# Edit default plot settings (colours from colorbrewer2.org)
plt.rc("font", size=14)
# data
y = np.array([93, 112, 122, 135, 122, 150, 118, 90, 124, 114])
# sufficient statistics
n = len(y)
s2 = np.var(y, ddof=1) # Here ddof=1 is used to get the sample estimate.
my = np.mean(y)
# Factorize the joint posterior p(mu,sigma2|y) to p(sigma2|y)p(mu|sigma2,y)
# Sample from the joint posterior using this factorization
# sample from p(sigma2|y)
nsamp = 1000
sigma2 = sinvchi2.rvs(n - 1, s2, size=nsamp)
# sample from p(mu|sigma2,y)
mu = my + np.sqrt(sigma2 / n) * np.random.randn(*sigma2.shape)
# display sigma instead of sigma2
sigma = np.sqrt(sigma2)
# For mu compute the density in these points
tl1 = [90, 150]
t1 = np.linspace(tl1[0], tl1[1], 1000)
# For sigma compute the density in these points
tl2 = [10, 60]
t2 = np.linspace(tl2[0], tl2[1], 1000)
# evaluate the joint density in a grid
# note that the following is not normalized, but for plotting
# contours it does not matter
plt.rc('axes',
color_cycle=('#377eb8', '#e41a1c', '#4daf4a', '#984ea3', '#ff7f00',
'#ffff33'))
# data
y = np.array([93, 112, 122, 135, 122, 150, 118, 90, 124, 114])
# sufficient statistics
n = len(y)
s2 = np.var(y, ddof=1) # Here ddof=1 is used to get the sample estimate.
my = np.mean(y)
# Factorize the joint posterior p(mu,sigma2|y) to p(sigma2|y)p(mu|sigma2,y)
# Sample from the joint posterior using this factorization
# sample from p(sigma2|y)
sigma2 = sinvchi2.rvs(n - 1, s2, size=1000)
# sample from p(mu|sigma2,y)
mu = my + np.sqrt(sigma2 / n) * np.random.randn(*sigma2.shape)
# display sigma instead of sigma2
sigma = np.sqrt(sigma2)
# For mu compute the density in these points
tl1 = [90, 150]
t1 = np.linspace(tl1[0], tl1[1], 1000)
# For sigma compute the density in these points
tl2 = [10, 60]
t2 = np.linspace(tl2[0], tl2[1], 1000)
# evaluate the joint density in a grid
# note that the following is not normalized, but for plotting
# contours it does not matter
# Edit default plot settings (colours from colorbrewer2.org)
plt.rc('font', size=14)
# data
y = np.array([93, 112, 122, 135, 122, 150, 118, 90, 124, 114])
# sufficient statistics
n = len(y)
s2 = np.var(y, ddof=1) # Here ddof=1 is used to get the sample estimate.
my = np.mean(y)
# Factorize the joint posterior p(mu,sigma2|y) to p(sigma2|y)p(mu|sigma2,y)
# Sample from the joint posterior using this factorization
# sample from p(sigma2|y)
nsamp = 1000
sigma2 = sinvchi2.rvs(n - 1, s2, size=nsamp)
# sample from p(mu|sigma2,y)
mu = my + np.sqrt(sigma2 / n) * np.random.randn(*sigma2.shape)
# display sigma instead of sigma2
sigma = np.sqrt(sigma2)
# For mu compute the density in these points
tl1 = [90, 150]
t1 = np.linspace(tl1[0], tl1[1], 1000)
# For sigma compute the density in these points
tl2 = [10, 60]
t2 = np.linspace(tl2[0], tl2[1], 1000)
# evaluate the joint density in a grid
# note that the following is not normalized, but for plotting
# contours it does not matter
plt.rc('lines', color='#377eb8')
plt.rc('axes', color_cycle=('#377eb8','#e41a1c','#4daf4a',
'#984ea3','#ff7f00','#ffff33'))
# data
y = np.array([93, 112, 122, 135, 122, 150, 118, 90, 124, 114])
# sufficient statistics
n = len(y)
s2 = np.var(y, ddof=1) # Here ddof=1 is used to get the sample estimate.
my = np.mean(y)
# Factorize the joint posterior p(mu,sigma2|y) to p(sigma2|y)p(mu|sigma2,y)
# Sample from the joint posterior using this factorization
# sample from p(sigma2|y)
sigma2 = sinvchi2.rvs(n-1, s2, size=1000)
# sample from p(mu|sigma2,y)
mu = my + np.sqrt(sigma2/n)*np.random.randn(*sigma2.shape)
# display sigma instead of sigma2
sigma = np.sqrt(sigma2)
# For mu compute the density in these points
tl1 = [90, 150]
t1 = np.linspace(tl1[0], tl1[1], 1000)
# For sigma compute the density in these points
tl2 = [10, 60]
t2 = np.linspace(tl2[0], tl2[1], 1000)
# evaluate the joint density in a grid
# note that the following is not normalized, but for plotting
# contours it does not matter