init=0.06541313854823212)
  end

  @random begin
    ηstd_1 ~ MvNormal(I(2))
    ηstd_2 ~ MvNormal(I(2))
    η_BOV   ~ MvNormal(3, sqrt(ω²η))
  end

  @covariates CrCL LBM OCC

  @pre begin
    η_1 = Diagonal(Ω_1) * (getchol(C_1).L * ηstd_1)
    η_2 = Diagonal(Ω_2) * (getchol(C_2).L * ηstd_2)

    CL          = (tvcl_other + (tvcl_GF * (CrCL/90))) * exp(η_1[1])
    Vc          = tvvc * ((LBM/55)^LBM_exp) * exp(η_1[2])
    Q           = tvq
    Vp          = tvvp
    Ka          = tvka * exp(η_2[1]) * exp(η_BOV[OCC])
    Tlag        = tvlag * exp(η_2[2])
  end

  @dosecontrol begin
    lags = (Depot = tvlag * exp(η_2[2]),)
  end

  @dynamics Depots1Central1Periph1

  @derived begin
    cp := @. (Central/Vc) 
    dv ~ @. Normal(cp, sqrt((cp^2) * (σ²_prop)))
  end
end

And, here is the error message:

[ Info: Checking the initial parameter values.
ERROR: TaskFailedException
Stacktrace:
  [1] wait
    @ ./task.jl:334 [inlined]
  [2] fetch
    @ ./task.jl:349 [inlined]
  [3] __tmapreduce(f::Pumas.var"#707#708"{Float64, Pumas.ThreadedBayesLogDensity{PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{ForwardDiff.GradientConfig{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8}}}}, Vector{DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}}, NamedTuple{(), Tuple{}}}, Vector{Float64}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Float64, Float64}}}, op::typeof(+), tasks::Vector{Task}, len::Int64, init::Float64, src::Tuple{UnitRange{Int64}}, batchargs::Tuple{})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:418
  [4] _tmapreduce
    @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:440 [inlined]
  [5] tmapreduce(f::Function, ::Type{Float64}, op::Function, src::Tuple{UnitRange{Int64}}, batchargs::Tuple{}; init::Float64, tasks::Vector{Task})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:451
  [6] _logdensity(b::Pumas.ThreadedBayesLogDensity{PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{ForwardDiff.GradientConfig{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8}}}}, Vector{DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}}, NamedTuple{(), Tuple{}}}, v::Vector{Float64})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:324
  [7] _check_initial_values(bayes::Pumas.ThreadedBayesLogDensity{PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{ForwardDiff.GradientConfig{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8}}}}, Vector{DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}}, NamedTuple{(), Tuple{}}}, vparam_aug::Vector{Float64})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/nuts.jl:393
  [8] pumas_sample(rngs::Vector{Xoshiro}, bayes::Vector{Pumas.ThreadedBayesLogDensity{PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{ForwardDiff.GradientConfig{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8}}}}, Vector{DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}}, NamedTuple{(), Tuple{}}}}, ::EnsembleThreads, nsamples::Int64, ess_per_chain::Int64, time_limit::Float64; ess_every::Int64, progress::Bool, balance_method::Symbol, update_progress_every::Int64, alg::AdvancedHMC.GeneralisedNoUTurn{Float64}, constantcoef::NamedTuple{(), Tuple{}}, kwargs::Base.Pairs{Symbol, Union{Nothing, Integer}, Tuple{Symbol, Symbol, Symbol}, NamedTuple{(:nadapts, :procs, :check_initial), Tuple{Int64, Nothing, Bool}}})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/nuts.jl:532
  [9] _fit_mcmc(model::PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, data::Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, param::NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, callback_update_thread::Int64, callback_update_process::Int64, ensemblealg::EnsembleThreads, parallel_subjects::Bool, parallel_chains::Bool, alg::BayesMCMC{AdvancedHMC.GeneralisedNoUTurn{Float64}, Float64, Int64, Int64, Int64, Int64, Int64, Float64, EnsembleThreads, Bool, Bool, Bool, Bool, TaskLocalRNG, NamedTuple{(), Tuple{}}, Bool, Int64, NamedTuple{(), Tuple{}}})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/nuts.jl:336
 [10] _fit(model::PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, data::Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, param::NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, alg::BayesMCMC{AdvancedHMC.GeneralisedNoUTurn{Float64}, Float64, Int64, Int64, Int64, Int64, Int64, Float64, EnsembleThreads, Bool, Bool, Bool, Bool, TaskLocalRNG, NamedTuple{(), Tuple{}}, Bool, Int64, NamedTuple{(), Tuple{}}})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/nuts.jl:230
 [11] #fit#769
    @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/nuts.jl:156 [inlined]
 [12] fit(model::PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, data::Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, param::NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, alg::BayesMCMC{AdvancedHMC.GeneralisedNoUTurn{Float64}, Float64, Int64, Int64, Missing, Missing, Missing, Missing, Missing, Missing, Missing, Missing, Missing, Missing, Missing, Missing, Missing, NamedTuple{(), Tuple{}}})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/nuts.jl:155
 [13] top-level scope
    @ ~/data/code/Veliparib/Bayes_PK/src/Veliparib_27Apr23_LKJ.jl:163

