A MAP method with nonparametric priors for estimating P-S-N curves

A Bayesian Nonparametric Method for estimating P-S-N curves is proposed in order to minimize the time and the number of specimens required for laboratory testing. Although the distributions of each stress level cannot be expressed as a single distribution, they are likely to follow some same distributional shape. A reasonable consideration is that how to use the history test data to construct a prior distribution. Once this prior distribution is known, inference can be made in an almost mechanic way by integrating out parameters to find the predictive distributions. Therefore, the prior distribution is the key to the estimation and its determination is the most important step. In order to obtain the prior, the Dirichlet process nonparametric model is used in this paper. The MAP method with the non-parametric priors shows several advantages over the maximum likelihood method. It takes a priori information into consideration, and the nonparametric models can avoid the arbitrariness and possibly unverifiable assumptions inherent in parametric models.