Evaluating Hypotheses

file.py

# We'll be working in log space as an optimization
# So that our numbers don't get so small that the computer 
# rounds them to zero.
# Start with an uninformative prior
# Every hypothesis gets an equal weighting.
# Not important that they sum to one, just that
# they're equally weighted.
hypothesis_likelihoods = np.log(np.array([1]))

for i, hypotheses_tuple in enumerate(hypotheses):
  a_hypothesis, h_hypothesis, k_hypothesis, sigma_hypothesis = hypotheses_tuple
  for x_datum, y_datum in zip(x_data, observed_y):
    # For the given hypothetical value of each parameter
    # let's compute a prediction and the error
    predicted_y = a_hypothesis * (x_datum - h_hypothesis)**2 + k_hypothesis
    prediction_error = y_datum - predicted_y
    
    # On average, the error should be centered around zero
    # just like in a standard regression (aka normal residuals).
    y_probability = ss.norm.pdf(0, loc=prediction_error, scale=sigma_hypothesis)
    
    # Multiply probability density but
    # we're in log space so just add them
    hypothesis_likelihoods[i] += np.log(y_probability)
    
hypothesis_probabilities = normalize(hypothesis_likelihoods)