Maximum Likelihood Reconstruction for Magnetic Resonance Fingerprinting
Zhao, Bo; Setsompop, Kawin; Ye, Huihui; Cauley, Stephen; Wald, Lawrence L.
2017-01-01
This paper introduces a statistical estimation framework for magnetic resonance (MR) fingerprinting, a recently proposed quantitative imaging paradigm. Within this framework, we present a maximum likelihood (ML) formalism to estimate multiple parameter maps directly from highly undersampled, noisy k-space data. A novel algorithm, based on variable splitting, the alternating direction method of multipliers, and the variable projection method, is developed to solve the resulting optimization problem. Representative results from both simulations and in vivo experiments demonstrate that the proposed approach yields significantly improved accuracy in parameter estimation, compared to the conventional MR fingerprinting reconstruction. Moreover, the proposed framework provides new theoretical insights into the conventional approach. We show analytically that the conventional approach is an approximation to the ML reconstruction; more precisely, it is exactly equivalent to the first iteration of the proposed algorithm for the ML reconstruction, provided that a gridding reconstruction is used as an initialization. PMID:26915119
Improved maximum likelihood reconstruction of complex multi-generational pedigrees.
Sheehan, Nuala A; Bartlett, Mark; Cussens, James
2014-11-01
The reconstruction of pedigrees from genetic marker data is relevant to a wide range of applications. Likelihood-based approaches aim to find the pedigree structure that gives the highest probability to the observed data. Existing methods either entail an exhaustive search and are hence restricted to small numbers of individuals, or they take a more heuristic approach and deliver a solution that will probably have high likelihood but is not guaranteed to be optimal. By encoding the pedigree learning problem as an integer linear program we can exploit efficient optimisation algorithms to construct pedigrees guaranteed to have maximal likelihood for the standard situation where we have complete marker data at unlinked loci and segregation of genes from parents to offspring is Mendelian. Previous work demonstrated efficient reconstruction of pedigrees of up to about 100 individuals. The modified method that we present here is not so restricted: we demonstrate its applicability with simulated data on a real human pedigree structure of over 1600 individuals. It also compares well with a very competitive approximate approach in terms of solving time and accuracy. In addition to identifying a maximum likelihood pedigree, we can obtain any number of pedigrees in decreasing order of likelihood. This is useful for assessing the uncertainty of a maximum likelihood solution and permits model averaging over high likelihood pedigrees when this would be appropriate. More importantly, when the solution is not unique, as will often be the case for large pedigrees, it enables investigation into the properties of maximum likelihood pedigree estimates which has not been possible up to now. Crucially, we also have a means of assessing the behaviour of other approximate approaches which all aim to find a maximum likelihood solution. Our approach hence allows us to properly address the question of whether a reasonably high likelihood solution that is easy to obtain is practically as
Penalized maximum-likelihood image reconstruction for lesion detection
NASA Astrophysics Data System (ADS)
Qi, Jinyi; Huesman, Ronald H.
2006-08-01
Detecting cancerous lesions is one major application in emission tomography. In this paper, we study penalized maximum-likelihood image reconstruction for this important clinical task. Compared to analytical reconstruction methods, statistical approaches can improve the image quality by accurately modelling the photon detection process and measurement noise in imaging systems. To explore the full potential of penalized maximum-likelihood image reconstruction for lesion detection, we derived simplified theoretical expressions that allow fast evaluation of the detectability of a random lesion. The theoretical results are used to design the regularization parameters to improve lesion detectability. We conducted computer-based Monte Carlo simulations to compare the proposed penalty function, conventional penalty function, and a penalty function for isotropic point spread function. The lesion detectability is measured by a channelized Hotelling observer. The results show that the proposed penalty function outperforms the other penalty functions for lesion detection. The relative improvement is dependent on the size of the lesion. However, we found that the penalty function optimized for a 5 mm lesion still outperforms the other two penalty functions for detecting a 14 mm lesion. Therefore, it is feasible to use the penalty function designed for small lesions in image reconstruction, because detection of large lesions is relatively easy.
Superfast maximum-likelihood reconstruction for quantum tomography
NASA Astrophysics Data System (ADS)
Shang, Jiangwei; Zhang, Zhengyun; Ng, Hui Khoon
2017-06-01
Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we provide a fast and reliable algorithm for maximum-likelihood reconstruction that avoids this slow convergence. Our method utilizes the state-of-the-art convex optimization scheme, an accelerated projected-gradient method, that allows one to accommodate the quantum nature of the problem in a different way than in the standard methods. We demonstrate the power of our approach by comparing its performance with other algorithms for n -qubit state tomography. In particular, an eight-qubit situation that purportedly took weeks of computation time in 2005 can now be completed in under a minute for a single set of data, with far higher accuracy than previously possible. This refutes the common claim that MLE reconstruction is slow and reduces the need for alternative methods that often come with difficult-to-verify assumptions. In fact, recent methods assuming Gaussian statistics or relying on compressed sensing ideas are demonstrably inapplicable for the situation under consideration here. Our algorithm can be applied to general optimization problems over the quantum state space; the philosophy of projected gradients can further be utilized for optimization contexts with general constraints.
Single particle maximum likelihood reconstruction from superresolution microscopy images
Verdier, Timothée; Gunzenhauser, Julia; Manley, Suliana; Castelnovo, Martin
2017-01-01
Point localization superresolution microscopy enables fluorescently tagged molecules to be imaged beyond the optical diffraction limit, reaching single molecule localization precisions down to a few nanometers. For small objects whose sizes are few times this precision, localization uncertainty prevents the straightforward extraction of a structural model from the reconstructed images. We demonstrate in the present work that this limitation can be overcome at the single particle level, requiring no particle averaging, by using a maximum likelihood reconstruction (MLR) method perfectly suited to the stochastic nature of such superresolution imaging. We validate this method by extracting structural information from both simulated and experimental PALM data of immature virus-like particles of the Human Immunodeficiency Virus (HIV-1). MLR allows us to measure the radii of individual viruses with precision of a few nanometers and confirms the incomplete closure of the viral protein lattice. The quantitative results of our analysis are consistent with previous cryoelectron microscopy characterizations. Our study establishes the framework for a method that can be broadly applied to PALM data to determine the structural parameters for an existing structural model, and is particularly well suited to heterogeneous features due to its single particle implementation. PMID:28253349
Single particle maximum likelihood reconstruction from superresolution microscopy images.
Verdier, Timothée; Gunzenhauser, Julia; Manley, Suliana; Castelnovo, Martin
2017-01-01
Point localization superresolution microscopy enables fluorescently tagged molecules to be imaged beyond the optical diffraction limit, reaching single molecule localization precisions down to a few nanometers. For small objects whose sizes are few times this precision, localization uncertainty prevents the straightforward extraction of a structural model from the reconstructed images. We demonstrate in the present work that this limitation can be overcome at the single particle level, requiring no particle averaging, by using a maximum likelihood reconstruction (MLR) method perfectly suited to the stochastic nature of such superresolution imaging. We validate this method by extracting structural information from both simulated and experimental PALM data of immature virus-like particles of the Human Immunodeficiency Virus (HIV-1). MLR allows us to measure the radii of individual viruses with precision of a few nanometers and confirms the incomplete closure of the viral protein lattice. The quantitative results of our analysis are consistent with previous cryoelectron microscopy characterizations. Our study establishes the framework for a method that can be broadly applied to PALM data to determine the structural parameters for an existing structural model, and is particularly well suited to heterogeneous features due to its single particle implementation.
Maximum likelihood pedigree reconstruction using integer linear programming.
Cussens, James; Bartlett, Mark; Jones, Elinor M; Sheehan, Nuala A
2013-01-01
Large population biobanks of unrelated individuals have been highly successful in detecting common genetic variants affecting diseases of public health concern. However, they lack the statistical power to detect more modest gene-gene and gene-environment interaction effects or the effects of rare variants for which related individuals are ideally required. In reality, most large population studies will undoubtedly contain sets of undeclared relatives, or pedigrees. Although a crude measure of relatedness might sometimes suffice, having a good estimate of the true pedigree would be much more informative if this could be obtained efficiently. Relatives are more likely to share longer haplotypes around disease susceptibility loci and are hence biologically more informative for rare variants than unrelated cases and controls. Distant relatives are arguably more useful for detecting variants with small effects because they are less likely to share masking environmental effects. Moreover, the identification of relatives enables appropriate adjustments of statistical analyses that typically assume unrelatedness. We propose to exploit an integer linear programming optimisation approach to pedigree learning, which is adapted to find valid pedigrees by imposing appropriate constraints. Our method is not restricted to small pedigrees and is guaranteed to return a maximum likelihood pedigree. With additional constraints, we can also search for multiple high-probability pedigrees and thus account for the inherent uncertainty in any particular pedigree reconstruction. The true pedigree is found very quickly by comparison with other methods when all individuals are observed. Extensions to more complex problems seem feasible. © 2012 Wiley Periodicals, Inc.
Penalized maximum likelihood reconstruction for x-ray differential phase-contrast tomography
Brendel, Bernhard; Teuffenbach, Maximilian von; Noël, Peter B.; Pfeiffer, Franz; Koehler, Thomas
2016-01-15
Purpose: The purpose of this work is to propose a cost function with regularization to iteratively reconstruct attenuation, phase, and scatter images simultaneously from differential phase contrast (DPC) acquisitions, without the need of phase retrieval, and examine its properties. Furthermore this reconstruction method is applied to an acquisition pattern that is suitable for a DPC tomographic system with continuously rotating gantry (sliding window acquisition), overcoming the severe smearing in noniterative reconstruction. Methods: We derive a penalized maximum likelihood reconstruction algorithm to directly reconstruct attenuation, phase, and scatter image from the measured detector values of a DPC acquisition. The proposed penalty comprises, for each of the three images, an independent smoothing prior. Image quality of the proposed reconstruction is compared to images generated with FBP and iterative reconstruction after phase retrieval. Furthermore, the influence between the priors is analyzed. Finally, the proposed reconstruction algorithm is applied to experimental sliding window data acquired at a synchrotron and results are compared to reconstructions based on phase retrieval. Results: The results show that the proposed algorithm significantly increases image quality in comparison to reconstructions based on phase retrieval. No significant mutual influence between the proposed independent priors could be observed. Further it could be illustrated that the iterative reconstruction of a sliding window acquisition results in images with substantially reduced smearing artifacts. Conclusions: Although the proposed cost function is inherently nonconvex, it can be used to reconstruct images with less aliasing artifacts and less streak artifacts than reconstruction methods based on phase retrieval. Furthermore, the proposed method can be used to reconstruct images of sliding window acquisitions with negligible smearing artifacts.
Pascazio, Vito; Schirinzi, Gilda
2002-01-01
In this paper, a technique that is able to reconstruct highly sloped and discontinuous terrain height profiles, starting from multifrequency wrapped phase acquired by interferometric synthetic aperture radar (SAR) systems, is presented. We propose an innovative unwrapping method, based on a maximum likelihood estimation technique, which uses multifrequency independent phase data, obtained by filtering the interferometric SAR raw data pair through nonoverlapping band-pass filters, and approximating the unknown surface by means of local planes. Since the method does not exploit the phase gradient, it assures the uniqueness of the solution, even in the case of highly sloped or piecewise continuous elevation patterns with strong discontinuities.
Béchet, Clémentine; Tallon, Michel; Thiébaut, Eric
2009-03-01
The performances of various estimators for wavefront sensing applications such as adaptive optics (AO) are compared. Analytical expressions for the bias and variance terms in the mean squared error (MSE) are derived for the minimum-norm maximum likelihood (MNML) and the maximum a posteriori (MAP) reconstructors. The MAP estimator is analytically demonstrated to yield an optimal trade-off that reduces the MSE, hence leading to a better Strehl ratio. The implications for AO applications are quantified thanks to simulations on 8-m- and 42-m-class telescopes. We show that the MAP estimator can achieve twice as low MSE as MNML methods do. Large AO systems can thus benefit from the high quality of MAP reconstruction in O(n) operations, thanks to the fast fractal iterative method (FrIM) algorithm (Thiébaut and Tallon, submitted to J. Opt. Soc. Am. A).
Van Slambrouck, Katrien; Stute, Simon; Comtat, Claude; Sibomana, Merence; van Velden, Floris H. P.; Boellaard, Ronald
2015-01-01
Positron emission tomography data are typically reconstructed with maximum likelihood expectation maximization (MLEM). However, MLEM suffers from positive bias due to the non-negativity constraint. This is particularly problematic for tracer kinetic modeling. Two reconstruction methods with bias reduction properties that do not use strict Poisson optimization are presented and compared to each other, to filtered backprojection (FBP), and to MLEM. The first method is an extension of NEGML, where the Poisson distribution is replaced by a Gaussian distribution for low count data points. The transition point between the Gaussian and the Poisson regime is a parameter of the model. The second method is a simplification of ABML. ABML has a lower and upper bound for the reconstructed image whereas AML has the upper bound set to infinity. AML uses a negative lower bound to obtain bias reduction properties. Different choices of the lower bound are studied. The parameter of both algorithms determines the effectiveness of the bias reduction and should be chosen large enough to ensure bias-free images. This means that both algorithms become more similar to least squares algorithms, which turned out to be necessary to obtain bias-free reconstructions. This comes at the cost of increased variance. Nevertheless, NEGML and AML have lower variance than FBP. Furthermore, randoms handling has a large influence on the bias. Reconstruction with smoothed randoms results in lower bias compared to reconstruction with unsmoothed randoms or randoms precorrected data. However, NEGML and AML yield both bias-free images for large values of their parameter. PMID:25137726
Van Slambrouck, Katrien; Stute, Simon; Comtat, Claude; Sibomana, Merence; van Velden, Floris H P; Boellaard, Ronald; Nuyts, Johan
2015-01-01
Positron emission tomography data are typically reconstructed with maximum likelihood expectation maximization (MLEM). However, MLEM suffers from positive bias due to the non-negativity constraint. This is particularly problematic for tracer kinetic modeling. Two reconstruction methods with bias reduction properties that do not use strict Poisson optimization are presented and compared to each other, to filtered backprojection (FBP), and to MLEM. The first method is an extension of NEGML, where the Poisson distribution is replaced by a Gaussian distribution for low count data points. The transition point between the Gaussian and the Poisson regime is a parameter of the model. The second method is a simplification of ABML. ABML has a lower and upper bound for the reconstructed image whereas AML has the upper bound set to infinity. AML uses a negative lower bound to obtain bias reduction properties. Different choices of the lower bound are studied. The parameter of both algorithms determines the effectiveness of the bias reduction and should be chosen large enough to ensure bias-free images. This means that both algorithms become more similar to least squares algorithms, which turned out to be necessary to obtain bias-free reconstructions. This comes at the cost of increased variance. Nevertheless, NEGML and AML have lower variance than FBP. Furthermore, randoms handling has a large influence on the bias. Reconstruction with smoothed randoms results in lower bias compared to reconstruction with unsmoothed randoms or randoms precorrected data. However, NEGML and AML yield both bias-free images for large values of their parameter.
Multi-energy penalized maximum-likelihood reconstruction for x-ray security imaging
NASA Astrophysics Data System (ADS)
Politte, David G.; Lu, Jingwei; O'Sullivan, Joseph A.; Johnson, Eric; Bosch, Carl
2017-05-01
X-ray imaging for security screening is a challenging application that requires simultaneous satisfaction of seemingly incompatible constraints, including low cost, high throughput, and reliable detection of threats. We take a principled computational imaging approach to system design. Mathematical models of the underlying physics and a Huber-class penalty function yield a penalized maximum-likelihood problem. We extend our iterative algorithm for computing linear attenuation coefficients to use multiple energy bins in the SureScan x1000, which has an unconventional, fixed-source geometry. The goal is to maintain the spatial resolution of the single-energy reconstruction while providing information for material characterization used for detection of threats.
Bian, Liheng; Suo, Jinli; Chung, Jaebum; Ou, Xiaoze; Yang, Changhuei; Chen, Feng; Dai, Qionghai
2016-01-01
Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval optimization process, in which we only obtain low resolution intensity images corresponding to the sub-bands of the sample’s high resolution (HR) spatial spectrum, and aim to retrieve the complex HR spectrum. In real setups, the measurements always suffer from various degenerations such as Gaussian noise, Poisson noise, speckle noise and pupil location error, which would largely degrade the reconstruction. To efficiently address these degenerations, we propose a novel FP reconstruction method under a gradient descent optimization framework in this paper. The technique utilizes Poisson maximum likelihood for better signal modeling, and truncated Wirtinger gradient for effective error removal. Results on both simulated data and real data captured using our laser-illuminated FPM setup show that the proposed method outperforms other state-of-the-art algorithms. Also, we have released our source code for non-commercial use. PMID:27283980
Maximum Likelihood Event Estimation and List-mode Image Reconstruction on GPU Hardware
Caucci, Luca; Furenlid, Lars R.; Barrett, Harrison H.
2010-01-01
The scintillation detectors commonly used in SPECT and PET imaging and in Compton cameras require estimation of the position and energy of each gamma ray interaction. Ideally, this process would yield images with no spatial distortion and the best possible spatial resolution. In addition, especially for Compton cameras, the computation must yield the best possible estimate of the energy of each interacting gamma ray. These goals can be achieved by use of maximum-likelihood (ML) estimation of the event parameters, but in the past the search for an ML estimate has not been computationally feasible. Now, however, graphics processing units (GPUs) make it possible to produce optimal, real-time estimates of position and energy, even from scintillation cameras with a large number of photodetectors. In addition, the mathematical properties of ML estimates make them very attractive for use as list entries in list-mode ML image reconstruction. This two-step ML process—using ML estimation once to get the list data and again to reconstruct the object—allows accurate modeling of the detector blur and, potentially, considerable improvement in reconstructed spatial resolution. PMID:21278803
Carson, R.E.; Yan, Y.; Chodkowski, B.; Yap, T.K.; Daube-Witherspoon, M.E. )
1994-09-01
The imaging characteristics of maximum likelihood (ML) reconstruction using the EM algorithm for emission tomography have been extensively evaluated. There has been less study of the precision and accuracy of ML estimates of regional radioactivity concentration. The authors developed a realistic brain slice simulation by segmenting a normal subject's MRI scan into gray matter, white matter, and CSF and produced PET sinogram data with a model that included detector resolution and efficiencies, attenuation, scatter, and randoms. Noisy realizations at different count levels were created, and ML and filtered backprojection (FBP) reconstructions were performed. The bias and variability of ROI values were determined. In addition, the effects of ML pixel size, image smoothing and region size reduction were assessed. ML estimates at 1,000 iterations (0.6 sec per iteration on a parallel computer) for 1-cm[sup 2] gray matter ROIs showed negative biases of 6% [+-] 2% which can be reduced to 0% [+-] 3% by removing the outer 1-mm rim of each ROI. FBP applied to the full-size ROIs had 15% [+-] 4% negative bias with 50% less noise than ML. Shrinking the FBP regions provided partial bias compensation with noise increases to levels similar to ML. Smoothing of ML images produced biases comparable to FBP with slightly less noise. Because of its heavy computational requirements, the ML algorithm will be most useful for applications in which achieving minimum bias is important.
Stsepankou, D; Arns, A; Ng, S K; Zygmanski, P; Hesser, J
2012-10-07
The objective of this paper is to evaluate an iterative maximum likelihood (ML) cone-beam computed tomography (CBCT) reconstruction with total variation (TV) regularization with respect to the robustness of the algorithm due to data inconsistencies. Three different and (for clinical application) typical classes of errors are considered for simulated phantom and measured projection data: quantum noise, defect detector pixels and projection matrix errors. To quantify those errors we apply error measures like mean square error, signal-to-noise ratio, contrast-to-noise ratio and streak indicator. These measures are derived from linear signal theory and generalized and applied for nonlinear signal reconstruction. For quality check, we focus on resolution and CT-number linearity based on a Catphan phantom. All comparisons are made versus the clinical standard, the filtered backprojection algorithm (FBP). In our results, we confirm and substantially extend previous results on iterative reconstruction such as massive undersampling of the number of projections. Errors of projection matrix parameters of up to 1° projection angle deviations are still in the tolerance level. Single defect pixels exhibit ring artifacts for each method. However using defect pixel compensation, allows up to 40% of defect pixels for passing the standard clinical quality check. Further, the iterative algorithm is extraordinarily robust in the low photon regime (down to 0.05 mAs) when compared to FPB, allowing for extremely low-dose image acquisitions, a substantial issue when considering daily CBCT imaging for position correction in radiotherapy. We conclude that the ML method studied herein is robust under clinical quality assurance conditions. Consequently, low-dose regime imaging, especially for daily patient localization in radiation therapy is possible without change of the current hardware of the imaging system.
A maximum-likelihood multi-resolution weak lensing mass reconstruction method
NASA Astrophysics Data System (ADS)
Khiabanian, Hossein
Gravitational lensing is formed when the light from a distant source is "bent" around a massive object. Lensing analysis has increasingly become the method of choice for studying dark matter, so much that it is one of the main tools that will be employed in the future surveys to study the dark energy and its equation of state as well as the evolution of galaxy clustering. Unlike other popular techniques for selecting galaxy clusters (such as studying the X-ray emission or observing the over-densities of galaxies), weak gravitational lensing does not have the disadvantage of relying on the luminous matter and provides a parameter-free reconstruction of the projected mass distribution in clusters without dependence on baryon content. Gravitational lensing also provides a unique test for the presence of truly dark clusters, though it is otherwise an expensive detection method. Therefore it is essential to make use of all the information provided by the data to improve the quality of the lensing analysis. This thesis project has been motivated by the limitations encountered with the commonly used direct reconstruction methods of producing mass maps. We have developed a multi-resolution maximum-likelihood reconstruction method for producing two dimensional mass maps using weak gravitational lensing data. To utilize all the shear information, we employ an iterative inverse method with a properly selected regularization coefficient which fits the deflection potential at the position of each galaxy. By producing mass maps with multiple resolutions in the different parts of the observed field, we can achieve a uniform signal to noise level by increasing the resolution in regions of higher distortions or regions with an over-density of background galaxies. In addition, we are able to better study the sub- structure of the massive clusters at a resolution which is not attainable in the rest of the observed field.
NASA Astrophysics Data System (ADS)
Stsepankou, D.; Arns, A.; Ng, S. K.; Zygmanski, P.; Hesser, J.
2012-10-01
The objective of this paper is to evaluate an iterative maximum likelihood (ML) cone-beam computed tomography (CBCT) reconstruction with total variation (TV) regularization with respect to the robustness of the algorithm due to data inconsistencies. Three different and (for clinical application) typical classes of errors are considered for simulated phantom and measured projection data: quantum noise, defect detector pixels and projection matrix errors. To quantify those errors we apply error measures like mean square error, signal-to-noise ratio, contrast-to-noise ratio and streak indicator. These measures are derived from linear signal theory and generalized and applied for nonlinear signal reconstruction. For quality check, we focus on resolution and CT-number linearity based on a Catphan phantom. All comparisons are made versus the clinical standard, the filtered backprojection algorithm (FBP). In our results, we confirm and substantially extend previous results on iterative reconstruction such as massive undersampling of the number of projections. Errors of projection matrix parameters of up to 1° projection angle deviations are still in the tolerance level. Single defect pixels exhibit ring artifacts for each method. However using defect pixel compensation, allows up to 40% of defect pixels for passing the standard clinical quality check. Further, the iterative algorithm is extraordinarily robust in the low photon regime (down to 0.05 mAs) when compared to FPB, allowing for extremely low-dose image acquisitions, a substantial issue when considering daily CBCT imaging for position correction in radiotherapy. We conclude that the ML method studied herein is robust under clinical quality assurance conditions. Consequently, low-dose regime imaging, especially for daily patient localization in radiation therapy is possible without change of the current hardware of the imaging system.
Chylla, Roger A; Hu, Kaifeng; Ellinger, James J; Markley, John L
2011-06-15
We have developed an algorithm called fast maximum likelihood reconstruction (FMLR) that performs spectral deconvolution of 1D-2D NMR spectra for the purpose of accurate signal quantification. FMLR constructs the simplest time-domain model (e.g., the model with the fewest number of signals and parameters) whose frequency spectrum matches the visible regions of the spectrum obtained from identical Fourier processing of the acquired data. We describe the application of FMLR to quantitative metabolomics and demonstrate the accuracy of the method by analysis of complex, synthetic mixtures of metabolites and liver extracts. The algorithm demonstrates greater accuracy (0.5-5.0% error) than peak height analysis and peak integral analysis with greatly reduced operator intervention. FMLR has been implemented in a Java-based framework that is available for download on multiple platforms and is interoperable with popular NMR display and processing software. Two-dimensional (1)H-(13)C spectra of mixtures can be acquired with acquisition times of 15 min and analyzed by FMLR in the range of 2-5 min per spectrum to identify and quantify constituents present at concentrations of 0.2 mM or greater.
NASA Astrophysics Data System (ADS)
Yang, Li; Ferrero, Andrea; Hagge, Rosalie J.; Badawi, Ramsey D.; Qi, Jinyi
2014-03-01
Detecting cancerous lesions is a major clinical application in emission tomography. In previous work, we have studied penalized maximum-likelihood (PML) image reconstruction for the detection task, where we used a multiview channelized Hotelling observer (mvCHO) to assess the lesion detectability in 3D images. It mimics the condition where a human observer examines three orthogonal views of a 3D image for lesion detection. We proposed a method to design a shift-variant quadratic penalty function to improve the detectability of lesions at unknown locations, and validated it using computer simulations. In this study we evaluated the bene t of the proposed penalty function for lesion detection using real data. A high-count real patient data with no identi able tumor inside the eld of view was used as the background data. A Na-22 point source was scanned in air at variable locations and the point source data were superimposed onto the patient data as arti cial lesions after being attenuated by the patient body. Independent Poisson noise was added to the high-count sinograms to generate 200 pairs of lesion-present and lesion-absent data sets, each mimicking a 5-minute scans. Lesion detectability was assessed using a multiview CHO and a human observer two alternative forced choice (2AFC) experiment. The results showed that the optimized penalty can improve lesion detection over the conventional quadratic penalty function.
Maximum likelihood signature estimation
NASA Technical Reports Server (NTRS)
Walker, H. F.
1975-01-01
Maximum-likelihood estimates are discussed which are based on an unlabeled sample of observations, of unknown parameters in a mixture of normal distributions. Several successive approximation procedures for obtaining such maximum-likelihood estimates are described. These procedures, which are theoretically justified by the local contractibility of certain maps, are designed to take advantage of good initial estimates of the unknown parameters. They can be applied to the signature extension problem, in which good initial estimates of the unknown parameters are obtained from segments which are geographically near the segments from which the unlabeled samples are taken. Additional problems to which these methods are applicable include: estimation of proportions and adaptive classification (estimation of mean signatures and covariances).
A Maximum Likelihood Method for Reconstruction of the Evolution of Eukaryotic Gene Structure
Carmel, Liran; Rogozin, Igor B.; Wolf, Yuri I.; Koonin, Eugene V.
2012-01-01
Spliceosomal introns are one of the principal distinctive features of eukaryotes. Nevertheless, different large-scale studies disagree about even the most basic features of their evolution. In order to come up with a more reliable reconstruction of intron evolution, we developed a model that is far more comprehensive than previous ones. This model is rich in parameters, and estimating them accurately is infeasible by straightforward likelihood maximization. Thus, we have developed an expectation-maximization algorithm that allows for efficient maximization. Here, we outline the model and describe the expectation-maximization algorithm in detail. Since the method works with intron presence–absence maps, it is expected to be instrumental for the analysis of the evolution of other binary characters as well. PMID:19381540
NASA Technical Reports Server (NTRS)
Pina, R. K.; Puetter, R. C.
1992-01-01
We have developed a new figure of merit, a 'maximum-residual-likelihood' (MRL) statistic, for the goodness of fit for Bayesian image restoration which explicitly incorporates spatial information. The MRL constraint provides a natural means of incorporating the prior knowledge that the residuals contain no spatial structure through the autocorrelation function of the residuals. We demonstrate that this statistic follows a Chi-square distribution and that forcing this statistic to have its most probable value leads to a restored image whose residuals are consistent with the noise model. Our numerical experiments suggest that image restoration using the MRL statistic alone is numerically robust and produces results which are independent of the initial guess for the restored image. However, we caution that using the MRL statistic without an image prior can result in overresolution in low SNR portions of the image.
NASA Technical Reports Server (NTRS)
Pina, R. K.; Puetter, R. C.
1992-01-01
We have developed a new figure of merit, a 'maximum-residual-likelihood' (MRL) statistic, for the goodness of fit for Bayesian image restoration which explicitly incorporates spatial information. The MRL constraint provides a natural means of incorporating the prior knowledge that the residuals contain no spatial structure through the autocorrelation function of the residuals. We demonstrate that this statistic follows a Chi-square distribution and that forcing this statistic to have its most probable value leads to a restored image whose residuals are consistent with the noise model. Our numerical experiments suggest that image restoration using the MRL statistic alone is numerically robust and produces results which are independent of the initial guess for the restored image. However, we caution that using the MRL statistic without an image prior can result in overresolution in low SNR portions of the image.
Maximum Likelihood, Profile Likelihood, and Penalized Likelihood: A Primer
Cole, Stephen R.; Chu, Haitao; Greenland, Sander
2014-01-01
The method of maximum likelihood is widely used in epidemiology, yet many epidemiologists receive little or no education in the conceptual underpinnings of the approach. Here we provide a primer on maximum likelihood and some important extensions which have proven useful in epidemiologic research, and which reveal connections between maximum likelihood and Bayesian methods. For a given data set and probability model, maximum likelihood finds values of the model parameters that give the observed data the highest probability. As with all inferential statistical methods, maximum likelihood is based on an assumed model and cannot account for bias sources that are not controlled by the model or the study design. Maximum likelihood is nonetheless popular, because it is computationally straightforward and intuitive and because maximum likelihood estimators have desirable large-sample properties in the (largely fictitious) case in which the model has been correctly specified. Here, we work through an example to illustrate the mechanics of maximum likelihood estimation and indicate how improvements can be made easily with commercial software. We then describe recent extensions and generalizations which are better suited to observational health research and which should arguably replace standard maximum likelihood as the default method. PMID:24173548
Llacer, J.; Veklerov, E.; Nolan, D. ); Grafton, S.T.; Mazziotta, J.C.; Hawkins, R.A.; Hoh, C.K.; Hoffman, E.J. )
1990-10-01
This paper will report on the progress to date in carrying out Receiver Operating Characteristics (ROC) studies comparing Maximum Likelihood Estimator (MLE) and Filtered Backprojection (FBP) reconstructions of normal and abnormal human brain PET data in a clinical setting. A previous statistical study of reconstructions of the Hoffman brain phantom with real data indicated that the pixel-to-pixel standard deviation in feasible MLE images is approximately proportional to the square root of the number of counts in a region, as opposed to a standard deviation which is high and largely independent of the number of counts in FBP. A preliminary ROC study carried out with 10 non-medical observers performing a relatively simple detectability task indicates that, for the majority of observers, lower standard deviation translates itself into a statistically significant detectability advantage in MLE reconstructions. The initial results of ongoing tests with four experienced neurologists/nuclear medicine physicians are presented. Normal cases of {sup 18}F -- fluorodeoxyglucose (FDG) cerebral metabolism studies and abnormal cases in which a variety of lesions have been introduced into normal data sets have been evaluated. We report on the results of reading the reconstructions of 90 data sets, each corresponding to a single brain slice. It has become apparent that the design of the study based on reading single brain slices is too insensitive and we propose a variation based on reading three consecutive slices at a time, rating only the center slice. 9 refs., 2 figs., 1 tab.
Papaconstadopoulos, P; Levesque, I R; Maglieri, R; Seuntjens, J
2016-02-07
Direct determination of the source intensity distribution of clinical linear accelerators is still a challenging problem for small field beam modeling. Current techniques most often involve special equipment and are difficult to implement in the clinic. In this work we present a maximum-likelihood expectation-maximization (MLEM) approach to the source reconstruction problem utilizing small fields and a simple experimental set-up. The MLEM algorithm iteratively ray-traces photons from the source plane to the exit plane and extracts corrections based on photon fluence profile measurements. The photon fluence profiles were determined by dose profile film measurements in air using a high density thin foil as build-up material and an appropriate point spread function (PSF). The effect of other beam parameters and scatter sources was minimized by using the smallest field size ([Formula: see text] cm(2)). The source occlusion effect was reproduced by estimating the position of the collimating jaws during this process. The method was first benchmarked against simulations for a range of typical accelerator source sizes. The sources were reconstructed with an accuracy better than 0.12 mm in the full width at half maximum (FWHM) to the respective electron sources incident on the target. The estimated jaw positions agreed within 0.2 mm with the expected values. The reconstruction technique was also tested against measurements on a Varian Novalis Tx linear accelerator and compared to a previously commissioned Monte Carlo model. The reconstructed FWHM of the source agreed within 0.03 mm and 0.11 mm to the commissioned electron source in the crossplane and inplane orientations respectively. The impact of the jaw positioning, experimental and PSF uncertainties on the reconstructed source distribution was evaluated with the former presenting the dominant effect.
A framelet-based iterative maximum-likelihood reconstruction algorithm for spectral CT
NASA Astrophysics Data System (ADS)
Wang, Yingmei; Wang, Ge; Mao, Shuwei; Cong, Wenxiang; Ji, Zhilong; Cai, Jian-Feng; Ye, Yangbo
2016-11-01
Standard computed tomography (CT) cannot reproduce spectral information of an object. Hardware solutions include dual-energy CT which scans the object twice in different x-ray energy levels, and energy-discriminative detectors which can separate lower and higher energy levels from a single x-ray scan. In this paper, we propose a software solution and give an iterative algorithm that reconstructs an image with spectral information from just one scan with a standard energy-integrating detector. The spectral information obtained can be used to produce color CT images, spectral curves of the attenuation coefficient μ (r,E) at points inside the object, and photoelectric images, which are all valuable imaging tools in cancerous diagnosis. Our software solution requires no change on hardware of a CT machine. With the Shepp-Logan phantom, we have found that although the photoelectric and Compton components were not perfectly reconstructed, their composite effect was very accurately reconstructed as compared to the ground truth and the dual-energy CT counterpart. This means that our proposed method has an intrinsic benefit in beam hardening correction and metal artifact reduction. The algorithm is based on a nonlinear polychromatic acquisition model for x-ray CT. The key technique is a sparse representation of iterations in a framelet system. Convergence of the algorithm is studied. This is believed to be the first application of framelet imaging tools to a nonlinear inverse problem.
NASA Astrophysics Data System (ADS)
Makeev, Andrey; Ikejimba, Lynda; Lo, Joseph Y.; Glick, Stephen J.
2016-03-01
Although digital mammography has reduced breast cancer mortality by approximately 30%, sensitivity and specificity are still far from perfect. In particular, the performance of mammography is especially limited for women with dense breast tissue. Two out of every three biopsies performed in the U.S. are unnecessary, thereby resulting in increased patient anxiety, pain, and possible complications. One promising tomographic breast imaging method that has recently been approved by the FDA is dedicated breast computed tomography (BCT). However, visualizing lesions with BCT can still be challenging for women with dense breast tissue due to the minimal contrast for lesions surrounded by fibroglandular tissue. In recent years there has been renewed interest in improving lesion conspicuity in x-ray breast imaging by administration of an iodinated contrast agent. Due to the fully 3-D imaging nature of BCT, as well as sub-optimal contrast enhancement while the breast is under compression with mammography and breast tomosynthesis, dedicated BCT of the uncompressed breast is likely to offer the best solution for injected contrast-enhanced x-ray breast imaging. It is well known that use of statistically-based iterative reconstruction in CT results in improved image quality at lower radiation dose. Here we investigate possible improvements in image reconstruction for BCT, by optimizing free regularization parameter in method of maximum likelihood and comparing its performance with clinical cone-beam filtered backprojection (FBP) algorithm.
