A Statistical Analysis of Morse Wavelet Coherence

Published versio

A Statistical Study of Temporally Smoothed Wavelet Coherence

Published versio

Analysis of point based image registration errors with applications in single molecule microscopy

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data.</p

Devising a fairer method for adjusting target scores in interrupted one-day international cricket

One-day international cricket matches face the problem of weather inter- ruption. In such circumstances, a so-called rain rule is used to decide the outcome. A variety of approaches for constructing such rules has been pro- posed, with the Duckworth-Lewis method being preferred in the sport. There are a number of issues to consider in reasoning about the e ↵ ectiveness of a rain rule, notably accuracy (does the rule make the right decision?) and fairness (are both teams treated equally?). We develop an approach that is a hybrid of resource-based and so-called probability-preserving approaches and provide empirical evidence that this hybrid method is superior in terms of fairness while competitive in terms of accuracy