Optim in Julia attempts extreme values that lead to numerical errors (NaN)

Question

I have an objective function that looks like

function myfun(θ, x)
    logτ = θ
    s(ϵ) = 1.0/sqrt(exp(logτ)) * ϵ
    p(ϵ) = 1/(1 + 0.5 * exp((0.5 - s(ϵ))*exp(log