Veklerov, E.; Llacer, J.; Hoffman, E.J.
1987-10-01
In order to study properties of the Maximum Likelihood Estimator (MLE) algorithm for image reconstruction in Positron Emission Tomographyy (PET), the algorithm is applied to data obtained by the ECAT-III tomograph from a brain phantom. The procedure for subtracting accidental coincidences from the data stream generated by this physical phantom is such that he resultant data are not Poisson distributed. This makes the present investigation different from other investigations based on computer-simulated phantoms. It is shown that the MLE algorithm is robust enough to yield comparatively good images, especially when the phantom is in the periphery of the field of view, even though the underlying assumption of the algorithm is violated. Two transition matrices are utilized. The first uses geometric considerations only. The second is derived by a Monte Carlo simulation which takes into account Compton scattering in the detectors, positron range, etc. in the detectors. It is demonstrated that the images obtained from the Monte Carlo matrix are superior in some specific ways. A stopping rule derived earlier and allowing the user to stop the iterative process before the images begin to deteriorate is tested. Since the rule is based on the Poisson assumption, it does not work well with the presently available data, although it is successful wit computer-simulated Poisson data.
Augmented Likelihood Image Reconstruction.
Stille, Maik; Kleine, Matthias; Hägele, Julian; Barkhausen, Jörg; Buzug, Thorsten M
2016-01-01
The presence of high-density objects remains an open problem in medical CT imaging. Data of projections passing through objects of high density, such as metal implants, are dominated by noise and are highly affected by beam hardening and scatter. Reconstructed images become less diagnostically conclusive because of pronounced artifacts that manifest as dark and bright streaks. A new reconstruction algorithm is proposed with the aim to reduce these artifacts by incorporating information about shape and known attenuation coefficients of a metal implant. Image reconstruction is considered as a variational optimization problem. The afore-mentioned prior knowledge is introduced in terms of equality constraints. An augmented Lagrangian approach is adapted in order to minimize the associated log-likelihood function for transmission CT. During iterations, temporally appearing artifacts are reduced with a bilateral filter and new projection values are calculated, which are used later on for the reconstruction. A detailed evaluation in cooperation with radiologists is performed on software and hardware phantoms, as well as on clinically relevant patient data of subjects with various metal implants. Results show that the proposed reconstruction algorithm is able to outperform contemporary metal artifact reduction methods such as normalized metal artifact reduction.
NASA Astrophysics Data System (ADS)
Bousse, Alexandre; Bertolli, Ottavia; Atkinson, David; Arridge, Simon; Ourselin, Sébastien; Hutton, Brian F.; Thielemans, Kris
2016-02-01
This work is an extension of our recent work on joint activity reconstruction/motion estimation (JRM) from positron emission tomography (PET) data. We performed JRM by maximization of the penalized log-likelihood in which the probabilistic model assumes that the same motion field affects both the activity distribution and the attenuation map. Our previous results showed that JRM can successfully reconstruct the activity distribution when the attenuation map is misaligned with the PET data, but converges slowly due to the significant cross-talk in the likelihood. In this paper, we utilize time-of-flight PET for JRM and demonstrate that the convergence speed is significantly improved compared to JRM with conventional PET data.
NASA Astrophysics Data System (ADS)
Islam, Fahima Fahmida
Sparse tomography is an efficient technique which saves time as well as minimizes cost. However, due to few angular data it implies the image reconstruction problem as ill-posed. In the ill posed problem, even with exact data constraints, the inversion cannot be uniquely performed. Therefore, selection of suitable method to optimize the reconstruction problems plays an important role in sparse data CT. Use of regularization function is a well-known method to control the artifacts in limited angle data acquisition. In this work, we propose directional total variation regularized ordered subset (OS) type image reconstruction method for neutron limited data CT. Total variation (TV) regularization works as edge preserving regularization which not only preserves the sharp edge but also reduces many of the artifacts that are very common in limited data CT. However TV itself is not direction dependent. Therefore, TV is not very suitable for images with a dominant direction. The images with dominant direction it is important to know the total variation at certain direction. Hence, here a directional TV is used as prior term. TV regularization assumes the constraint of piecewise smoothness. As the original image is not piece wise constant image, sparsifying transform is used to convert the image in to sparse image or piecewise constant image. Along with this regularized function (D TV) the likelihood function which is adapted as objective function. To optimize this objective function a OS type algorithm is used. Generally there are two methods available to make OS method convergent. This work proposes OS type directional TV regularized likelihood reconstruction method which yields fast convergence as well as good quality image. Initial iteration starts with the filtered back projection (FBP) reconstructed image. The indication of convergence is determined by the convergence index between two successive reconstructed images. The quality of the image is assessed by showing
NASA Astrophysics Data System (ADS)
Missert, Andrew D.; T2K Collaboration
2017-09-01
A new event reconstruction algorithm, fiTQun, has been developed for the Super-Kamiokande detector. Super-Kamiokande is a ring-imaging water Cherenkov detector with a 22.5-kton fiducial volume located 1000 m underground in the Kamioka Mine in Japan. Neutrino events in the detector’s central volume produce charged particles whose Cherenkov rings are imaged by more than 11,000 photomultiplier tubes (PMTs) that line the walls of the detector. This new reconstruction software is able to reconstruct the detailed kinematics of the neutrino interaction from the charge and timing information of each PMT. In contrast to previous reconstruction algorithms that use image processing and pattern recognition techniques, fiTQun uses a maximum-likelihood approach that takes advantage of the known Cherenkov emission profiles and the detector response to evaluate the likelihood of a given reconstruction hypothesis. This approach provides a unifying framework for all aspects of the event reconstruction, including kinematics, ring counting, and particle identification. Using fiTQun to reconstruct neutrino events for the Tokai-to-Kamioka (T2K) experiment can greatly improve the current event selection by reducing pion backgrounds, improving separation of electrons and muons, and reconstructing the neutrino energy with greater precision. These improvements should significantly increase T2K’s sensitivity to the oscillation parameters.
The Sherpa Maximum Likelihood Estimator
NASA Astrophysics Data System (ADS)
Nguyen, D.; Doe, S.; Evans, I.; Hain, R.; Primini, F.
2011-07-01
A primary goal for the second release of the Chandra Source Catalog (CSC) is to include X-ray sources with as few as 5 photon counts detected in stacked observations of the same field, while maintaining acceptable detection efficiency and false source rates. Aggressive source detection methods will result in detection of many false positive source candidates. Candidate detections will then be sent to a new tool, the Maximum Likelihood Estimator (MLE), to evaluate the likelihood that a detection is a real source. MLE uses the Sherpa modeling and fitting engine to fit a model of a background and source to multiple overlapping candidate source regions. A background model is calculated by simultaneously fitting the observed photon flux in multiple background regions. This model is used to determine the quality of the fit statistic for a background-only hypothesis in the potential source region. The statistic for a background-plus-source hypothesis is calculated by adding a Gaussian source model convolved with the appropriate Chandra point spread function (PSF) and simultaneously fitting the observed photon flux in each observation in the stack. Since a candidate source may be located anywhere in the field of view of each stacked observation, a different PSF must be used for each observation because of the strong spatial dependence of the Chandra PSF. The likelihood of a valid source being detected is a function of the two statistics (for background alone, and for background-plus-source). The MLE tool is an extensible Python module with potential for use by the general Chandra user.
Alam, M S; Bognar, J G; Cain, S; Yasuda, B J
1998-03-10
During the process of microscanning a controlled vibrating mirror typically is used to produce subpixel shifts in a sequence of forward-looking infrared (FLIR) images. If the FLIR is mounted on a moving platform, such as an aircraft, uncontrolled random vibrations associated with the platform can be used to generate the shifts. Iterative techniques such as the expectation-maximization (EM) approach by means of the maximum-likelihood algorithm can be used to generate high-resolution images from multiple randomly shifted aliased frames. In the maximum-likelihood approach the data are considered to be Poisson random variables and an EM algorithm is developed that iteratively estimates an unaliased image that is compensated for known imager-system blur while it simultaneously estimates the translational shifts. Although this algorithm yields high-resolution images from a sequence of randomly shifted frames, it requires significant computation time and cannot be implemented for real-time applications that use the currently available high-performance processors. The new image shifts are iteratively calculated by evaluation of a cost function that compares the shifted and interlaced data frames with the corresponding values in the algorithm's latest estimate of the high-resolution image. We present a registration algorithm that estimates the shifts in one step. The shift parameters provided by the new algorithm are accurate enough to eliminate the need for iterative recalculation of translational shifts. Using this shift information, we apply a simplified version of the EM algorithm to estimate a high-resolution image from a given sequence of video frames. The proposed modified EM algorithm has been found to reduce significantly the computational burden when compared with the original EM algorithm, thus making it more attractive for practical implementation. Both simulation and experimental results are presented to verify the effectiveness of the proposed technique.
Vestige: Maximum likelihood phylogenetic footprinting
Wakefield, Matthew J; Maxwell, Peter; Huttley, Gavin A
2005-01-01
Background Phylogenetic footprinting is the identification of functional regions of DNA by their evolutionary conservation. This is achieved by comparing orthologous regions from multiple species and identifying the DNA regions that have diverged less than neutral DNA. Vestige is a phylogenetic footprinting package built on the PyEvolve toolkit that uses probabilistic molecular evolutionary modelling to represent aspects of sequence evolution, including the conventional divergence measure employed by other footprinting approaches. In addition to measuring the divergence, Vestige allows the expansion of the definition of a phylogenetic footprint to include variation in the distribution of any molecular evolutionary processes. This is achieved by displaying the distribution of model parameters that represent partitions of molecular evolutionary substitutions. Examination of the spatial incidence of these effects across regions of the genome can identify DNA segments that differ in the nature of the evolutionary process. Results Vestige was applied to a reference dataset of the SCL locus from four species and provided clear identification of the known conserved regions in this dataset. To demonstrate the flexibility to use diverse models of molecular evolution and dissect the nature of the evolutionary process Vestige was used to footprint the Ka/Ks ratio in primate BRCA1 with a codon model of evolution. Two regions of putative adaptive evolution were identified illustrating the ability of Vestige to represent the spatial distribution of distinct molecular evolutionary processes. Conclusion Vestige provides a flexible, open platform for phylogenetic footprinting. Underpinned by the PyEvolve toolkit, Vestige provides a framework for visualising the signatures of evolutionary processes across the genome of numerous organisms simultaneously. By exploiting the maximum-likelihood statistical framework, the complex interplay between mutational processes, DNA repair and
NASA Astrophysics Data System (ADS)
Tran, A. P.; Vanclooster, M.; Lambot, S.
2013-07-01
The vertical profile of shallow unsaturated zone soil moisture plays a key role in many hydro-meteorological and agricultural applications. We propose a closed-loop data assimilation procedure based on the maximum likelihood ensemble filter algorithm to update the vertical soil moisture profile from time-lapse ground-penetrating radar (GPR) data. A hydrodynamic model is used to propagate the system state in time and a radar electromagnetic model and petrophysical relationships to link the state variable with the observation data, which enables us to directly assimilate the GPR data. Instead of using the surface soil moisture only, the approach allows to use the information of the whole soil moisture profile for the assimilation. We validated our approach through a synthetic study. We constructed a synthetic soil column with a depth of 80 cm and analyzed the effects of the soil type on the data assimilation by considering 3 soil types, namely, loamy sand, silt and clay. The assimilation of GPR data was performed to solve the problem of unknown initial conditions. The numerical soil moisture profiles generated by the Hydrus-1D model were used by the GPR model to produce the "observed" GPR data. The results show that the soil moisture profile obtained by assimilating the GPR data is much better than that of an open-loop forecast. Compared to the loamy sand and silt, the updated soil moisture profile of the clay soil converges to the true state much more slowly. Decreasing the update interval from 60 down to 10 h only slightly improves the effectiveness of the GPR data assimilation for the loamy sand but significantly for the clay soil. The proposed approach appears to be promising to improve real-time prediction of the soil moisture profiles as well as to provide effective estimates of the unsaturated hydraulic properties at the field scale from time-lapse GPR measurements.
Ritter, André; Anton, Gisela; Weber, Thomas
2016-01-01
A maximum-likelihood reconstruction technique for X-ray Talbot-Lau tomography is presented. This technique allows the iterative simultaneous reconstruction of discrete distributions of absorption coefficient, refractive index and a dark-field scattering coefficient. This technique avoids prior phase retrieval in the tomographic projection images and thus in principle allows reconstruction from tomographic data with less than three phase steps per projection. A numerical phantom is defined which is used to evaluate convergence of the technique with regard to photon statistics and with regard to the number of projection angles and phase steps used. It is shown that the use of a random phase sampling pattern allows the reconstruction even for the extreme case of only one single phase step per projection. The technique is successfully applied to measured tomographic data of a mouse. In future, this reconstruction technique might also be used to implement enhanced imaging models for X-ray Talbot-Lau tomography. These enhancements might be suited to correct for example beam hardening and dispersion artifacts and improve overall image quality of X-ray Talbot-Lau tomography. PMID:27695126
Ritter, André; Anton, Gisela; Weber, Thomas
2016-01-01
A maximum-likelihood reconstruction technique for X-ray Talbot-Lau tomography is presented. This technique allows the iterative simultaneous reconstruction of discrete distributions of absorption coefficient, refractive index and a dark-field scattering coefficient. This technique avoids prior phase retrieval in the tomographic projection images and thus in principle allows reconstruction from tomographic data with less than three phase steps per projection. A numerical phantom is defined which is used to evaluate convergence of the technique with regard to photon statistics and with regard to the number of projection angles and phase steps used. It is shown that the use of a random phase sampling pattern allows the reconstruction even for the extreme case of only one single phase step per projection. The technique is successfully applied to measured tomographic data of a mouse. In future, this reconstruction technique might also be used to implement enhanced imaging models for X-ray Talbot-Lau tomography. These enhancements might be suited to correct for example beam hardening and dispersion artifacts and improve overall image quality of X-ray Talbot-Lau tomography.
Maximum-Likelihood Detection Of Noncoherent CPM
NASA Technical Reports Server (NTRS)
Divsalar, Dariush; Simon, Marvin K.
1993-01-01
Simplified detectors proposed for use in maximum-likelihood-sequence detection of symbols in alphabet of size M transmitted by uncoded, full-response continuous phase modulation over radio channel with additive white Gaussian noise. Structures of receivers derived from particular interpretation of maximum-likelihood metrics. Receivers include front ends, structures of which depends only on M, analogous to those in receivers of coherent CPM. Parts of receivers following front ends have structures, complexity of which would depend on N.
Lee, Seunghee; Johnson, John E.
2011-01-01
Many micro- to nano-scale 3-D biological objects have a helical symmetry. Cryo electron microscopy provides 2-D projection images where, however, the images have low SNR and unknown projection directions. The object is described as a helical array of identical motifs, where both the parameters of the helical symmetry and the motif are unknown. Using a detailed image formation model, a maximum likelihood estimator for the parameters of the symmetry and the 3-D motif based on images of many objects and algorithms for computing the estimate are described. The possibility that the objects are not identical but rather come from a small set of homogeneous classes is included. The first example is based on 316 128×100 pixel experimental images of Tobacco Mosaic Virus, has one class, and achieves 12.40Å spatial resolution in the reconstruction. The second example is based on 400 128 × 128 pixel synthetic images of helical objects constructed from NaK ion channel pore macromolecular complexes, has two classes differing in helical symmetry, and achieves 7.84Å and 7.90Å spatial resolution in the reconstructions for the two classes. PMID:21335314
Meng, L. J.; Li, Nan
2016-01-01
This paper presents a non-uniform object-space pixelation (NUOP) approach for image reconstruction using the penalized maximum likelihood methods. This method was developed for use with a single photon emission microscope (SPEM) system that offers an ultrahigh spatial resolution for a targeted local region inside mouse brain. In this approach, the object-space is divided with non-uniform pixel sizes, which are chosen adaptively based on object-dependent criteria. These include (a) some known characteristics of a target-region, (b) the associated Fisher Information that measures the weighted correlation between the responses of the system to gamma ray emissions occurred at different spatial locations, and (c) the linear distance from a given location to the target-region. In order to quantify the impact of this non-uniform pixelation approach on image quality, we used the Modified Uniform Cramer-Rao bound (MUCRB) to evaluate the local resolution-variance and bias-variance tradeoffs achievable with different pixelation strategies. As demonstrated in this paper, an efficient object-space pixelation could improve the speed of computation by 1–2 orders of magnitude, whilst maintaining an excellent reconstruction for the target-region. This improvement is crucial for making the SPEM system a practical imaging tool for mouse brain studies. The proposed method also allows rapid computation of the first and second order statistics of reconstructed images using analytical approximations, which is the key for the evaluation of several analytical system performance indices for system design and optimization.
Maximum likelihood estimates of pairwise rearrangement distances.
Serdoz, Stuart; Egri-Nagy, Attila; Sumner, Jeremy; Holland, Barbara R; Jarvis, Peter D; Tanaka, Mark M; Francis, Andrew R
2017-06-21
Accurate estimation of evolutionary distances between taxa is important for many phylogenetic reconstruction methods. Distances can be estimated using a range of different evolutionary models, from single nucleotide polymorphisms to large-scale genome rearrangements. Corresponding corrections for genome rearrangement distances fall into 3 categories: Empirical computational studies, Bayesian/MCMC approaches, and combinatorial approaches. Here, we introduce a maximum likelihood estimator for the inversion distance between a pair of genomes, using a group-theoretic approach to modelling inversions introduced recently. This MLE functions as a corrected distance: in particular, we show that because of the way sequences of inversions interact with each other, it is quite possible for minimal distance and MLE distance to differently order the distances of two genomes from a third. The second aspect tackles the problem of accounting for the symmetries of circular arrangements. While, generally, a frame of reference is locked, and all computation made accordingly, this work incorporates the action of the dihedral group so that distance estimates are free from any a priori frame of reference. The philosophy of accounting for symmetries can be applied to any existing correction method, for which examples are offered. Copyright © 2017 Elsevier Ltd. All rights reserved.
Maximum likelihood inference of reticulate evolutionary histories
Yu, Yun; Dong, Jianrong; Liu, Kevin J.; Nakhleh, Luay
2014-01-01
Hybridization plays an important role in the evolution of certain groups of organisms, adaptation to their environments, and diversification of their genomes. The evolutionary histories of such groups are reticulate, and methods for reconstructing them are still in their infancy and have limited applicability. We present a maximum likelihood method for inferring reticulate evolutionary histories while accounting simultaneously for incomplete lineage sorting. Additionally, we propose methods for assessing confidence in the amount of reticulation and the topology of the inferred evolutionary history. Our method obtains accurate estimates of reticulate evolutionary histories on simulated datasets. Furthermore, our method provides support for a hypothesis of a reticulate evolutionary history inferred from a set of house mouse (Mus musculus) genomes. As evidence of hybridization in eukaryotic groups accumulates, it is essential to have methods that infer reticulate evolutionary histories. The work we present here allows for such inference and provides a significant step toward putting phylogenetic networks on par with phylogenetic trees as a model of capturing evolutionary relationships. PMID:25368173
Maximum likelihood inference of reticulate evolutionary histories.
Yu, Yun; Dong, Jianrong; Liu, Kevin J; Nakhleh, Luay
2014-11-18
Hybridization plays an important role in the evolution of certain groups of organisms, adaptation to their environments, and diversification of their genomes. The evolutionary histories of such groups are reticulate, and methods for reconstructing them are still in their infancy and have limited applicability. We present a maximum likelihood method for inferring reticulate evolutionary histories while accounting simultaneously for incomplete lineage sorting. Additionally, we propose methods for assessing confidence in the amount of reticulation and the topology of the inferred evolutionary history. Our method obtains accurate estimates of reticulate evolutionary histories on simulated datasets. Furthermore, our method provides support for a hypothesis of a reticulate evolutionary history inferred from a set of house mouse (Mus musculus) genomes. As evidence of hybridization in eukaryotic groups accumulates, it is essential to have methods that infer reticulate evolutionary histories. The work we present here allows for such inference and provides a significant step toward putting phylogenetic networks on par with phylogenetic trees as a model of capturing evolutionary relationships.
Collaborative Double Robust Targeted Maximum Likelihood Estimation*
van der Laan, Mark J.; Gruber, Susan
2010-01-01
Collaborative double robust targeted maximum likelihood estimators represent a fundamental further advance over standard targeted maximum likelihood estimators of a pathwise differentiable parameter of a data generating distribution in a semiparametric model, introduced in van der Laan, Rubin (2006). The targeted maximum likelihood approach involves fluctuating an initial estimate of a relevant factor (Q) of the density of the observed data, in order to make a bias/variance tradeoff targeted towards the parameter of interest. The fluctuation involves estimation of a nuisance parameter portion of the likelihood, g. TMLE has been shown to be consistent and asymptotically normally distributed (CAN) under regularity conditions, when either one of these two factors of the likelihood of the data is correctly specified, and it is semiparametric efficient if both are correctly specified. In this article we provide a template for applying collaborative targeted maximum likelihood estimation (C-TMLE) to the estimation of pathwise differentiable parameters in semi-parametric models. The procedure creates a sequence of candidate targeted maximum likelihood estimators based on an initial estimate for Q coupled with a succession of increasingly non-parametric estimates for g. In a departure from current state of the art nuisance parameter estimation, C-TMLE estimates of g are constructed based on a loss function for the targeted maximum likelihood estimator of the relevant factor Q that uses the nuisance parameter to carry out the fluctuation, instead of a loss function for the nuisance parameter itself. Likelihood-based cross-validation is used to select the best estimator among all candidate TMLE estimators of Q0 in this sequence. A penalized-likelihood loss function for Q is suggested when the parameter of interest is borderline-identifiable. We present theoretical results for “collaborative double robustness,” demonstrating that the collaborative targeted maximum
Maximum likelihood for genome phylogeny on gene content.
Zhang, Hongmei; Gu, Xun
2004-01-01
With the rapid growth of entire genome data, reconstructing the phylogenetic relationship among different genomes has become a hot topic in comparative genomics. Maximum likelihood approach is one of the various approaches, and has been very successful. However, there is no reported study for any applications in the genome tree-making mainly due to the lack of an analytical form of a probability model and/or the complicated calculation burden. In this paper we studied the mathematical structure of the stochastic model of genome evolution, and then developed a simplified likelihood function for observing a specific phylogenetic pattern under four genome situation using gene content information. We use the maximum likelihood approach to identify phylogenetic trees. Simulation results indicate that the proposed method works well and can identify trees with a high correction rate. Real data application provides satisfied results. The approach developed in this paper can serve as the basis for reconstructing phylogenies of more than four genomes.
Maximum Likelihood and Bayesian Parameter Estimation in Item Response Theory.
ERIC Educational Resources Information Center
Lord, Frederic M.
There are currently three main approaches to parameter estimation in item response theory (IRT): (1) joint maximum likelihood, exemplified by LOGIST, yielding maximum likelihood estimates; (2) marginal maximum likelihood, exemplified by BILOG, yielding maximum likelihood estimates of item parameters (ability parameters can be estimated…
Maximum likelihood continuity mapping for fraud detection
Hogden, J.
1997-05-01
The author describes a novel time-series analysis technique called maximum likelihood continuity mapping (MALCOM), and focuses on one application of MALCOM: detecting fraud in medical insurance claims. Given a training data set composed of typical sequences, MALCOM creates a stochastic model of sequence generation, called a continuity map (CM). A CM maximizes the probability of sequences in the training set given the model constraints, CMs can be used to estimate the likelihood of sequences not found in the training set, enabling anomaly detection and sequence prediction--important aspects of data mining. Since MALCOM can be used on sequences of categorical data (e.g., sequences of words) as well as real valued data, MALCOM is also a potential replacement for database search tools such as N-gram analysis. In a recent experiment, MALCOM was used to evaluate the likelihood of patient medical histories, where ``medical history`` is used to mean the sequence of medical procedures performed on a patient. Physicians whose patients had anomalous medical histories (according to MALCOM) were evaluated for fraud by an independent agency. Of the small sample (12 physicians) that has been evaluated, 92% have been determined fraudulent or abusive. Despite the small sample, these results are encouraging.
Maximum Likelihood Estimation of Population Parameters
Fu, Y. X.; Li, W. H.
1993-01-01
One of the most important parameters in population genetics is θ = 4N(e)μ where N(e) is the effective population size and μ is the rate of mutation per gene per generation. We study two related problems, using the maximum likelihood method and the theory of coalescence. One problem is the potential improvement of accuracy in estimating the parameter θ over existing methods and the other is the estimation of parameter λ which is the ratio of two θ's. The minimum variances of estimates of the parameter θ are derived under two idealized situations. These minimum variances serve as the lower bounds of the variances of all possible estimates of θ in practice. We then show that Watterson's estimate of θ based on the number of segregating sites is asymptotically an optimal estimate of θ. However, for a finite sample of sequences, substantial improvement over Watterson's estimate is possible when θ is large. The maximum likelihood estimate of λ = θ(1)/θ(2) is obtained and the properties of the estimate are discussed. PMID:8375660
Maximum likelihood estimation of population parameters
Fu, Y.X.; Li, W.H. )
1993-08-01
One of the most important parameters in population genetics is [theta] = 4N[sub e][mu] where N[sub e] is the effective population size and [mu] is the rate of mutation per gene per generation. The authors study two related problems, using the maximum likelihood method and the theory of coalescence. One problem is the potential improvement of accuracy in estimating the parameter [theta] over existing methods and the other is the estimation of parameter [lambda] which is the ratio of two [theta]'s. The minimum variances serve as the lower bounds of the variances of all possible estimates of [theta] in practice. The authors then show that Watterson's estimate of [theta] based on the number of segregating sites is asymptotically an optimal estimate of [theta]. However, for a finite sample of sequences, substantial improvement over Watterson's estimate is possible when [theta] is large. The maximum likelihood estimate of [lambda] = [theta][sub 1]/[theta][sub 2] is obtained and the properties of the estimate are discussed. 9 refs., 3 figs., 3 tabs.
Maximum likelihood decoding of Reed Solomon Codes
Sudan, M.
1996-12-31
We present a randomized algorithm which takes as input n distinct points ((x{sub i}, y{sub i})){sup n}{sub i=1} from F x F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in at least t places (i.e., y{sub i} = f (x{sub i}) for at least t values of i), provided t = {Omega}({radical}nd). The running time is bounded by a polynomial in n. This immediately provides a maximum likelihood decoding algorithm for Reed Solomon Codes, which works in a setting with a larger number of errors than any previously known algorithm. To the best of our knowledge, this is the first efficient (i.e., polynomial time bounded) algorithm which provides some maximum likelihood decoding for any efficient (i.e., constant or even polynomial rate) code.
Maximum Likelihood Analysis in the PEN Experiment
NASA Astrophysics Data System (ADS)
Lehman, Martin
2013-10-01
The experimental determination of the π+ -->e+ ν (γ) decay branching ratio currently provides the most accurate test of lepton universality. The PEN experiment at PSI, Switzerland, aims to improve the present world average experimental precision of 3 . 3 ×10-3 to 5 ×10-4 using a stopped beam approach. During runs in 2008-10, PEN has acquired over 2 ×107 πe 2 events. The experiment includes active beam detectors (degrader, mini TPC, target), central MWPC tracking with plastic scintillator hodoscopes, and a spherical pure CsI electromagnetic shower calorimeter. The final branching ratio will be calculated using a maximum likelihood analysis. This analysis assigns each event a probability for 5 processes (π+ -->e+ ν , π+ -->μ+ ν , decay-in-flight, pile-up, and hadronic events) using Monte Carlo verified probability distribution functions of our observables (energies, times, etc). A progress report on the PEN maximum likelihood analysis will be presented. Work supported by NSF grant PHY-0970013.
Approximate maximum likelihood decoding of block codes
NASA Technical Reports Server (NTRS)
Greenberger, H. J.
1979-01-01
Approximate maximum likelihood decoding algorithms, based upon selecting a small set of candidate code words with the aid of the estimated probability of error of each received symbol, can give performance close to optimum with a reasonable amount of computation. By combining the best features of various algorithms and taking care to perform each step as efficiently as possible, a decoding scheme was developed which can decode codes which have better performance than those presently in use and yet not require an unreasonable amount of computation. The discussion of the details and tradeoffs of presently known efficient optimum and near optimum decoding algorithms leads, naturally, to the one which embodies the best features of all of them.
ERIC Educational Resources Information Center
Boedeker, Peter
2017-01-01
Hierarchical linear modeling (HLM) is a useful tool when analyzing data collected from groups. There are many decisions to be made when constructing and estimating a model in HLM including which estimation technique to use. Three of the estimation techniques available when analyzing data with HLM are maximum likelihood, restricted maximum…
Physically constrained maximum likelihood mode filtering.
Papp, Joseph C; Preisig, James C; Morozov, Andrey K
2010-04-01
Mode filtering is most commonly implemented using the sampled mode shapes or pseudoinverse algorithms. Buck et al. [J. Acoust. Soc. Am. 103, 1813-1824 (1998)] placed these techniques in the context of a broader maximum a posteriori (MAP) framework. However, the MAP algorithm requires that the signal and noise statistics be known a priori. Adaptive array processing algorithms are candidates for improving performance without the need for a priori signal and noise statistics. A variant of the physically constrained, maximum likelihood (PCML) algorithm [A. L. Kraay and A. B. Baggeroer, IEEE Trans. Signal Process. 55, 4048-4063 (2007)] is developed for mode filtering that achieves the same performance as the MAP mode filter yet does not need a priori knowledge of the signal and noise statistics. The central innovation of this adaptive mode filter is that the received signal's sample covariance matrix, as estimated by the algorithm, is constrained to be that which can be physically realized given a modal propagation model and an appropriate noise model. Shallow water simulation results are presented showing the benefit of using the PCML method in adaptive mode filtering.
Cases In Which Ancestral Maximum Likelihood Will Be Confusingly Misleading.
Handelman, Tomer; Chor, Benny
2017-03-02
Ancestral maximum likelihood (AML) is a phylogenetic tree reconstruction criteria that "lies between" maximum parsimony (MP) and maximum likelihood (ML). ML has long been known to be statistically consistent. On the other hand, Felsenstein (1978) showed that MP is statistically inconsistent, and even positively misleading: There are cases where the parsimony criteria, applied to data generated according to one tree topology, will be optimized on a different tree topology. The question of weather AML is statistically consistent or not has been open for a long time. Mosel, Roch, and Steel (2009) have shown that AML can "shrink" short tree edges, resulting in a star tree with no internal resolution, which yields a better AML score than the original (resolved) model. This result implies that AML is statistically inconsistent, but not that it is positively misleading, because the star tree is compatible with any other topology. We show that AML is confusingly misleading: For some simple, four taxa (resolved) tree, the ancestral likelihood optimization criteria is maximized on an incorrect (resolved) tree topology, as well as on a star tree (both with specific edge lengths), while the tree with the original, correct topology, has strictly lower ancestral likelihood. Interestingly, the two short edges in the incorrect, resolved tree topology are of length zero, and are not adjacent, so this resolved tree is in fact a simple path. While for MP, the underlying phenomenon can be described as long edge attraction, it turns out that here we have long edge repulsion.
Maximum Likelihood Estimation of Multivariate Polyserial and Polychoric Correlation Coefficients.
ERIC Educational Resources Information Center
Poon, Wai-Yin; Lee, Sik-Yum
1987-01-01
Reparameterization is used to find the maximum likelihood estimates of parameters in a multivariate model having some component variable observable only in polychotomous form. Maximum likelihood estimates are found by a Fletcher Powell algorithm. In addition, the partition maximum likelihood method is proposed and illustrated. (Author/GDC)
Maximum likelihood estimates of polar motion parameters
NASA Technical Reports Server (NTRS)
Wilson, Clark R.; Vicente, R. O.
1990-01-01
Two estimators developed by Jeffreys (1940, 1968) are described and used in conjunction with polar-motion data to determine the frequency (Fc) and quality factor (Qc) of the Chandler wobble. Data are taken from a monthly polar-motion series, satellite laser-ranging results, and optical astrometry and intercompared for use via interpolation techniques. Maximum likelihood arguments were employed to develop the estimators, and the assumption that polar motion relates to a Gaussian random process is assessed in terms of the accuracies of the estimators. The present results agree with those from Jeffreys' earlier study but are inconsistent with the later estimator; a Monte Carlo evaluation of the estimators confirms that the 1968 method is more accurate. The later estimator method shows good performance because the Fourier coefficients derived from the data have signal/noise levels that are superior to those for an individual datum. The method is shown to be valuable for general spectral-analysis problems in which isolated peaks must be analyzed from noisy data.
Maximum Log-Likelihood Method with Weighting Penalty for CRISM Hyperspectral Images
NASA Astrophysics Data System (ADS)
He, L.; Arvidson, R. E.; O'Sullivan, J. A.; Politte, D. V.
2017-06-01
We develop the Maximum Log-likelihood Method with weighting penalties to denoise and reconstruct the CRISM data. Spatial and spectral weights determined by sampling degrees and noise levels are introduced to remove spatial and spectral artifacts.
Likelihood Principle and Maximum Likelihood Estimator of Location Parameter for Cauchy Distribution.
1986-05-01
consistency (or strong consistency) of maximum likelihood estimator has been studied by many researchers, for example, Wald (1949), Wolfowitz (1953, 1965...20, 595-601. [25] Wolfowitz , J. (1953). The method of maximum likelihood and Wald theory of decision functions. Indag. Math., Vol. 15, 114-119. [26...Probability Letters Vol. 1, No. 3, 197-202. [24] Wald , A. (1949). Note on the consistency of maximum likelihood estimates. Ann. Math. Statist., Vol
Evolution of photosynthetic prokaryotes: a maximum-likelihood mapping approach.
Raymond, Jason; Zhaxybayeva, Olga; Gogarten, J Peter; Blankenship, Robert E
2003-01-01
Reconstructing the early evolution of photosynthesis has been guided in part by the geological record, but the complexity and great antiquity of these early events require molecular genetic techniques as the primary tools of inference. Recent genome sequencing efforts have made whole genome data available from representatives of each of the five phyla of bacteria with photosynthetic members, allowing extensive phylogenetic comparisons of these organisms. Here, we have undertaken whole genome comparisons using maximum likelihood to compare 527 unique sets of orthologous genes from all five photosynthetic phyla. Substantiating recent whole genome analyses of other prokaryotes, our results indicate that horizontal gene transfer (HGT) has played a significant part in the evolution of these organisms, resulting in genomes with mosaic evolutionary histories. A small plurality phylogenetic signal was observed, which may be a core of remnant genes not subject to HGT, or may result from a propensity for gene exchange between two or more of the photosynthetic organisms compared. PMID:12594930
Convex Accelerated Maximum Entropy Reconstruction
Worley, Bradley
2016-01-01
Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm – called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm – is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra. PMID:26894476
Convex accelerated maximum entropy reconstruction.
Worley, Bradley
2016-04-01
Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm - called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm - is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra. Copyright © 2016 Elsevier Inc. All rights reserved.
Convex accelerated maximum entropy reconstruction
NASA Astrophysics Data System (ADS)
Worley, Bradley
2016-04-01
Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm - called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm - is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra.
Convolutional codes. II - Maximum-likelihood decoding. III - Sequential decoding
NASA Technical Reports Server (NTRS)
Forney, G. D., Jr.
