Wavelet shrinkage is an effective nonparametric regression technique, especially when the underlying curve has irregular features such as spikes or discontinuities. The basic idea is simple: take the discrete wavelet transform (DWT) of data consisting of a signal corrupted by noise; shrink or remove the wavelet coefficients to remove the noise; and then… (More)
We use cumulants to derive Bayesian credible intervals for wavelet regression estimates. The first four cumulants of the posterior distribution of the estimates are expressed in terms of the observed data and integer powers of the mother wavelet functions. These powers are closely approximated by linear combinations of wavelet scaling functions at an… (More)
SUMMARY We extend the optimal symmetric group sequential tests of Eales & Jennison (1992) to the broader class of asymmetric designs. Two forms of asymmetry are considered, involving unequal type I and type II error rates and different emphases on expected sample sizes at the null and alternative hypotheses. We discuss the properties of our optimal designs… (More)
1 Wavelets in one and two dimensions Wavelets are a special type of basis function which are localised in both time and frequency. To generate a wavelet basis, a mother wavelet Two dimensional data such as images can be decomposed with respect to a more complicated wavelet basis which is still determined solely by the choice of mother wavelet Although the… (More)
Horizontal shifts in the top layer of highly oriented pyrolytic graphite, induced by a scanning tunneling microscope (STM) tip, are presented. Excellent agreement is found between STM images and those simulated using density functional theory. First-principle calculations identify that the low-energy barrier direction of the top layer displacement is toward… (More)
This report details the results of extensive simulations carried out to compare the wavelet shrinkage methods proposed by Barber & Nason (2003) to a range of other existing wavelet shrinkage techniques.
One of the key ingredients in drug discovery is the derivation of conceptual templates called pharmacophores. A pharmacophore model characterises the physico-chemical properties common to all active molecules, called ligands, bound to a particular protein receptor, together with their relative spatial arrangement. Motivated by this important application, we… (More)
We develop a Bayesian model for the alignment of two point configurations under the full similarity transformations of rotation, translation and scaling. Other work in this area has concentrated on rigid body transformations, where scale information is preserved, motivated by problems involving molecular data; this is known as form analysis. We concentrate… (More)