
import pymc as pm
import numpy as np
import arviz as az
import matplotlib.pyplot as plt

# Given Data
N = 11  # Number of observations
x = np.array([-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10])
y = np.array([4.75906, 1.59423, 2.99548, 5.27501, 1.66472, 2.24347, 2.8914, 4.08681, 4.60588, 0.802364, 3.92136])
k = np.array([40, 37, 29, 12, 4, 3, 9, 19, 77, 82, 33])

with pm.Model() as m:
	# Define priors for the GP parameters
	sigma = pm.HalfNormal("sigma", sigma=10)
	rho = pm.HalfNormal("rho", sigma=10)
	eta = pm.HalfNormal("eta", sigma=10)

	# Define the GP model
	gp = pm.gp.Latent(cov_func=pm.gp.cov.Matern52(1, ls=rho, sigma=sigma))

	# Define the likelihood
	y_obs = pm.Poisson("y_obs", mu=gp(x), observed=y)

	# Sample the posterior
	trace = pm.sample(1000, tune=1000, chains=4, return_inferencedata=True, idata_kwargs={"log_likelihood": True})

	# Posterior diagnostics
	summary = az.summary(trace)
