Incorporating forcing functions in the ODE model

vembha · October 21, 2021, 7:47am

Hello,

I am new to Turing and Julia, and need some help!

I have been trying to estimate the parameters of a model with a discrete forcing function q(t), where the values of q(t) are discrete and are read from a file. Consider the ODE to be following:

function my_model(du, u, p, t)
    α, β = p
    du = α*q(t)*u - β
end

Here, alpha and beta are my parameters, which I tried to estimate by building a model as follows, where I am passing the forcing function data explicitly as a vector:

@model function fitting_model(observ_data, forcing_data)
    # Some priors...
    α ~ truncated(Normal(0.25, 0.1), 0.1, 0.5)
    β ~ truncated(Normal(0.65, 0.1), 0, 2)
    
    # Parameter vector
    p = [β, α, forcing_data];

    # Defining other required variables like u0, tspan, etc...

    # Then, the (usual) subsequent steps to estimate parameters
    problem = ODEProblem(my_model, u0, tspan, p);
    predicted = solve(problem, Tsit5(), saveat=1.0);

    # Finally matching the predicted data with observ_data
end

But running this code resulted in TypeError: in typeassert, expected Float64, got a value of type ForwardDiff.Dual{Nothing, Float64, 7}. I am at a dead end, and don’t know how to resolve this issue.

Please, please help me out!

tomaklutfu · October 21, 2021, 7:55am

Can you add whole code you try to run? If not, check the code for hard coded types. The error suggest you hard coded the type Float64 somewhere and you got a dual number along the way.

vembha · October 21, 2021, 8:46am

Thank you for the quick reply @tomaklutfu! Please check the complete code below:

#=
Section 1: Import required packages
=#

using Turing, Distributions, DifferentialEquations, Interpolations
using MCMCChains, Plots, StatsPlots
using CSV, XLSX, DataFrames
using Random
Random.seed!(18431)

#=
Section 2: Read the data file containing observation data and get the NPI data into arrays
=#

my_data = DataFrame(XLSX.readtable("observation_data.xlsx","Sheet1")...);

total_weeks = 36;   # Total number of time points
N = 67081000;       # Population

y_time = 1:1:total_weeks;               # Timepoints (weeks)

y_S = Float64.(my_data.Susceptible);    # Susceptible
y_S = y_S[1:total_weeks];

y_D = Float64.(my_data.Deceased);       # Deceased
y_D = y_D[1:total_weeks];

y_HC = Float64.(my_data.Hosp_critical); # Critical hospitalizations
y_HC = y_HC[1:total_weeks];

y_T = Float64.(my_data.Hosp_total);     # Total hospitalizations
y_T = y_T[1:total_weeks];
y_HNC = y_T - y_HC;                     # Non-critical hospitalizations

observation_data = [y_S y_D y_HC y_HNC];

wet_data = DataFrame(XLSX.readtable("Wetdata.xlsx","Wetdata")...);
# IPTCC is a forcing function
IPTCC = wet_data.Normalized_IPTCC;
IPTCC = IPTCC[1:total_weeks];

mobil_data = DataFrame(XLSX.readtable("Mobdata.xlsx","Mobdata")...);
# mobil is another forcing function
mobil = mobil_data.Mean;
mobil = mobil[1:total_weeks];

wet_forcing = interpolate(IPTCC, BSpline(Linear()));
mobil_forcing = interpolate(mobil, BSpline(Linear()));

forcing_params = (wet_forcing, mobil_forcing);

#=
Section 3: Define the model and the respective parameters
=#

function epidemic_wildtype(dy, y, p, t)
    S, E, I, Hᵪ, Hₙ, R, D = y;
    β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w, m = p;
    N = 67081000;

    dy[1] = -β*w(t)*m(t)*I*S/N + λ*R;  # S
    dy[2] = β*w(t)*m(t)*I*S/N - α*E;   # E
    dy[3] = α*E - (γ + θᵪ + θₙ)*I;     # I
    dy[4] = θₙ*I - γₙ*Hᵪ;               # HNC
    dy[5] = θᵪ*I - (γᵪ + δᵪ)*Hₙ;       # HC
    dy[6] = γ*I + γₙ*Hₙ + γᵪ*Hᵪ - λ*R;  # R
    dy[7] = δᵪ*Hᵪ;                     # D
end