1974-01-01
Maximum-likelihood decoding is characterized as the determination of the shortest path through a topological structure called a trellis. Aspects of code structure are discussed along with questions regarding maximum-likelihood decoding on memoryless channels. A general bounding technique is introduced. The technique is used to obtain asymptotic bounds on the probability of error for maximum-likelihood decoding and list-of-2 decoding. The basic features of sequential algorithms are discussed along with a stack algorithm, questions of computational distribution, and the martingale approach to computational bounds.
Weibull distribution based on maximum likelihood with interval inspection data
NASA Technical Reports Server (NTRS)
Rheinfurth, M. H.
1985-01-01
The two Weibull parameters based upon the method of maximum likelihood are determined. The test data used were failures observed at inspection intervals. The application was the reliability analysis of the SSME oxidizer turbine blades.
Maximum Likelihood Factor Structure of the Family Environment Scale.
ERIC Educational Resources Information Center
Fowler, Patrick C.
1981-01-01
Presents the maximum likelihood factor structure of the Family Environment Scale. The first bipolar dimension, "cohesion v conflict," measures relationship-centered concerns, while the second unipolar dimension is an index of "organizational and control" activities. (Author)
Low-complexity approximations to maximum likelihood MPSK modulation classification
NASA Technical Reports Server (NTRS)
Hamkins, Jon
2004-01-01
We present a new approximation to the maximum likelihood classifier to discriminate between M-ary and M'-ary phase-shift-keying transmitted on an additive white Gaussian noise (AWGN) channel and received noncoherentl, partially coherently, or coherently.
Maximum likelihood estimation of finite mixture model for economic data
NASA Astrophysics Data System (ADS)
Phoong, Seuk-Yen; Ismail, Mohd Tahir
2014-06-01
Finite mixture model is a mixture model with finite-dimension. This models are provides a natural representation of heterogeneity in a finite number of latent classes. In addition, finite mixture models also known as latent class models or unsupervised learning models. Recently, maximum likelihood estimation fitted finite mixture models has greatly drawn statistician's attention. The main reason is because maximum likelihood estimation is a powerful statistical method which provides consistent findings as the sample sizes increases to infinity. Thus, the application of maximum likelihood estimation is used to fit finite mixture model in the present paper in order to explore the relationship between nonlinear economic data. In this paper, a two-component normal mixture model is fitted by maximum likelihood estimation in order to investigate the relationship among stock market price and rubber price for sampled countries. Results described that there is a negative effect among rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia.
Maximum likelihood solution for inclination-only data in paleomagnetism
NASA Astrophysics Data System (ADS)
Arason, P.; Levi, S.
2010-08-01
We have developed a new robust maximum likelihood method for estimating the unbiased mean inclination from inclination-only data. In paleomagnetic analysis, the arithmetic mean of inclination-only data is known to introduce a shallowing bias. Several methods have been introduced to estimate the unbiased mean inclination of inclination-only data together with measures of the dispersion. Some inclination-only methods were designed to maximize the likelihood function of the marginal Fisher distribution. However, the exact analytical form of the maximum likelihood function is fairly complicated, and all the methods require various assumptions and approximations that are often inappropriate. For some steep and dispersed data sets, these methods provide estimates that are significantly displaced from the peak of the likelihood function to systematically shallower inclination. The problem locating the maximum of the likelihood function is partly due to difficulties in accurately evaluating the function for all values of interest, because some elements of the likelihood function increase exponentially as precision parameters increase, leading to numerical instabilities. In this study, we succeeded in analytically cancelling exponential elements from the log-likelihood function, and we are now able to calculate its value anywhere in the parameter space and for any inclination-only data set. Furthermore, we can now calculate the partial derivatives of the log-likelihood function with desired accuracy, and locate the maximum likelihood without the assumptions required by previous methods. To assess the reliability and accuracy of our method, we generated large numbers of random Fisher-distributed data sets, for which we calculated mean inclinations and precision parameters. The comparisons show that our new robust Arason-Levi maximum likelihood method is the most reliable, and the mean inclination estimates are the least biased towards shallow values.
Properties of maximum likelihood male fertility estimation in plant populations.
Morgan, M T
1998-01-01
Computer simulations are used to evaluate maximum likelihood methods for inferring male fertility in plant populations. The maximum likelihood method can provide substantial power to characterize male fertilities at the population level. Results emphasize, however, the importance of adequate experimental design and evaluation of fertility estimates, as well as limitations to inference (e.g., about the variance in male fertility or the correlation between fertility and phenotypic trait value) that can be reasonably drawn. PMID:9611217
Investigating bias in maximum-likelihood quantum-state tomography
NASA Astrophysics Data System (ADS)
Silva, G. B.; Glancy, S.; Vasconcelos, H. M.
2017-02-01
Maximum-likelihood quantum-state tomography yields estimators that are consistent, provided that the likelihood model is correct, but the maximum-likelihood estimators may have bias for any finite data set. The bias of an estimator is the difference between the expected value of the estimate and the true value of the parameter being estimated. This paper investigates bias in the widely used maximum-likelihood quantum-state tomography. Our goal is to understand how the amount of bias depends on factors such as the purity of the true state, the number of measurements performed, and the number of different bases in which the system is measured. For this, we perform numerical experiments that simulate optical homodyne tomography of squeezed thermal states under various conditions, perform tomography, and estimate bias in the purity of the estimated state. We find that estimates of higher purity states exhibit considerable bias, such that the estimates have lower purities than the true states.
Relevance Data for Language Models Using Maximum Likelihood.
ERIC Educational Resources Information Center
Bodoff, David; Wu, Bin; Wong, K. Y. Michael
2003-01-01
Presents a preliminary empirical test of a maximum likelihood approach to using relevance data for training information retrieval parameters. Discusses similarities to language models; the unification of document-oriented and query-oriented views; tests on data sets; algorithms and scalability; and the effectiveness of maximum likelihood…
Maximum-likelihood estimation of haplotype frequencies in nuclear families.
Becker, Tim; Knapp, Michael
2004-07-01
The importance of haplotype analysis in the context of association fine mapping of disease genes has grown steadily over the last years. Since experimental methods to determine haplotypes on a large scale are not available, phase has to be inferred statistically. For individual genotype data, several reconstruction techniques and many implementations of the expectation-maximization (EM) algorithm for haplotype frequency estimation exist. Recent research work has shown that incorporating available genotype information of related individuals largely increases the precision of haplotype frequency estimates. We, therefore, implemented a highly flexible program written in C, called FAMHAP, which calculates maximum likelihood estimates (MLEs) of haplotype frequencies from general nuclear families with an arbitrary number of children via the EM-algorithm for up to 20 SNPs. For more loci, we have implemented a locus-iterative mode of the EM-algorithm, which gives reliable approximations of the MLEs for up to 63 SNP loci, or less when multi-allelic markers are incorporated into the analysis. Missing genotypes can be handled as well. The program is able to distinguish cases (haplotypes transmitted to the first affected child of a family) from pseudo-controls (non-transmitted haplotypes with respect to the child). We tested the performance of FAMHAP and the accuracy of the obtained haplotype frequencies on a variety of simulated data sets. The implementation proved to work well when many markers were considered and no significant differences between the estimates obtained with the usual EM-algorithm and those obtained in its locus-iterative mode were observed. We conclude from the simulations that the accuracy of haplotype frequency estimation and reconstruction in nuclear families is very reliable in general and robust against missing genotypes.
Parameter estimation in X-ray astronomy using maximum likelihood
NASA Technical Reports Server (NTRS)
Wachter, K.; Leach, R.; Kellogg, E.
1979-01-01
Methods of estimation of parameter values and confidence regions by maximum likelihood and Fisher efficient scores starting from Poisson probabilities are developed for the nonlinear spectral functions commonly encountered in X-ray astronomy. It is argued that these methods offer significant advantages over the commonly used alternatives called minimum chi-squared because they rely on less pervasive statistical approximations and so may be expected to remain valid for data of poorer quality. Extensive numerical simulations of the maximum likelihood method are reported which verify that the best-fit parameter value and confidence region calculations are correct over a wide range of input spectra.
Maximum-likelihood block detection of noncoherent continuous phase modulation
NASA Technical Reports Server (NTRS)
Simon, Marvin K.; Divsalar, Dariush
1993-01-01
This paper examines maximum-likelihood block detection of uncoded full response CPM over an additive white Gaussian noise (AWGN) channel. Both the maximum-likelihood metrics and the bit error probability performances of the associated detection algorithms are considered. The special and popular case of minimum-shift-keying (MSK) corresponding to h = 0.5 and constant amplitude frequency pulse is treated separately. The many new receiver structures that result from this investigation can be compared to the traditional ones that have been used in the past both from the standpoint of simplicity of implementation and optimality of performance.
Maximum likelihood classification of synthetic aperture radar imagery
NASA Technical Reports Server (NTRS)
Frost, V. S.; Yurovsky, L. S.
1985-01-01
Classification of synthetic aperture radar (SAR) images has important applications in geology, agriculture, and the military. A statistical model for SAR images is reviewed and a maximum likelihood classification algorithm developed for the classification of agricultural fields based on the model. It is first assumed that the target feature information is known a priori. The performance of the algorithm is then evaluated in terms of the probability of incorrect classification. A technique is also presented to extract the needed feature information from a SAR image; then both the feature extraction and the maximum likelihood classification algorithms are tested on a SEASAT-A SAR image.
Semiparametric maximum likelihood for nonlinear regression with measurement errors.
Suh, Eun-Young; Schafer, Daniel W
2002-06-01
This article demonstrates semiparametric maximum likelihood estimation of a nonlinear growth model for fish lengths using imprecisely measured ages. Data on the species corvina reina, found in the Gulf of Nicoya, Costa Rica, consist of lengths and imprecise ages for 168 fish and precise ages for a subset of 16 fish. The statistical problem may therefore be classified as nonlinear errors-in-variables regression with internal validation data. Inferential techniques are based on ideas extracted from several previous works on semiparametric maximum likelihood for errors-in-variables problems. The illustration of the example clarifies practical aspects of the associated computational, inferential, and data analytic techniques.
Mixture Rasch Models with Joint Maximum Likelihood Estimation
ERIC Educational Resources Information Center
Willse, John T.
2011-01-01
This research provides a demonstration of the utility of mixture Rasch models. Specifically, a model capable of estimating a mixture partial credit model using joint maximum likelihood is presented. Like the partial credit model, the mixture partial credit model has the beneficial feature of being appropriate for analysis of assessment data…
A Unified Maximum Likelihood Approach to Document Retrieval.
ERIC Educational Resources Information Center
Bodoff, David; Enache, Daniel; Kambil, Ajit; Simon, Gary; Yukhimets, Alex
2001-01-01
Addresses the query- versus document-oriented dichotomy in information retrieval. Introduces a maximum likelihood approach to utilizing feedback data that can be used to construct a concrete object function that estimates both document and query parameters in accordance with all available feedback data. (AEF)
Maximum Likelihood Detection of Electro-Optic Moving Targets
1992-01-16
The description of a maximum likelihood algorithm to detect moving targets in electro - optic data is presented. The algorithm is based on processing...optimum algorithm to determine the performance loss. A processing architecture concept is also described. Electro - optic sensor, detection, infrared sensor, moving target, binary integration, velocity filter.
Mixture Rasch Models with Joint Maximum Likelihood Estimation
ERIC Educational Resources Information Center
Willse, John T.
2011-01-01
This research provides a demonstration of the utility of mixture Rasch models. Specifically, a model capable of estimating a mixture partial credit model using joint maximum likelihood is presented. Like the partial credit model, the mixture partial credit model has the beneficial feature of being appropriate for analysis of assessment data…
Maximum likelihood Jukes-Cantor triplets: analytic solutions.
Chor, Benny; Hendy, Michael D; Snir, Sagi
2006-03-01
Maximum likelihood (ML) is a popular method for inferring a phylogenetic tree of the evolutionary relationship of a set of taxa, from observed homologous aligned genetic sequences of the taxa. Generally, the computation of the ML tree is based on numerical methods, which in a few cases, are known to converge to a local maximum on a tree, which is suboptimal. The extent of this problem is unknown, one approach is to attempt to derive algebraic equations for the likelihood equation and find the maximum points analytically. This approach has so far only been successful in the very simplest cases, of three or four taxa under the Neyman model of evolution of two-state characters. In this paper we extend this approach, for the first time, to four-state characters, the Jukes-Cantor model under a molecular clock, on a tree T on three taxa, a rooted triple. We employ spectral methods (Hadamard conjugation) to express the likelihood function parameterized by the path-length spectrum. Taking partial derivatives, we derive a set of polynomial equations whose simultaneous solution contains all critical points of the likelihood function. Using tools of algebraic geometry (the resultant of two polynomials) in the computer algebra packages (Maple), we are able to find all turning points analytically. We then employ this method on real sequence data and obtain realistic results on the primate-rodents divergence time.
Nonparametric maximum likelihood estimation for the multisample Wicksell corpuscle problem
Chan, Kwun Chuen Gary; Qin, Jing
2016-01-01
We study nonparametric maximum likelihood estimation for the distribution of spherical radii using samples containing a mixture of one-dimensional, two-dimensional biased and three-dimensional unbiased observations. Since direct maximization of the likelihood function is intractable, we propose an expectation-maximization algorithm for implementing the estimator, which handles an indirect measurement problem and a sampling bias problem separately in the E- and M-steps, and circumvents the need to solve an Abel-type integral equation, which creates numerical instability in the one-sample problem. Extensions to ellipsoids are studied and connections to multiplicative censoring are discussed. PMID:27279657
ERIC Educational Resources Information Center
Wothke, Werner; Burket, George; Chen, Li-Sue; Gao, Furong; Shu, Lianghua; Chia, Mike
2011-01-01
It has been known for some time that item response theory (IRT) models may exhibit a likelihood function of a respondent's ability which may have multiple modes, flat modes, or both. These conditions, often associated with guessing of multiple-choice (MC) questions, can introduce uncertainty and bias to ability estimation by maximum likelihood…
ERIC Educational Resources Information Center
Wothke, Werner; Burket, George; Chen, Li-Sue; Gao, Furong; Shu, Lianghua; Chia, Mike
2011-01-01
It has been known for some time that item response theory (IRT) models may exhibit a likelihood function of a respondent's ability which may have multiple modes, flat modes, or both. These conditions, often associated with guessing of multiple-choice (MC) questions, can introduce uncertainty and bias to ability estimation by maximum likelihood…
A maximum-likelihood estimation of pairwise relatedness for autopolyploids
Huang, K; Guo, S T; Shattuck, M R; Chen, S T; Qi, X G; Zhang, P; Li, B G
2015-01-01
Relatedness between individuals is central to ecological genetics. Multiple methods are available to quantify relatedness from molecular data, including method-of-moment and maximum-likelihood estimators. We describe a maximum-likelihood estimator for autopolyploids, and quantify its statistical performance under a range of biologically relevant conditions. The statistical performances of five additional polyploid estimators of relatedness were also quantified under identical conditions. When comparing truncated estimators, the maximum-likelihood estimator exhibited lower root mean square error under some conditions and was more biased for non-relatives, especially when the number of alleles per loci was low. However, even under these conditions, this bias was reduced to be statistically insignificant with more robust genetic sampling. We also considered ambiguity in polyploid heterozygote genotyping and developed a weighting methodology for candidate genotypes. The statistical performances of three polyploid estimators under both ideal and actual conditions (including inbreeding and double reduction) were compared. The software package POLYRELATEDNESS is available to perform this estimation and supports a maximum ploidy of eight. PMID:25370210
Hu, Kaifeng; Ellinger, James J; Chylla, Roger A; Markley, John L
2011-12-15
Time-zero 2D (13)C HSQC (HSQC(0)) spectroscopy offers advantages over traditional 2D NMR for quantitative analysis of solutions containing a mixture of compounds because the signal intensities are directly proportional to the concentrations of the constituents. The HSQC(0) spectrum is derived from a series of spectra collected with increasing repetition times within the basic HSQC block by extrapolating the repetition time to zero. Here we present an alternative approach to data collection, gradient-selective time-zero (1)H-(13)C HSQC(0) in combination with fast maximum likelihood reconstruction (FMLR) data analysis and the use of two concentration references for absolute concentration determination. Gradient-selective data acquisition results in cleaner spectra, and NMR data can be acquired in both constant-time and non-constant-time mode. Semiautomatic data analysis is supported by the FMLR approach, which is used to deconvolute the spectra and extract peak volumes. The peak volumes obtained from this analysis are converted to absolute concentrations by reference to the peak volumes of two internal reference compounds of known concentration: DSS (4,4-dimethyl-4-silapentane-1-sulfonic acid) at the low concentration limit (which also serves as chemical shift reference) and MES (2-(N-morpholino)ethanesulfonic acid) at the high concentration limit. The linear relationship between peak volumes and concentration is better defined with two references than with one, and the measured absolute concentrations of individual compounds in the mixture are more accurate. We compare results from semiautomated gsHSQC(0) with those obtained by the original manual phase-cycled HSQC(0) approach. The new approach is suitable for automatic metabolite profiling by simultaneous quantification of multiple metabolites in a complex mixture.
Skewness for Maximum Likelihood Estimators of the Negative Binomial Distribution
Bowman, Kimiko o
2007-01-01
The probability generating function of one version of the negative binomial distribution being (p + 1 - pt){sup -k}, we study elements of the Hessian and in particular Fisher's discovery of a series form for the variance of k, the maximum likelihood estimator, and also for the determinant of the Hessian. There is a link with the Psi function and its derivatives. Basic algebra is excessively complicated and a Maple code implementation is an important task in the solution process. Low order maximum likelihood moments are given and also Fisher's examples relating to data associated with ticks on sheep. Efficiency of moment estimators is mentioned, including the concept of joint efficiency. In an Addendum we give an interesting formula for the difference of two Psi functions.
Use of historical information in a maximum-likelihood framework
Cohn, T.A.; Stedinger, J.R.
1987-01-01
This paper discusses flood-quantile estimators which can employ historical and paleoflood information, both when the magnitudes of historical flood peaks are known, and when only threshold-exceedance information is available. Maximum likelihood, quasi-maximum likelihood and curve fitting methods for simultaneous estimation of 1, 2 and 3 unknown parameters are examined. The information contained in a 100 yr record of historical observations, during which the flood perception threshold was near the 10 yr flood level (i.e., on average, one flood in ten is above the threshold and hence is recorded), is equivalent to roughly 43, 64 and 78 years of systematic record in terms of the improvement of the precision of 100 yr flood estimators when estimating 1, 2 and 3 parameters, respectively. With the perception threshold at the 100 yr flood level, the historical data was worth 13, 20 and 46 years of systematic data when estimating 1, 2 and 3 parameters, respectively. ?? 1987.
Chylla, Roger A; Van Acker, Rebecca; Kim, Hoon; Azapira, Ali; Mukerjee, Purba; Markley, John L; Storme, Véronique; Boerjan, Wout; Ralph, John
2013-04-26
Interest in the detailed lignin and polysaccharide composition of plant cell walls has surged within the past decade partly as a result of biotechnology research aimed at converting biomass to biofuels. High-resolution, solution-state 2D 1H-13C HSQC NMR spectroscopy has proven to be an effective tool for rapid and reproducible fingerprinting of the numerous polysaccharides and lignin components in unfractionated plant cell wall materials, and is therefore a powerful tool for cell wall profiling based on our ability to simultaneously identify and comparatively quantify numerous components within spectra generated in a relatively short time. However, assigning peaks in new spectra, integrating them to provide relative component distributions, and producing color-assigned spectra, are all current bottlenecks to the routine use of such NMR profiling methods. We have assembled a high-throughput software platform for plant cell wall profiling that uses spectral deconvolution by Fast Maximum Likelihood Reconstruction (FMLR) to construct a mathematical model of the signals present in a set of related NMR spectra. Combined with a simple region of interest (ROI) table that maps spectral regions to NMR chemical shift assignments of chemical entities, the reconstructions can provide rapid and reproducible fingerprinting of numerous polysaccharide and lignin components in unfractionated cell wall material, including derivation of lignin monomer unit (S:G:H) ratios or the so-called SGH profile. Evidence is presented that ROI-based amplitudes derived from FMLR provide a robust feature set for subsequent multivariate analysis. The utility of this approach is demonstrated on a large transgenic study of Arabidopsis requiring concerted analysis of 91 ROIs (including both assigned and unassigned regions) in the lignin and polysaccharide regions of almost 100 related 2D 1H-13C HSQC spectra. We show that when a suitable number of replicates are obtained per sample group, the correlated
Maximum Likelihood Estimation with Emphasis on Aircraft Flight Data
NASA Technical Reports Server (NTRS)
Iliff, K. W.; Maine, R. E.
1985-01-01
Accurate modeling of flexible space structures is an important field that is currently under investigation. Parameter estimation, using methods such as maximum likelihood, is one of the ways that the model can be improved. The maximum likelihood estimator has been used to extract stability and control derivatives from flight data for many years. Most of the literature on aircraft estimation concentrates on new developments and applications, assuming familiarity with basic estimation concepts. Some of these basic concepts are presented. The maximum likelihood estimator and the aircraft equations of motion that the estimator uses are briefly discussed. The basic concepts of minimization and estimation are examined for a simple computed aircraft example. The cost functions that are to be minimized during estimation are defined and discussed. Graphic representations of the cost functions are given to help illustrate the minimization process. Finally, the basic concepts are generalized, and estimation from flight data is discussed. Specific examples of estimation of structural dynamics are included. Some of the major conclusions for the computed example are also developed for the analysis of flight data.
Noncoherent Maximum Likelihood Detection for Differential Spatial Multiplexing MIMO Systems
NASA Astrophysics Data System (ADS)
Jia, Ziyan; Yoshii, Katsunobu; Handa, Shiro; Sasamori, Fumihito; Oshita, Shinjiro
In this paper, we propose a novel noncoherent maximum likelihood detection (NMLD) method for differential spatial multiplexing (SM) multiple-input multiple-output (MIMO) systems. Unlike the conventional maximum likelihood detection (MLD) method which needs the knowledge of channel state information (CSI) at the receiver, NMLD method has no need of CSI at either the transmitter orreceiver. After repartitioning the observation block of multiple-symbol differential detection (MSDD) and following a decision feedback process, the decision metric of NMLD is derived by reforming that of MSDD. Since the maximum Doppler frequency and noise power are included in the derived decision metric, estimations of both maximum Doppler frequency and noise power are needed at the receiver for NMLD. A fast calculation algorithm (FCA) is applied to reduce the computational complexity of NMLD. The feasibility of the proposed NMLD is demonstrated by computer simulations in both slow and fast fading environments. Simulation results show that the proposed NMLD has good bit error rate (BER) performance, approaching that of the conventional coherent MLD with the extension of reference symbols interval. It is also proved that the BER performance is not sensitive to the estimation errors in maximum Doppler frequency and noise power.
Approximate maximum likelihood estimation of scanning observer templates
NASA Astrophysics Data System (ADS)
Abbey, Craig K.; Samuelson, Frank W.; Wunderlich, Adam; Popescu, Lucretiu M.; Eckstein, Miguel P.; Boone, John M.
2015-03-01
In localization tasks, an observer is asked to give the location of some target or feature of interest in an image. Scanning linear observer models incorporate the search implicit in this task through convolution of an observer template with the image being evaluated. Such models are becoming increasingly popular as predictors of human performance for validating medical imaging methodology. In addition to convolution, scanning models may utilize internal noise components to model inconsistencies in human observer responses. In this work, we build a probabilistic mathematical model of this process and show how it can, in principle, be used to obtain estimates of the observer template using maximum likelihood methods. The main difficulty of this approach is that a closed form probability distribution for a maximal location response is not generally available in the presence of internal noise. However, for a given image we can generate an empirical distribution of maximal locations using Monte-Carlo sampling. We show that this probability is well approximated by applying an exponential function to the scanning template output. We also evaluate log-likelihood functions on the basis of this approximate distribution. Using 1,000 trials of simulated data as a validation test set, we find that a plot of the approximate log-likelihood function along a single parameter related to the template profile achieves its maximum value near the true value used in the simulation. This finding holds regardless of whether the trials are correctly localized or not. In a second validation study evaluating a parameter related to the relative magnitude of internal noise, only the incorrect localization images produces a maximum in the approximate log-likelihood function that is near the true value of the parameter.
Gaussian maximum likelihood and contextual classification algorithms for multicrop classification
NASA Technical Reports Server (NTRS)
Di Zenzo, Silvano; Bernstein, Ralph; Kolsky, Harwood G.; Degloria, Stephen D.
1987-01-01
The paper reviews some of the ways in which context has been handled in the remote-sensing literature, and additional possibilities are introduced. The problem of computing exhaustive and normalized class-membership probabilities from the likelihoods provided by the Gaussian maximum likelihood classifier (to be used as initial probability estimates to start relaxation) is discussed. An efficient implementation of probabilistic relaxation is proposed, suiting the needs of actual remote-sensing applications. A modified fuzzy-relaxation algorithm using generalized operations between fuzzy sets is presented. Combined use of the two relaxation algorithms is proposed to exploit context in multispectral classification of remotely sensed data. Results on both one artificially created image and one MSS data set are reported.
Gaussian maximum likelihood and contextual classification algorithms for multicrop classification
NASA Technical Reports Server (NTRS)
Di Zenzo, Silvano; Bernstein, Ralph; Kolsky, Harwood G.; Degloria, Stephen D.
1987-01-01
The paper reviews some of the ways in which context has been handled in the remote-sensing literature, and additional possibilities are introduced. The problem of computing exhaustive and normalized class-membership probabilities from the likelihoods provided by the Gaussian maximum likelihood classifier (to be used as initial probability estimates to start relaxation) is discussed. An efficient implementation of probabilistic relaxation is proposed, suiting the needs of actual remote-sensing applications. A modified fuzzy-relaxation algorithm using generalized operations between fuzzy sets is presented. Combined use of the two relaxation algorithms is proposed to exploit context in multispectral classification of remotely sensed data. Results on both one artificially created image and one MSS data set are reported.
Last Glacial Maximum Salinity Reconstruction
NASA Astrophysics Data System (ADS)
Homola, K.; Spivack, A. J.
2016-12-01
It has been previously demonstrated that salinity can be reconstructed from sediment porewater. The goal of our study is to reconstruct high precision salinity during the Last Glacial Maximum (LGM). Salinity is usually determined at high precision via conductivity, which requires a larger volume of water than can be extracted from a sediment core, or via chloride titration, which yields lower than ideal precision. It has been demonstrated for water column samples that high precision density measurements can be used to determine salinity at the precision of a conductivity measurement using the equation of state of seawater. However, water column seawater has a relatively constant composition, in contrast to porewater, where variations from standard seawater composition occur. These deviations, which affect the equation of state, must be corrected for through precise measurements of each ion's concentration and knowledge of apparent partial molar density in seawater. We have developed a density-based method for determining porewater salinity that requires only 5 mL of sample, achieving density precisions of 10-6 g/mL. We have applied this method to porewater samples extracted from long cores collected along a N-S transect across the western North Atlantic (R/V Knorr cruise KN223). Density was determined to a precision of 2.3x10-6 g/mL, which translates to salinity uncertainty of 0.002 gms/kg if the effect of differences in composition is well constrained. Concentrations of anions (Cl-, and SO4-2) and cations (Na+, Mg+, Ca+2, and K+) were measured. To correct salinities at the precision required to unravel LGM Meridional Overturning Circulation, our ion precisions must be better than 0.1% for SO4-/Cl- and Mg+/Na+, and 0.4% for Ca+/Na+, and K+/Na+. Alkalinity, pH and Dissolved Inorganic Carbon of the porewater were determined to precisions better than 4% when ratioed to Cl-, and used to calculate HCO3-, and CO3-2. Apparent partial molar densities in seawater were
Tamura, Koichiro; Peterson, Daniel; Peterson, Nicholas; Stecher, Glen; Nei, Masatoshi; Kumar, Sudhir
2011-01-01
Comparative analysis of molecular sequence data is essential for reconstructing the evolutionary histories of species and inferring the nature and extent of selective forces shaping the evolution of genes and species. Here, we announce the release of Molecular Evolutionary Genetics Analysis version 5 (MEGA5), which is a user-friendly software for mining online databases, building sequence alignments and phylogenetic trees, and using methods of evolutionary bioinformatics in basic biology, biomedicine, and evolution. The newest addition in MEGA5 is a collection of maximum likelihood (ML) analyses for inferring evolutionary trees, selecting best-fit substitution models (nucleotide or amino acid), inferring ancestral states and sequences (along with probabilities), and estimating evolutionary rates site-by-site. In computer simulation analyses, ML tree inference algorithms in MEGA5 compared favorably with other software packages in terms of computational efficiency and the accuracy of the estimates of phylogenetic trees, substitution parameters, and rate variation among sites. The MEGA user interface has now been enhanced to be activity driven to make it easier for the use of both beginners and experienced scientists. This version of MEGA is intended for the Windows platform, and it has been configured for effective use on Mac OS X and Linux desktops. It is available free of charge from http://www.megasoftware.net. PMID:21546353
A Maximum-Likelihood Approach to Force-Field Calibration.
Zaborowski, Bartłomiej; Jagieła, Dawid; Czaplewski, Cezary; Hałabis, Anna; Lewandowska, Agnieszka; Żmudzińska, Wioletta; Ołdziej, Stanisław; Karczyńska, Agnieszka; Omieczynski, Christian; Wirecki, Tomasz; Liwo, Adam
2015-09-28
A new approach to the calibration of the force fields is proposed, in which the force-field parameters are obtained by maximum-likelihood fitting of the calculated conformational ensembles to the experimental ensembles of training system(s). The maximum-likelihood function is composed of logarithms of the Boltzmann probabilities of the experimental conformations, calculated with the current energy function. Because the theoretical distribution is given in the form of the simulated conformations only, the contributions from all of the simulated conformations, with Gaussian weights in the distances from a given experimental conformation, are added to give the contribution to the target function from this conformation. In contrast to earlier methods for force-field calibration, the approach does not suffer from the arbitrariness of dividing the decoy set into native-like and non-native structures; however, if such a division is made instead of using Gaussian weights, application of the maximum-likelihood method results in the well-known energy-gap maximization. The computational procedure consists of cycles of decoy generation and maximum-likelihood-function optimization, which are iterated until convergence is reached. The method was tested with Gaussian distributions and then applied to the physics-based coarse-grained UNRES force field for proteins. The NMR structures of the tryptophan cage, a small α-helical protein, determined at three temperatures (T = 280, 305, and 313 K) by Hałabis et al. ( J. Phys. Chem. B 2012 , 116 , 6898 - 6907 ), were used. Multiplexed replica-exchange molecular dynamics was used to generate the decoys. The iterative procedure exhibited steady convergence. Three variants of optimization were tried: optimization of the energy-term weights alone and use of the experimental ensemble of the folded protein only at T = 280 K (run 1); optimization of the energy-term weights and use of experimental ensembles at all three temperatures (run 2
Fast maximum likelihood joint estimation of frequency and frequency rate
NASA Astrophysics Data System (ADS)
Abatzoglou, Theagenis J.
1986-11-01
A fast maximum likelihood algorithm is presented that jointly estimates the frequency and frequency rate of a sinusoid corrupted by additive Gaussian white noise. It consists of a coarse search and a fine search. First, the two-dimensional frequency-frequency rate plane is subdivided into parallelograms whose size depends on the region of convergence of Newton's method used in maximizing the log-likelihood function (LLF). The size of the parallelogram is explicitly computed and is optimal for the method used. The coarse search consists of maximizing the LLF over the vertices of the parallelograms. Then, starting at the vertex where the LLF attained its maximum, a two-dimensional Newton's method to find the absolute maximum of the LLF is implemented. This last step consists of the fine search. The rate of convergence of Newton's method is cubic, and is extremely fast. Furthermore, Newton's method will converge after two iterations when the starting point used in the method lies within 75 percent of the distances defined by the parallelogram of convergence whose center coincides with the true values of frequency and frequency rate. In this case, the rms errors for frequency and frequency rate are practically equal to the Cramer-Rao bound at all signal-to-noise ratio of equal to or greater than 15 dB. The frequency-frequency rate ambiguity function is shown to be even, and its periodicities are extracted.
Optimized Large-scale CMB Likelihood and Quadratic Maximum Likelihood Power Spectrum Estimation
NASA Astrophysics Data System (ADS)
Gjerløw, E.; Colombo, L. P. L.; Eriksen, H. K.; Górski, K. M.; Gruppuso, A.; Jewell, J. B.; Plaszczynski, S.; Wehus, I. K.
2015-11-01
We revisit the problem of exact cosmic microwave background (CMB) likelihood and power spectrum estimation with the goal of minimizing computational costs through linear compression. This idea was originally proposed for CMB purposes by Tegmark et al., and here we develop it into a fully functioning computational framework for large-scale polarization analysis, adopting WMAP as a working example. We compare five different linear bases (pixel space, harmonic space, noise covariance eigenvectors, signal-to-noise covariance eigenvectors, and signal-plus-noise covariance eigenvectors) in terms of compression efficiency, and find that the computationally most efficient basis is the signal-to-noise eigenvector basis, which is closely related to the Karhunen-Loeve and Principal Component transforms, in agreement with previous suggestions. For this basis, the information in 6836 unmasked WMAP sky map pixels can be compressed into a smaller set of 3102 modes, with a maximum error increase of any single multipole of 3.8% at ℓ ≤ 32 and a maximum shift in the mean values of a joint distribution of an amplitude-tilt model of 0.006σ. This compression reduces the computational cost of a single likelihood evaluation by a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust likelihood by implicitly regularizing nearly degenerate modes. Finally, we use the same compression framework to formulate a numerically stable and computationally efficient variation of the Quadratic Maximum Likelihood implementation, which requires less than 3 GB of memory and 2 CPU minutes per iteration for ℓ ≤ 32, rendering low-ℓ QML CMB power spectrum analysis fully tractable on a standard laptop.
Maximum likelihood estimation for life distributions with competing failure modes
NASA Technical Reports Server (NTRS)
Sidik, S. M.
1979-01-01
Systems which are placed on test at time zero, function for a period and die at some random time were studied. Failure may be due to one of several causes or modes. The parameters of the life distribution may depend upon the levels of various stress variables the item is subject to. Maximum likelihood estimation methods are discussed. Specific methods are reported for the smallest extreme-value distributions of life. Monte-Carlo results indicate the methods to be promising. Under appropriate conditions, the location parameters are nearly unbiased, the scale parameter is slight biased, and the asymptotic covariances are rapidly approached.
Efficient maximum likelihood parameterization of continuous-time Markov processes
McGibbon, Robert T.; Pande, Vijay S.
2015-01-01
Continuous-time Markov processes over finite state-spaces are widely used to model dynamical processes in many fields of natural and social science. Here, we introduce a maximum likelihood estimator for constructing such models from data observed at a finite time interval. This estimator is dramatically more efficient than prior approaches, enables the calculation of deterministic confidence intervals in all model parameters, and can easily enforce important physical constraints on the models such as detailed balance. We demonstrate and discuss the advantages of these models over existing discrete-time Markov models for the analysis of molecular dynamics simulations. PMID:26203016
Maximum-likelihood analysis of the COBE angular correlation function
NASA Technical Reports Server (NTRS)
Seljak, Uros; Bertschinger, Edmund
1993-01-01
We have used maximum-likelihood estimation to determine the quadrupole amplitude Q(sub rms-PS) and the spectral index n of the density fluctuation power spectrum at recombination from the COBE DMR data. We find a strong correlation between the two parameters of the form Q(sub rms-PS) = (15.7 +/- 2.6) exp (0.46(1 - n)) microK for fixed n. Our result is slightly smaller than and has a smaller statistical uncertainty than the 1992 estimate of Smoot et al.
