82 - Statistical Principles for Seismologists

This chapter discusses statistical principles used by seismologists. Seismology is primarily an observational science; its scientists rarely have the opportunity to control the levels of variables (such as temperature, stress, or depth) that might influence their results. Consequently, classical design considerations, which dominate the subjects of agricultural trials or sample surveys, play a relatively minor role in most seismological experiments. The groundwork for any statistical analysis is laid by the careful summary and display of data. Probability has been interpreted as the strength of belief associated with members of a family of propositions, the asymptotic relative frequency of different outcomes from a repeated experiment, and an abstract measure associated with members of a family of admissible subsets. Model fitting involves finding that member of a chosen class of models, which in some sense is “closest” to a given data set (sample). Usually the class of models is a parametric family, the members of which are defined up to a small number of numerical parameters. The model testing stage involves checking the agreement between selected features of the model and the corresponding features of the sample. A test is specified by computing an appropriate “distance” (the test statistic) between the sample and model features selected. Bayesian methods provided the first and still the most logically attractive approach to the “inverse problem’ of probability: Given the data, establish probability statements concerning the parameters.

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