  In this article the issues are discussed with the Bayesian approach,
least-square fits, and most-likely fits. Trying to counter these issues, a
method, based on weighted confidence, is proposed for estimating probabilities
and other observables. This method sums over different model parameter
combinations but does not require the need for making assumptions on priors or
underlying probability functions. Moreover, by construction the results are
invariant under reparametrization of the model parameters. In one case the
result appears similar as in Bayesian statistics but in general there is no
agreement. The binomial distribution is also studied which turns out to be
useful for making predictions on production processes without the need to make
further assumptions. In the last part, the case of a simple linear fit (a
multi-variate example) is studied using the standard approaches and the
confidence weighted approach.
