Variance estimation is central to many questions in finance and economics. Until now ex post variance estimation has been based on infill asymptotic assumptions that exploit high-frequency data. This article offers a new exact finite sample approach to estimating ex post variance using Bayesian nonparametric methods. In contrast to the classical counterpart, the proposed method exploits pooling over high-frequency observations with similar variances. Bayesian nonparametric variance estimators under no noise, heteroskedastic and serially correlated microstructure noise are introduced and discussed. Monte Carlo simulation results show that the proposed approach can increase the accuracy of variance estimation. Applications to equity data and comparison with realized variance and realized kernel estimators are included
