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In order to solve the problem consistently with our beliefs, we
have to avoid the intermediate
inference^{9.5}
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}]
(********************************************************)
Figure:
Inference on obtained from a direct inference
on , starting from a uniform prior in this quantity.

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
20030515