Do nhu cầu tính toán vốn có trong việc đưa ra phương pháp phản ứng nhanh hơn, nhiều dấu vết tìm kiếm không phải là hữu ích và chúng ta nên đưa ra các quy tắc tìm kiếm heuristic. Các phản ứng của các cấp độ hoạt động chỉ ra rằng chúng ta chỉ có thể giải quyết vấn đề với một vài biến hoặc một chức năng đơn giản mục tiêu. | 150 MODELLING UNCERTAINTY and we know a priori the probabilities for the hypothesis P H the evidence P E and the evidence assuming the hypothesis is true P E H . Bayes theorem gives us now the probability of the hypothesis based on the evidence P H E P HC E P E which we can rewrite as P E H P H P H E J 1 P E More generally if we have a set of n hypotheses H0 H1 . Hn-1 Bayes theorem can be restated as P P E Hi -P Hi E n-iPEH Hj provided that the whole event space equals ui 0 Hi Hi n Hj 0 when i j and P E 0. Bayes theorem has assumptions that restrict its usability First all the statistical data regarding the evidence with the various hypotheses is assumed to be known. Because Bayesian reasoning requires complete and up-to-date probabilities we have to adjust them whenever we find a new connection between a hypothesis and an evidence. Second the terms P E Hi must be independent of one another . the hypotheses are alternative explanations for the evidence . Both of these assumptions can be quite problematic to establish in the real world. Let us take a simple but instructive example of Bayes theorem. Suppose there is a 10 probability that an alpha-tested computer game has a bug in it. From past experience we have observed that the likelihood of a detected bug to have resulted from an actual bug in the program is 90 . The likelihood of detecting a bug when it is not present . it is caused by the test arrangement is 10 . Now the components are as follows H - there is a bug in the code E - a bug is detected in the test E H - a bug is detected in the test given that there is a bug in the code H E - there is a bug in the code given that a bug is detected in the test. The known probabilities are as follows P H P E H P E H . By using the law of total probability we can calculate for partitions H and H P E P E H P H P E H P H . MODELLING UNCERTAINTY 151 To get the probability of detecting an actual bug in the code we apply Equation .
