Bayesian models are challenging to implement on hardware with the conventional design methodologies due to their high computational complexity. Conventional digital architectures are designed for deterministic computation and are not optimal for implementing probabilistic algorithms on hardware. In this work, we propose an alternative method to implement the probabilistic algorithms such as Bayesian models on hardware using a stochastic computation (SC) framework. This framework leverages on the probabilistic nature of the Bayesian models and facilitates the implementation of complex probabilistic models using simple logic gates. From an application standpoint, we propose a novel Bayesian source localization model (BSLM) that estimates a source's position in a noisy environment by solving the Bayesian recursive equation implemented on Field Programmable Gate Array (FPGA) with low resource utilization. The proposed SC design framework will pave the way to build complex probabilistic algorithms for real-time edge computing applications.