This article proposes a Bayesian estimation method of the demand function under block rate pricing, mainly focusing on increasing block rat epricing. Block rate pricing is often observed in public sectors, such as water and electricity. Under this price structure, price changes when consumption exceeds a certain threshold, and the demand function is subject to a piece wise-linear budget constraint. We apply a discrete/continuous choice model to analyze household behavior with such a price system and take a hierarchical Bayesian approach to estimate its demand function. Moreover, a separability condition is additionally considered to obtain proper estimates. The model is extended to allow random coefficients for panel data and spatial correlation to account for consumer heterogeneity of spatial data. The proposed method is applied to estimate the Japanese residential water demand function under increasing block rate pricing.