Bayesian algorithms for one-dimensional global optimization

In this paper Bayesian analysis and Wiener process are used in order to build an algorithm to solve the problem of global optimization. The paper is divided in two main parts. In the first part an already known algorithm is considered: a new (Bayesian) stopping rule is added to it and some results are given, such as an upper bound for the number of iterations under the new stopping rule. In the second part a new algorithm is introduced in which the Bayesian approach is exploited not only in the choice of the Wiener model but also in the estimation of the parameter sigma(2) of the Wiener process, whose value appears to be quite crucial. Some results about this algorithm are also given.