The document discusses modeling retail demand when out-of-stock situations are partially observed. It proposes a joint model of sales and availability that accounts for consumer heterogeneity and substitution. The model is estimated using a Gibbs sampling approach on aggregate store data to simulate individual choices constrained by sales and inventory data. Empirical results show the model can estimate lost sales due to out-of-stocks more accurately than ignoring availability. Extensions including backorders, price endogeneity and in-store shopping behavior are also discussed.