Two measures of the influence of the prior distribution p(θ) in Bayes estimation are proposed. Both involve comparing with alternative priors proportional to p(θ), for s ≥ 0. The first one, the influence curve for the prior distribution is simply the curve of parameter values which are obtained as estimates when the estimation is made using p(θ) instead of p(θ). It measures the overall influenc...

Curve estimation from observed noisy data has broad applications. In certain applications, the underlying regression curve may have singularities, including jumps and roofs/valleys (i.e., jumps in the first order derivative of the regression curve), at some unknown positions, representing structural changes of the related process. Detection of such singularities is important for understanding t...

Abstract In 2006, the Special Region of Yogyakarta was shaken by a destructive earthquake. The United States Geological Survey (USGS) recorded that earthquake had magnitude 6.3 M w at depth 12.5 km below surface triggered strike slip fault activity. severe damage occurred in Bantul district and Klaten district, where area location were far from epicenter. This proves source distance are not onl...