How to apply the surrogate model to Bayesian method?

Questions
1

Hi everyone,
I have the surrogate function of the input and output. with the input follow the uniform distribution.

I have input: x = uniform distribution (0,1)
the surrogate function of input and output: y = 2.3 x^4-9.8x^3+15.2x^2-10.334x+2.7 ( where x is the input, and y is the output)
how to apply Bayesian method to find the posterior distribution?
thanks you

2

So you have observed y and you want to find the posterior of x? If that’s the case the current workaround is something like:

with pm.Model() as m:
    x = pm.Uniform('x', 0, 1)
    obs = pm.Normal('y', mu=2.3 * x**4 - 9.8 * x**3 + 15.2 * x**2 - 10.334 * x + 2.7, sd=.1
                  observed=y)