"""

Example inference instances for Assignment 04.

Created 2015-03-13 by Tom Loredo

"""

import numpy as np

import scipy

import matplotlib as mpl

from matplotlib.pyplot import *

from scipy import *

from scipy import stats

from poisson_binomial_cauchy import PoissonRateInference, BinomialInference, \

CauchyLocationInference

try:

import myplot

from myplot import close_all

except ImportError:

pass

ion() # for interactive use in a terminal session

def g_mean(params):

return params

have_laplace = False

#-------------------------------------------------------------------------------

# 1st case: Poisson, const prior, (n,T) = (16, 2)

r_u = 20. # upper limit for PDF calculation and plotting

# Create a PRI instance and plot the PDF.

prior_l, prior_u = 0., 1e5

flat_pdf = 1./(prior_u - prior_l)

n, T = 16, 2

pri = PoissonRateInference(T, n, flat_pdf, r_u)

pri.plot(alpha=.5)

xlabel(r'Rate (s$^{-1}$)')

ylabel('PDF (s)')

title('Poisson case')

if have_laplace:

# Laplace approx for the marg. like. and the mean:

ampl, locn, sig, ml = pri.laplace()

laplace_mean = pri.laplace(g_mean)

post_mean_l = laplace_mean[3]/ml

# Use results to plot a Gaussian PDF here.

# Print using string formatting:

print 'Poisson case:'

print 'Marg. like.: {:.4e} (quad), {:.4e} (Laplace)'.format(pri.mlike, ml)

print 'Posterior mean: {:4.2f} (quad), {:4.2f} (Laplace)'.format(pri.post_mean, post_mean_l)

print

#-------------------------------------------------------------------------------

# 2nd case: Binomial, const prior, (n, n_trials) = (8, 12)

# Define the data.

n, n_trials = 8, 12

bi = BinomialInference(n, n_trials)

bfig = figure() # separate figure for binomial case

bi.plot(alpha=.5)

xlabel(r'$\alpha$')

ylabel('Posterior PDF')

title('Binomial case')

if have_laplace:

# Laplace approx for the marg. like. and the mean:

laplace_ml = bi.laplace()

laplace_mean = bi.laplace(g_mean)

post_mean_l = laplace_mean[3]/laplace_ml[3]

# Use results to plot a Gaussian PDF here.

# Print using string formatting:

print 'Beta case:'

print 'Marg. like.: {:10.4e} (quad), {:10.4e} (Laplace)'.format(bi.mlike, laplace_ml[3])

print 'Posterior mean: {:4.2f} (quad), {:4.2f} (Laplace)'.format(bi.post_mean, post_mean_l)

print

#-------------------------------------------------------------------------------

# 3rd case: Cauchy, const prior

x0, d = 5., 3.

data = stats.cauchy(x0, d).rvs(5)

flat_pdf = .001 # e.g., for prior range 1e3

cli = CauchyLocationInference(d, data, flat_pdf, (-15., 25.))

cfig = figure()

cli.plot(alpha=.5)

xlim(-10, 15.)

xlabel('$x_0$')

ylabel('Posterior PDF')

title('Cauchy case; CDF method')

samps = []

for i in range(10000):

samps.append(cli.samp_cdf())

samps = array(samps)

hist(samps, 50, normed=True, color='g', alpha=.5)

if have_laplace:

# Laplace approx for the marg. like. and the mean:

ampl, locn, sig, ml = cli.laplace()

laplace_mean = cli.laplace(g_mean)

post_mean_l = laplace_mean[3]/ml

# Use results to plot a Gaussian PDF here.

# Print using string formatting:

print 'Poisson case:'

print 'Marg. like.: {:.4e} (quad), {:.4e} (Laplace)'.format(cli.mlike, ml)

print 'Posterior mean: {:4.2f} (quad), {:4.2f} (Laplace)'.format(cli.post_mean, post_mean_l)