#!/usr/bin/env python
# -*- coding: utf-8 -*-
from __future__ import division, print_function
import numpy as np
import matplotlib.pyplot as pl
from plot_setup import setup, SQUARE_FIGSIZE, COLORS, savefig
setup() # initialize the plotting styles
np.random.seed(42)
def compute_stats(K, a=0.0, b=1.0):
a, b = sorted((a, b))
x = np.random.uniform(a, b, size=K)
# Analytic results:
p = 1. / (b - a)
a_mu = 0.5 * p * (b**2 - a**2)
a_var = p * ((b - a_mu)**3 - (a - a_mu)**3) / 3.
a_skew = 0.25 * p * ((b-a_mu)**4-(a-a_mu)**4) / a_var**(3./2)
a_kurt = p * ((b-a_mu)**5-(a-a_mu)**5) / a_var**2 / 5.0
# Sample estimates of stats:
s_mu = np.mean(x)
s_var = np.var(x)
s_skew = np.mean((x - s_mu)**3) / s_var**(3./2)
s_kurt = np.mean((x - s_mu)**4) / s_var**2
from __future__ import division, print_function
import emcee3
import fitsio
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from plot_setup import setup, get_figsize, COLORS
import celerite
from celerite import terms
np.random.seed(123)
setup()
# Define the custom kernel
class RotationTerm(terms.Term):
parameter_names = ("log_amp", "log_timescale", "log_period", "log_factor")
def get_real_coefficients(self):
f = np.exp(self.log_factor)
return (
np.exp(self.log_amp) * (1.0 + f) / (2.0 + f),
np.exp(-self.log_timescale),
)
def get_complex_coefficients(self):
f = np.exp(self.log_factor)
#!/usr/bin/env python
# -*- coding: utf-8 -*-
from __future__ import division, print_function
import corner
import numpy as np
from plot_setup import setup, savefig
setup() # initialize the plotting styles
np.random.seed(42)
def log_p_gauss(x):
V = np.array([[2.0, 1.2], [1.2, 2.0]])
alpha = np.linalg.solve(V, x)
return -0.5 * np.dot(x, alpha)
def run_mcmc(log_p, x, prop_sigma=1.0, nsteps=2e4, thin=1):
lp = log_p(x)
chain = np.empty((nsteps // thin, len(x)))
acc = 0
for step in range(len(chain)):
for i in range(thin):
x_prime = np.array(x)
x_prime[np.random.randint(
len(x))] += prop_sigma * np.random.randn()
lp_prime = log_p(x_prime)
if np.random.rand() <= np.exp(lp_prime - lp):