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## Correct procedure

In order to solve the problem consistently with our beliefs, we have to avoid the intermediate inference9.5 on , and write prior and likelihood directly in terms of :

 (9.18)

with    constant. Let us do it again with Mathematica:
(********************************************************)
(* Now let's do it right: *)

lik=Exp[-lambda]
norm=NIntegrate[lik, {m, 0, eba}]

(* fa(m) is the final distribution from experiment A,
under the condition that m < eba *)

fa=lik/norm
Plot[fa, {m, 0.06, eba}, AxesLabel -> {m, f}]
(********************************************************)

The final distribution is shown in Fig. . It is now reasonable and consistent with the expectations: The values of mass which are less believable are those which could have been produced easier, given the kinematics. From we can calculate several results, for example a 95% upper limit, the average and the standard deviation:
(********************************************************)
NIntegrate[fa, {m, 0, 0.0782}]
ava = NIntegrate[m*fa, {m, 0, eba}]
stda = Sqrt[NIntegrate[m*fa, {m, 0, eba}] - ava^2]
(********************************************************)

We get:
 with 95% probability (9.19) E (9.20) (9.21)

Next: Interpretation of the results Up: Constraining the mass of Previous: Naïve procedure   Contents
Giulio D'Agostini 2003-05-15