#=
Section 4: Define the priors and the Bayesian model
=#

Turing.setadbackend(:forwarddiff)
@model function fitting_epidemic_wildtype(observ_data, w_forcing, m_forcing)
    # Priors of model parameters
    β ~ truncated(Normal(0.65, 0.1), 0, 2)
    λ ~ truncated(Normal(0.5, 0.1), 0, 5)
    α ~ truncated(Normal(0.25, 0.1), 0.1, 0.5)
    γ ~ truncated(Normal(0.05, 0.1), 0, 5)
    γₙ ~ Uniform(0.05, 0.1)
    γᵪ ~ Uniform(0.05, 0.1)
    θₙ ~ Uniform(0.09, 0.75)
    θᵪ ~ Uniform(0.09, 0.75)
    δᵪ ~ Uniform(0.1, 0.8)

    p = [β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w_forcing, m_forcing];

    # Priors of standard deviations
    σ₁ ~ InverseGamma(1, 1) # Susceptible
    σ₂ ~ InverseGamma(1, 1) # Deceased
    σ₃ ~ InverseGamma(2, 3) # Critically hospitalized
    σ₄ ~ InverseGamma(1, 1) # Non-critically hospitalized

    # Initial conditions
    N = 67081000;
    S0 = N;
    I0 = 100;
    y0 = [S0, 0, I0, 0, 0, 0, 0];
    y0 = eltype(p).(y0);

    # Solve the model and compare with observed data
    problem = ODEProblem(epidemic_wildtype, y0, (1, 36), p)
    predicted = solve(problem, Tsit5(), saveat=1.0)

    for i = 1:length(predicted)
        observ_data[i,1] ~ Normal(predicted[1,i], σ₁)
        observ_data[i,2] ~ Normal(predicted[7,i], σ₂)
        observ_data[i,3] ~ Normal(predicted[5,i], σ₃)
        observ_data[i,4] ~ Normal(predicted[4,i], σ₄)
    end
end

#=
Section 5: Run the model-inference system and save the chains
=#

model = fitting_epidemic_wildtype(observation_data, wet_forcing, mobil_forcing);
number_of_chains = 1;
chain = sample(model, NUTS(0.65), MCMCThreads(), 10000, number_of_chains);

Hope it helps to debug! Thanks in advance.

baggepinnen · October 21, 2021, 10:45am

This array might be expecting a Float64 eltype. The eltype of this array is likely defined to be the same as that of y0. I would try to update y0 to

y0 = eltype(p).(y0)

this makes y0 an array of the same element type as the parameter vector p, which is probably of type Dual.

vembha · October 21, 2021, 11:23am

Thank you @baggepinnen for the quick response. Unfortunately, it looks like the eltype still doesn’t solve it. The error now is MethodError: no constructors have been defined for Any. As far as I can see, all the data is of Float64 type, so don’t really know how/where the Any type is coming from!

Any help is really appreciated!

nilshg · October 21, 2021, 12:10pm

DataFrame(XLSX.readtable("observation_data.xlsx","Sheet1")...)

Will mean that all your data will be of type Any - try the infer_eltypes = true kwarg.

ChrisRackauckas · October 21, 2021, 12:44pm

Post the whole error. That stacktrace that you are ignoring is the most important part.

vembha · October 21, 2021, 1:39pm

My bad! Just realized that the whole stacktrace is important. Here it is:

┌ Warning: Only a single thread available: MCMC chains are not sampled in parallel      
└ @ AbstractMCMC C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:291
ERROR: LoadError: TaskFailedException

    nested task error: TaskFailedException       
    Stacktrace:
     [1] wait
       @ .\task.jl:322 [inlined]
     [2] threading_run(func::Function)
       @ Base.Threads .\threadingconstructs.jl:34
     [3] macro expansion
       @ .\threadingconstructs.jl:93 [inlined]   
     [4] macro expansion
       @ C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:342 [inlined]
     [5] (::AbstractMCMC.var"#31#41"{Bool, Base.Iterators.Pairs{Symbol, UnionAll, Tuple{Symbol}, NamedTuple{(:chain_type,), Tuple{UnionAll}}}, Int64, Int64, Vector{Any}, Vector{UInt64}, Vector{DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}}, Vector{DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}}, Vector{Random._GLOBAL_RNG}})()
       @ AbstractMCMC .\task.jl:411

