(9.24) |

Taking a uniform prior, we get the following posterior:

(9.25) |

where comes from the integral . So, we get our solution () for . In general, the probability that is smaller than 1 and decreases for increasing . For the parameters of experiment the integral in the denominator is equal to 0.0058. Therefore, if, for example,

There is another reasoning which leads to the same conclusion. At the detector has zero sensitivity. For this reason, in case of null observation, this values gets the maximum degree of belief. As far as larger values are concerned, the odds ratios with respect to must be invariant, since they are not influenced by the experimental observations, i.e.

(9.26) |

Since we are using, for the moment, a uniform distribution, the condition gives:

(9.27) |

We easily get the result shown in
Fig. by this piece of *Mathematica* code:

(********************************************************) famax=fa/.m->eba f2a=If[m<eba, fa, famax] (* f2a(m) represents instead the (improper) distribution extended also for values larger that eba, in the light of a flat prior and of the Experiment A *) Plot[f2a, {m,0.06,0.15}] (********************************************************)

The curve is extended on the right side up to a limit which cannot be determined by this experiment, it could virtually go to infinity. For this reason the ratio of probabilities