New framework for Bayesian statistical analysis and interpolation of residual stress measurements

•Various measured residual stress data are analyzed using Bayesian statistical approach.•The simplicity and accuracy of different probability density functions are compared.•Modified Shepard method with new interpolant and weight functions is used to interpolate data.

In the present study, different residual stress and strain data measured from various techniques are analyzed using a Bayesian statistical approach and finally interpolated utilizing modified Shepard method. This research is carried out to compare the capability, simplicity and accuracy of Bayesian approach with different probability density functions. Three different probability density functions: Gaussian, Cauchy and Sivia's distribution are studied and compared here. Finally the modified Shepard method is utilized with new interpolant and weight functions, to interpolate the scattered measured data. The proposed framework is then applied to two sets of measured residual data obtained from various experimental techniques.