PyMC3 : Using a parameter as a limit of integral

Questions
3

@junpenglao, thanks for your reply. I modified my code as per your suggestions. However, I got this error when I tried doing so :

AsTensorError: ('Cannot convert <function mu at 0x1c2ab42ea0> to TensorType', <class 'function'>)

I tried modifying the code further by converting the return value of the function to a tensor. This is the modified code :

basic_model = pymc3.Model()

with basic_model:
    start=pymc3.Uniform('start',0,0)
    a=pymc3.Uniform('a',0.01,0.1)

    b=pymc3.Uniform('b',0.001,0.01)

    e=pymc3.Normal("e",mu=0,sd=a+b*x)
    def mu(e):
        t = tt.dscalar('t')
        t.tag.test_value = np.zeros(())
        z=(1+0.2*((1+t)**float(3)-1))**float(-0.5)
        def f1(xp):
            integrate = Integrate(z,t)

            val=integrate(start, x+e)
            return val
        f2=f1(x+e)
        return tf.convert_to_tensor((f2*(1+x+e)))
    y=pymc3.Normal('y',mu=mu,sd=0.5,observed=y_obs)

But I still get the same error. This is the full traceback :

Traceback (most recent call last):

  File "<ipython-input-10-b47f07234c39>", line 21, in <module>
    y=pymc3.Normal('y',mu=mu,sd=0.5,observed=y_obs)

  File "/anaconda3/lib/python3.6/site-packages/pymc3/distributions/distribution.py", line 38, in __new__
    dist = cls.dist(*args, **kwargs)

  File "/anaconda3/lib/python3.6/site-packages/pymc3/distributions/distribution.py", line 49, in dist
    dist.__init__(*args, **kwargs)

  File "/anaconda3/lib/python3.6/site-packages/pymc3/distributions/continuous.py", line 386, in __init__
    self.mean = self.median = self.mode = self.mu = mu = tt.as_tensor_variable(mu)

  File "/anaconda3/lib/python3.6/site-packages/theano/tensor/basic.py", line 200, in as_tensor_variable
    raise AsTensorError("Cannot convert %s to TensorType" % str_x, type(x))

AsTensorError: ('Cannot convert <function mu at 0x1c2ab42ea0> to TensorType', <class 'function'>)

Is there any alternate way to define this function? I also tried using tf.py_func(), but this too doesn’t seem to work. Thanks in advance.