POTENTIAL OF BAYE’S THEOREM IN ERE

ABSTRACT

In probability theory and statistics, Bayes’ theorem (alternatively Bayes’ law or Bayes’ rule) describes the probability of an event, based on conditions that might be related to the event. For example, suppose one is interested in whether a person has cancer, and knows the person’s age. If cancer is related to age, then, using Bayes’ theorem, information about the person’s age can be used to more accurately assess the probability that they have cancer. When applied, the probabilities involved in Bayes’ theorem may have different probability interpretations. In one of these interpretations, the theorem is used directly as part of a particular approach to statistical inference. With the Bayesian probability interpretation the theorem expresses how a subjective degree of belief should rationally change to account for evidence: this is Bayesian inference, which is fundamental to Bayesian statistics. However, Bayes’ theorem has applications in a wide range of calculations involving probabilities, not just in Bayesian inference. The paper illustrates, via four independent examples, the (potential) utility of Bayes’ rule in ERE. Due to the currently insufficient availability of appropriate experimental information in the research literature, hypothetical numerical data are employed with the sole purpose of indicating the course of analysis to which appropriate experimental data could be subjected. With the intention of stimulating at least a modest appetite at present for Bayes’ rule, the illustrations are realistic but uncomplicated on purpose. Specific exploratory applications to electrochemical processes and technology at various levels of complexity are relatively recent.

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