Bayesian analysis of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi>Sr</mml:mi><mml:mprescripts/><mml:none/><mml:mn>86</mml:mn></mml:mmultiscripts><mml:mo>(</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>)</mml:mo></mml:mrow>

The Alpha Optical Model Potential (\aomp \!) is a phenomenological approach used to describe elastic scattering where multiple reaction channels are open. It is one of the most critical inputs for the calculation of thermonuclear reaction rates in explosive stellar environments, but uncertainties within the $\alpha$-OMP lead to imprecise predictions hindering comparisons between calculations and observations. In order to improve the precision of the $\alpha$-OMP, additional nuclear physics data are required. In this paper, a measurement of the $^{86}$Sr($\alpha$, $\alpha$) elastic scattering cross section at multiple energies is reported. A local optical potential is constructed via a fully Bayesian analysis of the elastic scattering data. The resulting uncertainties on the low energy cross sections relevant to nuclear astrophysics are then calculated and shown to be on the order of $50 \%$.