Selection of the Predictive Model Class

In order to examine the suitability of the predictive model class in Equation (6.75) and to propose the most suitable one, model class candidates are constructed. Here, predictive model classes are considered in a similar functional form of Equation (6.75) but to include different combinations of terms in different model classes. Eirst of all, the constant b is necessary to serve as a scaling factor of the PGA for any model class so all model classes contain b. As will be discussed later in Section 6.5.3.1 that only strong-motion records with moment magnitude M 3.5 are utilized, Mq = 3.5 is taken in this study. Eor the site properties, the terms b Gs and bjGc are either included or excluded together in a model class. Therefore, there are 2 = 32 model class candidates, namely Ci, C2, , C32. 

Let V denote the data that include the measured PGA and the corresponding earthquake magnitude, observation station-to-hypocenter distance and site foundation properties. 

Bayesian Methods for Structural Dynamics and Civil Engineering 

By solving the following simultaneous linear algebraic equations 97g(b V, Cj)/dbi = 0, I = 1,2. Nb, the closed-form solution of the most probable coefficient vector b can be 

Similarly, the most plausible value of the predictive/fitting error variance can be found by solving dp 6 V, Cj) da = 0 and is readily obtained by  

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