1. A method for posterior estimation of variables in water distribution networks, the method comprising: receiving, by one or more processors, a set of data inputs based on information received from one or more sensors within a water distribution system; determining, by the one or more processors, a first model of the water distribution network based on the set of data inputs, uncertainty information, and design parameters, wherein the design parameters comprise a rating associated with a distribution pump, a design output pressure associated with the distribution pump, a number of branches within the water distribution system, a number of branch connections within the water distribution system, and one or more elevations associated with the water distribution network; determining, by the one or more processors, a second model of the water distribution network based on the set of data inputs, and the first model; performing, by the one or more processors, a real-time recursive posterior estimation of the first model, wherein the recursive posterior estimation process continuously increases accuracy of a statistical distribution associated with the first model; displaying, by the one or more processors, the recursive posterior estimation to a user; and causing, by the one or more processors, the user to be notified of a malfunction of a piece of equipment within the water distribution system.