CCD data processor for maximum likelihood feature classification
NASA Technical Reports Server (NTRS)
Benz, H. F.; Kelly, W. L.; Husson, C.; Culotta, P. W.; Snyder, W. E.
1980-01-01
The paper describes an advanced technology development which utilizes a high speed analog/binary CCD correlator to perform the matrix multiplications necessary to implement onboard feature classification. The matrix manipulation module uses the maximum likelihood classification algorithm assuming a Gaussian probability density function. The module will process 16 element multispectral vectors at rates in excess of 500 thousand multispectral vector elements per second. System design considerations for the optimum use of this module are discussed, test results from initial device fabrication runs are presented, and the performance in typical processing applications is described
Maximum likelihood estimation for distributed parameter models of flexible spacecraft
NASA Technical Reports Server (NTRS)
Taylor, L. W., Jr.; Williams, J. L.
1989-01-01
A distributed-parameter model of the NASA Solar Array Flight Experiment spacecraft structure is constructed on the basis of measurement data and analyzed to generate a priori estimates of modal frequencies and mode shapes. A Newton-Raphson maximum-likelihood algorithm is applied to determine the unknown parameters, using a truncated model for the estimation and the full model for the computation of the higher modes. Numerical results are presented in a series of graphs and briefly discussed, and the significant improvement in computation speed obtained by parallel implementation of the method on a supercomputer is noted.
A 3D approximate maximum likelihood localization solver
2016-09-23
A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with acoustic transmitters and vocalizing marine mammals to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives and support Marine Renewable Energy. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
Precision of maximum likelihood estimation in adaptive designs.
Graf, Alexandra Christine; Gutjahr, Georg; Brannath, Werner
2016-03-15
There has been increasing interest in trials that allow for design adaptations like sample size reassessment or treatment selection at an interim analysis. Ignoring the adaptive and multiplicity issues in such designs leads to an inflation of the type 1 error rate, and treatment effect estimates based on the maximum likelihood principle become biased. Whereas the methodological issues concerning hypothesis testing are well understood, it is not clear how to deal with parameter estimation in designs were adaptation rules are not fixed in advanced so that, in practice, the maximum likelihood estimate (MLE) is used. It is therefore important to understand the behavior of the MLE in such designs. The investigation of Bias and mean squared error (MSE) is complicated by the fact that the adaptation rules need not be fully specified in advance and, hence, are usually unknown. To investigate Bias and MSE under such circumstances, we search for the sample size reassessment and selection rules that lead to the maximum Bias or maximum MSE. Generally, this leads to an overestimation of Bias and MSE, which can be reduced by imposing realistic constraints on the rules like, for example, a maximum sample size. We consider designs that start with k treatment groups and a common control and where selection of a single treatment and control is performed at the interim analysis with the possibility to reassess each of the sample sizes. We consider the case of unlimited sample size reassessments as well as several realistically restricted sample size reassessment rules. Copyright © 2015 John Wiley & Sons, Ltd.
Maximum likelihood tuning of a vehicle motion filter
NASA Technical Reports Server (NTRS)
Trankle, Thomas L.; Rabin, Uri H.
1990-01-01
This paper describes the use of maximum likelihood parameter estimation unknown parameters appearing in a nonlinear vehicle motion filter. The filter uses the kinematic equations of motion of a rigid body in motion over a spherical earth. The nine states of the filter represent vehicle velocity, attitude, and position. The inputs to the filter are three components of translational acceleration and three components of angular rate. Measurements used to update states include air data, altitude, position, and attitude. Expressions are derived for the elements of filter matrices needed to use air data in a body-fixed frame with filter states expressed in a geographic frame. An expression for the likelihood functions of the data is given, along with accurate approximations for the function's gradient and Hessian with respect to unknown parameters. These are used by a numerical quasi-Newton algorithm for maximizing the likelihood function of the data in order to estimate the unknown parameters. The parameter estimation algorithm is useful for processing data from aircraft flight tests or for tuning inertial navigation systems.
Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions
Barrett, Harrison H.; Dainty, Christopher; Lara, David
2008-01-01
Maximum-likelihood (ML) estimation in wavefront sensing requires careful attention to all noise sources and all factors that influence the sensor data. We present detailed probability density functions for the output of the image detector in a wavefront sensor, conditional not only on wavefront parameters but also on various nuisance parameters. Practical ways of dealing with nuisance parameters are described, and final expressions for likelihoods and Fisher information matrices are derived. The theory is illustrated by discussing Shack–Hartmann sensors, and computational requirements are discussed. Simulation results show that ML estimation can significantly increase the dynamic range of a Shack–Hartmann sensor with four detectors and that it can reduce the residual wavefront error when compared with traditional methods. PMID:17206255
Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions
NASA Astrophysics Data System (ADS)
Barrett, Harrison H.; Dainty, Christopher; Lara, David
2007-02-01
Maximum-likelihood (ML) estimation in wavefront sensing requires careful attention to all noise sources and all factors that influence the sensor data. We present detailed probability density functions for the output of the image detector in a wavefront sensor, conditional not only on wavefront parameters but also on various nuisance parameters. Practical ways of dealing with nuisance parameters are described, and final expressions for likelihoods and Fisher information matrices are derived. The theory is illustrated by discussing Shack-Hartmann sensors, and computational requirements are discussed. Simulation results show that ML estimation can significantly increase the dynamic range of a Shack-Hartmann sensor with four detectors and that it can reduce the residual wavefront error when compared with traditional methods.
Targeted Maximum Likelihood Estimation for Causal Inference in Observational Studies.
Schuler, Megan S; Rose, Sherri
2017-01-01
Estimation of causal effects using observational data continues to grow in popularity in the epidemiologic literature. While many applications of causal effect estimation use propensity score methods or G-computation, targeted maximum likelihood estimation (TMLE) is a well-established alternative method with desirable statistical properties. TMLE is a doubly robust maximum-likelihood-based approach that includes a secondary "targeting" step that optimizes the bias-variance tradeoff for the target parameter. Under standard causal assumptions, estimates can be interpreted as causal effects. Because TMLE has not been as widely implemented in epidemiologic research, we aim to provide an accessible presentation of TMLE for applied researchers. We give step-by-step instructions for using TMLE to estimate the average treatment effect in the context of an observational study. We discuss conceptual similarities and differences between TMLE and 2 common estimation approaches (G-computation and inverse probability weighting) and present findings on their relative performance using simulated data. Our simulation study compares methods under parametric regression misspecification; our results highlight TMLE's property of double robustness. Additionally, we discuss best practices for TMLE implementation, particularly the use of ensembled machine learning algorithms. Our simulation study demonstrates all methods using super learning, highlighting that incorporation of machine learning may outperform parametric regression in observational data settings.
Effects of parameter estimation on maximum-likelihood bootstrap analysis.
Ripplinger, Jennifer; Abdo, Zaid; Sullivan, Jack
2010-08-01
Bipartition support in maximum-likelihood (ML) analysis is most commonly assessed using the nonparametric bootstrap. Although bootstrap replicates should theoretically be analyzed in the same manner as the original data, model selection is almost never conducted for bootstrap replicates, substitution-model parameters are often fixed to their maximum-likelihood estimates (MLEs) for the empirical data, and bootstrap replicates may be subjected to less rigorous heuristic search strategies than the original data set. Even though this approach may increase computational tractability, it may also lead to the recovery of suboptimal tree topologies and affect bootstrap values. However, since well-supported bipartitions are often recovered regardless of method, use of a less intensive bootstrap procedure may not significantly affect the results. In this study, we investigate the impact of parameter estimation (i.e., assessment of substitution-model parameters and tree topology) on ML bootstrap analysis. We find that while forgoing model selection and/or setting substitution-model parameters to their empirical MLEs may lead to significantly different bootstrap values, it probably would not change their biological interpretation. Similarly, even though the use of reduced search methods often results in significant differences among bootstrap values, only omitting branch swapping is likely to change any biological inferences drawn from the data. Copyright 2010 Elsevier Inc. All rights reserved.
NASA Astrophysics Data System (ADS)
Singh, Harpreet; Arvind; Dorai, Kavita
2016-09-01
Estimation of quantum states is an important step in any quantum information processing experiment. A naive reconstruction of the density matrix from experimental measurements can often give density matrices which are not positive, and hence not physically acceptable. How do we ensure that at all stages of reconstruction, we keep the density matrix positive? Recently a method has been suggested based on maximum likelihood estimation, wherein the density matrix is guaranteed to be positive definite. We experimentally implement this protocol on an NMR quantum information processor. We discuss several examples and compare with the standard method of state estimation.
GNSS Spoofing Detection and Mitigation Based on Maximum Likelihood Estimation
Li, Hong; Lu, Mingquan
2017-01-01
Spoofing attacks are threatening the global navigation satellite system (GNSS). The maximum likelihood estimation (MLE)-based positioning technique is a direct positioning method originally developed for multipath rejection and weak signal processing. We find this method also has a potential ability for GNSS anti-spoofing since a spoofing attack that misleads the positioning and timing result will cause distortion to the MLE cost function. Based on the method, an estimation-cancellation approach is presented to detect spoofing attacks and recover the navigation solution. A statistic is derived for spoofing detection with the principle of the generalized likelihood ratio test (GLRT). Then, the MLE cost function is decomposed to further validate whether the navigation solution obtained by MLE-based positioning is formed by consistent signals. Both formulae and simulations are provided to evaluate the anti-spoofing performance. Experiments with recordings in real GNSS spoofing scenarios are also performed to validate the practicability of the approach. Results show that the method works even when the code phase differences between the spoofing and authentic signals are much less than one code chip, which can improve the availability of GNSS service greatly under spoofing attacks. PMID:28665318
Assessing allelic dropout and genotype reliability using maximum likelihood.
Miller, Craig R; Joyce, Paul; Waits, Lisette P
2002-01-01
A growing number of population genetic studies utilize nuclear DNA microsatellite data from museum specimens and noninvasive sources. Genotyping errors are elevated in these low quantity DNA sources, potentially compromising the power and accuracy of the data. The most conservative method for addressing this problem is effective, but requires extensive replication of individual genotypes. In search of a more efficient method, we developed a maximum-likelihood approach that minimizes errors by estimating genotype reliability and strategically directing replication at loci most likely to harbor errors. The model assumes that false and contaminant alleles can be removed from the dataset and that the allelic dropout rate is even across loci. Simulations demonstrate that the proposed method marks a vast improvement in efficiency while maintaining accuracy. When allelic dropout rates are low (0-30%), the reduction in the number of PCR replicates is typically 40-50%. The model is robust to moderate violations of the even dropout rate assumption. For datasets that contain false and contaminant alleles, a replication strategy is proposed. Our current model addresses only allelic dropout, the most prevalent source of genotyping error. However, the developed likelihood framework can incorporate additional error-generating processes as they become more clearly understood. PMID:11805071
Pattern recognition using maximum likelihood estimation and orthogonal subspace projection
NASA Astrophysics Data System (ADS)
Islam, M. M.; Alam, M. S.
2006-08-01
Hyperspectral sensor imagery (HSI) is a relatively new area of research, however, it is extensively being used in geology, agriculture, defense, intelligence and law enforcement applications. Much of the current research focuses on the object detection with low false alarm rate. Over the past several years, many object detection algorithms have been developed which include linear detector, quadratic detector, adaptive matched filter etc. In those methods the available data cube was directly used to determine the background mean and the covariance matrix, assuming that the number of object pixels is low compared to that of the data pixels. In this paper, we have used the orthogonal subspace projection (OSP) technique to find the background matrix from the given image data. Our algorithm consists of three parts. In the first part, we have calculated the background matrix using the OSP technique. In the second part, we have determined the maximum likelihood estimates of the parameters. Finally, we have considered the likelihood ratio, commonly known as the Neyman Pearson quadratic detector, to recognize the objects. The proposed technique has been investigated via computer simulation where excellent performance has been observed.
Maximum Likelihood Analysis of Low Energy CDMS II Germanium Data
Agnese, R.
2015-03-30
We report on the results of a search for a Weakly Interacting Massive Particle (WIMP) signal in low-energy data of the Cryogenic Dark Matter Search experiment using a maximum likelihood analysis. A background model is constructed using GEANT4 to simulate the surface-event background from Pb210decay-chain events, while using independent calibration data to model the gamma background. Fitting this background model to the data results in no statistically significant WIMP component. In addition, we also perform fits using an analytic ad hoc background model proposed by Collar and Fields, who claimed to find a large excess of signal-like events in our data. Finally, we confirm the strong preference for a signal hypothesis in their analysis under these assumptions, but excesses are observed in both single- and multiple-scatter events, which implies the signal is not caused by WIMPs, but rather reflects the inadequacy of their background model.
Pointwise nonparametric maximum likelihood estimator of stochastically ordered survivor functions.
Park, Yongseok; Taylor, Jeremy M G; Kalbfleisch, John D
2012-06-01
In this paper, we consider estimation of survivor functions from groups of observations with right-censored data when the groups are subject to a stochastic ordering constraint. Many methods and algorithms have been proposed to estimate distribution functions under such restrictions, but none have completely satisfactory properties when the observations are censored. We propose a pointwise constrained nonparametric maximum likelihood estimator, which is defined at each time t by the estimates of the survivor functions subject to constraints applied at time t only. We also propose an efficient method to obtain the estimator. The estimator of each constrained survivor function is shown to be nonincreasing in t, and its consistency and asymptotic distribution are established. A simulation study suggests better small and large sample properties than for alternative estimators. An example using prostate cancer data illustrates the method.
Pointwise nonparametric maximum likelihood estimator of stochastically ordered survivor functions
Park, Yongseok; Taylor, Jeremy M. G.; Kalbfleisch, John D.
2012-01-01
In this paper, we consider estimation of survivor functions from groups of observations with right-censored data when the groups are subject to a stochastic ordering constraint. Many methods and algorithms have been proposed to estimate distribution functions under such restrictions, but none have completely satisfactory properties when the observations are censored. We propose a pointwise constrained nonparametric maximum likelihood estimator, which is defined at each time t by the estimates of the survivor functions subject to constraints applied at time t only. We also propose an efficient method to obtain the estimator. The estimator of each constrained survivor function is shown to be nonincreasing in t, and its consistency and asymptotic distribution are established. A simulation study suggests better small and large sample properties than for alternative estimators. An example using prostate cancer data illustrates the method. PMID:23843661
A maximum likelihood approach to estimating correlation functions
Baxter, Eric Jones; Rozo, Eduardo
2013-12-10
We define a maximum likelihood (ML for short) estimator for the correlation function, ξ, that uses the same pair counting observables (D, R, DD, DR, RR) as the standard Landy and Szalay (LS for short) estimator. The ML estimator outperforms the LS estimator in that it results in smaller measurement errors at any fixed random point density. Put another way, the ML estimator can reach the same precision as the LS estimator with a significantly smaller random point catalog. Moreover, these gains are achieved without significantly increasing the computational requirements for estimating ξ. We quantify the relative improvement of the ML estimator over the LS estimator and discuss the regimes under which these improvements are most significant. We present a short guide on how to implement the ML estimator and emphasize that the code alterations required to switch from an LS to an ML estimator are minimal.
Evaluating maximum likelihood estimation methods to determine the hurst coefficients
NASA Astrophysics Data System (ADS)
Kendziorski, C. M.; Bassingthwaighte, J. B.; Tonellato, P. J.
1999-12-01
A maximum likelihood estimation method implemented in S-PLUS ( S-MLE) to estimate the Hurst coefficient ( H) is evaluated. The Hurst coefficient, with 0.5< H<1, characterizes long memory time series by quantifying the rate of decay of the autocorrelation function. S-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is difficult to distinguish between fd processes and fractional Gaussian noise (fGn) processes. Thus, the method is evaluated for estimating H for both fd and fGn processes. S-MLE gave biased results of H for fGn processes of any length and for fd processes of lengths less than 2 10. A modified method is proposed to correct for this bias. It gives reliable estimates of H for both fd and fGn processes of length greater than or equal to 2 11.
Maximum-Likelihood Continuity Mapping (MALCOM): An Alternative to HMMs
Nix, D.A.; Hogden, J.E.
1998-12-01
The authors describe Maximum-Likelihood Continuity Mapping (MALCOM) as an alternative to hidden Markov models (HMMs) for processing sequence data such as speech. While HMMs have a discrete ''hidden'' space constrained by a fixed finite-automata architecture, MALCOM has a continuous hidden space (a continuity map) that is constrained only by a smoothness requirement on paths through the space. MALCOM fits into the same probabilistic framework for speech recognition as HMMs, but it represents a far more realistic model of the speech production process. The authors support this claim by generating continuity maps for three speakers and using the resulting MALCOM paths to predict measured speech articulator data. The correlations between the MALCOM paths (obtained from only the speech acoustics) and the actual articulator movements average 0.77 on an independent test set not used to train MALCOM nor the predictor. On average, this unsupervised model achieves 92% of performance obtained using the corresponding supervised method.
Bayesian and maximum likelihood estimation of hierarchical response time models
Farrell, Simon; Ludwig, Casimir
2008-01-01
Hierarchical (or multilevel) statistical models have become increasingly popular in psychology in the last few years. We consider the application of multilevel modeling to the ex-Gaussian, a popular model of response times. Single-level estimation is compared with hierarchical estimation of parameters of the ex-Gaussian distribution. Additionally, for each approach maximum likelihood (ML) estimation is compared with Bayesian estimation. A set of simulations and analyses of parameter recovery show that although all methods perform adequately well, hierarchical methods are better able to recover the parameters of the ex-Gaussian by reducing the variability in recovered parameters. At each level, little overall difference was observed between the ML and Bayesian methods. PMID:19001592
Numerical Experimentation with Maximum Likelihood Identification in Static Distributed Systems
NASA Technical Reports Server (NTRS)
Scheid, R. E., Jr.; Rodriguez, G.
1985-01-01
Many important issues in the control of large space structures are intimately related to the fundamental problem of parameter identification. One might also ask how well this identification process can be carried out in the presence of noisy data since no sensor system is perfect. With these considerations in mind the algorithms herein are designed to treat both the case of uncertainties in the modeling and uncertainties in the data. The analytical aspects of maximum likelihood identification are considered in some detail in another paper. The questions relevant to the implementation of these schemes are dealt with, particularly as they apply to models of large space structures. The emphasis is on the influence of the infinite dimensional character of the problem on finite dimensional implementations of the algorithms. Those areas of current and future analysis are highlighted which indicate the interplay between error analysis and possible truncations of the state and parameter spaces.
Maximum likelihood: Extracting unbiased information from complex networks
NASA Astrophysics Data System (ADS)
Garlaschelli, Diego; Loffredo, Maria I.
2008-07-01
The choice of free parameters in network models is subjective, since it depends on what topological properties are being monitored. However, we show that the maximum likelihood (ML) principle indicates a unique, statistically rigorous parameter choice, associated with a well-defined topological feature. We then find that, if the ML condition is incompatible with the built-in parameter choice, network models turn out to be intrinsically ill defined or biased. To overcome this problem, we construct a class of safely unbiased models. We also propose an extension of these results that leads to the fascinating possibility to extract, only from topological data, the “hidden variables” underlying network organization, making them “no longer hidden.” We test our method on World Trade Web data, where we recover the empirical gross domestic product using only topological information.
A calibration method of self-referencing interferometry based on maximum likelihood estimation
NASA Astrophysics Data System (ADS)
Zhang, Chen; Li, Dahai; Li, Mengyang; E, Kewei; Guo, Guangrao
2015-05-01
Self-referencing interferometry has been widely used in wavefront sensing. However, currently the results of wavefront measurement include two parts, one is the real phase information of wavefront under test and the other is the system error in self-referencing interferometer. In this paper, a method based on maximum likelihood estimation is presented to calibrate the system error in self-referencing interferometer. Firstly, at least three phase difference distributions are obtained by three position measurements of the tested component: one basic position, one rotation and one lateral translation. Then, combining the three phase difference data and using the maximum likelihood method to create a maximum likelihood function, reconstructing the wavefront under test and the system errors by least square estimation and Zernike polynomials. The simulation results show that the proposed method can deal with the issue of calibration of a self-referencing interferometer. The method can be used to reduce the effect of system errors on extracting and reconstructing the wavefront under test, and improve the measurement accuracy of the self-referencing interferometer.
Maximum-likelihood estimation of recent shared ancestry (ERSA)
Huff, Chad D.; Witherspoon, David J.; Simonson, Tatum S.; Xing, Jinchuan; Watkins, W. Scott; Zhang, Yuhua; Tuohy, Therese M.; Neklason, Deborah W.; Burt, Randall W.; Guthery, Stephen L.; Woodward, Scott R.; Jorde, Lynn B.
2011-01-01
Accurate estimation of recent shared ancestry is important for genetics, evolution, medicine, conservation biology, and forensics. Established methods estimate kinship accurately for first-degree through third-degree relatives. We demonstrate that chromosomal segments shared by two individuals due to identity by descent (IBD) provide much additional information about shared ancestry. We developed a maximum-likelihood method for the estimation of recent shared ancestry (ERSA) from the number and lengths of IBD segments derived from high-density SNP or whole-genome sequence data. We used ERSA to estimate relationships from SNP genotypes in 169 individuals from three large, well-defined human pedigrees. ERSA is accurate to within one degree of relationship for 97% of first-degree through fifth-degree relatives and 80% of sixth-degree and seventh-degree relatives. We demonstrate that ERSA's statistical power approaches the maximum theoretical limit imposed by the fact that distant relatives frequently share no DNA through a common ancestor. ERSA greatly expands the range of relationships that can be estimated from genetic data and is implemented in a freely available software package. PMID:21324875
Cosmic shear measurement with maximum likelihood and maximum a posteriori inference
NASA Astrophysics Data System (ADS)
Hall, Alex; Taylor, Andy
2017-06-01
We investigate the problem of noise bias in maximum likelihood and maximum a posteriori estimators for cosmic shear. We derive the leading and next-to-leading order biases and compute them in the context of galaxy ellipticity measurements, extending previous work on maximum likelihood inference for weak lensing. We show that a large part of the bias on these point estimators can be removed using information already contained in the likelihood when a galaxy model is specified, without the need for external calibration. We test these bias-corrected estimators on simulated galaxy images similar to those expected from planned space-based weak lensing surveys, with promising results. We find that the introduction of an intrinsic shape prior can help with mitigation of noise bias, such that the maximum a posteriori estimate can be made less biased than the maximum likelihood estimate. Second-order terms offer a check on the convergence of the estimators, but are largely subdominant. We show how biases propagate to shear estimates, demonstrating in our simple set-up that shear biases can be reduced by orders of magnitude and potentially to within the requirements of planned space-based surveys at mild signal-to-noise ratio. We find that second-order terms can exhibit significant cancellations at low signal-to-noise ratio when Gaussian noise is assumed, which has implications for inferring the performance of shear-measurement algorithms from simplified simulations. We discuss the viability of our point estimators as tools for lensing inference, arguing that they allow for the robust measurement of ellipticity and shear.
Accelerated maximum likelihood parameter estimation for stochastic biochemical systems.
Daigle, Bernie J; Roh, Min K; Petzold, Linda R; Niemi, Jarad
2012-05-01
A prerequisite for the mechanistic simulation of a biochemical system is detailed knowledge of its kinetic parameters. Despite recent experimental advances, the estimation of unknown parameter values from observed data is still a bottleneck for obtaining accurate simulation results. Many methods exist for parameter estimation in deterministic biochemical systems; methods for discrete stochastic systems are less well developed. Given the probabilistic nature of stochastic biochemical models, a natural approach is to choose parameter values that maximize the probability of the observed data with respect to the unknown parameters, a.k.a. the maximum likelihood parameter estimates (MLEs). MLE computation for all but the simplest models requires the simulation of many system trajectories that are consistent with experimental data. For models with unknown parameters, this presents a computational challenge, as the generation of consistent trajectories can be an extremely rare occurrence. We have developed Monte Carlo Expectation-Maximization with Modified Cross-Entropy Method (MCEM(2)): an accelerated method for calculating MLEs that combines advances in rare event simulation with a computationally efficient version of the Monte Carlo expectation-maximization (MCEM) algorithm. Our method requires no prior knowledge regarding parameter values, and it automatically provides a multivariate parameter uncertainty estimate. We applied the method to five stochastic systems of increasing complexity, progressing from an analytically tractable pure-birth model to a computationally demanding model of yeast-polarization. Our results demonstrate that MCEM(2) substantially accelerates MLE computation on all tested models when compared to a stand-alone version of MCEM. Additionally, we show how our method identifies parameter values for certain classes of models more accurately than two recently proposed computationally efficient methods. This work provides a novel, accelerated version
NASA Technical Reports Server (NTRS)
Papadopoulos, G. D.
1975-01-01
The output of a radio interferometer is the Fourier transform of the object under investigation. Due to the limited coverage of the Fourier plane, the reconstruction of the image of the source is blurred by the beam of the synthesized array. A maximum-likelihood processing technique is described which uses the statistical properties of the received noise-like signals. This technique has been used extensively in the processing of large-aperture seismic arrays. This inversion method results in a synthesized beam that is more uniform, has lower sidelobes, and higher resolution than the normal Fourier transform methods. The maximum-likelihood method algorithm was applied successfully to very long baseline and short baseline interferometric data.
Rayleigh-maximum-likelihood bilateral filter for ultrasound image enhancement.
Li, Haiyan; Wu, Jun; Miao, Aimin; Yu, Pengfei; Chen, Jianhua; Zhang, Yufeng
2017-04-17
Ultrasound imaging plays an important role in computer diagnosis since it is non-invasive and cost-effective. However, ultrasound images are inevitably contaminated by noise and speckle during acquisition. Noise and speckle directly impact the physician to interpret the images and decrease the accuracy in clinical diagnosis. Denoising method is an important component to enhance the quality of ultrasound images; however, several limitations discourage the results because current denoising methods can remove noise while ignoring the statistical characteristics of speckle and thus undermining the effectiveness of despeckling, or vice versa. In addition, most existing algorithms do not identify noise, speckle or edge before removing noise or speckle, and thus they reduce noise and speckle while blurring edge details. Therefore, it is a challenging issue for the traditional methods to effectively remove noise and speckle in ultrasound images while preserving edge details. To overcome the above-mentioned limitations, a novel method, called Rayleigh-maximum-likelihood switching bilateral filter (RSBF) is proposed to enhance ultrasound images by two steps: noise, speckle and edge detection followed by filtering. Firstly, a sorted quadrant median vector scheme is utilized to calculate the reference median in a filtering window in comparison with the central pixel to classify the target pixel as noise, speckle or noise-free. Subsequently, the noise is removed by a bilateral filter and the speckle is suppressed by a Rayleigh-maximum-likelihood filter while the noise-free pixels are kept unchanged. To quantitatively evaluate the performance of the proposed method, synthetic ultrasound images contaminated by speckle are simulated by using the speckle model that is subjected to Rayleigh distribution. Thereafter, the corrupted synthetic images are generated by the original image multiplied with the Rayleigh distributed speckle of various signal to noise ratio (SNR) levels and
Pedestrian cue detection: colour inverse maximum likelihood ratio
NASA Astrophysics Data System (ADS)
Braik, Malik; Pycock, David
2013-12-01
This paper presents an adaptable method for identifying pedestrian cues. Cue detection is investigated for adults in isolation and groups. The aim is to detect a single cue for each pedestrian. Colour Inverse Maximum Likelihood Ratio (IMLR) criteria are employed to distinguish object and background regions using a mask designed to accommodate a wide range of appearances. The adaptability and specificity of the method is demonstrated using images containing trees and street furniture; structures that are often confused with pedestrians by computer vision systems. Test images of low contrast are also included to assess the sensitivity of the cue detection process. Evaluation with over 250 images gives a false positive error rate of 10% and a false negative error rate of 1.5% % under exacting detection criteria with a complexity of where n is the number of image points considered. The speed of execution is 8 mS per frame for images of 640 by 480 pixels on an Intel core i3-2310MTM CPU running at 2.10GHz with 4.00GB RAM.
Maximum-likelihood estimation of circle parameters via convolution.
Zelniker, Emanuel E; Clarkson, I Vaughan L
2006-04-01
The accurate fitting of a circle to noisy measurements of circumferential points is a much studied problem in the literature. In this paper, we present an interpretation of the maximum-likelihood estimator (MLE) and the Delogne-Kåsa estimator (DKE) for circle-center and radius estimation in terms of convolution on an image which is ideal in a certain sense. We use our convolution-based MLE approach to find good estimates for the parameters of a circle in digital images. In digital images, it is then possible to treat these estimates as preliminary estimates into various other numerical techniques which further refine them to achieve subpixel accuracy. We also investigate the relationship between the convolution of an ideal image with a "phase-coded kernel" (PCK) and the MLE. This is related to the "phase-coded annulus" which was introduced by Atherton and Kerbyson who proposed it as one of a number of new convolution kernels for estimating circle center and radius. We show that the PCK is an approximate MLE (AMLE). We compare our AMLE method to the MLE and the DKE as well as the Cramér-Rao Lower Bound in ideal images and in both real and synthetic digital images.
An updated maximum likelihood approach to open cluster distance determination
NASA Astrophysics Data System (ADS)
Palmer, M.; Arenou, F.; Luri, X.; Masana, E.
2014-04-01
Aims: An improved method for estimating distances to open clusters is presented and applied to Hipparcos data for the Pleiades and the Hyades. The method is applied in the context of the historic Pleiades distance problem, with a discussion of previous criticisms of Hipparcos parallaxes. This is followed by an outlook for Gaia, where the improved method could be especially useful. Methods: Based on maximum likelihood estimation, the method combines parallax, position, apparent magnitude, colour, proper motion, and radial velocity information to estimate the parameters describing an open cluster precisely and without bias. Results: We find the distance to the Pleiades to be 120.3 ± 1.5 pc, in accordance with previously published work using the same dataset. We find that error correlations cannot be responsible for the still present discrepancy between Hipparcos and photometric methods. Additionally, the three-dimensional space velocity and physical structure of Pleiades is parametrised, where we find strong evidence of mass segregation. The distance to the Hyades is found to be 46.35 ± 0.35 pc, also in accordance with previous results. Through the use of simulations, we confirm that the method is unbiased, so will be useful for accurate open cluster parameter estimation with Gaia at distances up to several thousand parsec. Appendices are available in electronic form at http://www.aanda.org
Maximum likelihood sequence estimation for optical complex direct modulation.
Che, Di; Yuan, Feng; Shieh, William
2017-04-17
Semiconductor lasers are versatile optical transmitters in nature. Through the direct modulation (DM), the intensity modulation is realized by the linear mapping between the injection current and the light power, while various angle modulations are enabled by the frequency chirp. Limited by the direct detection, DM lasers used to be exploited only as 1-D (intensity or angle) transmitters by suppressing or simply ignoring the other modulation. Nevertheless, through the digital coherent detection, simultaneous intensity and angle modulations (namely, 2-D complex DM, CDM) can be realized by a single laser diode. The crucial technique of CDM is the joint demodulation of intensity and differential phase with the maximum likelihood sequence estimation (MLSE), supported by a closed-form discrete signal approximation of frequency chirp to characterize the MLSE transition probability. This paper proposes a statistical method for the transition probability to significantly enhance the accuracy of the chirp model. Using the statistical estimation, we demonstrate the first single-channel 100-Gb/s PAM-4 transmission over 1600-km fiber with only 10G-class DM lasers.
Maximum likelihood estimation for cytogenetic dose-response curves
Frome, E.L; DuFrain, R.J.
1983-10-01
In vitro dose-response curves are used to describe the relation between the yield of dicentric chromosome aberrations and radiation dose for human lymphocytes. The dicentric yields follow the Poisson distribution, and the expected yield depends on both the magnitude and the temporal distribution of the dose for low LET radiation. A general dose-response model that describes this relation has been obtained by Kellerer and Rossi using the theory of dual radiation action. The yield of elementary lesions is kappa(..gamma..d + g(t, tau)d/sup 2/), where t is the time and d is dose. The coefficient of the d/sup 2/ term is determined by the recovery function and the temporal mode of irradiation. Two special cases of practical interest are split-dose and continuous exposure experiments, and the resulting models are intrinsically nonlinear in the parameters. A general purpose maximum likelihood estimation procedure is described and illustrated with numerical examples from both experimental designs. Poisson regression analysis is used for estimation, hypothesis testing, and regression diagnostics. Results are discussed in the context of exposure assessment procedures for both acute and chronic human radiation exposure.
Maximum likelihood estimation in meta-analytic structural equation modeling.
Oort, Frans J; Jak, Suzanne
2016-06-01
Meta-analytic structural equation modeling (MASEM) involves fitting models to a common population correlation matrix that is estimated on the basis of correlation coefficients that are reported by a number of independent studies. MASEM typically consist of two stages. The method that has been found to perform best in terms of statistical properties is the two-stage structural equation modeling, in which maximum likelihood analysis is used to estimate the common correlation matrix in the first stage, and weighted least squares analysis is used to fit structural equation models to the common correlation matrix in the second stage. In the present paper, we propose an alternative method, ML MASEM, that uses ML estimation throughout. In a simulation study, we use both methods and compare chi-square distributions, bias in parameter estimates, false positive rates, and true positive rates. Both methods appear to yield unbiased parameter estimates and false and true positive rates that are close to the expected values. ML MASEM parameter estimates are found to be significantly less bias than two-stage structural equation modeling estimates, but the differences are very small. The choice between the two methods may therefore be based on other fundamental or practical arguments. Copyright © 2016 John Wiley & Sons, Ltd.
Correcting for sequencing error in maximum likelihood phylogeny inference.
Kuhner, Mary K; McGill, James
2014-11-04
Accurate phylogenies are critical to taxonomy as well as studies of speciation processes and other evolutionary patterns. Accurate branch lengths in phylogenies are critical for dating and rate measurements. Such accuracy may be jeopardized by unacknowledged sequencing error. We use simulated data to test a correction for DNA sequencing error in maximum likelihood phylogeny inference. Over a wide range of data polymorphism and true error rate, we found that correcting for sequencing error improves recovery of the branch lengths, even if the assumed error rate is up to twice the true error rate. Low error rates have little effect on recovery of the topology. When error is high, correction improves topological inference; however, when error is extremely high, using an assumed error rate greater than the true error rate leads to poor recovery of both topology and branch lengths. The error correction approach tested here was proposed in 2004 but has not been widely used, perhaps because researchers do not want to commit to an estimate of the error rate. This study shows that correction with an approximate error rate is generally preferable to ignoring the issue.
Maximum Likelihood Analysis of Low Energy CDMS II Germanium Data
Agnese, R.
2015-03-30
We report on the results of a search for a Weakly Interacting Massive Particle (WIMP) signal in low-energy data of the Cryogenic Dark Matter Search experiment using a maximum likelihood analysis. A background model is constructed using GEANT4 to simulate the surface-event background from Pb210decay-chain events, while using independent calibration data to model the gamma background. Fitting this background model to the data results in no statistically significant WIMP component. In addition, we also perform fits using an analytic ad hoc background model proposed by Collar and Fields, who claimed to find a large excess of signal-like events in ourmore » data. Finally, we confirm the strong preference for a signal hypothesis in their analysis under these assumptions, but excesses are observed in both single- and multiple-scatter events, which implies the signal is not caused by WIMPs, but rather reflects the inadequacy of their background model.« less
Bayesian Monte Carlo and Maximum Likelihood Approach for ...
Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood estimation (BMCML) to calibrate a lake oxygen recovery model. We first derive an analytical solution of the differential equation governing lake-averaged oxygen dynamics as a function of time-variable wind speed. Statistical inferences on model parameters and predictive uncertainty are then drawn by Bayesian conditioning of the analytical solution on observed daily wind speed and oxygen concentration data obtained from an earlier study during two recovery periods on a eutrophic lake in upper state New York. The model is calibrated using oxygen recovery data for one year and statistical inferences were validated using recovery data for another year. Compared with essentially two-step, regression and optimization approach, the BMCML results are more comprehensive and performed relatively better in predicting the observed temporal dissolved oxygen levels (DO) in the lake. BMCML also produced comparable calibration and validation results with those obtained using popular Markov Chain Monte Carlo technique (MCMC) and is computationally simpler and easier to implement than the MCMC. Next, using the calibrated model, we derive an optimal relationship between liquid film-transfer coefficien
Bayesian Monte Carlo and Maximum Likelihood Approach for ...
Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood estimation (BMCML) to calibrate a lake oxygen recovery model. We first derive an analytical solution of the differential equation governing lake-averaged oxygen dynamics as a function of time-variable wind speed. Statistical inferences on model parameters and predictive uncertainty are then drawn by Bayesian conditioning of the analytical solution on observed daily wind speed and oxygen concentration data obtained from an earlier study during two recovery periods on a eutrophic lake in upper state New York. The model is calibrated using oxygen recovery data for one year and statistical inferences were validated using recovery data for another year. Compared with essentially two-step, regression and optimization approach, the BMCML results are more comprehensive and performed relatively better in predicting the observed temporal dissolved oxygen levels (DO) in the lake. BMCML also produced comparable calibration and validation results with those obtained using popular Markov Chain Monte Carlo technique (MCMC) and is computationally simpler and easier to implement than the MCMC. Next, using the calibrated model, we derive an optimal relationship between liquid film-transfer coefficien
Maximum likelihood techniques applied to quasi-elastic light scattering
NASA Technical Reports Server (NTRS)
Edwards, Robert V.
1992-01-01
There is a necessity of having an automatic procedure for reliable estimation of the quality of the measurement of particle size from QELS (Quasi-Elastic Light Scattering). Getting the measurement itself, before any error estimates can be made, is a problem because it is obtained by a very indirect measurement of a signal derived from the motion of particles in the system and requires the solution of an inverse problem. The eigenvalue structure of the transform that generates the signal is such that an arbitrarily small amount of noise can obliterate parts of any practical inversion spectrum. This project uses the Maximum Likelihood Estimation (MLE) as a framework to generate a theory and a functioning set of software to oversee the measurement process and extract the particle size information, while at the same time providing error estimates for those measurements. The theory involved verifying a correct form of the covariance matrix for the noise on the measurement and then estimating particle size parameters using a modified histogram approach.
Maximum likelihood estimation for cytogenetic dose-response curves
Frome, E.L.; DuFrain, R.J.
1986-03-01
In vitro dose-response curves are used to describe the relation between chromosome aberrations and radiation dose for human lymphocytes. The lymphocytes are exposed to low-LET radiation, and the resulting dicentric chromosome aberrations follow the Poisson distribution. The expected yield depends on both the magnitude and the temporal distribution of the dose. A general dose-response model that describes this relation has been presented by Kellerer and Rossi (1972, Current Topics on Radiation Research Quarterly 8, 85-158; 1978, Radiation Research 75, 471-488) using the theory of dual radiation action. Two special cases of practical interest are split-dose and continuous exposure experiments, and the resulting dose-time-response models are intrinsically nonlinear in the parameters. A general-purpose maximum likelihood estimation procedure is described, and estimation for the nonlinear models is illustrated with numerical examples from both experimental designs. Poisson regression analysis is used for estimation, hypothesis testing, and regression diagnostics. Results are discussed in the context of exposure assessment procedures for both acute and chronic human radiation exposure.
Covariance of maximum likelihood evolutionary distances between sequences aligned pairwise.
Dessimoz, Christophe; Gil, Manuel
2008-06-23
The estimation of a distance between two biological sequences is a fundamental process in molecular evolution. It is usually performed by maximum likelihood (ML) on characters aligned either pairwise or jointly in a multiple sequence alignment (MSA). Estimators for the covariance of pairs from an MSA are known, but we are not aware of any solution for cases of pairs aligned independently. In large-scale analyses, it may be too costly to compute MSAs every time distances must be compared, and therefore a covariance estimator for distances estimated from pairs aligned independently is desirable. Knowledge of covariances improves any process that compares or combines distances, such as in generalized least-squares phylogenetic tree building, orthology inference, or lateral gene transfer detection. In this paper, we introduce an estimator for the covariance of distances from sequences aligned pairwise. Its performance is analyzed through extensive Monte Carlo simulations, and compared to the well-known variance estimator of ML distances. Our covariance estimator can be used together with the ML variance estimator to form covariance matrices. The estimator performs similarly to the ML variance estimator. In particular, it shows no sign of bias when sequence divergence is below 150 PAM units (i.e. above ~29% expected sequence identity). Above that distance, the covariances tend to be underestimated, but then ML variances are also underestimated.
Parallel computation of a maximum-likelihood estimator of a physical map.
Bhandarkar, S M; Machaka, S A; Shete, S S; Kota, R N
2001-01-01
Reconstructing a physical map of a chromosome from a genomic library presents a central computational problem in genetics. Physical map reconstruction in the presence of errors is a problem of high computational complexity that provides the motivation for parallel computing. Parallelization strategies for a maximum-likelihood estimation-based approach to physical map reconstruction are presented. The estimation procedure entails a gradient descent search for determining the optimal spacings between probes for a given probe ordering. The optimal probe ordering is determined using a stochastic optimization algorithm such as simulated annealing or microcanonical annealing. A two-level parallelization strategy is proposed wherein the gradient descent search is parallelized at the lower level and the stochastic optimization algorithm is simultaneously parallelized at the higher level. Implementation and experimental results on a distributed-memory multiprocessor cluster running the parallel virtual machine (PVM) environment are presented using simulated and real hybridization data. PMID:11238392
Nonparametric maximum likelihood estimation of probability densities by penalty function methods
NASA Technical Reports Server (NTRS)
Demontricher, G. F.; Tapia, R. A.; Thompson, J. R.
1974-01-01
When it is known a priori exactly to which finite dimensional manifold the probability density function gives rise to a set of samples, the parametric maximum likelihood estimation procedure leads to poor estimates and is unstable; while the nonparametric maximum likelihood procedure is undefined. A very general theory of maximum penalized likelihood estimation which should avoid many of these difficulties is presented. It is demonstrated that each reproducing kernel Hilbert space leads, in a very natural way, to a maximum penalized likelihood estimator and that a well-known class of reproducing kernel Hilbert spaces gives polynomial splines as the nonparametric maximum penalized likelihood estimates.
Maximum likelihood random galaxy catalogues and luminosity function estimation
NASA Astrophysics Data System (ADS)
Cole, Shaun
2011-09-01
We present a new algorithm to generate a random (unclustered) version of an magnitude limited observational galaxy redshift catalogue. It takes into account both galaxy evolution and the perturbing effects of large-scale structure. The key to the algorithm is a maximum likelihood (ML) method for jointly estimating both the luminosity function (LF) and the overdensity as a function of redshift. The random catalogue algorithm then works by cloning each galaxy in the original catalogue, with the number of clones determined by the ML solution. Each of these cloned galaxies is then assigned a random redshift uniformly distributed over the accessible survey volume, taking account of the survey magnitude limit(s) and, optionally, both luminosity and number density evolution. The resulting random catalogues, which can be employed in traditional estimates of galaxy clustering, make fuller use of the information available in the original catalogue and hence are superior to simply fitting a functional form to the observed redshift distribution. They are particularly well suited to studies of the dependence of galaxy clustering on galaxy properties as each galaxy in the random catalogue has the same list of attributes as measured for the galaxies in the genuine catalogue. The derivation of the joint overdensity and LF estimator reveals the limit in which the ML estimate reduces to the standard 1/Vmax LF estimate, namely when one makes the prior assumption that the are no fluctuations in the radial overdensity. The new ML estimator can be viewed as a generalization of the 1/Vmax estimate in which Vmax is replaced by a density corrected Vdc, max.
Likelihood maximization for list-mode emission tomographic image reconstruction.
Byrne, C
2001-10-01
The maximum a posteriori (MAP) Bayesian iterative algorithm using priors that are gamma distributed, due to Lange, Bahn and Little, is extended to include parameter choices that fall outside the gamma distribution model. Special cases of the resulting iterative method include the expectation maximization maximum likelihood (EMML) method based on the Poisson model in emission tomography, as well as algorithms obtained by Parra and Barrett and by Huesman et al. that converge to maximum likelihood and maximum conditional likelihood estimates of radionuclide intensities for list-mode emission tomography. The approach taken here is optimization-theoretic and does not rely on the usual expectation maximization (EM) formalism. Block-iterative variants of the algorithms are presented. A self-contained, elementary proof of convergence of the algorithm is included.
Maximum-Likelihood Methods for Processing Signals From Gamma-Ray Detectors
Barrett, Harrison H.; Hunter, William C. J.; Miller, Brian William; Moore, Stephen K.; Chen, Yichun; Furenlid, Lars R.
2009-01-01
In any gamma-ray detector, each event produces electrical signals on one or more circuit elements. From these signals, we may wish to determine the presence of an interaction; whether multiple interactions occurred; the spatial coordinates in two or three dimensions of at least the primary interaction; or the total energy deposited in that interaction. We may also want to compute listmode probabilities for tomographic reconstruction. Maximum-likelihood methods provide a rigorous and in some senses optimal approach to extracting this information, and the associated Fisher information matrix provides a way of quantifying and optimizing the information conveyed by the detector. This paper will review the principles of likelihood methods as applied to gamma-ray detectors and illustrate their power with recent results from the Center for Gamma-ray Imaging. PMID:20107527
The Multi-Mission Maximum Likelihood Framework (3ML)
NASA Astrophysics Data System (ADS)
Burgess, J. M.; Vianello, G.
2016-10-01
We introduce a new tool for multi-messenger astronomy capable of fitting data from multiple instruments properly via the use of independent likelihood plugins. 3ML represents a step forward in spectral and spatial analysis across all wavelengths.
The numerical evaluation of the maximum-likelihood estimate of a subset of mixture proportions
NASA Technical Reports Server (NTRS)
Peters, B. C., Jr.; Walker, H. F.
1976-01-01
Necessary and sufficient conditions are given for a maximum likelihood estimate of a subset of mixture proportions. From these conditions, likelihood equations are derived satisfied by the maximum-likelihood estimate and a successive-approximations procedure is discussed as suggested by equations for numerically evaluating the maximum-likelihood estimate. It is shown that, with probability one for large samples, this procedure converges locally to the maximum-likelihood estimate whenever a certain step-size lies between zero and two. Furthermore, optimal rates of local convergence are obtained for a step-size which is bounded below by a number between one and two.
Maximum-likelihood estimation of gene location by linkage disequilibrium
Hill, W.G. ); Weir, B.S. )
1994-04-01
Linkage disequilibrium, D, between a polymorphic disease and mapped markers can, in principle, be used to help find the map position of the disease gene. Likelihoods are therefore derived for the value of D conditional on the observed number of haplotypes in the sample and on the population parameter Nc, where N is the effective population size and c the recombination fraction between the disease and marker loci. The likelihood is computed explicitly for the case of two loci with heterozygote superiority and, more generally, by computer simulations assuming a steady state of constant population size and selective pressures or neutrality. It is found that the likelihood is, in general, not very dependent on the degree of selection at the loci and is very flat. This suggests that precise information on map position will not be obtained from estimates of linkage disequilibrium. 15 refs., 5 figs., 21 tabs.
Maximum Marginal Likelihood Estimation for Semiparametric Item Analysis.
ERIC Educational Resources Information Center
Ramsay, J. O.; Winsberg, S.
1991-01-01
A method is presented for estimating the item characteristic curve (ICC) using polynomial regression splines. Estimation of spline ICCs is described by maximizing the marginal likelihood formed by integrating ability over a beta prior distribution. Simulation results compare this approach with the joint estimation of ability and item parameters.…
Maximum-likelihood estimation of admixture proportions from genetic data.
Wang, Jinliang
2003-01-01
For an admixed population, an important question is how much genetic contribution comes from each parental population. Several methods have been developed to estimate such admixture proportions, using data on genetic markers sampled from parental and admixed populations. In this study, I propose a likelihood method to estimate jointly the admixture proportions, the genetic drift that occurred to the admixed population and each parental population during the period between the hybridization and sampling events, and the genetic drift in each ancestral population within the interval between their split and hybridization. The results from extensive simulations using various combinations of relevant parameter values show that in general much more accurate and precise estimates of admixture proportions are obtained from the likelihood method than from previous methods. The likelihood method also yields reasonable estimates of genetic drift that occurred to each population, which translate into relative effective sizes (N(e)) or absolute average N(e)'s if the times when the relevant events (such as population split, admixture, and sampling) occurred are known. The proposed likelihood method also has features such as relatively low computational requirement compared with previous ones, flexibility for admixture models, and marker types. In particular, it allows for missing data from a contributing parental population. The method is applied to a human data set and a wolflike canids data set, and the results obtained are discussed in comparison with those from other estimators and from previous studies. PMID:12807794
Maximum likelihood estimation for periodic autoregressive moving average models
Vecchia, A.V.
1985-01-01
A useful class of models for seasonal time series that cannot be filtered or standardized to achieve second-order stationarity is that of periodic autoregressive moving average (PARMA) models, which are extensions of ARMA models that allow periodic (seasonal) parameters. An approximation to the exact likelihood for Gaussian PARMA processes is developed, and a straightforward algorithm for its maximization is presented. The algorithm is tested on several periodic ARMA(1, 1) models through simulation studies and is compared to moment estimation via the seasonal Yule-Walker equations. Applicability of the technique is demonstrated through an analysis of a seasonal stream-flow series from the Rio Caroni River in Venezuela.
Simultaneous maximum a posteriori longitudinal PET image reconstruction
NASA Astrophysics Data System (ADS)
Ellis, Sam; Reader, Andrew J.
2017-09-01
Positron emission tomography (PET) is frequently used to monitor functional changes that occur over extended time scales, for example in longitudinal oncology PET protocols that include routine clinical follow-up scans to assess the efficacy of a course of treatment. In these contexts PET datasets are currently reconstructed into images using single-dataset reconstruction methods. Inspired by recently proposed joint PET-MR reconstruction methods, we propose to reconstruct longitudinal datasets simultaneously by using a joint penalty term in order to exploit the high degree of similarity between longitudinal images. We achieved this by penalising voxel-wise differences between pairs of longitudinal PET images in a one-step-late maximum a posteriori (MAP) fashion, resulting in the MAP simultaneous longitudinal reconstruction (SLR) method. The proposed method reduced reconstruction errors and visually improved images relative to standard maximum likelihood expectation-maximisation (ML-EM) in simulated 2D longitudinal brain tumour scans. In reconstructions of split real 3D data with inserted simulated tumours, noise across images reconstructed with MAP-SLR was reduced to levels equivalent to doubling the number of detected counts when using ML-EM. Furthermore, quantification of tumour activities was largely preserved over a variety of longitudinal tumour changes, including changes in size and activity, with larger changes inducing larger biases relative to standard ML-EM reconstructions. Similar improvements were observed for a range of counts levels, demonstrating the robustness of the method when used with a single penalty strength. The results suggest that longitudinal regularisation is a simple but effective method of improving reconstructed PET images without using resolution degrading priors.
Maximum likelihood density modification by pattern recognition of structural motifs
Terwilliger, Thomas C.
2004-04-13
An electron density for a crystallographic structure having protein regions and solvent regions is improved by maximizing the log likelihood of a set of structures factors {F.sub.h } using a local log-likelihood function: (x)+p(.rho.(x).vertline.SOLV)p.sub.SOLV (x)+p(.rho.(x).vertline.H)p.sub.H (x)], where p.sub.PROT (x) is the probability that x is in the protein region, p(.rho.(x).vertline.PROT) is the conditional probability for .rho.(x) given that x is in the protein region, and p.sub.SOLV (x) and p(.rho.(x).vertline.SOLV) are the corresponding quantities for the solvent region, p.sub.H (x) refers to the probability that there is a structural motif at a known location, with a known orientation, in the vicinity of the point x; and p(.rho.(x).vertline.H) is the probability distribution for electron density at this point given that the structural motif actually is present. One appropriate structural motif is a helical structure within the crystallographic structure.
MXLKID: a maximum likelihood parameter identifier. [In LRLTRAN for CDC 7600
Gavel, D.T.
1980-07-01
MXLKID (MaXimum LiKelihood IDentifier) is a computer program designed to identify unknown parameters in a nonlinear dynamic system. Using noisy measurement data from the system, the maximum likelihood identifier computes a likelihood function (LF). Identification of system parameters is accomplished by maximizing the LF with respect to the parameters. The main body of this report briefly summarizes the maximum likelihood technique and gives instructions and examples for running the MXLKID program. MXLKID is implemented LRLTRAN on the CDC7600 computer at LLNL. A detailed mathematical description of the algorithm is given in the appendices. 24 figures, 6 tables.
On the existence of maximum likelihood estimates for presence-only data
Hefley, Trevor J.; Hooten, Mevin B.
2015-01-01
It is important to identify conditions for which maximum likelihood estimates are unlikely to be identifiable from presence-only data. In data sets where the maximum likelihood estimates do not exist, penalized likelihood and Bayesian methods will produce coefficient estimates, but these are sensitive to the choice of estimation procedure and prior or penalty term. When sample size is small or it is thought that habitat preferences are strong, we propose a suite of estimation procedures researchers can consider using.
A Comparison of a Bayesian and a Maximum Likelihood Tailored Testing Procedure.
ERIC Educational Resources Information Center
McKinley, Robert L.; Reckase, Mark D.
A study was conducted to compare tailored testing procedures based on a Bayesian ability estimation technique and on a maximum likelihood ability estimation technique. The Bayesian tailored testing procedure selected items so as to minimize the posterior variance of the ability estimate distribution, while the maximum likelihood tailored testing…
Item Parameter Estimation via Marginal Maximum Likelihood and an EM Algorithm: A Didactic.
ERIC Educational Resources Information Center
Harwell, Michael R.; And Others
1988-01-01
The Bock and Aitkin Marginal Maximum Likelihood/EM (MML/EM) approach to item parameter estimation is an alternative to the classical joint maximum likelihood procedure of item response theory. This paper provides the essential mathematical details of a MML/EM solution and shows its use in obtaining consistent item parameter estimates. (TJH)
The recursive maximum likelihood proportion estimator: User's guide and test results
NASA Technical Reports Server (NTRS)
Vanrooy, D. L.
1976-01-01
Implementation of the recursive maximum likelihood proportion estimator is described. A user's guide to programs as they currently exist on the IBM 360/67 at LARS, Purdue is included, and test results on LANDSAT data are described. On Hill County data, the algorithm yields results comparable to the standard maximum likelihood proportion estimator.
W-IQ-TREE: a fast online phylogenetic tool for maximum likelihood analysis.
Trifinopoulos, Jana; Nguyen, Lam-Tung; von Haeseler, Arndt; Minh, Bui Quang
2016-07-08
This article presents W-IQ-TREE, an intuitive and user-friendly web interface and server for IQ-TREE, an efficient phylogenetic software for maximum likelihood analysis. W-IQ-TREE supports multiple sequence types (DNA, protein, codon, binary and morphology) in common alignment formats and a wide range of evolutionary models including mixture and partition models. W-IQ-TREE performs fast model selection, partition scheme finding, efficient tree reconstruction, ultrafast bootstrapping, branch tests, and tree topology tests. All computations are conducted on a dedicated computer cluster and the users receive the results via URL or email. W-IQ-TREE is available at http://iqtree.cibiv.univie.ac.at It is free and open to all users and there is no login requirement.
W-IQ-TREE: a fast online phylogenetic tool for maximum likelihood analysis
Trifinopoulos, Jana; Nguyen, Lam-Tung; von Haeseler, Arndt; Minh, Bui Quang
2016-01-01
This article presents W-IQ-TREE, an intuitive and user-friendly web interface and server for IQ-TREE, an efficient phylogenetic software for maximum likelihood analysis. W-IQ-TREE supports multiple sequence types (DNA, protein, codon, binary and morphology) in common alignment formats and a wide range of evolutionary models including mixture and partition models. W-IQ-TREE performs fast model selection, partition scheme finding, efficient tree reconstruction, ultrafast bootstrapping, branch tests, and tree topology tests. All computations are conducted on a dedicated computer cluster and the users receive the results via URL or email. W-IQ-TREE is available at http://iqtree.cibiv.univie.ac.at. It is free and open to all users and there is no login requirement. PMID:27084950
Maximum likelihood positioning and energy correction for scintillation detectors.
Lerche, Christoph W; Salomon, André; Goldschmidt, Benjamin; Lodomez, Sarah; Weissler, Björn; Solf, Torsten
2016-02-21
An algorithm for determining the crystal pixel and the gamma ray energy with scintillation detectors for PET is presented. The algorithm uses Likelihood Maximisation (ML) and therefore is inherently robust to missing data caused by defect or paralysed photo detector pixels. We tested the algorithm on a highly integrated MRI compatible small animal PET insert. The scintillation detector blocks of the PET gantry were built with the newly developed digital Silicon Photomultiplier (SiPM) technology from Philips Digital Photon Counting and LYSO pixel arrays with a pitch of 1 mm and length of 12 mm. Light sharing was used to readout the scintillation light from the 30 × 30 scintillator pixel array with an 8 × 8 SiPM array. For the performance evaluation of the proposed algorithm, we measured the scanner's spatial resolution, energy resolution, singles and prompt count rate performance, and image noise. These values were compared to corresponding values obtained with Center of Gravity (CoG) based positioning methods for different scintillation light trigger thresholds and also for different energy windows. While all positioning algorithms showed similar spatial resolution, a clear advantage for the ML method was observed when comparing the PET scanner's overall single and prompt detection efficiency, image noise, and energy resolution to the CoG based methods. Further, ML positioning reduces the dependence of image quality on scanner configuration parameters and was the only method that allowed achieving highest energy resolution, count rate performance and spatial resolution at the same time.
Binomial and Poisson Mixtures, Maximum Likelihood, and Maple Code
Bowman, Kimiko o; Shenton, LR
2006-01-01
The bias, variance, and skewness of maximum likelihoood estimators are considered for binomial and Poisson mixture distributions. The moments considered are asymptotic, and they are assessed using the Maple code. Question of existence of solutions and Karl Pearson's study are mentioned, along with the problems of valid sample space. Large samples to reduce variances are not unusual; this also applies to the size of the asymptotic skewness.
Maximum likelihood positioning and energy correction for scintillation detectors
NASA Astrophysics Data System (ADS)
Lerche, Christoph W.; Salomon, André; Goldschmidt, Benjamin; Lodomez, Sarah; Weissler, Björn; Solf, Torsten
2016-02-01
An algorithm for determining the crystal pixel and the gamma ray energy with scintillation detectors for PET is presented. The algorithm uses Likelihood Maximisation (ML) and therefore is inherently robust to missing data caused by defect or paralysed photo detector pixels. We tested the algorithm on a highly integrated MRI compatible small animal PET insert. The scintillation detector blocks of the PET gantry were built with the newly developed digital Silicon Photomultiplier (SiPM) technology from Philips Digital Photon Counting and LYSO pixel arrays with a pitch of 1 mm and length of 12 mm. Light sharing was used to readout the scintillation light from the 30× 30 scintillator pixel array with an 8× 8 SiPM array. For the performance evaluation of the proposed algorithm, we measured the scanner’s spatial resolution, energy resolution, singles and prompt count rate performance, and image noise. These values were compared to corresponding values obtained with Center of Gravity (CoG) based positioning methods for different scintillation light trigger thresholds and also for different energy windows. While all positioning algorithms showed similar spatial resolution, a clear advantage for the ML method was observed when comparing the PET scanner’s overall single and prompt detection efficiency, image noise, and energy resolution to the CoG based methods. Further, ML positioning reduces the dependence of image quality on scanner configuration parameters and was the only method that allowed achieving highest energy resolution, count rate performance and spatial resolution at the same time.
C-arm perfusion imaging with a fast penalized maximum-likelihood approach
NASA Astrophysics Data System (ADS)
Frysch, Robert; Pfeiffer, Tim; Bannasch, Sebastian; Serowy, Steffen; Gugel, Sebastian; Skalej, Martin; Rose, Georg
2014-03-01
Perfusion imaging is an essential method for stroke diagnostics. One of the most important factors for a successful therapy is to get the diagnosis as fast as possible. Therefore our approach aims at perfusion imaging (PI) with a cone beam C-arm system providing perfusion information directly in the interventional suite. For PI the imaging system has to provide excellent soft tissue contrast resolution in order to allow the detection of small attenuation enhancement due to contrast agent in the capillary vessels. The limited dynamic range of flat panel detectors as well as the sparse sampling of the slow rotating C-arm in combination with standard reconstruction methods results in limited soft tissue contrast. We choose a penalized maximum-likelihood reconstruction method to get suitable results. To minimize the computational load, the 4D reconstruction task is reduced to several static 3D reconstructions. We also include an ordered subset technique with transitioning to a small number of subsets, which adds sharpness to the image with less iterations while also suppressing the noise. Instead of the standard multiplicative EM correction, we apply a Newton-based optimization to further accelerate the reconstruction algorithm. The latter optimization reduces the computation time by up to 70%. Further acceleration is provided by a multi-GPU implementation of the forward and backward projection, which fulfills the demands of cone beam geometry. In this preliminary study we evaluate this procedure on clinical data. Perfusion maps are computed and compared with reference images from magnetic resonance scans. We found a high correlation between both images.
Speech processing using conditional observable maximum likelihood continuity mapping
Hogden, John; Nix, David
2004-01-13
A computer implemented method enables the recognition of speech and speech characteristics. Parameters are initialized of first probability density functions that map between the symbols in the vocabulary of one or more sequences of speech codes that represent speech sounds and a continuity map. Parameters are also initialized of second probability density functions that map between the elements in the vocabulary of one or more desired sequences of speech transcription symbols and the continuity map. The parameters of the probability density functions are then trained to maximize the probabilities of the desired sequences of speech-transcription symbols. A new sequence of speech codes is then input to the continuity map having the trained first and second probability function parameters. A smooth path is identified on the continuity map that has the maximum probability for the new sequence of speech codes. The probability of each speech transcription symbol for each input speech code can then be output.
Maximum a posteriori CMB lensing reconstruction
NASA Astrophysics Data System (ADS)
Carron, Julien; Lewis, Antony
2017-09-01
Gravitational lensing of the cosmic microwave background (CMB) is a valuable cosmological signal that correlates to tracers of large-scale structure and acts as a important source of confusion for primordial B -mode polarization. State-of-the-art lensing reconstruction analyses use quadratic estimators, which are easily applicable to data. However, these estimators are known to be suboptimal, in particular for polarization, and large improvements are expected to be possible for high signal-to-noise polarization experiments. We develop a method and numerical code, lensit, that is able to find efficiently the most probable lensing map, introducing no significant approximations to the lensed CMB likelihood, and applicable to beamed and masked data with inhomogeneous noise. It works by iteratively reconstructing the primordial unlensed CMB using a deflection estimate and its inverse, and removing residual lensing from these maps with quadratic estimator techniques. Roughly linear computational cost is maintained due to fast convergence of iterative searches, combined with the local nature of lensing. The method achieves the maximal improvement in signal to noise expected from analytical considerations on the unmasked parts of the sky. Delensing with this optimal map leads to forecast tensor-to-scalar ratio parameter errors improved by a factor ≃2 compared to the quadratic estimator in a CMB stage IV configuration.
Bias Correction for the Maximum Likelihood Estimate of Ability. Research Report. ETS RR-05-15
ERIC Educational Resources Information Center
Zhang, Jinming
2005-01-01
Lord's bias function and the weighted likelihood estimation method are effective in reducing the bias of the maximum likelihood estimate of an examinee's ability under the assumption that the true item parameters are known. This paper presents simulation studies to determine the effectiveness of these two methods in reducing the bias when the item…
On the Relationships between Sum Score Based Estimation and Joint Maximum Likelihood Estimation
ERIC Educational Resources Information Center
del Pino, Guido; San Martin, Ernesto; Gonzalez, Jorge; De Boeck, Paul
2008-01-01
This paper analyzes the sum score based (SSB) formulation of the Rasch model, where items and sum scores of persons are considered as factors in a logit model. After reviewing the evolution leading to the equality between their maximum likelihood estimates, the SSB model is then discussed from the point of view of pseudo-likelihood and of…
Application of a maximum likelihood algorithm to ultrasound modulated optical tomography.
Huynh, Nam T; He, Diwei; Hayes-Gill, Barrie R; Crowe, John A; Walker, John G; Mather, Melissa L; Rose, Felicity R A J; Parker, Nicholas G; Povey, Malcolm J W; Morgan, Stephen P
2012-02-01
In pulsed ultrasound modulated optical tomography (USMOT), an ultrasound (US) pulse performs as a scanning probe within the sample as it propagates, modulating the scattered light spatially distributed along its propagation axis. Detecting and processing the modulated signal can provide a 1-dimensional image along the US axis. A simple model is developed wherein the detected signal is modelled as a convolution of the US pulse and the properties (ultrasonic/optical) of the medium along the US axis. Based upon this model, a maximum likelihood (ML) method for image reconstruction is established. For the first time to our knowledge, the ML technique for an USMOT signal is investigated both theoretically and experimentally. The ML method inverts the data to retrieve the spatially varying properties of the sample along the US axis, and a signal proportional to the optical properties can be acquired. Simulated results show that the ML method can serve as a useful reconstruction tool for a pulsed USMOT signal even when the signal-to-noise ratio (SNR) is close to unity. Experimental data using 5 cm thick tissue phantoms (scattering coefficient μ(s) = 6.5 cm(-1), anisotropy factor g=0.93) demonstrate that the axial resolution is 160 μm and the lateral resolution is 600 μm using a 10 MHz transducer.
A maximum likelihood method for high resolution proton radiography/proton CT.
Collins-Fekete, Charles-Antoine; Brousmiche, Sébastien; Portillo, Stephen K N; Beaulieu, Luc; Seco, Joao
2016-12-07
Multiple Coulomb scattering (MCS) is the largest contributor to blurring in proton imaging. In this work, we developed a maximum likelihood least squares estimator that improves proton radiography's spatial resolution. The water equivalent thickness (WET) through projections defined from the source to the detector pixels were estimated such that they maximizes the likelihood of the energy loss of every proton crossing the volume. The length spent in each projection was calculated through the optimized cubic spline path estimate. The proton radiographies were produced using Geant4 simulations. Three phantoms were studied here: a slanted cube in a tank of water to measure 2D spatial resolution, a voxelized head phantom for clinical performance evaluation as well as a parametric Catphan phantom (CTP528) for 3D spatial resolution. Two proton beam configurations were used: a parallel and a conical beam. Proton beams of 200 and 330 MeV were simulated to acquire the radiography. Spatial resolution is increased from 2.44 lp cm(-1) to 4.53 lp cm(-1) in the 200 MeV beam and from 3.49 lp cm(-1) to 5.76 lp cm(-1) in the 330 MeV beam. Beam configurations do not affect the reconstructed spatial resolution as investigated between a radiography acquired with the parallel (3.49 lp cm(-1) to 5.76 lp cm(-1)) or conical beam (from 3.49 lp cm(-1) to 5.56 lp cm(-1)). The improved images were then used as input in a photon tomography algorithm. The proton CT reconstruction of the Catphan phantom shows high spatial resolution (from 2.79 to 5.55 lp cm(-1) for the parallel beam and from 3.03 to 5.15 lp cm(-1) for the conical beam) and the reconstruction of the head phantom, although qualitative, shows high contrast in the gradient region. The proposed formulation of the optimization demonstrates serious potential to increase the spatial resolution (up by 65[Formula: see text]) in proton radiography and greatly accelerate proton computed tomography reconstruction.
A maximum likelihood method for high resolution proton radiography/proton CT
NASA Astrophysics Data System (ADS)
Collins-Fekete, Charles-Antoine; Brousmiche, Sébastien; Portillo, Stephen K. N.; Beaulieu, Luc; Seco, Joao
2016-12-01
Multiple Coulomb scattering (MCS) is the largest contributor to blurring in proton imaging. In this work, we developed a maximum likelihood least squares estimator that improves proton radiography’s spatial resolution. The water equivalent thickness (WET) through projections defined from the source to the detector pixels were estimated such that they maximizes the likelihood of the energy loss of every proton crossing the volume. The length spent in each projection was calculated through the optimized cubic spline path estimate. The proton radiographies were produced using Geant4 simulations. Three phantoms were studied here: a slanted cube in a tank of water to measure 2D spatial resolution, a voxelized head phantom for clinical performance evaluation as well as a parametric Catphan phantom (CTP528) for 3D spatial resolution. Two proton beam configurations were used: a parallel and a conical beam. Proton beams of 200 and 330 MeV were simulated to acquire the radiography. Spatial resolution is increased from 2.44 lp cm-1 to 4.53 lp cm-1 in the 200 MeV beam and from 3.49 lp cm-1 to 5.76 lp cm-1 in the 330 MeV beam. Beam configurations do not affect the reconstructed spatial resolution as investigated between a radiography acquired with the parallel (3.49 lp cm-1 to 5.76 lp cm-1) or conical beam (from 3.49 lp cm-1 to 5.56 lp cm-1). The improved images were then used as input in a photon tomography algorithm. The proton CT reconstruction of the Catphan phantom shows high spatial resolution (from 2.79 to 5.55 lp cm-1 for the parallel beam and from 3.03 to 5.15 lp cm-1 for the conical beam) and the reconstruction of the head phantom, although qualitative, shows high contrast in the gradient region. The proposed formulation of the optimization demonstrates serious potential to increase the spatial resolution (up by 65 % ) in proton radiography and greatly accelerate proton computed tomography reconstruction.
Marginal Maximum Likelihood Estimation for the One-Parameter Logistic Model.
ERIC Educational Resources Information Center
Thissen, David
1982-01-01
Two algorithms for marginal maximum likelihood estimation for the Rasch model are provided. The more efficient of the two algorithms is extended to estimation for the linear logistic model. Numerical examples of both procedures are presented. (Author/JKS)
A Primer on Maximum Likelihood Algorithms Available for Use with Missing Data. Teacher's Corner.
ERIC Educational Resources Information Center
Enders, Craig K.
2001-01-01
Provides a comprehensive, nontechnical overview of the three maximum likelihood algorithms available for use with missing data and discusses multiple imputation, frequently used in conjunction with the EM algorithm. (SLD)
Nielsen, R
1998-04-01
In this paper, a maximum likelihood estimator of population divergence time based on the infinite sites model is developed. It is demonstrated how this estimator may be applied to obtain maximum likelihood estimates of the topology of population phylogenies. This approach addresses several classical problems occurring in the inference of the phylogenetic relationship of populations, most notably the problem of shared ancestral polymorphisms. The method is applied to previously published data sets of human African populations and of Caribbean hawksbill turtles.
Adaptive Trellis Using Interim Maximum-Likelihood Detector Output for a Holographic Storage System
NASA Astrophysics Data System (ADS)
Kim, Gukhui; Kim, Jinyoung; Lee, Jaejin
2011-09-01
The performance of partial response maximum likelihood (PRML) for holographic data storage can be reduced by asymmetric channel characteristics such as radial/tangential tilts. Therefore, we proposed the adaptive trellis scheme to improve performance. The proposed algorithm updates the reference branch values through using interim maximum-likelihood detector output, using the changed channel condition. Thus, this system guarantees better bit error rate performance than conventional PRML detection.
