1977 年 30 巻 2 号 p. 179-185
Two kinds of probabilities p1 and p2 are considered in connection with the earthquake prediction, p1 is the probability that a prediction will be successful, and p2 is the probability that an earthquake will be predicted. Both “prediction” and “earthquake” have been defined by some criteria X and Y, respectively. The status of the prediction based on each observational element can be indicated by a point on the p1-p2 plane. The effectiveness of the prediction is related to p1 and p2 by an equation in the form E=p2(a-b/p1)-c where a, b and c are constants. If two or more observational elements are considered, p1 and p2 for the combined elements are calculated from p1 and p2 for each element under some assumptions. Formulas for such calculation have been derived. In these formulas the probability p0 that a random prediction (under criterion Y) will be successful plays an important role. For example, if a prediction is done when precursorlike anomalous phenomena are observed for two independent elements A and B, the probability of successful prediction is given by p1(A ∩ B)=1/1+(1/Ap1-1)(1/Bp1-1)/(1/p0-1) where Ap1 or Bp1 is the p1-value for element A or B alone. The effectiveness of the multielement prediction is discussed by using these formulas.