    nested task error: UndefVarError: η_2 not defined
    Stacktrace:
      [1] (::var"#28#37")(_param#476::NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Float64, Float64}}, _random#477::NamedTuple{(:ηstd_1, :ηstd_2, :η_BOV), Tuple{Vector{Float64}, Vector{Float64}, Vector{Float64}}}, _subject#474::Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}})
        @ Main /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/dsl/model_macro.jl:788
      [2] TimeDispatcher
        @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/dsl/model_macro.jl:471 [inlined]
      [3] TimeDispatcher
        @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/dsl/model_macro.jl:465 [inlined]
      [4] dcp(model::PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, subject::Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}, param::NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Float64, Float64}}, randeffs::NamedTuple{(:ηstd_1, :ηstd_2, :η_BOV), Tuple{Vector{Float64}, Vector{Float64}, Vector{Float64}}})
        @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/models/model_api.jl:2146
      [5] #_derived#317
        @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/models/model_api.jl:1257 [inlined]
      [6] #conditional_nll#496
        @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/likelihoods.jl:862 [inlined]
      [7] _penalized_conditional_nll(model::PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, subject::Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}, param::NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Float64, Float64}}, vrandeffsorth::SubArray{Float64, 1, Vector{Float64}, Tuple{UnitRange{Int64}}, true}, diffeq_options::NamedTuple{(), Tuple{}})
        @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/likelihoods.jl:920
      [8] (::Pumas.var"#707#708"{Float64, Pumas.ThreadedBayesLogDensity{PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{ForwardDiff.GradientConfig{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8}}}}, Vector{DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}}, NamedTuple{(), Tuple{}}}, Vector{Float64}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Float64, Float64}}})(i::Int64)
        @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:332
      [9] macro expansion
        @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:432 [inlined]
     [10] macro expansion
        @ ./simdloop.jl:77 [inlined]
     [11] batch_mapreduce
        @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:430 [inlined]
     [12] (::Pumas.var"#711#712"{Float64, UnitRange{Int64}, Pumas.var"#707#708"{Float64, Pumas.ThreadedBayesLogDensity{PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{ForwardDiff.GradientConfig{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8}}}}, Vector{DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}}, NamedTuple{(), Tuple{}}}, Vector{Float64}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Float64, Float64}}}, typeof(+), Tuple{UnitRange{Int64}}, Tuple{}})()
        @ Pumas ./threadingconstructs.jl:178

Thank you for your help in advance.

storopoli · April 28, 2023, 5:17pm

What are the initial values that are you passing to fit?

Sooyoung.Lee · April 28, 2023, 6:01pm

Hello, @storopoli

I used the following values for my initial values:

params = (tvcl_other = 7.97,
tvcl_GF = 8.52,
tvvc = 122.7,
tvq = 10.1,
tvvp = 97.9,
tvka = 2.15,
tvlag = 0.22,
LBM_exp = 0.92,
C_1 = [1 0.83; 0.83 1],
C_2 = [1 -0.79; -0.79 1],
Ω_1 = [0.114, 0.081],
Ω_2 = [0.047, 0.0056],
ω²η = 1.0006437368552639,
σ²_prop = 0.06541313854823212,)

However, I have found the cause of the problem elsewhere.