Cramer-Rao Bound, MUSIC, and Maximum Likelihood. Effects of Temporal Phase Difference
1990-11-01
Technical Report 1373 November 1990 Cramer-Rao Bound, MUSIC , And Maximum Likelihood Effects of Temporal Phase o Difference C. V. TranI OTIC Approved... MUSIC , and Maximum Likelihood (ML) asymptotic variances corresponding to the two-source direction-of-arrival estimation where sources were modeled as...1pI = 1.00, SNR = 20 dB ..................................... 27 2. MUSIC for two equipowered signals impinging on a 5-element ULA (a) IpI = 0.50, SNR
Using maximum likelihood to estimate population size from temporal changes in allele frequencies.
Williamson, E G; Slatkin, M
1999-01-01
We develop a maximum-likelihood framework for using temporal changes in allele frequencies to estimate the number of breeding individuals in a population. We use simulations to compare the performance of this estimator to an F-statistic estimator of variance effective population size. The maximum-likelihood estimator had a lower variance and smaller bias. Taking advantage of the likelihood framework, we extend the model to include exponential growth and show that temporal allele frequency data from three or more sampling events can be used to test for population growth. PMID:10353915
Maximum Likelihood Inference for the Cox Regression Model with Applications to Missing Covariates.
Chen, Ming-Hui; Ibrahim, Joseph G; Shao, Qi-Man
2009-10-01
In this paper, we carry out an in-depth theoretical investigation for existence of maximum likelihood estimates for the Cox model (Cox, 1972, 1975) both in the full data setting as well as in the presence of missing covariate data. The main motivation for this work arises from missing data problems, where models can easily become difficult to estimate with certain missing data configurations or large missing data fractions. We establish necessary and sufficient conditions for existence of the maximum partial likelihood estimate (MPLE) for completely observed data (i.e., no missing data) settings as well as sufficient conditions for existence of the maximum likelihood estimate (MLE) for survival data with missing covariates via a profile likelihood method. Several theorems are given to establish these conditions. A real dataset from a cancer clinical trial is presented to further illustrate the proposed methodology.
Maximum Likelihood Inference for the Cox Regression Model with Applications to Missing Covariates
Chen, Ming-Hui; Ibrahim, Joseph G.; Shao, Qi-Man
2009-01-01
In this paper, we carry out an in-depth theoretical investigation for existence of maximum likelihood estimates for the Cox model (Cox, 1972, 1975) both in the full data setting as well as in the presence of missing covariate data. The main motivation for this work arises from missing data problems, where models can easily become difficult to estimate with certain missing data configurations or large missing data fractions. We establish necessary and sufficient conditions for existence of the maximum partial likelihood estimate (MPLE) for completely observed data (i.e., no missing data) settings as well as sufficient conditions for existence of the maximum likelihood estimate (MLE) for survival data with missing covariates via a profile likelihood method. Several theorems are given to establish these conditions. A real dataset from a cancer clinical trial is presented to further illustrate the proposed methodology. PMID:19802375
Tong, Wenxu; Wei, Ying; Murga, Leonel F; Ondrechen, Mary Jo; Williams, Ronald J
2009-01-01
A new monotonicity-constrained maximum likelihood approach, called Partial Order Optimum Likelihood (POOL), is presented and applied to the problem of functional site prediction in protein 3D structures, an important current challenge in genomics. The input consists of electrostatic and geometric properties derived from the 3D structure of the query protein alone. Sequence-based conservation information, where available, may also be incorporated. Electrostatics features from THEMATICS are combined with multidimensional isotonic regression to form maximum likelihood estimates of probabilities that specific residues belong to an active site. This allows likelihood ranking of all ionizable residues in a given protein based on THEMATICS features. The corresponding ROC curves and statistical significance tests demonstrate that this method outperforms prior THEMATICS-based methods, which in turn have been shown previously to outperform other 3D-structure-based methods for identifying active site residues. Then it is shown that the addition of one simple geometric property, the size rank of the cleft in which a given residue is contained, yields improved performance. Extension of the method to include predictions of non-ionizable residues is achieved through the introduction of environment variables. This extension results in even better performance than THEMATICS alone and constitutes to date the best functional site predictor based on 3D structure only, achieving nearly the same level of performance as methods that use both 3D structure and sequence alignment data. Finally, the method also easily incorporates such sequence alignment data, and when this information is included, the resulting method is shown to outperform the best current methods using any combination of sequence alignments and 3D structures. Included is an analysis demonstrating that when THEMATICS features, cleft size rank, and alignment-based conservation scores are used individually or in combination
Li, Si; Choi, Kwok Pui; Wu, Taoyang; Zhang, Louxin
2013-01-01
Evolutionary history of protein-protein interaction (PPI) networks provides valuable insight into molecular mechanisms of network growth. In this paper, we study how to infer the evolutionary history of a PPI network from its protein duplication relationship. We show that for a plausible evolutionary history of a PPI network, its relative quality, measured by the so-called loss number, is independent of the growth parameters of the network and can be computed efficiently. This finding leads us to propose two fast maximum likelihood algorithms to infer the evolutionary history of a PPI network given the duplication history of its proteins. Simulation studies demonstrated that our approach, which takes advantage of protein duplication information, outperforms NetArch, the first maximum likelihood algorithm for PPI network history reconstruction. Using the proposed method, we studied the topological change of the PPI networks of the yeast, fruitfly, and worm.
Maximum Likelihood Reconstruction for Ising Models with Asynchronous Updates
NASA Astrophysics Data System (ADS)
Zeng, Hong-Li; Alava, Mikko; Aurell, Erik; Hertz, John; Roudi, Yasser
2013-05-01
We describe how the couplings in an asynchronous kinetic Ising model can be inferred. We consider two cases: one in which we know both the spin history and the update times and one in which we know only the spin history. For the first case, we show that one can average over all possible choices of update times to obtain a learning rule that depends only on spin correlations and can also be derived from the equations of motion for the correlations. For the second case, the same rule can be derived within a further decoupling approximation. We study all methods numerically for fully asymmetric Sherrington-Kirkpatrick models, varying the data length, system size, temperature, and external field. Good convergence is observed in accordance with the theoretical expectations.
Reconstruction of 3-D Positron Emission with Maximum Likelihood
1988-11-01
rMedical Command Nashinton. DC 20372-5210 89 36 UNCLASSIFIED SEC.-RIT CLASSFCATION OF "HIS PAGE REPORT DOCUMENTATION PAGE Ia . REPORT SECURITY CLASSIFICATION...complex :image identified by their simulated anato )rc location: shoulder (top) and lung (bottom). 27 0.! COMPLEX OBJECT VARIABILITY SHOULDER 7B BOXES 2- 1.5
NASA Technical Reports Server (NTRS)
Peters, B. C., Jr.; Walker, H. F.
1975-01-01
A general iterative procedure is given for determining the consistent maximum likelihood estimates of normal distributions. In addition, a local maximum of the log-likelihood function, Newtons's method, a method of scoring, and modifications of these procedures are discussed.
ERIC Educational Resources Information Center
Choi, Jaehwa; Kim, Sunhee; Chen, Jinsong; Dannels, Sharon
2011-01-01
The purpose of this study is to compare the maximum likelihood (ML) and Bayesian estimation methods for polychoric correlation (PCC) under diverse conditions using a Monte Carlo simulation. Two new Bayesian estimates, maximum a posteriori (MAP) and expected a posteriori (EAP), are compared to ML, the classic solution, to estimate PCC. Different…
ERIC Educational Resources Information Center
Magis, David; Raiche, Gilles
2010-01-01
In this article the authors focus on the issue of the nonuniqueness of the maximum likelihood (ML) estimator of proficiency level in item response theory (with special attention to logistic models). The usual maximum a posteriori (MAP) method offers a good alternative within that framework; however, this article highlights some drawbacks of its…
ERIC Educational Resources Information Center
Choi, Jaehwa; Kim, Sunhee; Chen, Jinsong; Dannels, Sharon
2011-01-01
The purpose of this study is to compare the maximum likelihood (ML) and Bayesian estimation methods for polychoric correlation (PCC) under diverse conditions using a Monte Carlo simulation. Two new Bayesian estimates, maximum a posteriori (MAP) and expected a posteriori (EAP), are compared to ML, the classic solution, to estimate PCC. Different…
ERIC Educational Resources Information Center
Magis, David; Raiche, Gilles
2010-01-01
In this article the authors focus on the issue of the nonuniqueness of the maximum likelihood (ML) estimator of proficiency level in item response theory (with special attention to logistic models). The usual maximum a posteriori (MAP) method offers a good alternative within that framework; however, this article highlights some drawbacks of its…
Estimating parameters of a multiple autoregressive model by the modified maximum likelihood method
NASA Astrophysics Data System (ADS)
Bayrak, Özlem Türker; Akkaya, Aysen D.
2010-02-01
We consider a multiple autoregressive model with non-normal error distributions, the latter being more prevalent in practice than the usually assumed normal distribution. Since the maximum likelihood equations have convergence problems (Puthenpura and Sinha, 1986) [11], we work out modified maximum likelihood equations by expressing the maximum likelihood equations in terms of ordered residuals and linearizing intractable nonlinear functions (Tiku and Suresh, 1992) [8]. The solutions, called modified maximum estimators, are explicit functions of sample observations and therefore easy to compute. They are under some very general regularity conditions asymptotically unbiased and efficient (Vaughan and Tiku, 2000) [4]. We show that for small sample sizes, they have negligible bias and are considerably more efficient than the traditional least squares estimators. We show that our estimators are robust to plausible deviations from an assumed distribution and are therefore enormously advantageous as compared to the least squares estimators. We give a real life example.
Determining the accuracy of maximum likelihood parameter estimates with colored residuals
NASA Technical Reports Server (NTRS)
Morelli, Eugene A.; Klein, Vladislav
1994-01-01
An important part of building high fidelity mathematical models based on measured data is calculating the accuracy associated with statistical estimates of the model parameters. Indeed, without some idea of the accuracy of parameter estimates, the estimates themselves have limited value. In this work, an expression based on theoretical analysis was developed to properly compute parameter accuracy measures for maximum likelihood estimates with colored residuals. This result is important because experience from the analysis of measured data reveals that the residuals from maximum likelihood estimation are almost always colored. The calculations involved can be appended to conventional maximum likelihood estimation algorithms. Simulated data runs were used to show that the parameter accuracy measures computed with this technique accurately reflect the quality of the parameter estimates from maximum likelihood estimation without the need for analysis of the output residuals in the frequency domain or heuristically determined multiplication factors. The result is general, although the application studied here is maximum likelihood estimation of aerodynamic model parameters from flight test data.
A maximum-likelihood search for neutrino point sources with the AMANDA-II detector
NASA Astrophysics Data System (ADS)
Braun, James R.
Neutrino astronomy offers a new window to study the high energy universe. The AMANDA-II detector records neutrino-induced muon events in the ice sheet beneath the geographic South Pole, and has accumulated 3.8 years of livetime from 2000 - 2006. After reconstructing muon tracks and applying selection criteria, we arrive at a sample of 6595 events originating from the Northern Sky, predominantly atmospheric neutrinos with primary energy 100 GeV to 8 TeV. We search these events for evidence of astrophysical neutrino point sources using a maximum-likelihood method. No excess above the atmospheric neutrino background is found, and we set upper limits on neutrino fluxes. Finally, a well-known potential dark matter signature is emission of high energy neutrinos from annihilation of WIMPs gravitationally bound to the Sun. We search for high energy neutrinos from the Sun and find no excess. Our limits on WIMP-nucleon cross section set new constraints on MSSM parameter space.
The optical synthetic aperture image restoration based on the improved maximum-likelihood algorithm
NASA Astrophysics Data System (ADS)
Geng, Zexun; Xu, Qing; Zhang, Baoming; Gong, Zhihui
2012-09-01
Optical synthetic aperture imaging (OSAI) can be envisaged in the future for improving the image resolution from high altitude orbits. Several future projects are based on optical synthetic aperture for science or earth observation. Comparing with equivalent monolithic telescopes, however, the partly filled aperture of OSAI induces the attenuation of the modulation transfer function of the system. Consequently, images acquired by OSAI instrument have to be post-processed to restore ones equivalent in resolution to that of a single filled aperture. The maximum-likelihood (ML) algorithm proposed by Benvenuto performed better than traditional Wiener filter did, but it didn't work stably and the point spread function (PSF), was assumed to be known and unchanged in iterative restoration. In fact, the PSF is unknown in most cases, and its estimation was expected to be updated alternatively in optimization. Facing these limitations of this method, an improved ML (IML) reconstruction algorithm was proposed in this paper, which incorporated PSF estimation by means of parameter identification into ML, and updated the PSF successively during iteration. Accordingly, the IML algorithm converged stably and reached better results. Experiment results showed that the proposed algorithm performed much better than ML did in peak signal to noise ratio, mean square error and the average contrast evaluation indexes.
NASA Astrophysics Data System (ADS)
Aioanei, Daniel; Samorì, Bruno; Brucale, Marco
2009-12-01
Single molecule force spectroscopy (SMFS) is extensively used to characterize the mechanical unfolding behavior of individual protein domains under applied force by pulling chimeric polyproteins consisting of identical tandem repeats. Constant velocity unfolding SMFS data can be employed to reconstruct the protein unfolding energy landscape and kinetics. The methods applied so far require the specification of a single stretching force increase function, either theoretically derived or experimentally inferred, which must then be assumed to accurately describe the entirety of the experimental data. The very existence of a suitable optimal force model, even in the context of a single experimental data set, is still questioned. Herein, we propose a maximum likelihood (ML) framework for the estimation of protein kinetic parameters which can accommodate all the established theoretical force increase models. Our framework does not presuppose the existence of a single force characteristic function. Rather, it can be used with a heterogeneous set of functions, each describing the protein behavior in the stretching time range leading to one rupture event. We propose a simple way of constructing such a set of functions via piecewise linear approximation of the SMFS force vs time data and we prove the suitability of the approach both with synthetic data and experimentally. Additionally, when the spontaneous unfolding rate is the only unknown parameter, we find a correction factor that eliminates the bias of the ML estimator while also reducing its variance. Finally, we investigate which of several time-constrained experiment designs leads to better estimators.
NASA Technical Reports Server (NTRS)
1979-01-01
The computer program Linear SCIDNT which evaluates rotorcraft stability and control coefficients from flight or wind tunnel test data is described. It implements the maximum likelihood method to maximize the likelihood function of the parameters based on measured input/output time histories. Linear SCIDNT may be applied to systems modeled by linear constant-coefficient differential equations. This restriction in scope allows the application of several analytical results which simplify the computation and improve its efficiency over the general nonlinear case.
Recent developments in maximum likelihood estimation of MTMM models for categorical data.
Jeon, Minjeong; Rijmen, Frank
2014-01-01
Maximum likelihood (ML) estimation of categorical multitrait-multimethod (MTMM) data is challenging because the likelihood involves high-dimensional integrals over the crossed method and trait factors, with no known closed-form solution. The purpose of the study is to introduce three newly developed ML methods that are eligible for estimating MTMM models with categorical responses: Variational maximization-maximization (e.g., Rijmen and Jeon, 2013), alternating imputation posterior (e.g., Cho and Rabe-Hesketh, 2011), and Monte Carlo local likelihood (e.g., Jeon et al., under revision). Each method is briefly described and its applicability for MTMM models with categorical data are discussed.
Maximum Likelihood Estimation for Multiple Camera Target Tracking on Grassmann Tangent Subspace.
Amini-Omam, Mojtaba; Torkamani-Azar, Farah; Ghorashi, Seyed Ali
2016-11-15
In this paper, we introduce a likelihood model for tracking the location of object in multiple view systems. Our proposed model transforms conventional nonlinear Euclidean estimation model to an estimation model based on the manifold tangent subspace. In this paper, we show that by decomposition of input noise into two parts and description of model by exponential map, real observations in the Euclidean geometry can be transformed to the manifold tangent subspace. Moreover, by obtained tangent subspace likelihood function, we propose two iterative and noniterative maximum likelihood estimation approaches which numerical results show their good performance.
Spackman, K. A.
1991-01-01
This paper presents maximum likelihood back-propagation (ML-BP), an approach to training neural networks. The widely reported original approach uses least squares back-propagation (LS-BP), minimizing the sum of squared errors (SSE). Unfortunately, least squares estimation does not give a maximum likelihood (ML) estimate of the weights in the network. Logistic regression, on the other hand, gives ML estimates for single layer linear models only. This report describes how to obtain ML estimates of the weights in a multi-layer model, and compares LS-BP to ML-BP using several examples. It shows that in many neural networks, least squares estimation gives inferior results and should be abandoned in favor of maximum likelihood estimation. Questions remain about the potential uses of multi-level connectionist models in such areas as diagnostic systems and risk-stratification in outcomes research. PMID:1807606
NASA Astrophysics Data System (ADS)
Khaninezhad, Mohammadreza M.; Jafarpour, Behnam
2014-07-01
Despite their apparent high dimensionality, spatially distributed hydraulic properties of geologic formations can often be compactly (sparsely) described in a properly designed basis. Hence, the estimation of high-dimensional subsurface flow properties from dynamic performance and monitoring data can be formulated and solved as a sparse reconstruction inverse problem. Recent advances in statistical signal processing, formalized under the compressed sensing paradigm, provide important guidelines on formulating and solving sparse inverse problems, primarily for linear models and using a deterministic framework. Given the uncertainty in describing subsurface physical properties, even after integration of the dynamic data, it is important to develop a practical sparse Bayesian inversion approach to enable uncertainty quantification. In this paper, we use sparse geologic dictionaries to compactly represent uncertain subsurface flow properties and develop a practical sparse Bayesian method for effective data integration and uncertainty quantification. The multi-Gaussian assumption that is widely used in classical probabilistic inverse theory is not appropriate for representing sparse prior models. Following the results presented by the compressed sensing paradigm, the Laplace (or double exponential) probability distribution is found to be more suitable for representing sparse parameters. However, combining Laplace priors with the frequently used Gaussian likelihood functions leads to neither a Laplace nor a Gaussian posterior distribution, which complicates the analytical characterization of the posterior. Here, we first express the form of the Maximum A-Posteriori (MAP) estimate for Laplace priors and then use the Monte-Carlo-based Randomize Maximum Likelihood (RML) method to generate approximate samples from the posterior distribution. The proposed Sparse RML (SpRML) approximate sampling approach can be used to assess the uncertainty in the calibrated model with a
A general methodology for maximum likelihood inference from band-recovery data
Conroy, M.J.; Williams, B.K.
1984-01-01
A numerical procedure is described for obtaining maximum likelihood estimates and associated maximum likelihood inference from band- recovery data. The method is used to illustrate previously developed one-age-class band-recovery models, and is extended to new models, including the analysis with a covariate for survival rates and variable-time-period recovery models. Extensions to R-age-class band- recovery, mark-recapture models, and twice-yearly marking are discussed. A FORTRAN program provides computations for these models.
Design of simplified maximum-likelihood receivers for multiuser CPM systems.
Bing, Li; Bai, Baoming
2014-01-01
A class of simplified maximum-likelihood receivers designed for continuous phase modulation based multiuser systems is proposed. The presented receiver is built upon a front end employing mismatched filters and a maximum-likelihood detector defined in a low-dimensional signal space. The performance of the proposed receivers is analyzed and compared to some existing receivers. Some schemes are designed to implement the proposed receivers and to reveal the roles of different system parameters. Analysis and numerical results show that the proposed receivers can approach the optimum multiuser receivers with significantly (even exponentially in some cases) reduced complexity and marginal performance degradation.
NASA Technical Reports Server (NTRS)
Thadani, S. G.
1977-01-01
The Maximum Likelihood Estimation of Signature Transformation (MLEST) algorithm is used to obtain maximum likelihood estimates (MLE) of affine transformation. The algorithm has been evaluated for three sets of data: simulated (training and recognition segment pairs), consecutive-day (data gathered from Landsat images), and geographical-extension (large-area crop inventory experiment) data sets. For each set, MLEST signature extension runs were made to determine MLE values and the affine-transformed training segment signatures were used to classify the recognition segments. The classification results were used to estimate wheat proportions at 0 and 1% threshold values.
Estimation of bias errors in measured airplane responses using maximum likelihood method
NASA Technical Reports Server (NTRS)
Klein, Vladiaslav; Morgan, Dan R.
1987-01-01
A maximum likelihood method is used for estimation of unknown bias errors in measured airplane responses. The mathematical model of an airplane is represented by six-degrees-of-freedom kinematic equations. In these equations the input variables are replaced by their measured values which are assumed to be without random errors. The resulting algorithm is verified with a simulation and flight test data. The maximum likelihood estimates from in-flight measured data are compared with those obtained by using a nonlinear-fixed-interval-smoother and an extended Kalmar filter.
Lemaire, H.; Barat, E.; Carrel, F.; Dautremer, T.; Dubos, S.; Limousin, O.; Montagu, T.; Normand, S.; Schoepff, V.; Amgarou, K.; Menaa, N.; Angelique, J.-C.; Patoz, A.
2015-07-01
In this work, we tested Maximum likelihood expectation-maximization (MLEM) algorithms optimized for gamma imaging applications on two recent coded mask gamma cameras. We respectively took advantage of the characteristics of the GAMPIX and Caliste HD-based gamma cameras: noise reduction thanks to mask/anti-mask procedure but limited energy resolution for GAMPIX, high energy resolution for Caliste HD. One of our short-term perspectives is the test of MAPEM algorithms integrating specific prior values for the data to reconstruct adapted to the gamma imaging topic. (authors)
Maximum-likelihood soft-decision decoding of block codes using the A* algorithm
NASA Technical Reports Server (NTRS)
Ekroot, L.; Dolinar, S.
1994-01-01
The A* algorithm finds the path in a finite depth binary tree that optimizes a function. Here, it is applied to maximum-likelihood soft-decision decoding of block codes where the function optimized over the codewords is the likelihood function of the received sequence given each codeword. The algorithm considers codewords one bit at a time, making use of the most reliable received symbols first and pursuing only the partially expanded codewords that might be maximally likely. A version of the A* algorithm for maximum-likelihood decoding of block codes has been implemented for block codes up to 64 bits in length. The efficiency of this algorithm makes simulations of codes up to length 64 feasible. This article details the implementation currently in use, compares the decoding complexity with that of exhaustive search and Viterbi decoding algorithms, and presents performance curves obtained with this implementation of the A* algorithm for several codes.
A multinomial maximum likelihood program /MUNOML/. [in modeling sensory and decision phenomena
NASA Technical Reports Server (NTRS)
Curry, R. E.
1975-01-01
A multinomial maximum likelihood program (MUNOML) for signal detection and for behavior models is discussed. It is found to be useful in day to day operation since it provides maximum flexibility with minimum duplicated effort. It has excellent convergence qualities and rarely goes beyond 10 iterations. A library of subroutines is being collected for use with MUNOML, including subroutines for a successive categories model and for signal detectability models.
An evaluation of percentile and maximum likelihood estimators of weibull paremeters
Stanley J. Zarnoch; Tommy R. Dell
1985-01-01
Two methods of estimating the three-parameter Weibull distribution were evaluated by computer simulation and field data comparison. Maximum likelihood estimators (MLB) with bias correction were calculated with the computer routine FITTER (Bailey 1974); percentile estimators (PCT) were those proposed by Zanakis (1979). The MLB estimators had superior smaller bias and...
Recovery of Weak Common Factors by Maximum Likelihood and Ordinary Least Squares Estimation.
ERIC Educational Resources Information Center
Briggs, Nancy E.; MacCallum, Robert C.
2003-01-01
Examined the relative performance of two commonly used methods of parameter estimation in factor analysis, maximum likelihood (ML) and ordinary least squares (OLS) through simulation. In situations with a moderate amount of error, ML often failed to recover the weak factor while OLS succeeded. Also presented an example using empirical data. (SLD)
An EM Algorithm for Maximum Likelihood Estimation of Process Factor Analysis Models
ERIC Educational Resources Information Center
Lee, Taehun
2010-01-01
In this dissertation, an Expectation-Maximization (EM) algorithm is developed and implemented to obtain maximum likelihood estimates of the parameters and the associated standard error estimates characterizing temporal flows for the latent variable time series following stationary vector ARMA processes, as well as the parameters defining the…
Marginal Maximum Likelihood Estimation of a Latent Variable Model with Interaction
ERIC Educational Resources Information Center
Cudeck, Robert; Harring, Jeffrey R.; du Toit, Stephen H. C.
2009-01-01
There has been considerable interest in nonlinear latent variable models specifying interaction between latent variables. Although it seems to be only slightly more complex than linear regression without the interaction, the model that includes a product of latent variables cannot be estimated by maximum likelihood assuming normality.…
ERIC Educational Resources Information Center
Enders, Craig K.; Bandalos, Deborah L.
2001-01-01
Used Monte Carlo simulation to examine the performance of four missing data methods in structural equation models: (1)full information maximum likelihood (FIML); (2) listwise deletion; (3) pairwise deletion; and (4) similar response pattern imputation. Results show that FIML estimation is superior across all conditions of the design. (SLD)
ERIC Educational Resources Information Center
Enders, Craig K.
2001-01-01
Examined the performance of a recently available full information maximum likelihood (FIML) estimator in a multiple regression model with missing data using Monte Carlo simulation and considering the effects of four independent variables. Results indicate that FIML estimation was superior to that of three ad hoc techniques, with less bias and less…
ERIC Educational Resources Information Center
Klein, Andreas G.; Muthen, Bengt O.
2007-01-01
In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly…
ERIC Educational Resources Information Center
Penfield, Randall D.; Bergeron, Jennifer M.
2005-01-01
This article applies a weighted maximum likelihood (WML) latent trait estimator to the generalized partial credit model (GPCM). The relevant equations required to obtain the WML estimator using the Newton-Raphson algorithm are presented, and a simulation study is described that compared the properties of the WML estimator to those of the maximum…
Bias and Efficiency in Structural Equation Modeling: Maximum Likelihood versus Robust Methods
ERIC Educational Resources Information Center
Zhong, Xiaoling; Yuan, Ke-Hai
2011-01-01
In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…
Maximum Likelihood Estimation of Nonlinear Structural Equation Models with Ignorable Missing Data
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan; Lee, John C. K.
2003-01-01
The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models…
ERIC Educational Resources Information Center
Casabianca, Jodi M.; Lewis, Charles
2015-01-01
Loglinear smoothing (LLS) estimates the latent trait distribution while making fewer assumptions about its form and maintaining parsimony, thus leading to more precise item response theory (IRT) item parameter estimates than standard marginal maximum likelihood (MML). This article provides the expectation-maximization algorithm for MML estimation…
ERIC Educational Resources Information Center
Luo, Guanzhong
2000-01-01
Extends joint maximum likelihood estimation for the hyperbolic cosine model to the situation in which the units of items are allowed to vary. Describes the four estimation cycles designed to address four important issues of model development and presents results from two sets of simulation studies that show reasonably accurate parameter recovery…
A New Maximum Likelihood Estimator for the Population Squared Multiple Correlation.
ERIC Educational Resources Information Center
Alf, Edward F., Jr.; Graf, Richard G.
2002-01-01
Developed a new estimator for the population squared multiple correlation using maximum likelihood estimation. Data from 72 air control school graduates demonstrate that the new estimator has greater accuracy than other estimators with values that fall within the parameter space. (SLD)
John Hogland; Nedret Billor; Nathaniel Anderson
2013-01-01
Discriminant analysis, referred to as maximum likelihood classification within popular remote sensing software packages, is a common supervised technique used by analysts. Polytomous logistic regression (PLR), also referred to as multinomial logistic regression, is an alternative classification approach that is less restrictive, more flexible, and easy to interpret. To...
Maximum Likelihood Item Easiness Models for Test Theory without an Answer Key
ERIC Educational Resources Information Center
France, Stephen L.; Batchelder, William H.
2015-01-01
Cultural consensus theory (CCT) is a data aggregation technique with many applications in the social and behavioral sciences. We describe the intuition and theory behind a set of CCT models for continuous type data using maximum likelihood inference methodology. We describe how bias parameters can be incorporated into these models. We introduce…
The Bias Function of the Maximum Likelihood Estimate of Ability for the Dichotomous Response Level.
ERIC Educational Resources Information Center
Samejima, Fumiko
1993-01-01
F. Samejima's approximation for the bias function for the maximum likelihood estimate of the latent trait in the general case where item responses are discrete is explored. Observations are made about the behavior of this bias function for the dichotomous response level in general. Empirical examples are given. (SLD)
An Alternative Estimator for the Maximum Likelihood Estimator for the Two Extreme Response Patterns.
ERIC Educational Resources Information Center
Samejima, Fumiko
In the methods and approaches developed for estimating the operating characteristics of the discrete item responses, the maximum likelihood estimate of the examinee based upon the "Old Test" has an important role. When Old Test does not provide a sufficient amount of test information for the upper and lower part of the ability interval,…
ERIC Educational Resources Information Center
Samejima, Fumiko
1977-01-01
A method of estimating item characteristic functions is proposed, in which a set of test items, whose operating characteristics are known and which give a constant test information function for a wide range of ability, are used. The method is based on maximum likelihood estimation procedures. (Author/JKS)
Indoor Ultra-Wide Band Network Adjustment using Maximum Likelihood Estimation
NASA Astrophysics Data System (ADS)
Koppanyi, Z.; Toth, C. K.
2014-11-01
This study is the part of our ongoing research on using ultra-wide band (UWB) technology for navigation at the Ohio State University. Our tests have indicated that the UWB two-way time-of-flight ranges under indoor circumstances follow a Gaussian mixture distribution that may be caused by the incompleteness of the functional model. In this case, to adjust the UWB network from the observed ranges, the maximum likelihood estimation (MLE) may provide a better solution for the node coordinates than the widely-used least squares approach. The prerequisite of the maximum likelihood method is to know the probability density functions. The 30 Hz sampling rate of the UWB sensors enables to estimate these functions between each node from the samples in static positioning mode. In order to prove the MLE hypothesis, an UWB network has been established in a multi-path density environment for test data acquisition. The least squares and maximum likelihood coordinate solutions are determined and compared, and the results indicate that better accuracy can be achieved with maximum likelihood estimation.
A Maximum Likelihood Method for Latent Class Regression Involving a Censored Dependent Variable.
ERIC Educational Resources Information Center
Jedidi, Kamel; And Others
1993-01-01
A method is proposed to simultaneously estimate regression functions and subject membership in "k" latent classes or groups given a censored dependent variable for a cross-section of subjects. Maximum likelihood estimates are obtained using an EM algorithm. The method is illustrated through a consumer psychology application. (SLD)
Bias and Efficiency in Structural Equation Modeling: Maximum Likelihood versus Robust Methods
ERIC Educational Resources Information Center
Zhong, Xiaoling; Yuan, Ke-Hai
2011-01-01
In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…
ERIC Educational Resources Information Center
Penfield, Randall D.; Bergeron, Jennifer M.
2005-01-01
This article applies a weighted maximum likelihood (WML) latent trait estimator to the generalized partial credit model (GPCM). The relevant equations required to obtain the WML estimator using the Newton-Raphson algorithm are presented, and a simulation study is described that compared the properties of the WML estimator to those of the maximum…
Bootstrap Standard Errors for Maximum Likelihood Ability Estimates When Item Parameters Are Unknown
ERIC Educational Resources Information Center
Patton, Jeffrey M.; Cheng, Ying; Yuan, Ke-Hai; Diao, Qi
2014-01-01
When item parameter estimates are used to estimate the ability parameter in item response models, the standard error (SE) of the ability estimate must be corrected to reflect the error carried over from item calibration. For maximum likelihood (ML) ability estimates, a corrected asymptotic SE is available, but it requires a long test and the…
Maximum Likelihood Item Easiness Models for Test Theory without an Answer Key
ERIC Educational Resources Information Center
France, Stephen L.; Batchelder, William H.
2015-01-01
Cultural consensus theory (CCT) is a data aggregation technique with many applications in the social and behavioral sciences. We describe the intuition and theory behind a set of CCT models for continuous type data using maximum likelihood inference methodology. We describe how bias parameters can be incorporated into these models. We introduce…
Constrained Maximum Likelihood Estimation for Two-Level Mean and Covariance Structure Models
ERIC Educational Resources Information Center
Bentler, Peter M.; Liang, Jiajuan; Tang, Man-Lai; Yuan, Ke-Hai
2011-01-01
Maximum likelihood is commonly used for the estimation of model parameters in the analysis of two-level structural equation models. Constraints on model parameters could be encountered in some situations such as equal factor loadings for different factors. Linear constraints are the most common ones and they are relatively easy to handle in…
A Maximum Likelihood Method for Latent Class Regression Involving a Censored Dependent Variable.
ERIC Educational Resources Information Center
Jedidi, Kamel; And Others
1993-01-01
A method is proposed to simultaneously estimate regression functions and subject membership in "k" latent classes or groups given a censored dependent variable for a cross-section of subjects. Maximum likelihood estimates are obtained using an EM algorithm. The method is illustrated through a consumer psychology application. (SLD)
ERIC Educational Resources Information Center
Enders, Craig K.; Bandalos, Deborah L.
2001-01-01
Used Monte Carlo simulation to examine the performance of four missing data methods in structural equation models: (1)full information maximum likelihood (FIML); (2) listwise deletion; (3) pairwise deletion; and (4) similar response pattern imputation. Results show that FIML estimation is superior across all conditions of the design. (SLD)
Maximum Likelihood Dynamic Factor Modeling for Arbitrary "N" and "T" Using SEM
ERIC Educational Resources Information Center
Voelkle, Manuel C.; Oud, Johan H. L.; von Oertzen, Timo; Lindenberger, Ulman
2012-01-01
This article has 3 objectives that build on each other. First, we demonstrate how to obtain maximum likelihood estimates for dynamic factor models (the direct autoregressive factor score model) with arbitrary "T" and "N" by means of structural equation modeling (SEM) and compare the approach to existing methods. Second, we go beyond standard time…
An EM Algorithm for Maximum Likelihood Estimation of Process Factor Analysis Models
ERIC Educational Resources Information Center
Lee, Taehun
2010-01-01
In this dissertation, an Expectation-Maximization (EM) algorithm is developed and implemented to obtain maximum likelihood estimates of the parameters and the associated standard error estimates characterizing temporal flows for the latent variable time series following stationary vector ARMA processes, as well as the parameters defining the…
On Muthen's Maximum Likelihood for Two-Level Covariance Structure Models
ERIC Educational Resources Information Center
Yuan, Ke-Hai; Hayashi, Kentaro
2005-01-01
Data in social and behavioral sciences are often hierarchically organized. Special statistical procedures that take into account the dependence of such observations have been developed. Among procedures for 2-level covariance structure analysis, Muthen's maximum likelihood (MUML) has the advantage of easier computation and faster convergence. When…
ERIC Educational Resources Information Center
Casabianca, Jodi M.; Lewis, Charles
2015-01-01
Loglinear smoothing (LLS) estimates the latent trait distribution while making fewer assumptions about its form and maintaining parsimony, thus leading to more precise item response theory (IRT) item parameter estimates than standard marginal maximum likelihood (MML). This article provides the expectation-maximization algorithm for MML estimation…
ERIC Educational Resources Information Center
Holt, Judith A.; Macready, George B.
