The Potential Distortion of Bayesian Reasoning

The Bayesian theorem was formulated in the 18th century and has been adopted as the theoretical basis of uncertainty management as well as the stochastic foundation for forecast-oriented expert systems. Through Bayesian reasoning, people accumulate evidences and draw hypothetical conclusions according to the evidences being observed within the problem domain. Mathematically, the reasoning steps can be represented by a sequence of probabilistic computations. However, without a good mapping to human mental models, Bayesian reasoning is neither nature nor intuitive. To reduce the mathematical complexity and make it workable with human mental models, an assumption is usually made. This assumption does simplify the probabilistic computation and make it more manageable from the perspective of human cognition. Nevertheless, the simplification also somehow introduces errors to the computation and makes it distorted from the real probabilistic result. The range of this potential error depends on how well is the assumption fitted to the real case being dealt with. In this paper, I present cases of probabilistic computations to elicit the range of the potential probabilistic distortion caused by Bayesian assumption. Instead of involving the detail but tedious probabilistic computations, I use graphical approach to visualize the distortion being introduced to the result by showing cases from best-fitted, partial-fitted to worst-fitted