Bootstrap in Global Sensitivity Analysis (GSA)

Specific Domains Modelling & Simulations
1

Hi There,

Running the basic example below the bootstrapping just returns

nothing

So no standard errors are returned at all. Playing with sobolsensitivity.jl package if I go in and hard code nboot I can return bootstrapped runs it appears the nboot keyword is not recognised in the package. I have tried my best at having a crack at this but I think I have become stuck in how to fix this.

I am sorry I could not help more, MWE is down below

Cheers,
Harry

using GlobalSensitivity, Statistics, OrdinaryDiffEq, QuasiMonteCarlo, Plots


function f(du,u,p,t)
    du[1] = p[1]*u[1] - p[2]*u[1]*u[2] #prey
    du[2] = -p[3]*u[2] + p[4]*u[1]*u[2] #predator
end

u0 = [1.0;1.0]
tspan = (0.0,10.0)
p = [1.5,1.0,3.0,1.0]
prob = ODEProblem(f,u0,tspan,p)
t = collect(range(0, stop=10, length=200))


f1 = function (p)
    prob1 = remake(prob;p=p)
    sol = solve(prob1,Tsit5();saveat=t)
    [mean(sol[1,:]), maximum(sol[2,:])]
end

samples = 10000
lb = [1.0, 1.0, 1.0, 1.0]
ub = [5.0, 5.0, 5.0, 5.0]
sampler = SobolSample()
A,B = QuasiMonteCarlo.generate_design_matrices(samples,lb,ub,sampler)

sobol_result = gsa(f1,Sobol(),A,B, nboot = 1000)

sobol_result.S1
sobol_result.S1_Conf_Int
2

gsa for Sobol (also) uses nboot set via Sobol(...) and the reason you get nothing is that the default of Sobol’s nboot is equal to 1. You can still set a nboot for gsa which is independent of the nboot passed to Sobol constructor. However, if you only pass nboot via Sobol, then the gsa’s nboot will be set to the same value. I hope this makes sense to you.

Try alter the relevant line in the following way:

# your previous code here

# please note `nboot` keyword in `Sobol` constructor
sobol_result = gsa(f1, Sobol(nboot=1000), A, B)

# you'll get a Matrix{Float64} here
sobol_result.S1_Conf_Int

Have fun.