When latent class parameters are estimated, maximum likelihood and Pearson chi-square statistics can be derived for assessing the fit of the model to the data. This study used simulated data to compare these two statistics, and is based on mixtures of latent binomial distributions, using data generated from five dichotomous manifest variables.…
Maximum Likelihood Analysis of a Two-Level Nonlinear Structural Equation Model with Fixed Covariates
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan
2005-01-01
In this article, a maximum likelihood (ML) approach for analyzing a rather general two-level structural equation model is developed for hierarchically structured data that are very common in educational and/or behavioral research. The proposed two-level model can accommodate nonlinear causal relations among latent variables as well as effects…
Some Contrasts between Maximum Likelihood Factor Analysis and Alpha Factor Analysis.
ERIC Educational Resources Information Center
Kaiser, Henry F.; Derflinger, Gerhard
1990-01-01
The fundamental mathematical model of L. L. Thurstone's common factor analysis is reviewed, and basic covariance matrices of maximum likelihood factor analysis and alpha factor analysis are presented. The methods are compared in terms of computational and scaling contrasts. Weighting and the appropriate number of common factors are considered.…
Li, Ruijie; Ding, Shengli; Dang, Anhong
2017-05-01
This paper investigates a detection scheme without channel state information for wireless optical communication systems. Employing conventional on-off keying signals, we supposed that conditional probability density function P(r|0) is much bigger than P(r|1) when r<0. Under this assumption, the suboptimal maximum likelihood scheme is obtained by utilizing the probability density function without channel information. Theoretical analysis shows the performance of the proposed scheme is close to the maximum likelihood symbol-by-symbol detection. Compared with the maximum likelihood symbol by symbol detection, Monte Carlo simulations show that the performance of the proposed scheme is about 0.62 dB loss for a gamma-gamma channel with a Rytov variance of 1 at the signal-to-noise ratio of 2 dB, but the efficient algorithm makes the real-time implementation of detection based on maximum likelihood feasible. Besides, the experiment is set up under 2 Gbps, and the experimental results match well with that of the theory and simulation.
Maximum Likelihood Dynamic Factor Modeling for Arbitrary "N" and "T" Using SEM
ERIC Educational Resources Information Center
Voelkle, Manuel C.; Oud, Johan H. L.; von Oertzen, Timo; Lindenberger, Ulman
2012-01-01
This article has 3 objectives that build on each other. First, we demonstrate how to obtain maximum likelihood estimates for dynamic factor models (the direct autoregressive factor score model) with arbitrary "T" and "N" by means of structural equation modeling (SEM) and compare the approach to existing methods. Second, we go beyond standard time…
ERIC Educational Resources Information Center
Enders, Craig K.
2001-01-01
Examined the performance of a recently available full information maximum likelihood (FIML) estimator in a multiple regression model with missing data using Monte Carlo simulation and considering the effects of four independent variables. Results indicate that FIML estimation was superior to that of three ad hoc techniques, with less bias and less…
Maximum Likelihood Estimation of Nonlinear Structural Equation Models with Ignorable Missing Data
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan; Lee, John C. K.
2003-01-01
The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models…
Maximum Likelihood Analysis of Nonlinear Structural Equation Models with Dichotomous Variables
ERIC Educational Resources Information Center
Song, Xin-Yuan; Lee, Sik-Yum
2005-01-01
In this article, a maximum likelihood approach is developed to analyze structural equation models with dichotomous variables that are common in behavioral, psychological and social research. To assess nonlinear causal effects among the latent variables, the structural equation in the model is defined by a nonlinear function. The basic idea of the…
On the Existence and Uniqueness of Maximum-Likelihood Estimates in the Rasch Model.
ERIC Educational Resources Information Center
Fischer, Gerhard H.
1981-01-01
Necessary and sufficient conditions for the existence and uniqueness of a solution of the so-called "unconditional" and the "conditional" maximum-likelihood estimation equations in the dichotomous Rasch model are given. It is shown how to apply the results in practical uses of the Rasch model. (Author/JKS)
A maximum pseudo-likelihood approach for estimating species trees under the coalescent model
2010-01-01
Background Several phylogenetic approaches have been developed to estimate species trees from collections of gene trees. However, maximum likelihood approaches for estimating species trees under the coalescent model are limited. Although the likelihood of a species tree under the multispecies coalescent model has already been derived by Rannala and Yang, it can be shown that the maximum likelihood estimate (MLE) of the species tree (topology, branch lengths, and population sizes) from gene trees under this formula does not exist. In this paper, we develop a pseudo-likelihood function of the species tree to obtain maximum pseudo-likelihood estimates (MPE) of species trees, with branch lengths of the species tree in coalescent units. Results We show that the MPE of the species tree is statistically consistent as the number M of genes goes to infinity. In addition, the probability that the MPE of the species tree matches the true species tree converges to 1 at rate O(M -1). The simulation results confirm that the maximum pseudo-likelihood approach is statistically consistent even when the species tree is in the anomaly zone. We applied our method, Maximum Pseudo-likelihood for Estimating Species Trees (MP-EST) to a mammal dataset. The four major clades found in the MP-EST tree are consistent with those in the Bayesian concatenation tree. The bootstrap supports for the species tree estimated by the MP-EST method are more reasonable than the posterior probability supports given by the Bayesian concatenation method in reflecting the level of uncertainty in gene trees and controversies over the relationship of four major groups of placental mammals. Conclusions MP-EST can consistently estimate the topology and branch lengths (in coalescent units) of the species tree. Although the pseudo-likelihood is derived from coalescent theory, and assumes no gene flow or horizontal gene transfer (HGT), the MP-EST method is robust to a small amount of HGT in the dataset. In addition
Estimation Methods for Non-Homogeneous Regression - Minimum CRPS vs Maximum Likelihood
NASA Astrophysics Data System (ADS)
Gebetsberger, Manuel; Messner, Jakob W.; Mayr, Georg J.; Zeileis, Achim
2017-04-01
Non-homogeneous regression models are widely used to statistically post-process numerical weather prediction models. Such regression models correct for errors in mean and variance and are capable to forecast a full probability distribution. In order to estimate the corresponding regression coefficients, CRPS minimization is performed in many meteorological post-processing studies since the last decade. In contrast to maximum likelihood estimation, CRPS minimization is claimed to yield more calibrated forecasts. Theoretically, both scoring rules used as an optimization score should be able to locate a similar and unknown optimum. Discrepancies might result from a wrong distributional assumption of the observed quantity. To address this theoretical concept, this study compares maximum likelihood and minimum CRPS estimation for different distributional assumptions. First, a synthetic case study shows that, for an appropriate distributional assumption, both estimation methods yield to similar regression coefficients. The log-likelihood estimator is slightly more efficient. A real world case study for surface temperature forecasts at different sites in Europe confirms these results but shows that surface temperature does not always follow the classical assumption of a Gaussian distribution. KEYWORDS: ensemble post-processing, maximum likelihood estimation, CRPS minimization, probabilistic temperature forecasting, distributional regression models
Fitak, Robert R; Johnsen, Sönke
2017-08-31
In studies of animal orientation, data are often represented as directions that can be analyzed using circular statistical methods. Although several circular statistical tests exist to detect the presence of a mean direction, likelihood-based approaches may offer advantages in hypothesis testing - especially when data are multimodal. Unfortunately, likelihood-based inference in animal orientation remains rare. Here, we discuss some of the assumptions and limitations of common circular tests and report a new R package called CircMLE to implement the maximum likelihood analysis of circular data. We illustrate the use of this package on both simulated datasets and an empirical example dataset in Chinook salmon (Oncorhynchus tshawytscha). Our software provides a convenient interface that facilitates the use of model-based approaches in animal orientation studies. © 2017. Published by The Company of Biologists Ltd.
Qi, Jinyi; Huesman, Ronald H
2006-05-01
Region of interest (ROI) quantification is an important task in emission tomography (e.g., positron emission tomography and single photon emission computed tomography). It is essential for exploring clinical factors such as tumor activity, growth rate, and the efficacy of therapeutic interventions. Statistical image reconstruction methods based on the penalized maximum-likelihood (PML) or maximum a posteriori principle have been developed for emission tomography to deal with the low signal-to-noise ratio of the emission data. Similar to the filter cut-off frequency in the filtered backprojection method, the regularization parameter in PML reconstruction controls the resolution and noise tradeoff and, hence, affects ROI quantification. In this paper, we theoretically analyze the performance of ROI quantification in PML reconstructions. Building on previous work, we derive simplified theoretical expressions for the bias, variance, and ensemble mean-squared-error (EMSE) of the estimated total activity in an ROI that is surrounded by a uniform background. When the mean and covariance matrix of the activity inside the ROI are known, the theoretical expressions are readily computable and allow for fast evaluation of image quality for ROI quantification with different regularization parameters. The optimum regularization parameter can then be selected to minimize the EMSE. Computer simulations are conducted for small ROIs with variable uniform uptake. The results show that the theoretical predictions match the Monte Carlo results reasonably well.
Penalized likelihood PET image reconstruction using patch-based edge-preserving regularization.
Wang, Guobao; Qi, Jinyi
2012-12-01
Iterative image reconstruction for positron emission tomography (PET) can improve image quality by using spatial regularization that penalizes image intensity difference between neighboring pixels. The most commonly used quadratic penalty often oversmoothes edges and fine features in reconstructed images. Nonquadratic penalties can preserve edges but often introduce piece-wise constant blocky artifacts and the results are also sensitive to the hyper-parameter that controls the shape of the penalty function. This paper presents a patch-based regularization for iterative image reconstruction that uses neighborhood patches instead of individual pixels in computing the nonquadratic penalty. The new regularization is more robust than the conventional pixel-based regularization in differentiating sharp edges from random fluctuations due to noise. An optimization transfer algorithm is developed for the penalized maximum likelihood estimation. Each iteration of the algorithm can be implemented in three simple steps: an EM-like image update, an image smoothing and a pixel-by-pixel image fusion. Computer simulations show that the proposed patch-based regularization can achieve higher contrast recovery for small objects without increasing background variation compared with the quadratic regularization. The reconstruction is also more robust to the hyper-parameter than conventional pixel-based nonquadratic regularizations. The proposed regularization method has been applied to real 3-D PET data.
NASA Astrophysics Data System (ADS)
Fu, Qiang; Luk, Wai-Shing; Tao, Jun; Zeng, Xuan; Cai, Wei
In this paper, a novel intra-die spatial correlation extraction method referred to as MLEMTC (Maximum Likelihood Estimation for Multiple Test Chips) is presented. In the MLEMTC method, a joint likelihood function is formulated by multiplying the set of individual likelihood functions for all test chips. This joint likelihood function is then maximized to extract a unique group of parameter values of a single spatial correlation function, which can be used for statistical circuit analysis and design. Moreover, to deal with the purely random component and measurement error contained in measurement data, the spatial correlation function combined with the correlation of white noise is used in the extraction, which significantly improves the accuracy of the extraction results. Furthermore, an LU decomposition based technique is developed to calculate the log-determinant of the positive definite matrix within the likelihood function, which solves the numerical stability problem encountered in the direct calculation. Experimental results have shown that the proposed method is efficient and practical.
NASA Technical Reports Server (NTRS)
Kelly, D. A.; Fermelia, A.; Lee, G. K. F.
1990-01-01
An adaptive Kalman filter design that utilizes recursive maximum likelihood parameter identification is discussed. At the center of this design is the Kalman filter itself, which has the responsibility for attitude determination. At the same time, the identification algorithm is continually identifying the system parameters. The approach is applicable to nonlinear, as well as linear systems. This adaptive Kalman filter design has much potential for real time implementation, especially considering the fast clock speeds, cache memory and internal RAM available today. The recursive maximum likelihood algorithm is discussed in detail, with special attention directed towards its unique matrix formulation. The procedure for using the algorithm is described along with comments on how this algorithm interacts with the Kalman filter.
A Maximum Likelihood Approach to Functional Mapping of Longitudinal Binary Traits
Wang, Chenguang; Li, Hongying; Wang, Zhong; Wang, Yaqun; Wang, Ningtao; Wang, Zuoheng; Wu, Rongling
2013-01-01
Despite their importance in biology and biomedicine, genetic mapping of binary traits that change over time has not been well explored. In this article, we develop a statistical model for mapping quantitative trait loci (QTLs) that govern longitudinal responses of binary traits. The model is constructed within the maximum likelihood framework by which the association between binary responses is modeled in terms of conditional log odds-ratios. With this parameterization, the maximum likelihood estimates (MLEs) of marginal mean parameters are robust to the misspecification of time dependence. We implement an iterative procedures to obtain the MLEs of QTL genotype-specific parameters that define longitudinal binary responses. The usefulness of the model was validated by analyzing a real example in rice. Simulation studies were performed to investigate the statistical properties of the model, showing that the model has power to identify and map specific QTLs responsible for the temporal pattern of binary traits. PMID:23183762
Donato, David I.
2012-01-01
This report presents the mathematical expressions and the computational techniques required to compute maximum-likelihood estimates for the parameters of the National Descriptive Model of Mercury in Fish (NDMMF), a statistical model used to predict the concentration of methylmercury in fish tissue. The expressions and techniques reported here were prepared to support the development of custom software capable of computing NDMMF parameter estimates more quickly and using less computer memory than is currently possible with available general-purpose statistical software. Computation of maximum-likelihood estimates for the NDMMF by numerical solution of a system of simultaneous equations through repeated Newton-Raphson iterations is described. This report explains the derivation of the mathematical expressions required for computational parameter estimation in sufficient detail to facilitate future derivations for any revised versions of the NDMMF that may be developed.
Constrained Maximum Likelihood Estimation for Two-level Mean and Covariance Structure Models.
Bentler, Peter M; Liang, Jiajuan; Tang, Man-Lai; Yuan, Ke-Hai
2011-03-22
Maximum likelihood is commonly used for estimation of model parameters in analysis of two-level structural equation models. Constraints on model parameters could be encountered in some situations such as equal factor loadings for different factors. Linear constraints are the most common ones and they are relatively easy to handle in maximum likelihood analysis. Nonlinear constraints could be encountered in complicated applications. In this paper we develop an EM-type algorithm for estimating model parameters with both linear and nonlinear constraints. The empirical performance of the algorithm is demonstrated by a Monte Carlo study. Application of the algorithm for linear constraints is illustrated by setting up a two-level mean and covariance structure model for a real two-level data set and running an EQS program.
Maximum-Likelihood Estimator of Clock Offset between Nanomachines in Bionanosensor Networks
Lin, Lin; Yang, Chengfeng; Ma, Maode
2015-01-01
Recent advances in nanotechnology, electronic technology and biology have enabled the development of bio-inspired nanoscale sensors. The cooperation among the bionanosensors in a network is envisioned to perform complex tasks. Clock synchronization is essential to establish diffusion-based distributed cooperation in the bionanosensor networks. This paper proposes a maximum-likelihood estimator of the clock offset for the clock synchronization among molecular bionanosensors. The unique properties of diffusion-based molecular communication are described. Based on the inverse Gaussian distribution of the molecular propagation delay, a two-way message exchange mechanism for clock synchronization is proposed. The maximum-likelihood estimator of the clock offset is derived. The convergence and the bias of the estimator are analyzed. The simulation results show that the proposed estimator is effective for the offset compensation required for clock synchronization. This work paves the way for the cooperation of nanomachines in diffusion-based bionanosensor networks. PMID:26690173
Maximum Likelihood Shift Estimation Using High Resolution Polarimetric SAR Clutter Model
NASA Astrophysics Data System (ADS)
Harant, Olivier; Bombrun, Lionel; Vasile, Gabriel; Ferro-Famil, Laurent; Gay, Michel
2011-03-01
This paper deals with a Maximum Likelihood (ML) shift estimation method in the context of High Resolution (HR) Polarimetric SAR (PolSAR) clutter. Texture modeling is exposed and the generalized ML texture tracking method is extended to the merging of various sensors. Some results on displacement estimation on the Argentiere glacier in the Mont Blanc massif using dual-pol TerraSAR-X (TSX) and quad-pol RADARSAT-2 (RS2) sensors are finally discussed.
Extraction of the Michel parameters from muon decay by a maximum likelihood method
McKee, R.J.
1980-01-01
A maximum likelihood method was developed for extracting the Michel parameters, which describe the decay spectrum of stopped polarized muons. The method was applied successfully in a Monte Carlo simulation of apparatus. A complete error matrix for the set of Michel parameters was also obtained. In an experiment of 10/sup 8/ muon decays the statistical errors can be reduced by more than an order of magnitude over the currently accepted limits on the Michel parameters. 5 tables.
NASA Astrophysics Data System (ADS)
Borkowski, Robert; Johannisson, Pontus; Wymeersch, Henk; Arlunno, Valeria; Caballero, Antonio; Zibar, Darko; Tafur Monroy, Idelfonso
2014-03-01
We perform an experimental investigation of a maximum likelihood-based (ML-based) algorithm for bulk chromatic dispersion estimation for digital coherent receivers operating in uncompensated optical networks. We demonstrate the robustness of the method at low optical signal-to-noise ratio (OSNR) and against differential group delay (DGD) in an experiment involving 112 Gbit/s polarization-division multiplexed (PDM) 16-ary quadrature amplitude modulation (16 QAM) and quaternary phase-shift keying (QPSK).
Wang, Changyuan; Zhang, Jing; Mu, Jing
2012-01-01
A new filter named the maximum likelihood-based iterated divided difference filter (MLIDDF) is developed to improve the low state estimation accuracy of nonlinear state estimation due to large initial estimation errors and nonlinearity of measurement equations. The MLIDDF algorithm is derivative-free and implemented only by calculating the functional evaluations. The MLIDDF algorithm involves the use of the iteration measurement update and the current measurement, and the iteration termination criterion based on maximum likelihood is introduced in the measurement update step, so the MLIDDF is guaranteed to produce a sequence estimate that moves up the maximum likelihood surface. In a simulation, its performance is compared against that of the unscented Kalman filter (UKF), divided difference filter (DDF), iterated unscented Kalman filter (IUKF) and iterated divided difference filter (IDDF) both using a traditional iteration strategy. Simulation results demonstrate that the accumulated mean-square root error for the MLIDDF algorithm in position is reduced by 63% compared to that of UKF and DDF algorithms, and by 7% compared to that of IUKF and IDDF algorithms. The new algorithm thus has better state estimation accuracy and a fast convergence rate.
Robust maximum likelihood estimation for stochastic state space model with observation outliers
NASA Astrophysics Data System (ADS)
AlMutawa, J.
2016-08-01
The objective of this paper is to develop a robust maximum likelihood estimation (MLE) for the stochastic state space model via the expectation maximisation algorithm to cope with observation outliers. Two types of outliers and their influence are studied in this paper: namely,the additive outlier (AO) and innovative outlier (IO). Due to the sensitivity of the MLE to AO and IO, we propose two techniques for robustifying the MLE: the weighted maximum likelihood estimation (WMLE) and the trimmed maximum likelihood estimation (TMLE). The WMLE is easy to implement with weights estimated from the data; however, it is still sensitive to IO and a patch of AO outliers. On the other hand, the TMLE is reduced to a combinatorial optimisation problem and hard to implement but it is efficient to both types of outliers presented here. To overcome the difficulty, we apply the parallel randomised algorithm that has a low computational cost. A Monte Carlo simulation result shows the efficiency of the proposed algorithms. An earlier version of this paper was presented at the 8th Asian Control Conference, Kaohsiung, Taiwan, 2011.
NASA Technical Reports Server (NTRS)
Lei, Ning; Chiang, Kwo-Fu; Oudrari, Hassan; Xiong, Xiaoxiong
2011-01-01
Optical sensors aboard Earth orbiting satellites such as the next generation Visible/Infrared Imager/Radiometer Suite (VIIRS) assume that the sensors radiometric response in the Reflective Solar Bands (RSB) is described by a quadratic polynomial, in relating the aperture spectral radiance to the sensor Digital Number (DN) readout. For VIIRS Flight Unit 1, the coefficients are to be determined before launch by an attenuation method, although the linear coefficient will be further determined on-orbit through observing the Solar Diffuser. In determining the quadratic polynomial coefficients by the attenuation method, a Maximum Likelihood approach is applied in carrying out the least-squares procedure. Crucial to the Maximum Likelihood least-squares procedure is the computation of the weight. The weight not only has a contribution from the noise of the sensor s digital count, with an important contribution from digitization error, but also is affected heavily by the mathematical expression used to predict the value of the dependent variable, because both the independent and the dependent variables contain random noise. In addition, model errors have a major impact on the uncertainties of the coefficients. The Maximum Likelihood approach demonstrates the inadequacy of the attenuation method model with a quadratic polynomial for the retrieved spectral radiance. We show that using the inadequate model dramatically increases the uncertainties of the coefficients. We compute the coefficient values and their uncertainties, considering both measurement and model errors.
NASA Astrophysics Data System (ADS)
Song, N.; He, B.; Wahl, R. L.; Frey, E. C.
2011-09-01
Optimizing targeted radionuclide therapy requires patient-specific estimation of organ doses. The organ doses are estimated from quantitative nuclear medicine imaging studies, many of which involve planar whole body scans. We have previously developed the quantitative planar (QPlanar) processing method and demonstrated its ability to provide more accurate activity estimates than conventional geometric-mean-based planar (CPlanar) processing methods using physical phantom and simulation studies. The QPlanar method uses the maximum likelihood-expectation maximization algorithm, 3D organ volume of interests (VOIs), and rigorous models of physical image degrading factors to estimate organ activities. However, the QPlanar method requires alignment between the 3D organ VOIs and the 2D planar projections and assumes uniform activity distribution in each VOI. This makes application to patients challenging. As a result, in this paper we propose an extended QPlanar (EQPlanar) method that provides independent-organ rigid registration and includes multiple background regions. We have validated this method using both Monte Carlo simulation and patient data. In the simulation study, we evaluated the precision and accuracy of the method in comparison to the original QPlanar method. For the patient studies, we compared organ activity estimates at 24 h after injection with those from conventional geometric mean-based planar quantification using a 24 h post-injection quantitative SPECT reconstruction as the gold standard. We also compared the goodness of fit of the measured and estimated projections obtained from the EQPlanar method to those from the original method at four other time points where gold standard data were not available. In the simulation study, more accurate activity estimates were provided by the EQPlanar method for all the organs at all the time points compared with the QPlanar method. Based on the patient data, we concluded that the EQPlanar method provided a
Song, N; He, B; Wahl, R L; Frey, E C
2011-09-07
Optimizing targeted radionuclide therapy requires patient-specific estimation of organ doses. The organ doses are estimated from quantitative nuclear medicine imaging studies, many of which involve planar whole body scans. We have previously developed the quantitative planar (QPlanar) processing method and demonstrated its ability to provide more accurate activity estimates than conventional geometric-mean-based planar (CPlanar) processing methods using physical phantom and simulation studies. The QPlanar method uses the maximum likelihood-expectation maximization algorithm, 3D organ volume of interests (VOIs), and rigorous models of physical image degrading factors to estimate organ activities. However, the QPlanar method requires alignment between the 3D organ VOIs and the 2D planar projections and assumes uniform activity distribution in each VOI. This makes application to patients challenging. As a result, in this paper we propose an extended QPlanar (EQPlanar) method that provides independent-organ rigid registration and includes multiple background regions. We have validated this method using both Monte Carlo simulation and patient data. In the simulation study, we evaluated the precision and accuracy of the method in comparison to the original QPlanar method. For the patient studies, we compared organ activity estimates at 24 h after injection with those from conventional geometric mean-based planar quantification using a 24 h post-injection quantitative SPECT reconstruction as the gold standard. We also compared the goodness of fit of the measured and estimated projections obtained from the EQPlanar method to those from the original method at four other time points where gold standard data were not available. In the simulation study, more accurate activity estimates were provided by the EQPlanar method for all the organs at all the time points compared with the QPlanar method. Based on the patient data, we concluded that the EQPlanar method provided a
Chen, Rui; Hyrien, Ollivier
2011-01-01
This article deals with quasi- and pseudo-likelihood estimation in a class of continuous-time multi-type Markov branching processes observed at discrete points in time. “Conventional” and conditional estimation are discussed for both approaches. We compare their properties and identify situations where they lead to asymptotically equivalent estimators. Both approaches possess robustness properties, and coincide with maximum likelihood estimation in some cases. Quasi-likelihood functions involving only linear combinations of the data may be unable to estimate all model parameters. Remedial measures exist, including the resort either to non-linear functions of the data or to conditioning the moments on appropriate sigma-algebras. The method of pseudo-likelihood may also resolve this issue. We investigate the properties of these approaches in three examples: the pure birth process, the linear birth-and-death process, and a two-type process that generalizes the previous two examples. Simulations studies are conducted to evaluate performance in finite samples. PMID:21552356
Maximum-LikelihoodSemiblind Equalization of Doubly Selective Channels Using the EM Algorithm
NASA Astrophysics Data System (ADS)
Kutz, Gideon; Raphaeli, Dan
2010-12-01
Maximum-likelihood semi-blind joint channel estimation and equalization for doubly selective channels and single-carrier systems is proposed. We model the doubly selective channel as an FIR filter where each filter tap is modeled as a linear combination of basis functions. This channel description is then integrated in an iterative scheme based on the expectation-maximization (EM) principle that converges to the channel description vector estimation. We discuss the selection of the basis functions and compare various functions sets. To alleviate the problem of convergence to a local maximum, we propose an initialization scheme to the EM iterations based on a small number of pilot symbols. We further derive a pilot positioning scheme targeted to reduce the probability of convergence to a local maximum. Our pilot positioning analysis reveals that for high Doppler rates it is better to spread the pilots evenly throughout the data block (and not to group them) even for frequency-selective channels. The resulting equalization algorithm is shown to be superior over previously proposed equalization schemes and to perform in many cases close to the maximum-likelihood equalizer with perfect channel knowledge. Our proposed method is also suitable for coded systems and as a building block for Turbo equalization algorithms.
Li, Dongming; Sun, Changming; Yang, Jinhua; Liu, Huan; Peng, Jiaqi; Zhang, Lijuan
2017-04-06
An adaptive optics (AO) system provides real-time compensation for atmospheric turbulence. However, an AO image is usually of poor contrast because of the nature of the imaging process, meaning that the image contains information coming from both out-of-focus and in-focus planes of the object, which also brings about a loss in quality. In this paper, we present a robust multi-frame adaptive optics image restoration algorithm via maximum likelihood estimation. Our proposed algorithm uses a maximum likelihood method with image regularization as the basic principle, and constructs the joint log likelihood function for multi-frame AO images based on a Poisson distribution model. To begin with, a frame selection method based on image variance is applied to the observed multi-frame AO images to select images with better quality to improve the convergence of a blind deconvolution algorithm. Then, by combining the imaging conditions and the AO system properties, a point spread function estimation model is built. Finally, we develop our iterative solutions for AO image restoration addressing the joint deconvolution issue. We conduct a number of experiments to evaluate the performances of our proposed algorithm. Experimental results show that our algorithm produces accurate AO image restoration results and outperforms the current state-of-the-art blind deconvolution methods.
Li, Dongming; Sun, Changming; Yang, Jinhua; Liu, Huan; Peng, Jiaqi; Zhang, Lijuan
2017-01-01
An adaptive optics (AO) system provides real-time compensation for atmospheric turbulence. However, an AO image is usually of poor contrast because of the nature of the imaging process, meaning that the image contains information coming from both out-of-focus and in-focus planes of the object, which also brings about a loss in quality. In this paper, we present a robust multi-frame adaptive optics image restoration algorithm via maximum likelihood estimation. Our proposed algorithm uses a maximum likelihood method with image regularization as the basic principle, and constructs the joint log likelihood function for multi-frame AO images based on a Poisson distribution model. To begin with, a frame selection method based on image variance is applied to the observed multi-frame AO images to select images with better quality to improve the convergence of a blind deconvolution algorithm. Then, by combining the imaging conditions and the AO system properties, a point spread function estimation model is built. Finally, we develop our iterative solutions for AO image restoration addressing the joint deconvolution issue. We conduct a number of experiments to evaluate the performances of our proposed algorithm. Experimental results show that our algorithm produces accurate AO image restoration results and outperforms the current state-of-the-art blind deconvolution methods. PMID:28383503
Maximum Likelihood Estimations and EM Algorithms with Length-biased Data
Qin, Jing; Ning, Jing; Liu, Hao; Shen, Yu
2012-01-01
SUMMARY Length-biased sampling has been well recognized in economics, industrial reliability, etiology applications, epidemiological, genetic and cancer screening studies. Length-biased right-censored data have a unique data structure different from traditional survival data. The nonparametric and semiparametric estimations and inference methods for traditional survival data are not directly applicable for length-biased right-censored data. We propose new expectation-maximization algorithms for estimations based on full likelihoods involving infinite dimensional parameters under three settings for length-biased data: estimating nonparametric distribution function, estimating nonparametric hazard function under an increasing failure rate constraint, and jointly estimating baseline hazards function and the covariate coefficients under the Cox proportional hazards model. Extensive empirical simulation studies show that the maximum likelihood estimators perform well with moderate sample sizes and lead to more efficient estimators compared to the estimating equation approaches. The proposed estimates are also more robust to various right-censoring mechanisms. We prove the strong consistency properties of the estimators, and establish the asymptotic normality of the semi-parametric maximum likelihood estimators under the Cox model using modern empirical processes theory. We apply the proposed methods to a prevalent cohort medical study. Supplemental materials are available online. PMID:22323840
ERIC Educational Resources Information Center
Mahmud, Jumailiyah; Sutikno, Muzayanah; Naga, Dali S.
2016-01-01
The aim of this study is to determine variance difference between maximum likelihood and expected A posteriori estimation methods viewed from number of test items of aptitude test. The variance presents an accuracy generated by both maximum likelihood and Bayes estimation methods. The test consists of three subtests, each with 40 multiple-choice…
NASA Technical Reports Server (NTRS)
Peters, B. C., Jr.; Walker, H. F.
1975-01-01
New results and insights concerning a previously published iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions were discussed. It was shown that the procedure converges locally to the consistent maximum likelihood estimate as long as a specified parameter is bounded between two limits. Bound values were given to yield optimal local convergence.
Changren Weng; Thomas L. Kubisiak; C. Dana Nelson; James P. Geaghan; Michael Stine
1999-01-01
Single marker regression and single marker maximum likelihood estimation were tied to detect quantitative trait loci (QTLs) controlling the early height growth of longleaf pine and slash pine using a ((longleaf pine x slash pine) x slash pine) BC, population consisting of 83 progeny. Maximum likelihood estimation was found to be more power than regression and could...
Pražnikar, Jure; Turk, Dušan
2014-12-01
The maximum-likelihood free-kick target, which calculates model error estimates from the work set and a randomly displaced model, proved superior in the accuracy and consistency of refinement of crystal structures compared with the maximum-likelihood cross-validation target, which calculates error estimates from the test set and the unperturbed model. The refinement of a molecular model is a computational procedure by which the atomic model is fitted to the diffraction data. The commonly used target in the refinement of macromolecular structures is the maximum-likelihood (ML) function, which relies on the assessment of model errors. The current ML functions rely on cross-validation. They utilize phase-error estimates that are calculated from a small fraction of diffraction data, called the test set, that are not used to fit the model. An approach has been developed that uses the work set to calculate the phase-error estimates in the ML refinement from simulating the model errors via the random displacement of atomic coordinates. It is called ML free-kick refinement as it uses the ML formulation of the target function and is based on the idea of freeing the model from the model bias imposed by the chemical energy restraints used in refinement. This approach for the calculation of error estimates is superior to the cross-validation approach: it reduces the phase error and increases the accuracy of molecular models, is more robust, provides clearer maps and may use a smaller portion of data for the test set for the calculation of R{sub free} or may leave it out completely.
NASA Astrophysics Data System (ADS)
Lei, Ning; Chiang, Kwo-Fu; Oudrari, Hassan; Xiong, Xiaoxiong
2011-10-01
Optical sensors aboard Earth orbiting satellites such as the next generation Visible/Infrared Imager Radiometer Suite (VIIRS) assume that the sensors' radiometric response in the Reflective Solar Bands (RSB) is described by a quadratic polynomial, in relating the aperture spectral radiance to the sensor Digital Number (DN) readout. For VIIRS Flight Unit 1 (FU1) (Butler, J., Xiong, X., Oudrari, H., Pan, C., and Gleason, J., "NASA Calibration and Characterization in the NPOESS Preparatory Project (NPP)", IGARSS, July 12-17, 2009, Cape Town, South Africa.), the coefficients are to be determined before launch by an attenuation method, although the linear coefficient will be further determined on-orbit through observing the Solar Diffuser. In determining the quadratic polynomial coefficients by the attenuation method, a Maximum Likelihood approach is applied in carrying out the least-squares procedure. Crucial to the Maximum Likelihood least-squares procedure is the computation of the weight. The weight not only has a contribution from the noise of the sensor's digital count, with an important contribution from digitization error, but also is affected heavily by the mathematical expression used to predict the value of the dependent variable, because both the independent and the dependent variables contain random noise. In addition, model errors have a major impact on the uncertainties of the coefficients. The Maximum Likelihood approach demonstrates the inadequacy of the quadratic model. We show that using the inadequate quadratic model dramatically increases the uncertainties of the coefficients. We compute the coefficient values and their uncertainties, considering both measurement and model errors.
NASA Astrophysics Data System (ADS)
Ghammraoui, Bahaa; Badal, Andreu; Popescu, Lucretiu M.
2016-04-01
Coherent scatter computed tomography (CSCT) is a reconstructive x-ray imaging technique that yields the spatially resolved coherent-scatter cross section of the investigated object revealing structural information of tissue under investigation. In the original CSCT proposals the reconstruction of images from coherently scattered x-rays is done at each scattering angle separately using analytic reconstruction. In this work we develop a maximum likelihood estimation of scatter components algorithm (ML-ESCA) that iteratively reconstructs images using a few material component basis functions from coherent scatter projection data. The proposed algorithm combines the measured scatter data at different angles into one reconstruction equation with only a few component images. Also, it accounts for data acquisition statistics and physics, modeling effects such as polychromatic energy spectrum and detector response function. We test the algorithm with simulated projection data obtained with a pencil beam setup using a new version of MC-GPU code, a Graphical Processing Unit version of PENELOPE Monte Carlo particle transport simulation code, that incorporates an improved model of x-ray coherent scattering using experimentally measured molecular interference functions. The results obtained for breast imaging phantoms using adipose and glandular tissue cross sections show that the new algorithm can separate imaging data into basic adipose and water components at radiation doses comparable with Breast Computed Tomography. Simulation results also show the potential for imaging microcalcifications. Overall, the component images obtained with ML-ESCA algorithm have a less noisy appearance than the images obtained with the conventional filtered back projection algorithm for each individual scattering angle. An optimization study for x-ray energy range selection for breast CSCT is also presented.
Ghammraoui, Bahaa; Badal, Andreu; Popescu, Lucretiu M
2016-04-21
Coherent scatter computed tomography (CSCT) is a reconstructive x-ray imaging technique that yields the spatially resolved coherent-scatter cross section of the investigated object revealing structural information of tissue under investigation. In the original CSCT proposals the reconstruction of images from coherently scattered x-rays is done at each scattering angle separately using analytic reconstruction. In this work we develop a maximum likelihood estimation of scatter components algorithm (ML-ESCA) that iteratively reconstructs images using a few material component basis functions from coherent scatter projection data. The proposed algorithm combines the measured scatter data at different angles into one reconstruction equation with only a few component images. Also, it accounts for data acquisition statistics and physics, modeling effects such as polychromatic energy spectrum and detector response function. We test the algorithm with simulated projection data obtained with a pencil beam setup using a new version of MC-GPU code, a Graphical Processing Unit version of PENELOPE Monte Carlo particle transport simulation code, that incorporates an improved model of x-ray coherent scattering using experimentally measured molecular interference functions. The results obtained for breast imaging phantoms using adipose and glandular tissue cross sections show that the new algorithm can separate imaging data into basic adipose and water components at radiation doses comparable with Breast Computed Tomography. Simulation results also show the potential for imaging microcalcifications. Overall, the component images obtained with ML-ESCA algorithm have a less noisy appearance than the images obtained with the conventional filtered back projection algorithm for each individual scattering angle. An optimization study for x-ray energy range selection for breast CSCT is also presented.
