Fig 1. Contour lines.

Plots show the contour lines of two functions, chosen to illustrate identifiable and non-identifiable cases. Plot (A) is an identifiable case illustrated by Booth function l_A(θ) = (θ₁+2θ₂−7)²+(2θ₁+θ₂−5)², which has known minimum l_A(1,3) = 0. Plot (B) illustrate non-identifiable case by Rosenbrock function $l_B\left(\mathit{\theta }\right)={\left({1-\theta }_1\right)}^2+{100({\theta }_2-{\theta }_1^2)}^2$ with minimum l_B(1,1) = 0. The star-shaped points mark the minima of the above functions. The bold contour represents the ${CR}_{\alpha }=\left\{\mathit{\theta }:l\left(\mathit{\theta }\right)-l_{\alpha }^{*}\le 0\right\}$ for $l_{\alpha }^{*}=200$. The dashed lines are profile paths projected on (θ₁, θ₂) Red circles mark the points where tangent hyperplanes correspond to parameters’ minimal or maximal values in CR_α. Red circles are CI endpoints. The contours were calculated using marching squares algorithm implemented in Contour.jl package (https://github.com/JuliaGeometry/Contour.jl). They are provided for illustrative purposes only.