A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.Comment: Published in at http://dx.doi.org/10.1214/12-STS406 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

The role of microstructure and phase distribution in the failure mechanisms and life prediction model for PSZ coatings

Partially Stabilized Zirconia (PSZ) may become widely used for Thermal Barrier Coatings (TBC). Failure of these coatings can occur due to thermal fatigue in oxidizing atmospheres. The failure is due to the strains that develop due to thermal gradients, differences in thermal expansion coefficients, and oxidation of the bond coating. The role of microstructure and the cubic, tetragonal, and monoclinic phase distribution in the strain development and subsequent failure will be discussed. An X-ray diffraction technique for accurate determination of the fraction of each phase in PSZ will be applied to understanding the phase transformations and strain development. These results will be discussed in terms of developing a model for life prediction in PSZ coatings during thermal cycling

A Model for Converting Dilatometric Strain Measurements to the Fraction of Phase Formed During the Transformation of Austenite to Martensite in Powder Metallurgy Steels

A model is developed to allow converting dilatometric strains that occur during the continuous cooling transformation (CCT) of austenite to martensite to volume fraction martensite formed in powder metallurgy steels. Unlike existing models, this model can accurately account for the observed decrease in the measured transformation strain with increased porosity. As a demonstration, the model is used to accurately calculate the volume fraction of martensite formed during the CCT of austenite to martensite in FL-4605 PM steel