This paper addresses the problem of prediction of grade variables over volumes (block estimation) for an autonomous mine. Resource estimation is usually concerned with the prediction of the quality of material over volumes (blocks in resource models). This problem is tackled by developing Bayesian block estimation with the Gaussian processes (GPs) framework. GPs are commonly used for nonparametric regression and classification and offer an elegant solution to deal with incomplete knowledge and information. A GP is defined by its mean and covariance function. The parameters of the covariance function can be learnt by maximising the marginal likelihood of the data. This offers a way of automating the covariance fitting process, while at the same time allowing for an assessment of how well the covariance function fits the data. Within the GP framework the calculation of the average grade over a volume can be performed using Bayesian quadrature, which treats an integral as a random variable. First, it is demonstrated that the block kriging equations in geostatistics are the same as Bayesian quadrature. Then, it is determined when closed form analytical solutions for the integrals are possible and quadrature approaches for approximations are briefly discussed.