Driving Markov chain Monte Carlo with a dependent random stream

Markov chain Monte Carlo is a widely-used technique for generating a dependent sequence of samples from complex distributions. Conventionally, these methods require a source of independent random variates. Most implementations use pseudo-random numbers instead because generating true independent variates with a physical system is not straightforward. In this paper we show how to modify some commonly used Markov chains to use a dependent stream of random numbers in place of independent uniform variates. The resulting Markov chains have the correct invariant distribution without requiring detailed knowledge of the stream's dependencies or even its marginal distribution. As a side-effect, sometimes far fewer random numbers are required to obtain accurate results.Comment: 16 pages, 4 figure

A rational spectral collocation method with adaptively transformed Chebyshev grid points

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are approximated by the locations of poles of Chebyshev-Padé approximants. Numerical experiments on two time-dependent problems, one with finite time blow-up and one with a moving front, indicate that the method far outperforms the standard Chebyshev spectral collocation method for problems whose solutions have singularities in the complex plan close to [-1,1]

A nonparametric HMM for genetic imputation and coalescent inference

Genetic sequence data are well described by hidden Markov models (HMMs) in which latent states correspond to clusters of similar mutation patterns. Theory from statistical genetics suggests that these HMMs are nonhomogeneous (their transition probabilities vary along the chromosome) and have large support for self transitions. We develop a new nonparametric model of genetic sequence data, based on the hierarchical Dirichlet process, which supports these self transitions and nonhomogeneity. Our model provides a parameterization of the genetic process that is more parsimonious than other more general nonparametric models which have previously been applied to population genetics. We provide truncation-free MCMC inference for our model using a new auxiliary sampling scheme for Bayesian nonparametric HMMs. In a series of experiments on male X chromosome data from the Thousand Genomes Project and also on data simulated from a population bottleneck we show the benefits of our model over the popular finite model fastPHASE, which can itself be seen as a parametric truncation of our model. We find that the number of HMM states found by our model is correlated with the time to the most recent common ancestor in population bottlenecks. This work demonstrates the flexibility of Bayesian nonparametrics applied to large and complex genetic data

Faster K-Means Cluster Estimation

There has been considerable work on improving popular clustering algorithm `K-means' in terms of mean squared error (MSE) and speed, both. However, most of the k-means variants tend to compute distance of each data point to each cluster centroid for every iteration. We propose a fast heuristic to overcome this bottleneck with only marginal increase in MSE. We observe that across all iterations of K-means, a data point changes its membership only among a small subset of clusters. Our heuristic predicts such clusters for each data point by looking at nearby clusters after the first iteration of k-means. We augment well known variants of k-means with our heuristic to demonstrate effectiveness of our heuristic. For various synthetic and real-world datasets, our heuristic achieves speed-up of up-to 3 times when compared to efficient variants of k-means.Comment: 6 pages, Accepted at ECIR 201

Complete spatial characterization of an optical wavefront using a variable-separation pinhole pair

We present a technique for measuring the transverse spatial properties of an optical wavefront. Intensity and phase profiles are recovered by analysis of a series of interference patterns produced by the combination of a scanning X-shaped slit and a static horizontal slit; the spatial coherence may be found from the same data. We demonstrate the technique by characterizing high harmonic radiation generated in a gas cell, however the method could be extended to a wide variety of light sources.Comment: 4 pages, 3 figures, 1 tabl

Rhinologic changes in Wegener's granulomatosis

Twenty-eight patients with a clinical diagnosis of sinonasal Wegener's granulomatosis were referred for imaging during the period 1990-2001. Of these, 10 had clinical symptoms and signs confined to the nose and sinuses and 18 had classical systemic Wegener's. The computed tomography (CT) and magnetic resonance (MRI) scans of the series were reviewed by a panel of one otolaryngologist and two radiologists. From the total of 28 patients, 85.7 per cent showed non-specific mucosal thickening in the nasal cavity or paranasal sinuses, 75 per cent showed evidence of bone destruction, and 50 per cent new bone formation in the walls of the sinus cavities. In addition the orbit was affected in 30 per cent of patients.The diagnosis of systemic Wegener's granulomatosis is made clinically but the condition may present characteristic features on imaging by CT and MRI. In a patient without a history of previous sinonasal surgery, a combination of bone destruction and new bone formation on CT is virtually diagnostic of Wegener's especially when accompanied on MRI by a fat signal from the sclerotic sinus wall. These changes are important diagnostically in localized sinonasal Wegener's granulomatosis where the clinical diagnosis may be uncertain and the cANCA test can be negative

A comparison of the physiological consequences of head-loading and back-loading for African and European women

The aim is to quantify the physiological cost of head-load carriage and to examine the ‘free ride’ hypothesis for head-load carriage in groups of women differing in their experience of head-loading. Twenty-four Xhosa women [13 experienced head-loaders (EXP), 11 with no experience of head-loading (NON)] attempted to carry loads of up to 70% of body mass on both their heads and backs whilst walking on a treadmill at a self-selected walking speed. Expired air was collected throughout. In a second study nine women, members of the British Territorial Army, carried similar loads, again at a self-selected speed. Maximum load carried was greater for the back than the head (54.7 ± 15.1 vs. 40.8 ± 13.2% BM, P <0.0005). Considering study one, head-loading required a greater oxygen rate than back-loading (10.1 ± 2.6 vs. 8.8 ± 2.3 ml kg bodymass−1 min−1, P = 0.043, for loads 10–25% BM) regardless of previous head-loading experience (P = 0.333). Percentage changes in oxygen consumption associated with head-loading were greater than the proportional load added in both studies but were smaller than the added load for the lighter loads carried on the back in study 1. All other physiological variables were consistent with changes in oxygen consumption. The data provides no support for the ‘free ride’ hypothesis for head-loading although there is some evidence of energy saving mechanisms for back-loading at low speed/load combinations. Investigating the large individual variation in response may help in identifying combinations of factors that contribute to improved economy