When I modified the lags in the dosecontrol block as shown below, rather than using tvlag * exp(η_2[2]),
the estimation proceeded successfully.
Modified lags: lags = (Depot = tvlag * exp( (Diagonal(Ω_2) * (getchol(C_2).L * ηstd_2))[2] ) ,)
So, is it impossible to use exp(η_2[2]) within the lags when using the LKJ distribution?
It was not a problem when using the inverse Wishart distribution.

Separate from this, I still have an unresolved question.

1. ω value
I wonder if I use input whether SD or SD^2 for the diagonal element in ω?

I saw the following code in the tutorial
(https://tutorials.pumas.ai/html/bayesian/02-bayes_random_effects.html):
ω ~ Constrained( MvNormal(zeros(2), Diagonal(0.4^2 * ones(2))); lower=zeros(2), upper=fill(Inf, 2), init=ones(2) )
Is this correct, assuming a prior SD of 0.4?

When considering the results of this calculation (η = Diagonal(ω) * (getchol(C).L * ηstd)),
I’m wondering why the value 0.4^2 was used for the diagonal elements in ω instead of 0.4, given that the SD is 0.4.

2. Correlation value adjust
I am still curious about how to adjust the strength of correlation.

When considering the arguments d and eta in the LKJCholesky function (LKJCholesky(d, eta)), there doesn’t seem to be a direct place to reflect the correlation value.
I am wondering if I want to make a strong informative prior, where to reflect the correlation value, such as 0.8 or -0.7.

storopoli · April 28, 2023, 6:57pm

What happens if you give a float.(Matrix(I(2))) initial value to all your C matrices?

squared

Just use a non-informative prior, like LKJCholesky(d, 1.0) or maybe LKJCholesky(d, 2.0) and let the MCMC sampler do his job.
If there’s signal in your data and your model has no major flaws, then it will converge to the true values of C.
These kind of priors don’t get in the way of the likelihood (signal in the data) when estimating the correlation matrix.

If you experience issues with these non-informative priors, then check section 3.10 of our new Bayesian Workflow pre-print [2304.04752] A Practitioner's Guide to Bayesian Inference in Pharmacometrics using Pumas

Sooyoung.Lee · April 28, 2023, 7:25pm

Thank you for your prompt response.
Many of my questions have been resolved.

As your advice, I set the initial values for both C_1 and C_2 to float.(Matrix(I(2))).
However, I am still encountering the error message when lags = (Depot = tvlag * exp(η_2[2])).
It seems to be the same error message.

