 # Complete the PyMC model definition within the 'with pm.Model() as m:' block below. Your output must define a complete Bayesian model with appropriate priors, likelihood, and then sample the posterior using, `pm.sample(1000, tune=1000, chains=4, return_inferencedata=True, idata_kwargs={"log_likelihood": True})`. Do not include any extra commentary or text outside the code. Follow best practices for expert-level Bayesian modeling.
    
# Description: Simulated data from a Poisson GP model.

    
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:
    
    