        nested task error: MethodError: no constructors have been defined for Any
        Stacktrace:
          [1] _broadcast_getindex_evalf
            @ .\broadcast.jl:648 [inlined]
          [2] _broadcast_getindex
            @ .\broadcast.jl:621 [inlined]
          [3] getindex
            @ .\broadcast.jl:575 [inlined]
          [4] copy
            @ .\broadcast.jl:922 [inlined]
          [5] materialize
            @ .\broadcast.jl:883 [inlined]
          [6] fitting_epidemic_wildtype(__model__::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, __varinfo__::DynamicPPL.UntypedVarInfo{DynamicPPL.Metadata{Dict{AbstractPPL.VarName, Int64}, Vector{Distribution}, Vector{AbstractPPL.VarName}, Vector{Real}, Vector{Set{DynamicPPL.Selector}}}, Float64}, __context__::DynamicPPL.SamplingContext{DynamicPPL.SampleFromUniform, DynamicPPL.DefaultContext, Random._GLOBAL_RNG}, observ_data::Matrix{Float64}, w_forcing::Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, m_forcing::Interpolations.BSplineInterpolation{Float64, 1, 
Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}})
            @ Main c:\Users\Bharadwaj\Indian Institute of Science\COVID-19 variant study - General\codes_wildtype_fitting\discourse_NPI_code.jl:100
          [7] macro expansion
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:465 [inlined]
          [8] _evaluate
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:448 [inlined]
          [9] evaluate_threadunsafe
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:421 [inlined]
         [10] Model
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:389 [inlined]
         [11] Model
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:383 [inlined]
         [12] VarInfo
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\varinfo.jl:127 [inlined]
         [13] VarInfo
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\varinfo.jl:126 [inlined]
         [14] step(rng::Random._GLOBAL_RNG, model::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, spl::DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}; resume_from::Nothing, kwargs::Base.Iterators.Pairs{Symbol, Int64, Tuple{Symbol}, NamedTuple{(:nadapts,), Tuple{Int64}}})
            @ DynamicPPL C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\sampler.jl:69
         [15] macro expansion
            @ C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:123 [inlined]
         [16] macro expansion
            @ C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\logging.jl:15 [inlined]
         [17] mcmcsample(rng::Random._GLOBAL_RNG, model::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, sampler::DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, N::Int64; progress::Bool, progressname::String, callback::Nothing, discard_initial::Int64, thinning::Int64, chain_type::Type, kwargs::Base.Iterators.Pairs{Symbol, Int64, Tuple{Symbol}, NamedTuple{(:nadapts,), Tuple{Int64}}})
            @ AbstractMCMC C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:114
         [18] #sample#40
            @ C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\hmc.jl:133 [inlined]
         [19] macro expansion
            @ C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:351 [inlined]
         [20] (::AbstractMCMC.var"#927#threadsfor_fun#42"{UnitRange{Int64}, Bool, Base.Iterators.Pairs{Symbol, UnionAll, Tuple{Symbol}, NamedTuple{(:chain_type,), Tuple{UnionAll}}}, Int64, Vector{Any}, Vector{UInt64}, Vector{DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}}, Vector{DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}}, Vector{Random._GLOBAL_RNG}})(onethread::Bool)
            @ AbstractMCMC .\threadingconstructs.jl:81
         [21] (::AbstractMCMC.var"#927#threadsfor_fun#42"{UnitRange{Int64}, Bool, Base.Iterators.Pairs{Symbol, UnionAll, Tuple{Symbol}, NamedTuple{(:chain_type,), Tuple{UnionAll}}}, Int64, Vector{Any}, Vector{UInt64}, Vector{DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}}, Vector{DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}}, Vector{Random._GLOBAL_RNG}})()
            @ AbstractMCMC .\threadingconstructs.jl:48
Stacktrace:
  [1] sync_end(c::Channel{Any})
    @ Base .\task.jl:369
  [2] macro expansion
    @ .\task.jl:388 [inlined]
  [3] macro expansion
    @ C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:320 [inlined]
  [4] macro expansion
    @ C:\Users\Bharadwaj\.julia\packages\ProgressLogging\6KXlp\src\ProgressLogging.jl:328 [inlined]
  [5] macro expansion
    @ C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\logging.jl:8 [inlined]
  [6] mcmcsample(rng::Random._GLOBAL_RNG, model::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, sampler::DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, ::MCMCThreads, N::Int64, nchains::Int64; progress::Bool, progressname::String, kwargs::Base.Iterators.Pairs{Symbol, UnionAll, Tuple{Symbol}, NamedTuple{(:chain_type,), Tuple{UnionAll}}})
    @ AbstractMCMC C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:314
  [7] sample(rng::Random._GLOBAL_RNG, model::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, sampler::DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, ensemble::MCMCThreads, N::Int64, n_chains::Int64; chain_type::Type, progress::Bool, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ Turing.Inference C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\Inference.jl:217
  [8] sample
    @ C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\Inference.jl:217 [inlined]
  [9] #sample#6
    @ C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\Inference.jl:202 [inlined]
 [10] sample
    @ C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\Inference.jl:202 [inlined]
 [11] #sample#5
    @ C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\Inference.jl:189 [inlined]
 [12] sample(model::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, alg::NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}, ensemble::MCMCThreads, N::Int64, n_chains::Int64)
    @ Turing.Inference C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\Inference.jl:189
 [13] top-level scope
    @ c:\Users\Bharadwaj\Indian Institute of Science\COVID-19 variant study - General\codes_wildtype_fitting\discourse_NPI_code.jl:120
in expression starting at c:\Users\Bharadwaj\Indian Institute of Science\COVID-19 variant study - General\codes_wildtype_fitting\discourse_NPI_code.jl:120

