When using household-level data to examine consumer demand it is common to find that consumers purchase only a subset of the available goods, setting the demand for the remaining goods to zero. Ignoring such censoring of the dependent variables can lead to estimators with poor statistical properties and estimates that lead to poor policy decisions. In this paper we investigate household demand for four types of breakfast cereals, such as whole grain ready-to-eat, non-whole grain ready-to-eat, whole grain hot and non-whole grain hot cereals, using a censored Al- most Ideal Demand System (AIDS) and estimate the parameters of the model via Bayesian methods. Using household level scanner data (ACNielsen Homescan) we find that demand for all types of breakfast cereals is inelastic to changes in prices. The expenditure elasticity is slightly above unity for the whole grain ready-to-eat cereals suggesting that as the expenditure on cereals increases households will allocate proportionally more on whole-grain ready-to-eat cereals and less on other cereals.