Public sentiment is a direct public-centric indicator for the success of effective action planning. Despite its importance, systematic modeling of public sentiment remains untapped in previous studies. This research aims to develop a Bayesian-based approach for quantitative public sentiment modeling, which is capable of incorporating uncertainty and guiding the selection of public sentiment measures. This study comprises three steps: (1) quantifying prior sentiment information and new sentiment observations with Dirichlet distribution and multinomial distribution respectively; (2) deriving the posterior distribution of sentiment probabilities through incorporating the Dirichlet distribution and multinomial distribution via Bayesian inference; and (3) measuring public sentiment through aggregating sampled sets of sentiment probabilities with an application-based measure. A case study on Hurricane Harvey is provided to demonstrate the feasibility and applicability of the proposed approach. The developed approach also has the potential to be generalized to model various types of probability-based measures.