This is the error I am getting after incorporating the suggestions of @baggepinnen and @nilshg. Please check this and help me out!

ChrisRackauckas · October 21, 2021, 2:21pm

which line is line 100 in your code?

vembha · October 21, 2021, 2:35pm

@ChrisRackauckas Hello! This was the line 100.

ChrisRackauckas · October 21, 2021, 2:45pm

Put an @show typeof(y0) and @show eltype(p) right before that line and share what they print out.

vembha · October 21, 2021, 3:11pm

This is the output from the two lines:

┌ Warning: Only a single thread available: MCMC chains are not sampled in parallel      
└ @ AbstractMCMC C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:291
typeof(y0) = Vector{Int64}
eltype(p) = Any
ERROR: LoadError: TaskFailedException

… and the previously mentioned error continues.

ChrisRackauckas · October 21, 2021, 3:29pm

eltype(p) is Any` because you put functions in there.

p = [β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w_forcing, m_forcing];

So instead you want to upconvert to just the scalar dual types. In fact, it would be better to do:

p = (β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w_forcing, m_forcing);

so that is type-stable, and then do:

y0 = typeof(β).(y0)

so it converts y0 to a dual.

vembha · October 21, 2021, 6:39pm

Tried the modifications you suggested, and this time got different error.

nested task error: BoundsError: attempt to access 36-element interpolate(::Vector{Float64}, BSpline(Linear())) with element type Float64 at index [NaN]
        Stacktrace:
          [1] throw_boundserror(A::Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, I::Tuple{Float64})
            @ Base .\abstractarray.jl:651
          [2] BSplineInterpolation
            @ C:\Users\vembh\.julia\packages\Interpolations\3gTQB\src\b-splines\indexing.jl:6 [inlined]
          [3] getindex(itp::Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, i::Float64)
            @ Interpolations .\deprecated.jl:72
          [4] epidemic_wildtype...

at line 61, where line 61 is dy[1] = -β*w(t)*m(t)*I*S/N + λ*R; and line 106 is predicted = solve(problem, Tsit5(), saveat=1.0).

