How to create Bayesian data fusion in python with pymc3?

Questions v3
4

Thank you for the reply.

In my code, I have two sensors where S2 is the weak sensor and S1 is the strong sensor, and what I am dealing with is same case as the Kalman Filter in 1 Dimension since I am dealing with 1D data.

So, I created Bayesian Fusion to follow the steps below:

  1. get the first data of S2 and getting their trace of the priors. ('Designing the Bayesian PDF for initial Sensor 2:')
  2. Use the priors trace to create a predictive priors based on the next data of S2. ('Designing the Bayesian PDF for predictive Sensor 2:')
  3. Update the distribution by using the predictive priors from the previous step into S1 and obtain the corrected custom distribution. ('Designing the Bayesian PDF for correction Sensor 1:')

I created this code following the same style as the in Kalman Filter in 1 Dimension since I am dealing with 1D data and changed the approach to fit in the Bayesian package (which is PyMC3).

mean = mean0
var = var0

plt.figure(figsize=(fw,5))
for m in range(len(positions)):
    
    # Predict
    var, mean = predict(var, mean, varMove, distances[m])
    #print('mean: %.2f\tvar:%.2f' % (mean, var))
    plt.plot(x,mlab.normpdf(x, mean, var), label='%i. step (Prediction)' % (m+1))
    
    # Correct
    var, mean = correct(var, mean, varSensor, positions[m])
    print('After correction:  mean= %.2f\tvar= %.2f' % (mean, var))
    plt.plot(x,mlab.normpdf(x, mean, var), label='%i. step (Correction)' % (m+1))
    
plt.ylim(0, 0.1);
plt.xlim(-20, 120)
plt.legend();

Based on your experience with pymc3, could any of the reasons that I mentioned would affect my results in the attempt of creating Bayesian fusion?