%matplotlib inline
from IPython.html.widgets import interact
from scipy import stats

f0=stats.norm(0,1)
f1=stats.norm(2,1)
fig,ax = subplots()
xi = linspace(-2,5,100)
ax.plot(xi,f0.pdf(xi),label=r'$f(x|C_0)$')
ax.plot(xi,f1.pdf(xi),label=r'$f(x|C_1)$')
ax.legend(fontsize=16,loc=(1,0))
ax.set_xlabel(r'$x$',fontsize=18)
ax.vlines(0,0,ax.axis()[-1]*1.1,linestyles='--',lw=3.)
ax.fill_between(xi,f1.pdf(xi),where=xi>0,alpha=.3,color='g')
ax.fill_between(xi,f0.pdf(xi),where=xi>0,alpha=.3,color='b')

def plot_roc_interact(c=0):
    xi = linspace(-3,5,100)
    fig,axs = subplots(1,2)
    fig.set_size_inches((10,3))
    ax = axs[0]
    ax.plot(xi,f0.pdf(xi),label=r'$f(x|C_0)$')
    ax.plot(xi,f1.pdf(xi),label=r'$f(x|C_1)$')
    ax.set_xlabel(r'$x$',fontsize=18)
    ax.vlines(c,0,ax.axis()[-1]*1.1,linestyles='--',lw=3.)
    ax.fill_between(xi,f1.pdf(xi),where=xi>c,alpha=.3,color='g')
    ax.fill_between(xi,f0.pdf(xi),where=xi>c,alpha=.3,color='b')
    ax.axis(xmin=-3,xmax=5)
    crange = linspace(-3,5,50)
    ax=axs[1]
    ax.plot(1-f0.cdf(crange),1-f1.cdf(crange))
    ax.plot(1-f0.cdf(c),1-f1.cdf(c),'o',ms=15.)
    ax.set_xlabel('False-alarm probability')
    ax.set_ylabel('Detection probability')

interact(plot_roc_interact,c=(-3,5,.05))

print 'p-value ',stats.wilcoxon(f1.rvs(30),f0.rvs(30))[1]