Mean of likelihood function for Bayesian regression

Questions
3

Hi @cluhmann,

To be more precise, I have a mean function that I know via Least square’s regression whose function is given by:

f(x) =      a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2) + 
              a3*exp(-((x-b3)/c3)^2) + a4*exp(-((x-b4)/c4)^2) + 
              a5*exp(-((x-b5)/c5)^2)

Here, “x” is the predictor variable and all others are the unknown parameters (a1,a2,…b1,b2,…c1,c2,…).

I want to model this in PyMC3 considering all these unknown parameters as RVs. I have already tried defining a function and using it as follows:

with pm.Model() as model:

  def sumGaussians(a,b,c,x):
      sum = tt.zeros (shape=(1,26))
      for g in range(numG):
           sum = sum + a[g] * pm.math.exp(pm.math.sqr((x - b[g])/c[g]))
      return sum

  a_ = pm.Normal("a_", mu=0, sigma=sigma_theta, shape=(numG, 1))
  b_ = pm.Normal("b_", mu=0, sigma=sigma_theta, shape=(numG, 1))
  c_ = pm.Normal("c_", mu=0, sigma=sigma_theta, shape=(numG, 1))
  
  mu_y = sumGaussians(a_,b_,c_,x)
  sigma_y = pm.InverseGamma("sigma_y",1,1)
  
  Y_obs = pm.Normal('Y_obs', mu_y, sigma_y, observed=obs_data)

This doesn’t work for me. What do you think is going wrong for me?