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Large deviations estimates forsome level crossing probabilities in Bayesian setting

The probabilities of rare events have 
interest in some network and risk 
problems and, in this paper, we 
concentrate our attention on some 
level crossing probabilities for 
Brownian motion and for Poisson 
process. We are interested in large 
deviation estimates and we present the Bayesian and the frequentist approaches 
which lead to different conclusions; 
more precisely, as argued in other works 
in the literature on this topic, the 
Bayesian approach is more conservative. 
In the Bayesian framework we always deal 
with conjugate families of prior 
distributions.