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Paper aims at establishing probability distributions of intensities and other earthquake parameters which are related to the probability distribu tions of structural responses at given locations and times intervals. The nor mal scarcity of records precludes a straight-forward statistical treatment. Rather, prior distributions of magnitudes in relevant volumes of the earth are established on the basis of major geologic features; through use of Bayes' theorem, statistical information is incorporated to obtain posterior distribu tions of magnitudes; semiempirical formulas lead then to probability dis. tribu tions of intensities and of other parameters at stations of interest. A new applications of Bayes' theorem permits incorporating available information about past earthquakes at those stations.