  The development of global sensitivity analysis of numerical model outputs has
recently raised new issues on 1-dimensional Poincar\'e inequalities. Typically
two kind of sensitivity indices are linked by a Poincar\'e type inequality,
which provide upper bounds of the most interpretable index by using the other
one, cheaper to compute. This allows performing a low-cost screening of
unessential variables. The efficiency of this screening then highly depends on
the accuracy of the upper bounds in Poincar\'e inequalities. The novelty in the
questions concern the wide range of probability distributions involved, which
are often truncated on intervals. After providing an overview of the existing
knowledge and techniques, we add some theory about Poincar\'e constants on
intervals, with improvements for symmetric intervals. Then we exploit the
spectral interpretation for computing exact value of Poincar\'e constants of
any admissible distribution on a given interval. We give semi-analytical
results for some frequent distributions (truncated exponential, triangular,
truncated normal), and present a numerical method in the general case. Finally,
an application is made to a hydrological problem, showing the benefits of the
new results in Poincar\'e inequalities to sensitivity analysis.
