In this paper, seismic hazard analysis is performed from a Bayesian perspective. First, by using historical seismic records, the relationship between peak ground acceleration and other important factors, such as magnitude of earthquake and hypocenter-to-site distance, arc, developed. Numerous studies were devoted to empirical relationship using the magnitude of earthquake, the site-to-fault distance and the site foundation properties. In this study, the Bayesianapproach is utilized to investigate the suitable form of empirical formula. It is obvious that a more complicated relationship (i.e. a formula with more free parameters) possesses smaller fitting error for a given set of data. However, this does not imply that the complicated relationship is more realistic since over-fitting may occur when the relationship has too many free parameters. The Bayesian model class selection method is used to identify, the most suitable relationship among all the candidate relationships. The plausibility of each candidate relationship is evaluated for a database of strong-motion records., obtained from the China Earthquake Data Center. The most plausible relationship is the one with the highest plausibility. It is robust since it has balance between the data fitting capability and the sensitivity,, to noise. It turns out that the most plausible relationship is simpler than the well known Boore-Joyner-Fumal seismic attenuation model. Parametric uncertainty is also quantified by the Bayesian probabilistic methodology. The most plausible Predictive formula provides a reliable basis for peak ground acceleration estimation. With the most plausible predictive formula and the uncertainty of the coefficients. Monte Carlo simulation can be performed to estimate the peak ground acceleration of a site and its uncertainty.