Bayesian methods and liquefaction Christian, John T.; Baecher, Gregory B.
Since the beginning of serious study of liquefaction in the 1960s, uncertainties in both observed data and in processing field and laboratory tests have been major concerns. Assigning reasonable coefficients of variation to the parameters and correction factors in the conventional deterministic analyses indicates that a site with SPT N values between 12 and 22 and deterministic factors of safety of 1.5 can actually have liquefaction probability above 20%. About a third of the variance in the factor of safety comes from uncertainty in the load (magnitude scaling, stress reduction factor, etc.), which is independent of the method used to estimate the resistance. Researchers have traditionally presented the results of case studies in the form of charts showing instances in which liquefaction did and did not occur and have developed relations to separate the two. Although the original researchers developed the separation lines informally, recent work has applied statistical methods, such as discriminant analysis and logistic regression or combinations of them. In their original form, these methods give the sampling distributions of the observed data (i.e., the probability of observing the data given the hypothesis) rather than the probability of the hypothesis given the data, but the engineer needs the latter, that is, the probability of liquefaction given a set of observations. Researchers have addressed this issue using Bayesian methods, adopting non-informative priors to develop the results. Published curves of liquefaction probabilities can thus be interpreted as likelihood ratios. Other, independent work demonstrates that geological, meteorological, and historical data can be used to develop prior liquefaction probabilities that are not non-informative, so it may not be necessary to assume a non-informative prior. The actual prior can then be combined with the previously developed likelihood ratios to provide rational probabilities of liquefaction.
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