heteroscedastic errors.
"""
# Author: Jake VanderPlas <*****@*****.**>
# License: BSD
# The figure produced by this code is published in the textbook
# "Statistics, Data Mining, and Machine Learning in Astronomy" (2013)
# For more information, see http://astroML.github.com
import numpy as np
from matplotlib import pyplot as plt
from scipy import optimize
from astroML.datasets import fetch_hogg2010test
#------------------------------------------------------------
# Get data: this includes outliers
data = fetch_hogg2010test()
x = data['x']
y = data['y']
dy = data['sigma_y']
# Define the standard squared-loss function
def squared_loss(m, b, x, y, dy):
y_fit = m * x + b
return np.sum(((y - y_fit) / dy) ** 2, -1)
# Define the log-likelihood via the Huber loss function
def huber_loss(m, b, x, y, dy, c=2):
y_fit = m * x + b
t = abs((y - y_fit) / dy)
import pymc
#----------------------------------------------------------------------
# This function adjusts matplotlib settings for a uniform feel in the textbook.
# Note that with usetex=True, fonts are rendered with LaTeX. This may
# result in an error if LaTeX is not installed on your system. In that case,
# you can set usetex to False.
if "setup_text_plots" not in globals():
from astroML.plotting import setup_text_plots
setup_text_plots(fontsize=8, usetex=True)
np.random.seed(0)
#------------------------------------------------------------
# Get data: this includes outliers
data = fetch_hogg2010test()
xi = data['x']
yi = data['y']
dyi = data['sigma_y']
#----------------------------------------------------------------------
# First model: no outlier correction
# define priors on beta = (slope, intercept)
@pymc.stochastic
def beta_M0(value=np.array([2., 100.])):
"""Slope and intercept parameters for a straight line.
The likelihood corresponds to the prior probability of the parameters."""
slope, intercept = value
prob_intercept = 1 + 0 * intercept
# uniform prior on theta = arctan(slope)