[ Info: Checking the initial parameter values.
ERROR: TaskFailedException
Stacktrace:
  [1] wait
    @ ./task.jl:334 [inlined]
  [2] fetch
    @ ./task.jl:349 [inlined]
  [3] __tmapreduce(f::Pumas.var"#707#708"{Float64, Pumas.ThreadedBayesLogDensity{PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{ForwardDiff.GradientConfig{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8}}}}, Vector{DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}}, NamedTuple{(), Tuple{}}}, Vector{Float64}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Float64, Float64}}}, op::typeof(+), tasks::Vector{Task}, len::Int64, init::Float64, src::Tuple{UnitRange{Int64}}, batchargs::Tuple{})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:418
  [4] _tmapreduce
    @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:440 [inlined]
  [5] tmapreduce(f::Function, ::Type{Float64}, op::Function, src::Tuple{UnitRange{Int64}}, batchargs::Tuple{}; init::Float64, tasks::Vector{Task})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:451
  [6] _logdensity(b::Pumas.ThreadedBayesLogDensity{PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{ForwardDiff.GradientConfig{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8}}}}, Vector{DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}}, NamedTuple{(), Tuple{}}}, v::Vector{Float64})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:324
  [7] _check_initial_values(bayes::Pumas.ThreadedBayesLogDensity{PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{ForwardDiff.GradientConfig{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8}}}}, Vector{DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}}, NamedTuple{(), Tuple{}}}, vparam_aug::Vector{Float64})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/nuts.jl:393
  [8] pumas_sample(rngs::Vector{Xoshiro}, bayes::Vector{Pumas.ThreadedBayesLogDensity{PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{ForwardDiff.GradientConfig{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8}}}}, Vector{DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}}, NamedTuple{(), Tuple{}}}}, ::EnsembleThreads, nsamples::Int64, ess_per_chain::Int64, time_limit::Float64; ess_every::Int64, progress::Bool, balance_method::Symbol, update_progress_every::Int64, alg::AdvancedHMC.GeneralisedNoUTurn{Float64}, constantcoef::NamedTuple{(), Tuple{}}, kwargs::Base.Pairs{Symbol, Union{Nothing, Integer}, Tuple{Symbol, Symbol, Symbol}, NamedTuple{(:nadapts, :procs, :check_initial), Tuple{Int64, Nothing, Bool}}})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/nuts.jl:532
  [9] _fit_mcmc(model::PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, data::Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, param::NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, callback_update_thread::Int64, callback_update_process::Int64, ensemblealg::EnsembleThreads, parallel_subjects::Bool, parallel_chains::Bool, alg::BayesMCMC{AdvancedHMC.GeneralisedNoUTurn{Float64}, Float64, Int64, Int64, Int64, Int64, Int64, Float64, EnsembleThreads, Bool, Bool, Bool, Bool, TaskLocalRNG, NamedTuple{(), Tuple{}}, Bool, Int64, NamedTuple{(), Tuple{}}})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/nuts.jl:336
 [10] _fit(model::PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, data::Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, param::NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, alg::BayesMCMC{AdvancedHMC.GeneralisedNoUTurn{Float64}, Float64, Int64, Int64, Int64, Int64, Int64, Float64, EnsembleThreads, Bool, Bool, Bool, Bool, TaskLocalRNG, NamedTuple{(), Tuple{}}, Bool, Int64, NamedTuple{(), Tuple{}}})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/nuts.jl:230
 [11] #fit#769
    @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/nuts.jl:156 [inlined]
 [12] fit(model::PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, data::Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, param::NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :C_2, :Ω_1, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Matrix{Float64}, Vector{Float64}, Vector{Float64}, Float64, Float64}}, alg::BayesMCMC{AdvancedHMC.GeneralisedNoUTurn{Float64}, Float64, Int64, Int64, Missing, Missing, Missing, Missing, Missing, Missing, Missing, Missing, Missing, Missing, Missing, Missing, Missing, NamedTuple{(), Tuple{}}})
    @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/nuts.jl:155
 [13] top-level scope
    @ ~/data/code/Veliparib/Bayes_PK/src/test_2.jl:164

