In this graduate student talk, basic ideas and examples on Bayesian numerical analysis will be introduced. The interest on the interface of Probabilistic integration and numerical methods dates back to Poincare(1896), while this idea got popular starting from late 20th century. In this talk, I will mainly review the paper of Diaconis(1988) and the results cited therein. We will see the idea of Poincare for the interpolation from the Bayesian perspective when we have some expensive integration to evaluate. Then we will come to the Eberlein's approach on quadrature to this problem, which is now viewed as the standard Bayesian quadrature.