ChrisRackauckas · October 21, 2021, 7:38pm

Are you solving past the time point where you interpolate? Before that line add @show t and figure out what the last point being interpolated is. That should make easy to then do w(t) or m(t) and reproduce the error without Turing.

vembha · October 22, 2021, 6:07am

I do not think I am solving beyond the last point of interpolation. The image below proves that! I am solving for time interval (1, 36) and the interpolated forcing functions have the values at the same time points.

I am posting the code here again for convenience and the error (which is completely new this time and does not show BoundsError) getting generated. Incorporating only your suggestions @ChrisRackauckas:

#=
Section 1: Import required packages
=#

using Turing, Distributions, DifferentialEquations, Interpolations
using MCMCChains, Plots, StatsPlots
using CSV, XLSX, DataFrames
using Random
Random.seed!(18431)

#=
Section 2: Read the data file containing observation data and get the NPI data into arrays
=#

my_data = DataFrame(XLSX.readtable("observation_data.xlsx","Sheet1"; infer_eltypes = true)...);

total_weeks = 36;   # Total number of time points
N = 67081000;       # Population

y_time = 1:1:total_weeks;               # Timepoints (weeks)

y_S = Float64.(my_data.Susceptible);    # Susceptible
y_S = y_S[1:total_weeks];

y_D = Float64.(my_data.Deceased);       # Deceased
y_D = y_D[1:total_weeks];

y_HC = Float64.(my_data.Hosp_critical); # Critical hospitalizations
y_HC = y_HC[1:total_weeks];

y_T = Float64.(my_data.Hosp_total);     # Total hospitalizations
y_T = y_T[1:total_weeks];
y_HNC = y_T - y_HC;                     # Non-critical hospitalizations

observation_data = [y_S y_D y_HC y_HNC];

wet_data = DataFrame(XLSX.readtable("Wetdata.xlsx","Wetdata"; infer_eltypes = true)...);
# IPTCC is a forcing function
IPTCC = wet_data.Normalized_IPTCC;
IPTCC = IPTCC[1:total_weeks];

mobil_data = DataFrame(XLSX.readtable("Mobdata.xlsx","Mobdata"; infer_eltypes = true)...);
# mobil is another forcing function
mobil = mobil_data.Mean;
mobil = mobil[1:total_weeks];

wet_forcing = interpolate(IPTCC, BSpline(Linear()));
mobil_forcing = interpolate(mobil, BSpline(Linear()));

forcing_params = (wet_forcing, mobil_forcing);

#=
Section 3: Define the model and the respective parameters
=#

function epidemic_wildtype(dy, y, p, t)
    S, E, I, Hᵪ, Hₙ, R, D = y;
    β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w, m = p;
    N = 67081000;

    dy[1] = -β*w(t)*m(t)*I*S/N + λ*R;  # S
    dy[2] = β*w(t)*m(t)*I*S/N - α*E;   # E
    dy[3] = α*E - (γ + θᵪ + θₙ)*I;     # I
    dy[4] = θₙ*I - γₙ*Hᵪ;               # HNC
    dy[5] = θᵪ*I - (γᵪ + δᵪ)*Hₙ;       # HC
    dy[6] = γ*I + γₙ*Hₙ + γᵪ*Hᵪ - λ*R;  # R
    dy[7] = δᵪ*Hᵪ;                     # D
end

#=
Section 4: Define the priors and the Bayesian model
=#

Turing.setadbackend(:forwarddiff)
@model function fitting_epidemic_wildtype(observ_data, w_forcing, m_forcing)
    # Priors of model parameters
    β ~ truncated(Normal(0.65, 0.1), 0, 2)
    λ ~ truncated(Normal(0.5, 0.1), 0, 5)
    α ~ truncated(Normal(0.25, 0.1), 0.1, 0.5)
    γ ~ truncated(Normal(0.05, 0.1), 0, 5)
    γₙ ~ Uniform(0.05, 0.1)
    γᵪ ~ Uniform(0.05, 0.1)
    θₙ ~ Uniform(0.09, 0.75)
    θᵪ ~ Uniform(0.09, 0.75)
    δᵪ ~ Uniform(0.1, 0.8)

    p = (β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w_forcing, m_forcing);

    # Priors of standard deviations
    σ₁ ~ InverseGamma(1, 1) # Susceptible
    σ₂ ~ InverseGamma(1, 1) # Deceased
    σ₃ ~ InverseGamma(2, 3) # Critically hospitalized
    σ₄ ~ InverseGamma(1, 1) # Non-critically hospitalized

