Hello everyone.

I hope I can show the problem I have using mainly (I think) pytensor and numpy.

I want to make inference over some physical parameter x which is a variable of a complicated physical model.

I have tried to make the inference using the physical model as it is but the graphs to be constructed are so complex that my desktop computer runs out of memory.

Therefore I have thought that if I generate an interpolating polynomial for the physical model and use it as an alternative I could solve the problem. But here a new problem arose: when I want to generate samples of the interpolated model, there is an incompatibility between the tensor variable used by pymc and the numerical input expected by the interpolating polynomial generated with numpy (the same problem occurs using scipy interpolators).

I suspect that the solution can be given by translating the tensor variable to a float variable, but I have not found the correct way to do it.

Below I copy a minimal outline of the code I have implemented. I hope someone knows how to deal with this kind of issues.

Thank you very much.

import pymc as pm

import pytensor

import pytensor.tensor as pt

import numpy as np

from multiprocessing import Pool

**1. Create the interpolated function evaluate a complicated physical model in a 1D-grid using p.map**

```
>>> def f_model(x):
# a complicated function of x and another (fixed for now) parameters
return f
```

```
>>> x_list = [ ]
>>> xRange = np.linspace(xmin, xmax, nx) # for some values of xmin, xmax and nx
>>> for j in range(nx):
x_list.append(xRange[j])
>>> p = Pool(6)
>>> f_sampled = p.map(f_model,x_list)
# generate the interpolation
>>> x_new = np.linspace(xmin, xmax, Nx) # same values for xmin and xmax; but now Nx much bigger than nx
>>> f_interp = np.interp(x_new, xRange, f_sampled)
```

here I plot together f_interp and f_sampled and the interpolation seems to be satisfactory. Also, I print some evaluation for the interpolation and I get

```
>>> f_out = np.interp(x_value,xRange,f_sampled) # for some numerical x_value
>>> print(str(f_out),type(f_out))
f_value <class 'numpy.float64'>
```

```
**2. Generate the inference for x given observed data**
## Define the deterministic model and the prior for x
```

```
>>> def data_model(x):
S1 = np.interp(x,xRange,f_sampled)
Dim = 1
a = pt.zeros(Dim)
a = S1
return a
```

```
>>> print('some evaluation: ', str(data_model(x_value))+' '+str(type(data_model(x_value))))
some evaluation: numerical_value <class 'numpy.float64'>
```

```
## Then I define the Model:
>>> with pm.Model() as model_bayes:
x_in = pm.Uniform('x', xmin, xmax)
def sampled_model(x_rnd = x_in):
return data_model(x_rnd)
>>> print('10 draws for x: ', str(pm.draw(x_in,10)))
>>> print('evaluation of the physical model:', str(sampled_model(pm.draw(x_in,1))))
>>> print('kind of variable: ', type(sampled_model(pm.draw(x_in,1))))
10 draws for x: [x0 x1 x2 x3 x4 x5 x6 x7 x8 x9]
evaluation of the physical model: a_numerical_value
kind of variable: <class 'numpy.float64'>
And here comes the error
>>> with model_bayes:
function_pm = pm.Deterministic('modelo', sampled_model())
TypeError Traceback (most recent call last)
<ipython-input-41-cd6021848196> in <cell line: 10>()
9
10 with model_bayes:
---> 11 function_pm = pm.Deterministic('modelo',sampled_model())
1 frames
<ipython-input-38-3c75629263ab> in data_model(x)
12
13
---> 14 x_in = float(x)
15
16 S1 = np.interp(x_in,xRange,f_sampled)
**TypeError: float() argument must be a string or a real number, not 'TensorVariable'**Preformatted text
```