Estimation of peak ground acceleration is one of the main issues in civil and earthquake engineering practice. The Boore-Joyner-Fumal empirical formula is well known for this purpose by estimating the peak ground acceleration using information such as the magnitude of earthquake, the site-to-fault distance and the site foundation properties. The complexity of this prediction formula is investigated in this study. For example, should we use a first-order or a second-order polynomial for the earthquake magnitude? It is obvious that a more complicated prediction model class (i.e., a formula with more free parameters) possesses smaller fitting error for a set of data. However, this does not imply that the complicated predictive formula is more realistic since over-fitting may occur if there are too many free parameters. In this chapter we propose to use the Bayesian probabilistic model class selection approach to obtain the most suitable prediction model class for the seismic attenuation formula. In this approach, each prediction model class is evaluated by the plausibility given the dataset. A complicated model class is penalized by the "Ockham factor", which is a natural consequence of the aforementioned plausibility, instead of any ad-hoc penalty terms. The optimal model class is robust in the sense that there is balance between the data fitting capability and the sensitivity to noise. A database of strong-motion records, obtained from the China Earthquake Data Center, is utilized for the analysis. The optimal prediction model class and its most plausible model parameters are determined. Quantification of the uncertainty of the parameters is allowed by the Bayesian probabilistic methodology and this can be used for uncertainty analysis of the predicted peak ground acceleration. It turns out that the optimal model class is simpler than the full order attenuation model suggested by Boore, Joyner and Fumal (1993). © 2008 Nova Science Publishers, Inc.