    # Initial conditions
    N = 67081000;
    S0 = N;
    I0 = 100;
    y0 = [S0, 0, I0, 0, 0, 0, 0];
    @show typeof(y0)
    @show eltype(p)
    y0 = typeof(β).(y0);

    # Solve the model and compare with observed data
    problem = ODEProblem(epidemic_wildtype, y0, (1, 36), p)
    predicted = solve(problem, Tsit5(), saveat=1)

    for i = 1:length(predicted)
        observ_data[i,1] ~ Normal(predicted[1,i], σ₁)
        observ_data[i,2] ~ Normal(predicted[7,i], σ₂)
        observ_data[i,3] ~ Normal(predicted[5,i], σ₃)
        observ_data[i,4] ~ Normal(predicted[4,i], σ₄)
    end
end

#=
Section 5: Run the model-inference system and save the chains
=#

model = fitting_epidemic_wildtype(observation_data, wet_forcing, mobil_forcing);
number_of_chains = 1;
chain = sample(model, NUTS(0.65), MCMCThreads(), 10000, number_of_chains);

Error without the Turing error part:

nested task error: InexactError: Int64(161//1000)
        Stacktrace:
          [1] Integer
            @ .\rational.jl:110 [inlined]
          [2] convert(#unused#::Type{Int64}, x::Rational{Int64})
            @ Base .\number.jl:7
          [3] OrdinaryDiffEq.Tsit5ConstantCache(T::Type, T2::Type)
            @ OrdinaryDiffEq C:\Users\Bharadwaj\.julia\packages\OrdinaryDiffEq\Zi9Zh\src\tableaus\low_order_rk_tableaus.jl:604
          [4] alg_cache(alg::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, u::Vector{Float64}, rate_prototype::Vector{Float64}, #unused#::Type{Float64}, #unused#::Type{Float64}, #unused#::Type{Int64}, uprev::Vector{Float64}, uprev2::Vector{Float64}, f::ODEFunction{true, typeof(epidemic_wildtype), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, 
Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, t::Int64, dt::Int64, reltol::Float64, p::Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, calck::Bool, #unused#::Val{true})
            @ OrdinaryDiffEq C:\Users\Bharadwaj\.julia\packages\OrdinaryDiffEq\Zi9Zh\src\caches\low_order_rk_caches.jl:350
          [5] __init(prob::ODEProblem{Vector{Float64}, Tuple{Int64, Int64}, true, Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, ODEFunction{true, typeof(epidemic_wildtype), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, alg::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{Val{true}}; saveat::Int64, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Int64, dtmin::Nothing, dtmax::Int64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{Int64}, abstol::Nothing, reltol::Nothing, qmin::Rational{Int64}, qmax::Int64, qsteady_min::Int64, qsteady_max::Int64, beta1::Nothing, beta2::Nothing, qoldinit::Rational{Int64}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), internalopnorm::typeof(LinearAlgebra.opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias_u0::Bool, alias_du0::Bool, initializealg::OrdinaryDiffEq.DefaultInit, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
            @ OrdinaryDiffEq C:\Users\Bharadwaj\.julia\packages\OrdinaryDiffEq\Zi9Zh\src\solve.jl:295
          [6] #__solve#471
            @ C:\Users\Bharadwaj\.julia\packages\OrdinaryDiffEq\Zi9Zh\src\solve.jl:4 [inlined]
          [7] #solve_call#42
            @ C:\Users\Bharadwaj\.julia\packages\DiffEqBase\FtYIB\src\solve.jl:61 [inlined]
          [8] solve_up(prob::ODEProblem{Vector{Float64}, Tuple{Int64, Int64}, true, Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, ODEFunction{true, typeof(epidemic_wildtype), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, sensealg::Nothing, u0::Vector{Float64}, p::Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, args::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}; kwargs::Base.Iterators.Pairs{Symbol, Int64, Tuple{Symbol}, NamedTuple{(:saveat,), Tuple{Int64}}})
            @ DiffEqBase C:\Users\Bharadwaj\.julia\packages\DiffEqBase\FtYIB\src\solve.jl:87
          [9] #solve#43
            @ C:\Users\Bharadwaj\.julia\packages\DiffEqBase\FtYIB\src\solve.jl:73 [inlined]
         [10] fitting_epidemic_wildtype(__model__::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, __varinfo__::DynamicPPL.UntypedVarInfo{DynamicPPL.Metadata{Dict{AbstractPPL.VarName, Int64}, Vector{Distribution}, Vector{AbstractPPL.VarName}, Vector{Real}, Vector{Set{DynamicPPL.Selector}}}, Float64}, __context__::DynamicPPL.SamplingContext{DynamicPPL.SampleFromUniform, DynamicPPL.DefaultContext, Random._GLOBAL_RNG}, observ_data::Matrix{Float64}, w_forcing::Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, m_forcing::Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}})
            @ Main c:\Users\Bharadwaj\Indian Institute of Science\COVID-19 variant study - General\codes_wildtype_fitting\discourse_NPI_code.jl:106
         [11] macro expansion
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:465 [inlined]
         [12] _evaluate
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:448 [inlined]
         [13] evaluate_threadunsafe
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:421 [inlined]
         [14] Model
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:389 [inlined]
         [15] Model
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:383 [inlined]
         [16] VarInfo
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\varinfo.jl:127 [inlined]
         [17] VarInfo
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\varinfo.jl:126 [inlined]
         [18] step(rng::Random._GLOBAL_RNG, model::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, spl::DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}; resume_from::Nothing, kwargs::Base.Iterators.Pairs{Symbol, Int64, Tuple{Symbol}, NamedTuple{(:nadapts,), Tuple{Int64}}})

