A Bayesian way to solve the pdf selection problem: an application in geotechnical analysis

J.G.M. Kerstens
Faculty of Architecture Building and Planning, Technical University Eindhoven, the Netherlands

Single probability density functions (pdf) are often selected based on a best-fit approach or the minimum description length (MDL) theorem that finds its description by the theory of complexity by Kolmogorov. However, it often occurs that random data cannot be accurately described by any of the commonly used pdf's. In this paper a method is presented which solves the problem of selecting single pdf's by predicting the probability of contending pdf's true given the data. These probabilities are combined when drawing inferences. The new method is illustrated on the prediction of the ultimate limit state (bearing capacity) of a single foundation pile. The Bayesian statistical method for combining information on pile capacity with the results of full-scale tests has been applied to establish the probability of contending pdf's of the model uncertainty. The results obtained by the Level II method have been used to obtain partial factors. The application of the new method to a single pile case is shown to be successful and has indicated a number of possible further applications.

Key words: Bayesian analysis, multiparameter probability density function, pile foundation