An Analysis upon Concept and Basics of Probability Theory: A Review | Original Article

ABSTRACT:

In recent years probabilistic knowledge-based systems such as Bayesian networks and influence diagrams have come to the fore as a means of representing and reasoning about complex real-world situations. Although some of the probabilities used in these models may be obtained statistically, where this is impossible or simply inconvenient, modellers rely on expert knowledge. Experts, however, typically find it difficult to specify exact probabilities and conventional representations cannot reflect any uncertainty they may have. In this way, the use of conventional point probabilities can damage the accuracy, robustness and interpretability of acquired models. In talking about no discrete probability spaces, it is difficult to avoid measure-theoretic concepts. However, to develop extensive formal machinery from measure theory before going into probability (as is done in most graduate programs in mathematics) would be inappropriate for the particular audience to whom the book is addressed. Thus I have tried to suggest, when possible, the underlying measure-theoretic ideas, while emphasizing the probabilistic way of thinking, which is likely to be quite novel to anyone studying this subject for the first time.