The Debiased Spatial Whittle likelihood.

We provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased Spatial Whittle likelihood, makes important corrections to the well-known Whittle likelihood to account for large sources of bias caused by boundary effects and aliasing. We generalize the approach to flexibly allow for significant volumes of missing data including those with lower-dimensional substructure, and for irregular sampling boundaries.

Network histograms and universality of blockmodel approximation.

In this paper we introduce the network histogram, a statistical summary of network interactions to be used as a tool for exploratory data analysis. A network histogram is obtained by fitting a stochastic blockmodel to a single observation of a network dataset. Blocks of edges play the role of histogram bins and community sizes that of histogram bandwidths or bin sizes.

A DNA methylation network interaction measure, and detection of network oncomarkers.

Epigenetic processes--including DNA methylation--are increasingly seen as having a fundamental role in chronic diseases like cancer. DNA methylation patterns offer a route to develop prognostic measures based directly on DNA measurements, rather than less-stable RNA measurements. A novel DNA methylation-based measure of the co-ordinated interactive behaviour of genes is developed, in a network context.

Corruption of the intra-gene DNA methylation architecture is a hallmark of cancer.

Epigenetic processes--including DNA methylation--are increasingly seen as having a fundamental role in chronic diseases like cancer. It is well known that methylation levels at particular genes or loci differ between normal and diseased tissue. Here we investigate whether the intra-gene methylation architecture is corrupted in cancer and whether the variability of levels of methylation of individual CpGs within a defined gene is able to discriminate cancerous from normal tissue, and is associated with heterogeneous tumour phenotype, as defined by gene expression.

The memory of spatial patterns: changes in local abundance and aggregation in a tropical forest.

The current spatial pattern of a population is the result of previous individual birth, death, and dispersal events. We present a simple model followed by a comparative analysis for a species-rich plant community to show how the current spatial aggregation of a population may hold information about recent population dynamics. Previous research has shown how locally restricted seed dispersal often leads to stronger aggregation in less abundant populations than it does in more abundant populations.

Hyperanalytic denoising.

A new threshold rule for the estimation of a deterministic image immersed in noise is proposed. The full estimation procedure is based on a separable wavelet decomposition of the observed image, and the estimation is improved by introducing the new threshold to estimate the decomposition coefficients. The observed wavelet coefficients are thresholded, using the magnitudes of wavelet transforms of a small number of "replicates" of the image.

Noise reduction in directional signals using multiple morse wavelets illustrated on quadrature Doppler ultrasound.

The use of multiple complex-valued Morse wavelets for the scalogram study of signals which are unidirectional at any time, but are bidirectional overall is considered. These wavelets are well-suited to identifying the forward and reverse components. Scalogram averaging which is possible due to the multiplicity of the complex-valued wavelets leads to a scalogram with reduced noise.