    nested task error: UndefVarError: η_2 not defined
    Stacktrace:
      [1] (::var"#28#37")(_param#472::NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Float64, Float64}}, _random#473::NamedTuple{(:ηstd_1, :ηstd_2, :η_BOV), Tuple{Vector{Float64}, Vector{Float64}, Vector{Float64}}}, _subject#470::Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}})
        @ Main /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/dsl/model_macro.jl:788
      [2] TimeDispatcher
        @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/dsl/model_macro.jl:471 [inlined]
      [3] TimeDispatcher
        @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/dsl/model_macro.jl:465 [inlined]
      [4] dcp(model::PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, subject::Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}, param::NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Float64, Float64}}, randeffs::NamedTuple{(:ηstd_1, :ηstd_2, :η_BOV), Tuple{Vector{Float64}, Vector{Float64}, Vector{Float64}}})
        @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/models/model_api.jl:2146
      [5] #_derived#317
        @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/models/model_api.jl:1257 [inlined]
      [6] #conditional_nll#496
        @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/likelihoods.jl:862 [inlined]
      [7] _penalized_conditional_nll(model::PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, subject::Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}, param::NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Float64, Float64}}, vrandeffsorth::SubArray{Float64, 1, Vector{Float64}, Tuple{UnitRange{Int64}}, true}, diffeq_options::NamedTuple{(), Tuple{}})
        @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/likelihoods.jl:920
      [8] (::Pumas.var"#707#708"{Float64, Pumas.ThreadedBayesLogDensity{PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{ForwardDiff.GradientConfig{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8}}}}, Vector{DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}}, NamedTuple{(), Tuple{}}}, Vector{Float64}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Float64, Float64}}})(i::Int64)
        @ Pumas /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:332
      [9] macro expansion
        @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:432 [inlined]
     [10] macro expansion
        @ ./simdloop.jl:77 [inlined]
     [11] batch_mapreduce
        @ /build/_work/PumasSystemImages/PumasSystemImages/julia_depot/packages/Pumas/Td3Jp/src/estimation/bayes/logdensity.jl:430 [inlined]
     [12] (::Pumas.var"#711#712"{Float64, UnitRange{Int64}, Pumas.var"#707#708"{Float64, Pumas.ThreadedBayesLogDensity{PumasModel{(tvcl_other = 1, tvcl_GF = 1, tvvc = 1, tvq = 1, tvvp = 1, tvka = 1, tvlag = 1, LBM_exp = 1, C_1 = 1, Ω_1 = 2, C_2 = 1, Ω_2 = 2, ω²η = 1, σ²_prop = 1), 7, (:Depot, :Central, :Peripheral), ParamSet{NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LogNormal{Float64}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, LKJCholesky{Float64}, Constrained{DiagNormal, VectorDomain{Vector{Float64}, Vector{TransformVariables.Infinity{true}}, Vector{Float64}}}, InverseGamma{Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#23#32", Pumas.TimeDispatcher{var"#24#33", var"#25#34"}, Pumas.TimeDispatcher{var"#27#36", var"#28#37"}, var"#29#38", Depots1Central1Periph1, var"#30#39", var"#31#40", Nothing}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Matrix{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Float64, Float64}}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantInterpolationStructArray{Vector{Float64}, NamedTuple{(:CrCL, :LBM, :OCC), Tuple{Vector{Float64}, Vector{Float64}, Vector{Int64}}}, Symbol}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{ForwardDiff.GradientConfig{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Pumas.Tag, Float64}, Float64, 8}}}}, Vector{DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}}, NamedTuple{(), Tuple{}}}, Vector{Float64}, NamedTuple{(:tvcl_other, :tvcl_GF, :tvvc, :tvq, :tvvp, :tvka, :tvlag, :LBM_exp, :C_1, :Ω_1, :C_2, :Ω_2, :ω²η, :σ²_prop), Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Pumas.CorrMat{Float64, PDMats.PDMat{Float64, Matrix{Float64}}}, Vector{Float64}, Float64, Float64}}}, typeof(+), Tuple{UnitRange{Int64}}, Tuple{}})()
        @ Pumas ./threadingconstructs.jl:178

When lags = (Depot = tvlag * exp((Diagonal(Ω_2) * (getchol(C_2).L * ηstd_2))[2])),
I was able to start the estimation without problems when setting both C_1 and C_2 to float.(Matrix(I(2))) as the initial values.

If you have any other suggestions, I would appreciate it.

mohamed82008 · May 19, 2023, 5:16pm

Sorry for the late response here. Is there a simulated data set you can share to help debug this?

mohamed82008 · May 19, 2023, 5:17pm

I think these need to be defined again in the @dosecontrol blocks. The @dosecontrol block does not see what’s inside the @pre block.

Sooyoung.Lee · May 23, 2023, 4:40am

Nice to meet you, @mohamed82008

I don’t know how to upload a CSV file here.
So I’m providing you with the code to generate simulated data.
I apologize for the inconvenience.

using Random
using Pumas

################# 1. Define model  #################
model_ = @model begin
  @metadata begin
      desc        = "two compartment model with first-order absorption and Tlag"
    end

  @param begin
      "Absorption Rate Constant (hr⁻¹)"
      tvka        ∈ RealDomain(lower=0.000001)
      "Volume of Central Compartment (L)"
      tvvc        ∈ RealDomain(lower=0.000001)
      "Volume of Peripheral Compartment (L)"
      tvvp        ∈ RealDomain(lower=0.000001)
      "Clearance (L/hr)"
      tvcl_other  ∈ RealDomain(lower=0.000001)
      tvcl_GF     ∈ RealDomain(lower=0.000001)
      "Intercompartmental Clearance (L/hr)"
      tvq         ∈ RealDomain(lower=0.000001)
      "LBM exponent"
      LBM_exp     ∈ RealDomain(lower=0.000001)
      "Lagtime (hr)"
      tvlag       ∈ RealDomain(lower=0.000001)
      "BSV and BOV"
      Ω_1        ∈ PSDDomain(2)
      Ω_2        ∈ PSDDomain(2)
      ω²η      ∈ RealDomain(lower=0.000001)
      "Proportional RUV"
      σ²_prop   ∈ RealDomain(lower=0.000001)
  end