where line 106 is predicted = solve(problem, Tsit5(), saveat=1). Hope this helps; sorry for the mess!

ChrisRackauckas · October 22, 2021, 2:13pm

Make your time a floating point type: (1.0,36.0). That should be caught and fixed automatically, but let’s see if that’s all that’s left now.

vembha · October 23, 2021, 6:38am

This brought back the BoundsError error that I posted previously! Posting the part of the (extremely long) error message stacktrace.

nested task error: BoundsError: attempt to access 36-element interpolate(::Vector{Float64}, BSpline(Linear())) with element type Float64 at index [NaN]
        Stacktrace:
          [1] throw_boundserror(A::Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, I::Tuple{Float64})
            @ Base .\abstractarray.jl:651
          [2] BSplineInterpolation
            @ C:\Users\Bharadwaj\.julia\packages\Interpolations\3gTQB\src\b-splines\indexing.jl:6 [inlined]
          [3] epidemic_wildtype(dy::Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:β, :λ, :α, :γ, :γₙ, :γᵪ, :θₙ, :θᵪ, :δᵪ, :σ₁, :σ₂, :σ₃, :σ₄), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:β, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:β, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:λ, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:λ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:α, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:α, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:γ, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:γ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:γₙ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:γₙ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:γᵪ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:γᵪ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:θₙ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:θₙ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:θᵪ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:θᵪ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:δᵪ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:δᵪ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ₁, Tuple{}}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ₁, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ₂, Tuple{}}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ₂, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ₃, Tuple{}}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ₃, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ₄, Tuple{}}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ₄, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 7}}, y::Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:β, :λ, :α, :γ, :γₙ, :γᵪ, :θₙ, :θᵪ, :δᵪ, :σ₁, :σ₂, :σ₃, :σ₄), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:β, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:β, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:λ, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:λ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:α, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:α, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:γ, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:γ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:γₙ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:γₙ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:γᵪ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:γᵪ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:θₙ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:θₙ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:θᵪ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:θᵪ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:δᵪ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:δᵪ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ₁, Tuple{}}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ₁, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ₂, Tuple{}}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ₂, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ₃, Tuple{}}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ₃, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ₄, Tuple{}}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ₄, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 7}}, p::Tuple{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:β, :λ, :α, :γ, :γₙ, :γᵪ, :θₙ, :θᵪ, :δᵪ, :σ₁, :σ₂, :σ₃, :σ₄), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:β, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:β, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:λ, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:λ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:α, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:α, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:γ, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:γ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:γₙ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:γₙ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:γᵪ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:γᵪ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:θₙ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:θₙ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:θᵪ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:θᵪ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:δᵪ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:δᵪ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ₁, Tuple{}}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ₁, Tuple{}}}, 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            @ Main C:\Users\Bharadwaj\Indian Institute of Science\COVID-19 variant study - General\codes_wildtype_fitting\discourse_NPI_code.jl:61

Here, line 61 is the first differential equation.

