in recent years, some statisticians have studied the signal detection problem by using the random field theory. in this paper we have considered point estimation of the gaussian scale space random field parameters in the bayesian approach. since the posterior distribution for the parameters of interest dose not have a closed form, we introduce the markov chain monte carlo (mcmc) algorithm to ap...

one of the main distinctions between geomaterials and other engineering materials is the spatial variation of their properties in different directions. this characteristic of geomaterials -so called heterogeneity- is studied herewith. several spatial distributions are introduced to describe probabilistic variation of geotechnical properties of soils. among all, the absolute normal distribution ...

ABSTRACT. Siegmund and Worsley (1995) considered the problem of testing for a signal with unknown location and scale in a Gaussian random field defined on N . The test statistic was the maximum of a Gaussian random field in an N 1 dimensional ‘scale space’, N dimensions for location and 1 dimension for the scale of a smoothing kernel. Siegmund and Worsley used two methods, one involving the exp...

Siegmund and Worsley considered the problem of testing for a signal with unknown location and scale in a Gaussian random field defined on RN . The test statistic was the maximum of a Gaussian random field in an (N + 1)-dimensional “scale space,” N dimensions for location and one dimension for the scale of a smoothing kernel. Siegmund and Worsley used two methods, one involving the expected Eule...

A novel nonlinear scale space framework is proposed for the purpose of multi-scale image representation. The scale space decomposition problem is formulated as a general Bayesian least-squares estimation problem. A quasi-random density estimation approach is introduced for estimating the posterior distribution between consecutive scale space realizations. In addition, the application of the pro...

We introduce a class of multi-scale models for random fields. The novel framework couples standard Markov models for the random field stochastic process at different levels of resolution, and links them via error models to induce a new and rich class of structured linear models reconciling modelling and information at different levels of resolution. Jeffrey’s rule of conditioning is used to rev...