Student t CDF as a function

Questions
1

I’m interested in using the CDF of the student t distribution as a function inside a model. I noticed that pm.StudentT has a logcdf method, so I grabbed the code and put it in a minimal example script:

import arviz as az
import numpy as np
import matplotlib.pyplot as plt
import pymc3 as pm
from pymc3.distributions.dist_math import incomplete_beta
from scipy.stats import t
import theano.tensor as tt


if __name__ == '__main__':

    with pm.Model():

        x = np.linspace(-8, 8)
        p = t.cdf(x, 1.1)
        y = np.random.binomial(40, p)

        _x = tt.as_tensor_variable(x)
        nu = pm.Exponential(name="nu", lam=1)

        sqrt_t2_nu = tt.sqrt(_x ** 2 + nu)
        __x = (_x + sqrt_t2_nu) / (2.0 * sqrt_t2_nu)
        _p = incomplete_beta(nu / 2., nu / 2., __x)  # <-- this line gives the error

        pm.Binomial(name="yhat", n=40, p=_p, observed=y)

        trace = pm.sample()
        az.plot_trace(trace)
        plt.show()

I get the following error:

Traceback (most recent call last):
  File "/Users/samuelrobertmathias/miniconda3/envs/psychoacoustics/lib/python3.8/site-packages/theano/tensor/type.py", line 254, in dtype_specs
    return {
KeyError: 'object'

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "/Users/samuelrobertmathias/miniconda3/envs/psychoacoustics/lib/python3.8/site-packages/theano/tensor/basic.py", line 246, in constant
    ttype = TensorType(dtype=x_.dtype, broadcastable=bcastable)
  File "/Users/samuelrobertmathias/miniconda3/envs/psychoacoustics/lib/python3.8/site-packages/theano/tensor/type.py", line 51, in __init__
    self.dtype_specs()  # error checking is done there
  File "/Users/samuelrobertmathias/miniconda3/envs/psychoacoustics/lib/python3.8/site-packages/theano/tensor/type.py", line 271, in dtype_specs
    raise TypeError("Unsupported dtype for %s: %s"
TypeError: Unsupported dtype for TensorType: object

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "/Users/samuelrobertmathias/miniconda3/envs/psychoacoustics/lib/python3.8/site-packages/theano/tensor/basic.py", line 194, in as_tensor_variable
    return constant(x, name=name, ndim=ndim)
  File "/Users/samuelrobertmathias/miniconda3/envs/psychoacoustics/lib/python3.8/site-packages/theano/tensor/basic.py", line 266, in constant
    raise TypeError("Could not convert %s to TensorType" % x, type(x))
TypeError: not all arguments converted during string formatting

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "/Users/samuelrobertmathias/PycharmProjects/TrialEffects/_test.py", line 23, in <module>
    p = incomplete_beta(nu / 2., nu / 2., __x)
  File "/Users/samuelrobertmathias/miniconda3/envs/psychoacoustics/lib/python3.8/site-packages/pymc3/distributions/dist_math.py", line 527, in incomplete_beta
    ps = incomplete_beta_ps(a, b, value)
  File "/Users/samuelrobertmathias/miniconda3/envs/psychoacoustics/lib/python3.8/site-packages/pymc3/distributions/dist_math.py", line 503, in incomplete_beta_ps
    tt.cast((t, s),
  File "/Users/samuelrobertmathias/miniconda3/envs/psychoacoustics/lib/python3.8/site-packages/theano/tensor/basic.py", line 1259, in cast
    _x = as_tensor_variable(x)
  File "/Users/samuelrobertmathias/miniconda3/envs/psychoacoustics/lib/python3.8/site-packages/theano/tensor/basic.py", line 200, in as_tensor_variable
    raise AsTensorError("Cannot convert %s to TensorType" % str_x, type(x))
theano.tensor.var.AsTensorError: ('Cannot convert (Elemwise{mul,no_inplace}.0, TensorConstant{0.0}) to TensorType', <class 'tuple'>)

I’m failing to understand this error. Can anyone give me any pointers?