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Maximum likelihood estimation of signal amplitude and noise variance from MR data. Magnetic Resonance in Medicine
, 2004
"... In magnetic resonance imaging, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian distributed noise. After applying an inverse Fourier transform the data remain complex valued and Gaussian distributed. If the signal amplitude is t ..."
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Cited by 22 (0 self)
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In magnetic resonance imaging, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian distributed noise. After applying an inverse Fourier transform the data remain complex valued and Gaussian distributed. If the signal amplitude is to be estimated, one has two options. It can be estimated directly from the complex valued data set, or one can first perform a magnitude operation on this data set, which changes the distribution of the data from Gaussian to Rician, and estimate the signal amplitude from the thus obtained magnitude image. Similarly, the noise variance can be estimated from both the complex and magnitude data sets. This paper addresses the question whether it is better to use complex valued data or magnitude data for the estimation of these parameters using the Maximum Likelihood method. As a performance criterion, the meansquared error (MSE) is used. 1
AUTOCORRELATED PROCESS MONITORING USING TRIGGERED CUSCORE CHARTS
"... Some of the most widelyinvestigated control charting techniques for autocorrelated data are based on time series residuals. If the mean shift in the autocorrelated process is a sudden step shift, the resulting mean shift in the residuals is time varying and has been referred to as the fault signatu ..."
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Cited by 9 (8 self)
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Some of the most widelyinvestigated control charting techniques for autocorrelated data are based on time series residuals. If the mean shift in the autocorrelated process is a sudden step shift, the resulting mean shift in the residuals is time varying and has been referred to as the fault signature. Traditional residual based charts, such as a Shewhart, CUSUM, or EWMA on the residuals, do not make use of the information contained in the dynamics of the fault signature. In contrast, methods such as the Cuscore chart or Generalized Likelihood Ratio Test (GLRT) do incorporate this information. In order for the Cuscore chart to fully benefit from this, its detector coefficients should coincide with the fault signature. This is impossible to ensure, however, since the exact form of the fault signature depends on the time of occurrence of the mean shift, which is generally not known apriori. Any mismatch between the detector and the fault signature will adversely affect the Cuscore performance. This paper proposes a CUSUMtriggered Cuscore chart to reduce the mismatch between the detector and fault signature. A variation to the CUSUMtriggered Cuscore chart that uses a GLRT to estimate the mean shift time of occurrence is also discussed. It is shown that the triggered Cuscore chart performs better than the standard Cuscore chart and the residualbased CUSUM chart. Examples are provided to illustrate its use. Copyright © 2002 John Wiley & Sons,
Methodological Review Phylogenetics by likelihood: Evolutionary modeling as a tool for understanding the genome
, 2005
"... www.elsevier.com/locate/yjbin Molecular evolutionary studies provide a means of investigating how cells function and how organisms adapt to their environment. The products of evolutionary studies provide medically important insights to the source of major diseases, such as HIV, and hold the key to u ..."
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www.elsevier.com/locate/yjbin Molecular evolutionary studies provide a means of investigating how cells function and how organisms adapt to their environment. The products of evolutionary studies provide medically important insights to the source of major diseases, such as HIV, and hold the key to understand the developing immunity of pathogenic bacteria to antibiotics. They have also helped mankind understand its place in nature, casting light on the selective forces and environmental conditions that resulted in modern humans. The use of likelihood as a framework for statistical modeling in phylogenetics has played a fundamental role in studying molecular evolution, enabling rigorous and robust conclusions to be drawn from sequence data. The first half of this article is a general introduction to the likelihood method for inferring phylogenies, the properties of the models used, and how it can be used for statistical testing. The latter half of the article focuses on the emerging new generation of phylogenetic models that describe heterogeneity in the evolutionary process along sequences, including the recoding of protein coding sequence data to amino acids and codons, and various approaches for describing dependencies between sites in a sequence. We conclude with a detailed case study examining how modern modeling approaches have been successfully
Maximum Likelihood estimation of signal
 Magn Reson Med
, 2004
"... In magnetic resonance imaging, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian distributed noise. After applying an inverse Fourier transform the data remain complex valued and Gaussian distributed. If the signal amplitude is ..."
Abstract
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In magnetic resonance imaging, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian distributed noise. After applying an inverse Fourier transform the data remain complex valued and Gaussian distributed. If the signal amplitude is to be estimated, one has two options. It can be estimated directly from the complex valued data set, or one can first perform a magnitude operation on this data set, which changes the distribution of the data from Gaussian to Rician, and estimate the signal amplitude from the thus obtained magnitude image. Similarly, the noise variance can be estimated from both the complex and magnitude data sets.
Directed Monitoring Using Cuscore Charts for Seasonal Time Series
"... The most commonly used statistical process control charts to detect special causes are Shewhart and Cusum charts. However, the Cuscore chart is a contemporary alternative that is especially well suited for detecting special causes that can be modeled in advance based on their characteristic effect o ..."
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The most commonly used statistical process control charts to detect special causes are Shewhart and Cusum charts. However, the Cuscore chart is a contemporary alternative that is especially well suited for detecting special causes that can be modeled in advance based on their characteristic effect on the system. In this paper, we develop the appropriate Cuscore statistic and the required control limits to detect a mean shift in a seasonal time series process. The work is motivated by an application involving blood platelet orders placed with the Red Cross. We also compare the performance of the Cuscore chart to the Cusum chart in this application and find that the performance of the Cuscore, in terms of time to signal the special cause, is better than the Cusum chart. We find that this result holds even when faced with the mismatch problem which pertains to the compatibility between the actual and expected information that the Cuscore statistic is predicated upon.
Transactions: physical sciences papers’.
"... foundations of theoretical statistics’. Phil. ..."
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Anatomical Arrangement of Neurons in Population Codes
"... This thesis has been submitted in fulfilment of the requirements for a postgraduate degree (e.g. PhD, MPhil, DClinPsychol) at the University of Edinburgh. Please note the following terms and conditions of use: • This work is protected by copyright and other intellectual property rights, which are re ..."
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This thesis has been submitted in fulfilment of the requirements for a postgraduate degree (e.g. PhD, MPhil, DClinPsychol) at the University of Edinburgh. Please note the following terms and conditions of use: • This work is protected by copyright and other intellectual property rights, which are retained by the thesis author, unless otherwise stated. • A copy can be downloaded for personal noncommercial research or study, without prior permission or charge. • This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the author. • The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the author. • When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given. Analysing the Information Contributions and
'C L INICALARTICLE TRIALS
"... Translational clinical trials: an entropybased approach to sample size ..."
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