  @random begin
      η_1         ~ MvNormal(Ω_1)
      η_2         ~ MvNormal(Ω_2)
      η_BOV       ~ MvNormal(3, sqrt(ω²η))
  end

  @covariates CrCL LBM OCC

  @pre begin
    CL          = (tvcl_other + (tvcl_GF * (CrCL/90))) * exp(η_1[1])
    Vc          = tvvc * ((LBM/55)^LBM_exp) * exp(η_1[2])
    Q           = tvq
    Vp          = tvvp
    Ka          = tvka * exp(η_2[1]) * exp(η_BOV[OCC])
    Tlag        = tvlag * exp(η_2[2])
    LBM_exp_out = LBM_exp
  end

  @dosecontrol begin
    lags = (Depot = tvlag * exp(η_2[2]),)
  end

  @dynamics Depots1Central1Periph1

  @derived begin
    cp = @. (Central/Vc) 
    dv ~ @. Normal(cp, sqrt((cp^2) * (σ²_prop)))
  end
end


################# 2. Define model parameters   #################
function cv_to_var(x)
  Var_val = log((x/100)^2+1)
  return Var_val
end

BSV_Ka_Var     = cv_to_var(21.9)
BSV_Tlag_Var   = cv_to_var(7.47)
BSV_CL_Var     = cv_to_var(34.7)
BSV_Vc_Var     = cv_to_var(29.0)
BOV_Ka_Var     = cv_to_var(131.53)
WSV_Pro_Var    = cv_to_var(26)
Cov_CL_Vc      = 0.83 * sqrt(BSV_CL_Var * BSV_Vc_Var)
Cov_Ka_Tlag    = -0.79 * sqrt(BSV_Ka_Var * BSV_Tlag_Var)

param = ( tvcl_other  = 7.97,
          tvcl_GF     = 8.52,
          tvvc        = 122.7,
          tvq         = 10.1,
          tvvp        = 97.91,
          tvka        = 2.15,
          tvlag       = 0.22,
          LBM_exp     = 0.92,          
          Ω_1        = [BSV_CL_Var Cov_CL_Vc
                          Cov_CL_Vc BSV_Vc_Var],
          Ω_2        = [BSV_Ka_Var Cov_Ka_Tlag
                          Cov_Ka_Tlag BSV_Tlag_Var],
          ω²η      = BOV_Ka_Var,
          σ²_prop   = WSV_Pro_Var)


################# 3. Define subject   #################
# Dose Regimem
group_n = 15
Dose = 80
ev  = DosageRegimen(Dose, ii=12, addl = 21*2 - 1, cmt = 1)

# Demographics
LBM = rand(truncated(Normal(53.6, 10.5), 33.67, 78.5), group_n)
CrCL = rand(truncated(Normal(90.5, 23.9), 32.1, 120), group_n)

# Time
time_obs = [24*7, 24*14, 24*21]
occ = [1,2,3] 

# Population covariates
pop_with_covariates = map(
	i -> Subject(;
		id=i,
		events = ev,
		time = time_obs,
		covariates_time = time_obs,
		covariates=(
			LBM = fill(LBM[i], length(time_obs)),
			CrCL = fill(CrCL[i],length(time_obs)),
			OCC = occ),
		observations = (; dv=nothing),
		),
	1:group_n,
  )


################# 4. Simulate #################
Random.seed!(1234)
sim_sub = simobs(model_, pop_with_covariates, param, obstimes=time_obs)

Sooyoung.Lee · May 23, 2023, 4:47am

I understand what you said.
As mentioned earlier, I realized how the estimation works when modifying the dose control block.

Thank you for your interest in my issue.

Topic		Replies	Views
Error with Bayesian Model Normal distribution for omegas bayesian	6	225	March 1, 2023
Error while running simobs using Bayesian fit bayesian	8	250	March 1, 2023
Bayesian model fails to estimate bayesian	1	211	January 10, 2023
Variance Covaraiance matrix error Estimation	1	93	February 8, 2024
Incorporating Inter-Occassion Variability in Bayesian Model bayesian	3	252	April 25, 2022

Converting variance-covariance matrix to LKJCholesky prior in Bayesian estimation

Related topics