Hope this helps you @ChrisRackauckas in helping me out…

vembha · October 23, 2021, 10:03am

By the way, when I am just solving the ODE with randomly chosen parameter values (and not using Turing) along with the forcing functions, the code runs error-free! Here is the part of the code without the Turing part:

#= 
Section 1: Import required packages =#

using Turing, Distributions, DifferentialEquations, Interpolations
using MCMCChains, Plots, StatsPlots
using CSV, XLSX, DataFrames
using Random
Random.seed!(18431)

#= 
Section 2: Read the data file containing observation data and get the NPI data into arrays =#

my_data = DataFrame(XLSX.readtable("UK_weekly_15_July.xlsx", "Sheet1"; infer_eltypes=true)...);

total_weeks = 36;   # Total number of time points
N = 67081000;       # Population

y_time = 1:1:total_weeks;               # Timepoints (weeks)

y_S = Float64.(my_data.Susceptible);    # Susceptible
y_S = y_S[1:total_weeks];

y_D = Float64.(my_data.Deceased);       # Deceased
y_D = y_D[1:total_weeks];

y_HC = Float64.(my_data.Hosp_critical); # Critical hospitalizations
y_HC = y_HC[1:total_weeks];

y_T = Float64.(my_data.Hosp_total);     # Total hospitalizations
y_T = y_T[1:total_weeks];
y_HNC = y_T - y_HC;                     # Non-critical hospitalizations

observation_data = [y_S y_D y_HC y_HNC];

wet_data = DataFrame(XLSX.readtable("Wetdata.xlsx", "Wetdata"; infer_eltypes=true)...);
# IPTCC is a forcing function
IPTCC = wet_data.Normalized_IPTCC;
IPTCC = IPTCC[1:total_weeks];

mobil_data = DataFrame(XLSX.readtable("Mobdata.xlsx", "Mobdata"; infer_eltypes=true)...);
# mobil is another forcing function
mobil = mobil_data.Mean;
mobil = mobil[1:total_weeks];

wet_forcing = interpolate(IPTCC, BSpline(Linear()));
mobil_forcing = interpolate(mobil, BSpline(Linear()));

#= 
Section 3: Define the model and the respective parameters =#

function epidemic_wildtype!(dy, y, p, t)
    S, E, I, Hᵪ, Hₙ, R, D = y;
    β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w, m = p;
    N = 67081000;

    dy[1] = -β * w(t) * m(t) * I * S / N + λ * R;  # S
    dy[2] = β * w(t) * m(t) * I * S / N - α * E;   # E
    dy[3] = α * E - (γ + θᵪ + θₙ) * I;     # I
    dy[4] = θₙ * I - γₙ * Hᵪ;               # HNC
    dy[5] = θᵪ * I - (γᵪ + δᵪ) * Hₙ;       # HC
    dy[6] = γ * I + γₙ * Hₙ + γᵪ * Hᵪ - λ * R;  # R
    dy[7] = δᵪ * Hᵪ;                     # D
end

#= 
Section 4: Solve it! =#

p = (0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, wet_forcing, mobil_forcing);
tspan = (1.0, 36.0);
N = 67081000;
S0 = N;
I0 = 100;
y0 = [S0, 0, I0, 0, 0, 0, 0];
problem1 = ODEProblem(epidemic_wildtype!, y0, tspan, p);
solution1 = solve(problem1, Tsit5(), saveat=1.0);

Also, even when I am defining the forcing functions as global variables rather than passing them as a part of the parameter vector p, the ODE system is being solved error-free. But the same BoundsError (mentioned in the previous post) is getting triggered.

tomaklutfu · October 23, 2021, 10:50am

Can you do @show t before that line and see what w(t) and m(t) give for the last t shown before the error? Most likely, those two throw somewhere.