A 2D sampling example

We show a 2D sampling example. The dimension of the model space is 2. We assume the ground truth is at the origin and the initial error range is R₁ = (8, 2).

Let delta=1.7, sigma_max=1000.

Based on equation (11) in the paper, we have:

R₁ = (8, 2)           Sigma₁ = (4.71 1000)    

R₂=(2.77 2.00)    Sigma₂ = (1.63 1.63)     

R₃=(0.96 0.96)    Sigma₃ = (0.56 0.56)     

The plot of feasible regions defined by R₁(black) , R₂(red), and R₃(green).  

The level 1 sampling results. R₁ = (8, 2)  and Sigma₁ = (4.71 1000).  The target function  q₁(C|I) is the normal distribution N(0, Sigma₁).  The sampling density function is the gradient magnitude of q₁(C|I).  The metropolis sampling is used to sample training examples.

The plot of q1(C|I)	The gradient magnitude of q1(C|I)	The sampled points using Metropolis algorithm.

The level 2 sampling results. R₂ = (2.77 2.00)  and Sigma₂ = (1.63 1.63).  The target function  q₂(C|I) is the normal distribution N(0, Sigma₂).  The sampling density function is the gradient magnitude of q₂(C|I).  The metropolis sampling is used to sample training examples.

The plot of q2(C|I)	The gradient magnitude of q2(C|I)	The sampled points using Metropolis algorithm.

The level 3 sampling results. R₃ = (0.96 0.96)  and Sigma₃ = (0.56 0.56).  The target function  q₃(C|I) is the normal distribution N(0, Sigma₃).  The sampling density function is the gradient magnitude of q₃(C|I).  The metropolis sampling is used to sample training examples.

The plot of q3(C|I)	The gradient magnitude of q3(C|I)	The sampled points using Metropolis algorithm.