CF in Rules

Confidence factors are also used to measure the degree of uncertainty in rules. Most of the rules in ECliPS are based in information that comes from empirical studies, which provide a large body of circumstantial evidence about the climate system. Many of those works are case studies involving a combination of synoptic, statistical, and conceptual physical reasoning. This knowledge is often presented in the form of production (IF-THEN) rules that links evidence (e) and hypothesis (h):

IF e THEN h, CF = [0…100].

Typically, the hypothesis is a statement regarding a category of the forecast (or target) variable (e.g., h: temperature = above normal). The CF in this case represents a subjective probability, or "guesstimate," that if e is true, then h is true as well. A numerical value of the CF is based upon experience and available information about the relationship between climatic processes presented in the rule. If the quantitative data is available, conventional statistical techniques (for example, correlation analysis) may also be used to determine the strength of a relationship between climate variables, and thereby provide an estimate of the CF. 

In assigning CFs to the rules, it is very important to maintain consistency in their values throughout the knowledge base. If the correlation analysis is used, the correlation coefficient (r) is converted to the CF as follows:

CF = k (r – CL),

where k is the correction coefficient based on the number of observations, and CL is the 95% confidence level determined using the Student’s t-test. The value for k is taken from the normal cumulative distribution with the mean of and standard deviation of 6 as in this figure. For example, in a sample of 15 pairs of data and r = 0.8, CF = 69 * (0.80 - 0.51) = 20. 

The CF value should be reduced if there is a serial correlation in the data and/or the distribution is not normal. The CF may also reflect the quality of the data, the accuracy the statistical analysis, how convincing its interpretation is, and maybe just the gut feeling of the users. In the case of categorical variables, the probabilities or odds may be converted into CFs as discussed in the section CFs and Probabilities.