I am learning how to data fit on python with importance sampling, I am trying to sample x and y values and find their weights but I am getting errors

Question

Basically, I am trying to sample x and y from a proposal distribution function and then find the weights for the sample, and create 10 different sets of n = 10,000 samples. I was given an array of 55 values for radius and mu and sigma, and I have 10,000 values of x and y as samples.

here is my code:

import numpy as np
import matplotlib.pyplot as plt 

GN = 4.302**-6
A = 8445.264

mu = np.array([1,1])
C = [[1,0],[0,1]]
num = 10**4
def chi_sq(x,y):
  r = np.zeros(len(radius))
  for s in range(len(radius)):
    f_xy = np.sqrt( GN * 10**y * radius[s] / (radius[s] + 10**x )**3 ) 
    chi_sqtotal = np.sum((f_xy - mu[s] )**2 / (sigma[s])**2)
    r += chi_sqtotal 
  return r 
def P(x,y):
  return A*np.exp(-0.5*chi_sq(x,y))
for i in range(10):
  def chi_sq(x,y):
    r = np.zeros(len(radius))
    for s in range(len(radius)):
      f_xy = np.sqrt( GN * 10**y * radius[s] / (radius[s] + 10**x )**3 ) 
      chi_sqtotal = np.sum((f_xy - mu[s] )**2 / (sigma[s])**2)
      r += chi_sqtotal 
    return r 
  def P(x,y):
    return A*np.exp(-0.5*chi_sq(x,y))
  detC = np.linalg.det(C)
  Cinv = np.linalg.inv(C)
  def Q(x,y):
    r = np.array([x,y]) - mu
    prefactor = 1/(2*np.pi*np.sqrt(detC))
    exponent = 0.5*(r @ Cinv @ r)
    return prefactor*np.exp(-exponent)
  r_samples = np.random.multivariate_normal(mu,C,num)
  x_samples = r_samples[:,0]
  y_samples = r_samples[:,1]
  w = np.zeros(num)
  for j in range(num):
    x, y = r_samples[j]
    
    w[j] = P(x,y)/Q(x,y)

Here is the error I am getting:

IndexError                                Traceback (most recent call last)
<ipython-input-114-638cc1a1b2e2> in <module>()
     41     x, y = r_samples[j]
     42 
---> 43     w[j] = P(x,y)/Q(x,y)

1 frames
<ipython-input-114-638cc1a1b2e2> in chi_sq(x, y)
     22     for s in range(len(radius)):
     23       f_xy = np.sqrt( GN * 10**y * radius[s] / (radius[s] + 10**x )**3 )
---> 24       chi_sqtotal = np.sum((f_xy - mu[s] )**2 / (sigma[s])**2)
     25       r += chi_sqtotal
     26     return r

IndexError: index 2 is out of bounds for axis 0 with size 2

Answer 1

The error is very descriptive:

IndexError: index 2 is out of bounds for axis 0 with size 2

If I have a numpy.ndarray , let's call it x , then the axes are as follows:

x[axis_0][axis_1]...

They are saying that the size of the axis is 2, and you're indexing it with 2, which is out of bounds. Notice

mu = np.array([1,1])

and the line with mu has the error. In this chunk:

for s in range(len(radius)):
  f_xy = np.sqrt( GN * 10**y * radius[s] / (radius[s] + 10**x )**3 ) 
  chi_sqtotal = np.sum((f_xy - mu[s] )**2 / (sigma[s])**2)
  r += chi_sqtotal 

s goes above 1, causing the error. You need to make a correction somewhere and not loop as high as len(radius) , because mu only has 2 elements.