In their simplest form, sensors are transducers that convert physical phenomena into electrical signals. By combining recent innovations in wireless technology, distributed computing, and transducer design, grids of sensors equipped with wireless communication can monitor large geographical areas. However, just getting the data is not enough. In order to react intelligently to the dynamics of the physical world, advances at the lower end of the computing spectrum are needed to endow sensor grids with some degree of intelligence at the sensor and the network levels. Integrating sensory data into representations conducive to intelligent decision making requires significant effort. By discovering relationships between seemingly unrelated data, efficient knowledge representations, known as Bayesian networks, can be constructed to endow sensor grids with the needed intelligence to support decision making under conditions of uncertainty. Because sensors have limited computational capabilities, methods are needed to reduce the complexity involved in Bayesian network inference. This paper discusses methods that simplify the calculation of probabilities in Bayesian networks and perform probabilistic inference with such a small footprint that the algorithms can be encoded in small computing devices, such as those used in wireless sensors and in personal digital assistants (PDAs).