  Bayesian optimization (BO) is a popular algorithm for solving challenging
optimization tasks. It is designed for problems where the objective function is
expensive to evaluate, perhaps not available in exact form, without gradient
information and possibly returning noisy values. Different versions of the
algorithm vary in the choice of the acquisition function, which recommends the
point to query the objective at next. Initially, researchers focused on
improvement-based acquisitions, while recently the attention has shifted to
more computationally expensive information-theoretical measures. In this paper
we present two major contributions to the literature. First, we propose a new
improvement-based acquisition function that recommends query points where the
improvement is expected to be high with high confidence. The proposed algorithm
is evaluated on a large set of benchmark functions from the global optimization
literature, where it turns out to perform at least as well as current
state-of-the-art acquisition functions, and often better. This suggests that it
is a powerful default choice for BO. The novel policy is then compared to
widely used global optimization solvers in order to confirm that BO methods
reduce the computational costs of the optimization by keeping the number of
function evaluations small. The second main contribution represents an
application to precision medicine, where the interest lies in the estimation of
parameters of a partial differential equations model of the human pulmonary
blood circulation system. Once inferred, these parameters can help clinicians
in diagnosing a patient with pulmonary hypertension without going through the
standard invasive procedure of right heart catheterization, which can lead to
side effects and complications (e.g. severe pain, internal bleeding,
thrombosis).
