def asimov_mu_ts0(self,ts):
"""Return the value of the signal strength parameter for which
the TS (-2*lnL) for discovery is equal to the given value."""
smin = 1E-3
smax = 1E3
while self.asimov_ts0_signal(smax) < ts: smax *= 10
while self.asimov_ts0_signal(smin) > ts: smin *= 0.1
mu = find_fn_root(self.asimov_ts0_signal,smin,smax,ts)
mu_err = np.sqrt(mu**2/ts)
return (mu,mu_err)
nexcess = ns+nb-mub
nexcess[nexcess<=0] = 0
ts_mc = -2*(poisson_lnl(ns+nb,mub) - poisson_lnl(ns+nb,ns+nb))
ts_asimov = fn_qmu(mus+mub,mus+mub,mub)
ul_mc = np.zeros(ntrial)
alpha = 0.05
dlnl = pval_to_sigma(alpha)**2
for i in range(ntrial):
xroot = find_fn_root(lambda t: fn_qmu((ns+nb)[:,i],
(mub+nexcess)[:,i],
(mub+nexcess)[:,i]+t),0,100,dlnl)
ul_mc[i] = nexcess[i]+xroot
sigma_mu_fn = lambda t: np.sqrt(t**2/fn_qmu(mub,mub,mub+t))
ul_asimov_qmu = find_fn_root(lambda t: fn_qmu(mub,mub,mub+t),0,100,dlnl)
sigma = np.sqrt(ul_asimov_qmu**2/dlnl)
ul_asimov = 1.64*sigma
ul_asimov_upper = (1.64+1)*sigma
ul_asimov_lower = (1.64-1)*sigma
print 'SIGMA ', sigma