Typo in smeared likelihood

[Roberto Trotta]

One of our users pointed out:

[***Question begins***]
In your paper (hep-ph/0602028, equ. 3.5) you have the likelyhood as:

sigma/sqrt(sigma^2 + tau^2)*exp((E_lim -E)^2/(2(sigma^2 +
tau^2)))*(1.0-Z_(t_lim)) + Z((x0-y)/tau)

where t_lim and Z(t_lim) was defined on equation 3.6. In the
Smearedbound function in SuperBayes, this quantity is multiplied by
sqrt(2 pi)*sigma:

lnprob = -LOG(sigma/sqrt((sigma**2+tau**2))*EXP(exparg)*(1-
Z_func(tstar)) + Zfunc2)

But, if this the whole quantity is multiplied by sqrt(2 pi)*sigma,
shouldn't the second term also be multiplied by this factor? In other
words:

lnprob = -LOG(sigma/sqrt((sigma**2+tau**2))*EXP(exparg)*(1-
Z_func(tstar))+ sqrt(2d0*pi)*sigma*Zfunc2)

[***Question ends***]

There is a regrettable typo in Eq. (3.5) of hep-ph/0602028, which
actually should read:

1/sqrt(2pi(sigma^2 + tau^2))*exp((E_lim - E)^2/(2(sigma^2 +
tau^2)))*(1.0-Z_(t_lim)) + Z((x0-y)/tau)/(sqrt(2pi)sigma)

The extra factor in the second term ensures the proper normalization.

In the code this is mutliplied by the constant sqrt(2pi)sigma, hence
the lnprob formula in the like, which is correct.