A semiparametric state space model

This paper considers the problem of estimating a linear univariate Time Series State Space model for which the shape of the distribution of the observation noise is not specified a priori. Although somewhat challenging computationally, the simultaneous estimation of the parameters of the model and the unknown observation noise density is made feasible through a combination of Gaussian-sum Filtering and Smoothing algorithms and Kernel Density Estimation methods. The bottleneck in these calculations consists in avoiding the geometric increase, with time, of the number of simultaneous Kalman filter components. It is the aim of this paper to show that this can be achieved by the use of standard techniques from Cluster Analysis and unsupervised Classification. An empirical illustration of this new methodology is included; this consists in the application of a semiparametric version of the Local Level model to the analysis of the wellknown river Nile data series

Signal Extraction in Continuous Time and the Generalized Hodrick- Prescott Filter

A widely used filter to extract a signal in a time series, in particular in the business cycle analysis, is the Hodrick-Prescott filter. The model that underlies the filter considers the data series as the sum of two unobserved component (signal and non signal) and a smoothing parameter which for quarterly series is set to a specified value. This paper proposes a generalization of the Hodrick-Prescott filter to a continuous time support, using the well-established relationship between cubic splines and state-space models. The spline formulation of the filter leads to a state space model with several practical advantages: first, the smoothing parameter can be either pre-specified or estimated as the other parameters in the model; second, the unobserved components can be modelled by the addition of particular ARIMA structures; lastly the model is capable of working in the presence of missing values or for irregular surveys. Monte Carlo experiments support these considerations.smoothing parameter, cubic spline, state-space model, irregular surveys.

Dynamic Thermal Imaging for Intraoperative Monitoring of Neuronal Activity and Cortical Perfusion

Neurosurgery is a demanding medical discipline that requires a complex interplay of several neuroimaging techniques. This allows structural as well as functional information to be recovered and then visualized to the surgeon. In the case of tumor resections this approach allows more fine-grained differentiation of healthy and pathological tissue which positively influences the postoperative outcome as well as the patient's quality of life. In this work, we will discuss several approaches to establish thermal imaging as a novel neuroimaging technique to primarily visualize neural activity and perfusion state in case of ischaemic stroke. Both applications require novel methods for data-preprocessing, visualization, pattern recognition as well as regression analysis of intraoperative thermal imaging. Online multimodal integration of preoperative and intraoperative data is accomplished by a 2D-3D image registration and image fusion framework with an average accuracy of 2.46 mm. In navigated surgeries, the proposed framework generally provides all necessary tools to project intraoperative 2D imaging data onto preoperative 3D volumetric datasets like 3D MR or CT imaging. Additionally, a fast machine learning framework for the recognition of cortical NaCl rinsings will be discussed throughout this thesis. Hereby, the standardized quantification of tissue perfusion by means of an approximated heating model can be achieved. Classifying the parameters of these models yields a map of connected areas, for which we have shown that these areas correlate with the demarcation caused by an ischaemic stroke segmented in postoperative CT datasets. Finally, a semiparametric regression model has been developed for intraoperative neural activity monitoring of the somatosensory cortex by somatosensory evoked potentials. These results were correlated with neural activity of optical imaging. We found that thermal imaging yields comparable results, yet doesn't share the limitations of optical imaging. In this thesis we would like to emphasize that thermal imaging depicts a novel and valid tool for both intraoperative functional and structural neuroimaging

Semiparametric Bayesian inference in smooth coefficient models

We describe procedures for Bayesian estimation and testing in cross-sectional, panel data and nonlinear smooth coefficient models. The smooth coefficient model is a generalization of the partially linear or additive model wherein coefficients on linear explanatory variables are treated as unknown functions of an observable covariate. In the approach we describe, points on the regression lines are regarded as unknown parameters and priors are placed on differences between adjacent points to introduce the potential for smoothing the curves. The algorithms we describe are quite simple to implement - for example, estimation, testing and smoothing parameter selection can be carried out analytically in the cross-sectional smooth coefficient model. We apply our methods using data from the National Longitudinal Survey of Youth (NLSY). Using the NLSY data we first explore the relationship between ability and log wages and flexibly model how returns to schooling vary with measured cognitive ability. We also examine a model of female labor supply and use this example to illustrate how the described techniques can been applied in nonlinear settings

Retinal blood vessels extraction using probabilistic modelling

© 2014 Kaba et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This article has been made available through the Brunel Open Access Publishing Fund.The analysis of retinal blood vessels plays an important role in detecting and treating retinal diseases. In this review, we present an automated method to segment blood vessels of fundus retinal image. The proposed method could be used to support a non-intrusive diagnosis in modern ophthalmology for early detection of retinal diseases, treatment evaluation or clinical study. This study combines the bias correction and an adaptive histogram equalisation to enhance the appearance of the blood vessels. Then the blood vessels are extracted using probabilistic modelling that is optimised by the expectation maximisation algorithm. The method is evaluated on fundus retinal images of STARE and DRIVE datasets. The experimental results are compared with some recently published methods of retinal blood vessels segmentation. The experimental results show that our method achieved the best overall performance and it is comparable to the performance of human experts.The Department of Information Systems, Computing and Mathematics, Brunel University

Degeneracy of gravitational waveforms in the context of GW150914

We study the degeneracy of theoretical gravitational waveforms for binary black hole mergers using an aligned-spin effective-one-body model. After appropriate truncation, bandpassing, and matching, we identify regions in the mass--spin parameter space containing waveforms similar to the template proposed for GW150914, with masses $m_1 = 36^{+5}_{-4} M_\odot$ and $m_2 = 29^{+4}_{-4} M_\odot$, using the cross-correlation coefficient as a measure of the similarity between waveforms. Remarkably high cross-correlations are found across broad regions of parameter space. The associated uncertanties exceed these from LIGO's Bayesian analysis considerably. We have shown that waveforms with greatly increased masses, such as $m_1 = 70 M_\odot$ and $m_2 = 35 M_\odot$, and strong anti-aligned spins ($\chi_1=0.95$ and $\chi_2=-0.95$) yield almost the same signal-to-noise ratio in the strain data for GW150914.Comment: Accepted for publication in JCA