Multiple sums and integrals as neutral BKP tau functions

We consider multiple sums and multi-integrals as tau functions of the BKP hierarchy using neutral fermions as the simplest tool for deriving these. The sums are over projective Schur functions $Q_{\alpha }$ for strict partitions $\alpha$. We consider two types of such sums: weighted sums of $Q_{\alpha }$ over strict partitions $\alpha$ and sums over products $Q_{\alpha }{Q}_{\gamma }$. In this way we obtain discrete analogues of the beta-ensembles ($\beta =1,2,4$). Continuous versions are represented as multiple integrals. Such sums and integrals are of interest in a number of problems in mathematics and physics.