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Nov 13th, 2021
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  1. import numpy as np
  2.  
  3. def sample_odds_path(p, s=0.05, N=2000):
  4.     x = []
  5.     xc = np.log(p) - np.log(1-p)
  6.  
  7.     for k in range(N):
  8.         x.append(xc)
  9.         f = np.exp(xc)
  10.         xc += np.random.normal(loc=0, scale=s) + s**2 * (f-1)/(f+1)
  11.  
  12.     x = np.array(x)
  13.     L = 1 - 1/(np.exp(x) + 1)
  14.  
  15.     return x, L
  16.  
  17. mean_scores = []
  18. log_scores = []
  19.  
  20. for _ in range(1000):
  21.     x, L = sample_odds_path(0.5, s = 0.15, N = 500)
  22.     q = np.random.choice(L, size=10)
  23.  
  24.     indicator = np.random.choice([0, 1], p=[1 - L[-1], L[-1]])
  25.  
  26.     mean_forecast = np.mean(q)
  27.     mean_log_odds = 1 - 1/(np.exp(np.mean(np.log(q/(1-q)))) + 1)
  28.  
  29.     mean_scores.append(np.log(mean_forecast) if indicator == 1 else np.log(1 - mean_forecast))
  30.     log_scores.append(np.log(mean_log_odds) if indicator == 1 else np.log(1 - mean_log_odds))
  31.  
  32. print(np.mean(mean_scores), np.mean(log_scores))
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