Maximum-likelihood approach to topological charge fluctuations in lattice gauge theory
NASA Astrophysics Data System (ADS)
Brower, R. C.; Cheng, M.; Fleming, G. T.; Lin, M. F.; Neil, E. T.; Osborn, J. C.; Rebbi, C.; Rinaldi, E.; Schaich, D.; Schroeder, C.; Voronov, G.; Vranas, P.; Weinberg, E.; Witzel, O.
2014-07-01
We present a novel technique for the determination of the topological susceptibility (related to the variance of the distribution of global topological charge) from lattice gauge theory simulations, based on maximum-likelihood analysis of the Markov-chain Monte Carlo time series. This technique is expected to be particularly useful in situations where relatively few tunneling events are observed. Restriction to a lattice subvolume on which topological charge is not quantized is explored, and may lead to further improvement when the global topology is poorly sampled. We test our proposed method on a set of lattice data, and compare it to traditional methods.
Method and apparatus for implementing a traceback maximum-likelihood decoder in a hypercube network
NASA Technical Reports Server (NTRS)
Pollara-Bozzola, Fabrizio (Inventor)
1989-01-01
A method and a structure to implement maximum-likelihood decoding of convolutional codes on a network of microprocessors interconnected as an n-dimensional cube (hypercube). By proper reordering of states in the decoder, only communication between adjacent processors is required. Communication time is limited to that required for communication only of the accumulated metrics and not the survivor parameters of a Viterbi decoding algorithm. The survivor parameters are stored at a local processor's memory and a trace-back method is employed to ascertain the decoding result. Faster and more efficient operation is enabled, and decoding of large constraint length codes is feasible using standard VLSI technology.
F-8C adaptive flight control extensions. [for maximum likelihood estimation
NASA Technical Reports Server (NTRS)
Stein, G.; Hartmann, G. L.
1977-01-01
An adaptive concept which combines gain-scheduled control laws with explicit maximum likelihood estimation (MLE) identification to provide the scheduling values is described. The MLE algorithm was improved by incorporating attitude data, estimating gust statistics for setting filter gains, and improving parameter tracking during changing flight conditions. A lateral MLE algorithm was designed to improve true air speed and angle of attack estimates during lateral maneuvers. Relationships between the pitch axis sensors inherent in the MLE design were examined and used for sensor failure detection. Design details and simulation performance are presented for each of the three areas investigated.
Gyro-based Maximum-Likelihood Thruster Fault Detection and Identification
NASA Technical Reports Server (NTRS)
Wilson, Edward; Lages, Chris; Mah, Robert; Clancy, Daniel (Technical Monitor)
2002-01-01
When building smaller, less expensive spacecraft, there is a need for intelligent fault tolerance vs. increased hardware redundancy. If fault tolerance can be achieved using existing navigation sensors, cost and vehicle complexity can be reduced. A maximum likelihood-based approach to thruster fault detection and identification (FDI) for spacecraft is developed here and applied in simulation to the X-38 space vehicle. The system uses only gyro signals to detect and identify hard, abrupt, single and multiple jet on- and off-failures. Faults are detected within one second and identified within one to five accords,
Eisenhauer, Philipp; Heckman, James J.; Mosso, Stefano
2015-01-01
We compare the performance of maximum likelihood (ML) and simulated method of moments (SMM) estimation for dynamic discrete choice models. We construct and estimate a simplified dynamic structural model of education that captures some basic features of educational choices in the United States in the 1980s and early 1990s. We use estimates from our model to simulate a synthetic dataset and assess the ability of ML and SMM to recover the model parameters on this sample. We investigate the performance of alternative tuning parameters for SMM. PMID:26494926
A maximum likelihood estimation framework for delay logistic differential equation model
NASA Astrophysics Data System (ADS)
Mahmoud, Ahmed Adly; Dass, Sarat Chandra; Muthuvalu, Mohana S.
2016-11-01
This paper will introduce the maximum likelihood method of estimation for delay differential equation model governed by unknown delay and other parameters of interest followed by a numerical solver approach. As an example we consider the delayed logistic differential equation. A grid based estimation framework is proposed. Our methodology estimates correctly the delay parameter as well as the initial starting value of the dynamical system based on simulation data. The computations have been carried out with help of mathematical software: MATLAB® 8.0 R2012b.
User's manual for MMLE3, a general FORTRAN program for maximum likelihood parameter estimation
NASA Technical Reports Server (NTRS)
Maine, R. E.; Iliff, K. W.
1980-01-01
A user's manual for the FORTRAN IV computer program MMLE3 is described. It is a maximum likelihood parameter estimation program capable of handling general bilinear dynamic equations of arbitrary order with measurement noise and/or state noise (process noise). The theory and use of the program is described. The basic MMLE3 program is quite general and, therefore, applicable to a wide variety of problems. The basic program can interact with a set of user written problem specific routines to simplify the use of the program on specific systems. A set of user routines for the aircraft stability and control derivative estimation problem is provided with the program.
An inconsistency in the standard maximum likelihood estimation of bulk flows
Nusser, Adi
2014-11-01
Maximum likelihood estimation of the bulk flow from radial peculiar motions of galaxies generally assumes a constant velocity field inside the survey volume. This assumption is inconsistent with the definition of bulk flow as the average of the peculiar velocity field over the relevant volume. This follows from a straightforward mathematical relation between the bulk flow of a sphere and the velocity potential on its surface. This inconsistency also exists for ideal data with exact radial velocities and full spatial coverage. Based on the same relation, we propose a simple modification to correct for this inconsistency.
Maximum-likelihood estimation optimizer for constrained, time-optimal satellite reorientation
NASA Astrophysics Data System (ADS)
Melton, Robert G.
2014-10-01
The Covariance Matrix Adaptation-Evolutionary Strategy (CMA-ES) method provides a high-quality estimate of the control solution for an unconstrained satellite reorientation problem, and rapid, useful guesses needed for high-fidelity methods that can solve time-optimal reorientation problems with multiple path constraints. The CMA-ES algorithm offers two significant advantages over heuristic methods such as Particle Swarm or Bacteria Foraging Optimisation: it builds an approximation to the covariance matrix for the cost function, and uses that to determine a direction of maximum likelihood for the search, reducing the chance of stagnation; and it achieves second-order, quasi-Newton convergence behaviour.
NASA Astrophysics Data System (ADS)
Magnard, C.; Small, D.; Meier, E.
2015-03-01
The phase estimation of cross-track multibaseline synthetic aperture interferometric data is usually thought to be very efficiently achieved using the maximum likelihood (ML) method. The suitability of this method is investigated here as applied to airborne single pass multibaseline data. Experimental interferometric data acquired with a Ka-band sensor were processed using (a) a ML method that fuses the complex data from all receivers and (b) a coarse-to-fine method that only uses the intermediate baselines to unwrap the phase values from the longest baseline. The phase noise was analyzed for both methods: in most cases, a small improvement was found when the ML method was used.
Khairuzzaman, Md; Zhang, Chao; Igarashi, Koji; Katoh, Kazuhiro; Kikuchi, Kazuro
2010-03-01
We describe a successful introduction of maximum-likelihood-sequence estimation (MLSE) into digital coherent receivers together with finite-impulse response (FIR) filters in order to equalize both linear and nonlinear fiber impairments. The MLSE equalizer based on the Viterbi algorithm is implemented in the offline digital signal processing (DSP) core. We transmit 20-Gbit/s quadrature phase-shift keying (QPSK) signals through a 200-km-long standard single-mode fiber. The bit-error rate performance shows that the MLSE equalizer outperforms the conventional adaptive FIR filter, especially when nonlinear impairments are predominant.
Maximum likelihood parametric blur identification based on a continuous spatial domain model.
Pavlovic, G; Tekalp, A M
1992-01-01
A formulation for maximum-likelihood (ML) blur identification based on parametric modeling of the blur in the continuous spatial coordinates is proposed. Unlike previous ML blur identification methods based on discrete spatial domain blur models, this formulation makes it possible to find the ML estimate of the extent, as well as other parameters, of arbitrary point spread functions that admit a closed-form parametric description in the continuous coordinates. Experimental results are presented for the cases of 1-D uniform motion blur, 2-D out-of-focus blur, and 2-D truncated Gaussian blur at different signal-to-noise ratios.
A New Maximum-Likelihood Change Estimator for Two-Pass SAR Coherent Change Detection.
Wahl, Daniel E.; Yocky, David A.; Jakowatz, Charles V,
2014-09-01
In this paper, we derive a new optimal change metric to be used in synthetic aperture RADAR (SAR) coherent change detection (CCD). Previous CCD methods tend to produce false alarm states (showing change when there is none) in areas of the image that have a low clutter-to-noise power ratio (CNR). The new estimator does not suffer from this shortcoming. It is a surprisingly simple expression, easy to implement, and is optimal in the maximum-likelihood (ML) sense. The estimator produces very impressive results on the CCD collects that we have tested.
Maximum likelihood estimation of the mixture of log-concave densities.
Hu, Hao; Wu, Yichao; Yao, Weixin
2016-09-01
Finite mixture models are useful tools and can be estimated via the EM algorithm. A main drawback is the strong parametric assumption about the component densities. In this paper, a much more flexible mixture model is considered, which assumes each component density to be log-concave. Under fairly general conditions, the log-concave maximum likelihood estimator (LCMLE) exists and is consistent. Numeric examples are also made to demonstrate that the LCMLE improves the clustering results while comparing with the traditional MLE for parametric mixture models.
Gang, Grace J.; Stayman, J. Webster; Zbijewski, Wojciech; Siewerdsen, Jeffrey H.
2014-08-15
Purpose: Nonstationarity is an important aspect of imaging performance in CT and cone-beam CT (CBCT), especially for systems employing iterative reconstruction. This work presents a theoretical framework for both filtered-backprojection (FBP) and penalized-likelihood (PL) reconstruction that includes explicit descriptions of nonstationary noise, spatial resolution, and task-based detectability index. Potential utility of the model was demonstrated in the optimal selection of regularization parameters in PL reconstruction. Methods: Analytical models for local modulation transfer function (MTF) and noise-power spectrum (NPS) were investigated for both FBP and PL reconstruction, including explicit dependence on the object and spatial location. For FBP, a cascaded systems analysis framework was adapted to account for nonstationarity by separately calculating fluence and system gains for each ray passing through any given voxel. For PL, the point-spread function and covariance were derived using the implicit function theorem and first-order Taylor expansion according toFessler [“Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): Applications to tomography,” IEEE Trans. Image Process. 5(3), 493–506 (1996)]. Detectability index was calculated for a variety of simple tasks. The model for PL was used in selecting the regularization strength parameter to optimize task-based performance, with both a constant and a spatially varying regularization map. Results: Theoretical models of FBP and PL were validated in 2D simulated fan-beam data and found to yield accurate predictions of local MTF and NPS as a function of the object and the spatial location. The NPS for both FBP and PL exhibit similar anisotropic nature depending on the pathlength (and therefore, the object and spatial location within the object) traversed by each ray, with the PL NPS experiencing greater smoothing along directions with higher noise. The MTF of FBP
NASA Astrophysics Data System (ADS)
Chen, C. E.; Lorenzelli, F.; Hudson, R. E.; Yao, K.
2007-12-01
We investigate the maximum likelihood (ML) direction-of-arrival (DOA) estimation of multiple wideband sources in the presence of unknown nonuniform sensor noise. New closed-form expression for the direction estimation Cramér-Rao-Bound (CRB) has been derived. The performance of the conventional wideband uniform ML estimator under nonuniform noise has been studied. In order to mitigate the performance degradation caused by the nonuniformity of the noise, a new deterministic wideband nonuniform ML DOA estimator is derived and two associated processing algorithms are proposed. The first algorithm is based on an iterative procedure which stepwise concentrates the log-likelihood function with respect to the DOAs and the noise nuisance parameters, while the second is a noniterative algorithm that maximizes the derived approximately concentrated log-likelihood function. The performance of the proposed algorithms is tested through extensive computer simulations. Simulation results show the stepwise-concentrated ML algorithm (SC-ML) requires only a few iterations to converge and both the SC-ML and the approximately-concentrated ML algorithm (AC-ML) attain a solution close to the derived CRB at high signal-to-noise ratio.
Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET
Gopich, Irina V.
2015-01-01
Photon sequences from single-molecule Förster resonance energy transfer (FRET) experiments can be analyzed using a maximum likelihood method. Parameters of the underlying kinetic model (FRET efficiencies of the states and transition rates between conformational states) are obtained by maximizing the appropriate likelihood function. In addition, the errors (uncertainties) of the extracted parameters can be obtained from the curvature of the likelihood function at the maximum. We study the standard deviations of the parameters of a two-state model obtained from photon sequences with recorded colors and arrival times. The standard deviations can be obtained analytically in a special case when the FRET efficiencies of the states are 0 and 1 and in the limiting cases of fast and slow conformational dynamics. These results are compared with the results of numerical simulations. The accuracy and, therefore, the ability to predict model parameters depend on how fast the transition rates are compared to the photon count rate. In the limit of slow transitions, the key parameters that determine the accuracy are the number of transitions between the states and the number of independent photon sequences. In the fast transition limit, the accuracy is determined by the small fraction of photons that are correlated with their neighbors. The relative standard deviation of the relaxation rate has a “chevron” shape as a function of the transition rate in the log-log scale. The location of the minimum of this function dramatically depends on how well the FRET efficiencies of the states are separated. PMID:25612692
Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET
Gopich, Irina V.
2015-01-21
Photon sequences from single-molecule Förster resonance energy transfer (FRET) experiments can be analyzed using a maximum likelihood method. Parameters of the underlying kinetic model (FRET efficiencies of the states and transition rates between conformational states) are obtained by maximizing the appropriate likelihood function. In addition, the errors (uncertainties) of the extracted parameters can be obtained from the curvature of the likelihood function at the maximum. We study the standard deviations of the parameters of a two-state model obtained from photon sequences with recorded colors and arrival times. The standard deviations can be obtained analytically in a special case when the FRET efficiencies of the states are 0 and 1 and in the limiting cases of fast and slow conformational dynamics. These results are compared with the results of numerical simulations. The accuracy and, therefore, the ability to predict model parameters depend on how fast the transition rates are compared to the photon count rate. In the limit of slow transitions, the key parameters that determine the accuracy are the number of transitions between the states and the number of independent photon sequences. In the fast transition limit, the accuracy is determined by the small fraction of photons that are correlated with their neighbors. The relative standard deviation of the relaxation rate has a “chevron” shape as a function of the transition rate in the log-log scale. The location of the minimum of this function dramatically depends on how well the FRET efficiencies of the states are separated.
On the use of maximum likelihood estimation for the assembly of Space Station Freedom
NASA Astrophysics Data System (ADS)
Taylor, Lawrence W., Jr.; Ramakrishnan, Jayant
Distributed parameter models of the Solar Array Flight Experiment, the Mini-MAST truss, and Space Station Freedom assembly are discussed. The distributed parameter approach takes advantage of (1) the relatively small number of model parameters associated with partial differential equation models of structural dynamics, (2) maximum-likelihood estimation using both prelaunch and on-orbit test data, (3) the inclusion of control system dynamics in the same equations, and (4) the incremental growth of the structural configurations. Maximum-likelihood parameter estimates for distributed parameter models were based on static compliance test results and frequency response measurements. Because the Space Station Freedom does not yet exist, the NASA Mini-MAST truss was used to test the procedure of modeling and parameter estimation. The resulting distributed parameter model of the Mini-MAST truss successfully demonstrated the approach taken. The computer program PDEMOD enables any configuration that can be represented by a network of flexible beam elements and rigid bodies to be remodeled.
On the use of maximum likelihood estimation for the assembly of Space Station Freedom
NASA Technical Reports Server (NTRS)
Taylor, Lawrence W., Jr.; Ramakrishnan, Jayant
1991-01-01
Distributed parameter models of the Solar Array Flight Experiment, the Mini-MAST truss, and Space Station Freedom assembly are discussed. The distributed parameter approach takes advantage of (1) the relatively small number of model parameters associated with partial differential equation models of structural dynamics, (2) maximum-likelihood estimation using both prelaunch and on-orbit test data, (3) the inclusion of control system dynamics in the same equations, and (4) the incremental growth of the structural configurations. Maximum-likelihood parameter estimates for distributed parameter models were based on static compliance test results and frequency response measurements. Because the Space Station Freedom does not yet exist, the NASA Mini-MAST truss was used to test the procedure of modeling and parameter estimation. The resulting distributed parameter model of the Mini-MAST truss successfully demonstrated the approach taken. The computer program PDEMOD enables any configuration that can be represented by a network of flexible beam elements and rigid bodies to be remodeled.
Schminkey, Donna L; von Oertzen, Timo; Bullock, Linda
2016-08-01
With increasing access to population-based data and electronic health records for secondary analysis, missing data are common. In the social and behavioral sciences, missing data frequently are handled with multiple imputation methods or full information maximum likelihood (FIML) techniques, but healthcare researchers have not embraced these methodologies to the same extent and more often use either traditional imputation techniques or complete case analysis, which can compromise power and introduce unintended bias. This article is a review of options for handling missing data, concluding with a case study demonstrating the utility of multilevel structural equation modeling using full information maximum likelihood (MSEM with FIML) to handle large amounts of missing data. MSEM with FIML is a parsimonious and hypothesis-driven strategy to cope with large amounts of missing data without compromising power or introducing bias. This technique is relevant for nurse researchers faced with ever-increasing amounts of electronic data and decreasing research budgets. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Maximum likelihood optimal and robust Support Vector Regression with lncosh loss function.
Karal, Omer
2017-10-01
In this paper, a novel and continuously differentiable convex loss function based on natural logarithm of hyperbolic cosine function, namely lncosh loss, is introduced to obtain Support Vector Regression (SVR) models which are optimal in the maximum likelihood sense for the hyper-secant error distributions. Most of the current regression models assume that the distribution of error is Gaussian, which corresponds to the squared loss function and has helpful analytical properties such as easy computation and analysis. However, in many real world applications, most observations are subject to unknown noise distributions, so the Gaussian distribution may not be a useful choice. The developed SVR model with the parameterized lncosh loss provides a possibility of learning a loss function leading to a regression model which is maximum likelihood optimal for a specific input-output data. The SVR models obtained with different parameter choices of lncosh loss with ε-insensitiveness feature, possess most of the desirable characteristics of well-known loss functions such as Vapnik's loss, the Squared loss, and Huber's loss function as special cases. In other words, it is observed in the extensive simulations that the mentioned lncosh loss function is entirely controlled by a single adjustable λ parameter and as a result, it allows switching between different losses depending on the choice of λ. The effectiveness and feasibility of lncosh loss function are validated through a number of synthetic and real world benchmark data sets for various types of additive noise distributions. Copyright © 2017 Elsevier Ltd. All rights reserved.
SAR automatic target recognition using maximum likelihood template-based classifiers
NASA Astrophysics Data System (ADS)
Saghri, John A.
2008-08-01
A review of several recently-developed maximum likelihood template-based automatic target recognition (ATR) algorithms for extended targets in synthetic aperture radar (SAR) imagery data is presented. The algorithms are based on 'gradient' peaks, 'ceiling' peaks, edges, corners, shadows, and rectangular-fits. A weight-based Bayesian maximum likelihood scheme to combine multiple template-based classifiers is presented. The feature weights are derived from prior recognition accuracies, i.e., confidence levels, achieved by individual template-based classifiers. Application of feature-based weights instead of target specific feature-based weights reduces the resulting ATR accuracy by only a small amount. Preliminary results indicate that (1) the ceiling peaks provide the most target-discriminating power, (2) inclusion of more target-discriminating features leads to higher classification accuracy. Dempster-Shaffer rule of combination is suggested as a potential alternative to the implemented Bayesian decision theory approach to resolve conflicting reports from multiple template-based classifiers.
A maximum likelihood approach to estimating articulator positions from speech acoustics
Hogden, J.
1996-09-23
This proposal presents an algorithm called maximum likelihood continuity mapping (MALCOM) which recovers the positions of the tongue, jaw, lips, and other speech articulators from measurements of the sound-pressure waveform of speech. MALCOM differs from other techniques for recovering articulator positions from speech in three critical respects: it does not require training on measured or modeled articulator positions, it does not rely on any particular model of sound propagation through the vocal tract, and it recovers a mapping from acoustics to articulator positions that is linearly, not topographically, related to the actual mapping from acoustics to articulation. The approach categorizes short-time windows of speech into a finite number of sound types, and assumes the probability of using any articulator position to produce a given sound type can be described by a parameterized probability density function. MALCOM then uses maximum likelihood estimation techniques to: (1) find the most likely smooth articulator path given a speech sample and a set of distribution functions (one distribution function for each sound type), and (2) change the parameters of the distribution functions to better account for the data. Using this technique improves the accuracy of articulator position estimates compared to continuity mapping -- the only other technique that learns the relationship between acoustics and articulation solely from acoustics. The technique has potential application to computer speech recognition, speech synthesis and coding, teaching the hearing impaired to speak, improving foreign language instruction, and teaching dyslexics to read. 34 refs., 7 figs.
Maximum-likelihood methods for array processing based on time-frequency distributions
NASA Astrophysics Data System (ADS)
Zhang, Yimin; Mu, Weifeng; Amin, Moeness G.
1999-11-01
This paper proposes a novel time-frequency maximum likelihood (t-f ML) method for direction-of-arrival (DOA) estimation for non- stationary signals, and compares this method with conventional maximum likelihood DOA estimation techniques. Time-frequency distributions localize the signal power in the time-frequency domain, and as such enhance the effective SNR, leading to improved DOA estimation. The localization of signals with different t-f signatures permits the division of the time-frequency domain into smaller regions, each contains fewer signals than those incident on the array. The reduction of the number of signals within different time-frequency regions not only reduces the required number of sensors, but also decreases the computational load in multi- dimensional optimizations. Compared to the recently proposed time- frequency MUSIC (t-f MUSIC), the proposed t-f ML method can be applied in coherent environments, without the need to perform any type of preprocessing that is subject to both array geometry and array aperture.
NASA Astrophysics Data System (ADS)
Rizzo, R. E.; Healy, D.; De Siena, L.
2017-02-01
The success of any predictive model is largely dependent on the accuracy with which its parameters are known. When characterising fracture networks in rocks, one of the main issues is accurately scaling the parameters governing the distribution of fracture attributes. Optimal characterisation and analysis of fracture lengths and apertures are fundamental to estimate bulk permeability and therefore fluid flow, especially for rocks with low primary porosity where most of the flow takes place within fractures. We collected outcrop data from a fractured upper Miocene biosiliceous mudstone formation (California, USA), which exhibits seepage of bitumen-rich fluids through the fractures. The dataset was analysed using Maximum Likelihood Estimators to extract the underlying scaling parameters, and we found a log-normal distribution to be the best representative statistic for both fracture lengths and apertures in the study area. By applying Maximum Likelihood Estimators on outcrop fracture data, we generate fracture network models with the same statistical attributes to the ones observed on outcrop, from which we can achieve more robust predictions of bulk permeability.
NASA Astrophysics Data System (ADS)
Cattivelli, Federico S.; Estabrook, Polly; Satorius, Edgar H.; Sayed, Ali H.
2008-11-01
One of the most crucial stages of the Mars exploration missions is the entry, descent, and landing (EDL) phase. During EDL, maintaining reliable communication from the spacecraft to Earth is extremely important for the success of future missions, especially in case of mission failure. EDL is characterized by very deep accelerations, caused by friction, parachute deployment and rocket firing among others. These dynamics cause a severe Doppler shift on the carrier communications link to Earth. Methods have been proposed to estimate the Doppler shift based on Maximum Likelihood. So far these methods have proved successful, but it is expected that the next Mars mission, known as the Mars Science Laboratory, will suffer from higher dynamics and lower SNR. Thus, improving the existing estimation methods becomes a necessity. We propose a Maximum Likelihood approach that takes into account the power in the data tones to enhance carrier recovery, and improve the estimation performance by up to 3 dB. Simulations are performed using real data obtained during the EDL stage of the Mars Exploration Rover B (MERB) mission.
Houle, D; Meyer, K
2015-08-01
We explore the estimation of uncertainty in evolutionary parameters using a recently devised approach for resampling entire additive genetic variance-covariance matrices (G). Large-sample theory shows that maximum-likelihood estimates (including restricted maximum likelihood, REML) asymptotically have a multivariate normal distribution, with covariance matrix derived from the inverse of the information matrix, and mean equal to the estimated G. This suggests that sampling estimates of G from this distribution can be used to assess the variability of estimates of G, and of functions of G. We refer to this as the REML-MVN method. This has been implemented in the mixed-model program WOMBAT. Estimates of sampling variances from REML-MVN were compared to those from the parametric bootstrap and from a Bayesian Markov chain Monte Carlo (MCMC) approach (implemented in the R package MCMCglmm). We apply each approach to evolvability statistics previously estimated for a large, 20-dimensional data set for Drosophila wings. REML-MVN and MCMC sampling variances are close to those estimated with the parametric bootstrap. Both slightly underestimate the error in the best-estimated aspects of the G matrix. REML analysis supports the previous conclusion that the G matrix for this population is full rank. REML-MVN is computationally very efficient, making it an attractive alternative to both data resampling and MCMC approaches to assessing confidence in parameters of evolutionary interest. © 2015 European Society For Evolutionary Biology. Journal of Evolutionary Biology © 2015 European Society For Evolutionary Biology.
NASA Technical Reports Server (NTRS)
Scholz, D.; Fuhs, N.; Hixson, M.
1979-01-01
The overall objective of this study was to apply and evaluate several of the currently available classification schemes for crop identification. The approaches examined were: (1) a per point Gaussian maximum likelihood classifier, (2) a per point sum of normal densities classifier, (3) a per point linear classifier, (4) a per point Gaussian maximum likelihood decision tree classifier, and (5) a texture sensitive per field Gaussian maximum likelihood classifier. Three agricultural data sets were used in the study: areas from Fayette County, Illinois, and Pottawattamie and Shelby Counties in Iowa. The segments were located in two distinct regions of the Corn Belt to sample variability in soils, climate, and agricultural practices.
SU-C-207A-01: A Novel Maximum Likelihood Method for High-Resolution Proton Radiography/proton CT
Collins-Fekete, C; Schulte, R; Beaulieu, L; Seco, J
2016-06-15
Purpose: Multiple Coulomb scattering is the largest contributor to blurring in proton imaging. Here we tested a maximum likelihood least squares estimator (MLLSE) to improve the spatial resolution of proton radiography (pRad) and proton computed tomography (pCT). Methods: The object is discretized into voxels and the average relative stopping power through voxel columns defined from the source to the detector pixels is optimized such that it maximizes the likelihood of the proton energy loss. The length spent by individual protons in each column is calculated through an optimized cubic spline estimate. pRad images were first produced using Geant4 simulations. An anthropomorphic head phantom and the Catphan line-pair module for 3-D spatial resolution were studied and resulting images were analyzed. Both parallel and conical beam have been investigated for simulated pRad acquisition. Then, experimental data of a pediatric head phantom (CIRS) were acquired using a recently completed experimental pCT scanner. Specific filters were applied on proton angle and energy loss data to remove proton histories that underwent nuclear interactions. The MTF10% (lp/mm) was used to evaluate and compare spatial resolution. Results: Numerical simulations showed improvement in the pRad spatial resolution for the parallel (2.75 to 6.71 lp/cm) and conical beam (3.08 to 5.83 lp/cm) reconstructed with the MLLSE compared to averaging detector pixel signals. For full tomographic reconstruction, the improved pRad were used as input into a simultaneous algebraic reconstruction algorithm. The Catphan pCT reconstruction based on the MLLSE-enhanced projection showed spatial resolution improvement for the parallel (2.83 to 5.86 lp/cm) and conical beam (3.03 to 5.15 lp/cm). The anthropomorphic head pCT displayed important contrast gains in high-gradient regions. Experimental results also demonstrated significant improvement in spatial resolution of the pediatric head radiography. Conclusion: The
Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood e...
Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood e...
Maximum likelihood, multiple imputation and regression calibration for measurement error adjustment.
Messer, Karen; Natarajan, Loki
2008-12-30
In epidemiologic studies of exposure-disease association, often only a surrogate measure of exposure is available for the majority of the sample. A validation sub-study may be conducted to estimate the relation between the surrogate measure and true exposure levels. In this article, we discuss three methods of estimation for such a main study/validation study design: (i) maximum likelihood (ML), (ii) multiple imputation (MI) and (iii) regression calibration (RC). For logistic regression, we show how each method depends on a different numerical approximation to the likelihood, and we adapt standard software to compute both MI and ML estimates. We use simulation to compare the performance of the estimators for both realistic and extreme settings, and for both internal and external validation designs. Our results indicate that with large measurement error or large enough sample sizes, ML performs as well as or better than MI and RC. However, for smaller measurement error and small sample sizes, either ML or RC may have the advantage. Interestingly, in most cases the relative advantage of RC versus ML was determined by the relative variance rather than the bias of the estimators. Software code for all three methods in SAS is provided.
NASA Technical Reports Server (NTRS)
Klein, V.
1980-01-01
A frequency domain maximum likelihood method is developed for the estimation of airplane stability and control parameters from measured data. The model of an airplane is represented by a discrete-type steady state Kalman filter with time variables replaced by their Fourier series expansions. The likelihood function of innovations is formulated, and by its maximization with respect to unknown parameters the estimation algorithm is obtained. This algorithm is then simplified to the output error estimation method with the data in the form of transformed time histories, frequency response curves, or spectral and cross-spectral densities. The development is followed by a discussion on the equivalence of the cost function in the time and frequency domains, and on advantages and disadvantages of the frequency domain approach. The algorithm developed is applied in four examples to the estimation of longitudinal parameters of a general aviation airplane using computer generated and measured data in turbulent and still air. The cost functions in the time and frequency domains are shown to be equivalent; therefore, both approaches are complementary and not contradictory. Despite some computational advantages of parameter estimation in the frequency domain, this approach is limited to linear equations of motion with constant coefficients.
Neandertal Admixture in Eurasia Confirmed by Maximum-Likelihood Analysis of Three Genomes
Lohse, Konrad; Frantz, Laurent A. F.
2014-01-01
Although there has been much interest in estimating histories of divergence and admixture from genomic data, it has proved difficult to distinguish recent admixture from long-term structure in the ancestral population. Thus, recent genome-wide analyses based on summary statistics have sparked controversy about the possibility of interbreeding between Neandertals and modern humans in Eurasia. Here we derive the probability of full mutational configurations in nonrecombining sequence blocks under both admixture and ancestral structure scenarios. Dividing the genome into short blocks gives an efficient way to compute maximum-likelihood estimates of parameters. We apply this likelihood scheme to triplets of human and Neandertal genomes and compare the relative support for a model of admixture from Neandertals into Eurasian populations after their expansion out of Africa against a history of persistent structure in their common ancestral population in Africa. Our analysis allows us to conclusively reject a model of ancestral structure in Africa and instead reveals strong support for Neandertal admixture in Eurasia at a higher rate (3.4−7.3%) than suggested previously. Using analysis and simulations we show that our inference is more powerful than previous summary statistics and robust to realistic levels of recombination. PMID:24532731
Maximum Likelihood Mapping of Quantitative Trait Loci Using Full-Sib Families
Knott, S. A.; Haley, C. S.
1992-01-01
A maximum likelihood method is presented for the detection of quantitative trait loci (QTL) using flanking markers in full-sib families. This method incorporates a random component for common family effects due to additional QTL or the environment. Simulated data have been used to investigate this method. With a fixed total number of full sibs power of detection decreased substantially with decreasing family size. Increasing the number of alleles at the marker loci (i.e., polymorphism information content) and decreasing the interval size about the QTL increased power. Flanking markers were more powerful than single markers. In testing for a linked QTL the test must be made against a model which allows for between family variation (i.e., including an unlinked QTL or a between family variance component) or the test statistic may be grossly inflated. Mean parameter estimates were close to the simulated values in all situations when fitting the full model (including a linked QTL and common family effect). If the common family component was omitted the QTL effect was overestimated in data in which additional genetic variance was simulated and when compared with an unlinked QTL model there was reduced power. The test statistic curves, reflecting the likelihood of the QTL at each position along the chromosome, have discontinuities at the markers caused by adjacent pairs of markers providing different amounts of information. This must be accounted for when using flanking markers to search for a QTL in an outbred population. PMID:1459438
Meyer, Karin; Kirkpatrick, Mark
2005-01-01
Principal component analysis is a widely used 'dimension reduction' technique, albeit generally at a phenotypic level. It is shown that we can estimate genetic principal components directly through a simple reparameterisation of the usual linear, mixed model. This is applicable to any analysis fitting multiple, correlated genetic effects, whether effects for individual traits or sets of random regression coefficients to model trajectories. Depending on the magnitude of genetic correlation, a subset of the principal component generally suffices to capture the bulk of genetic variation. Corresponding estimates of genetic covariance matrices are more parsimonious, have reduced rank and are smoothed, with the number of parameters required to model the dispersion structure reduced from k(k + 1)/2 to m(2k - m + 1)/2 for k effects and m principal components. Estimation of these parameters, the largest eigenvalues and pertaining eigenvectors of the genetic covariance matrix, via restricted maximum likelihood using derivatives of the likelihood, is described. It is shown that reduced rank estimation can reduce computational requirements of multivariate analyses substantially. An application to the analysis of eight traits recorded via live ultrasound scanning of beef cattle is given. PMID:15588566
Huebner, Alan R; Wang, Chun; Quinlan, Kari; Seubert, Lauren
2016-12-01
Item bank stratification has been shown to be an effective method for combating item overexposure in both uni- and multidimensional computer adaptive testing. However, item bank stratification cannot guarantee that items will not be overexposed-that is, exposed at a rate exceeding some prespecified threshold. In this article, we propose enhancing stratification for multidimensional computer adaptive tests by combining it with the item eligibility method, a technique for controlling the maximum exposure rate in computerized tests. The performance of the method was examined via a simulation study and compared to existing methods of item selection and exposure control. Also, for the first time, maximum likelihood (MLE) and expected a posteriori (EAP) estimation of examinee ability were compared side by side in a multidimensional computer adaptive test. The simulation suggested that the proposed method is effective in suppressing the maximum item exposure rate with very little loss of measurement accuracy and precision. As compared to MLE, EAP generates smaller mean squared errors of the ability estimates in all simulation conditions.
Huang, Jinxin; Clarkson, Eric; Kupinski, Matthew; Lee, Kye-Sung; Maki, Kara L; Ross, David S; Aquavella, James V; Rolland, Jannick P
2013-01-01
Understanding tear film dynamics is a prerequisite for advancing the management of Dry Eye Disease (DED). In this paper, we discuss the use of optical coherence tomography (OCT) and statistical decision theory to analyze the tear film dynamics of a digital phantom. We implement a maximum-likelihood (ML) estimator to interpret OCT data based on mathematical models of Fourier-Domain OCT and the tear film. With the methodology of task-based assessment, we quantify the tradeoffs among key imaging system parameters. We find, on the assumption that the broadband light source is characterized by circular Gaussian statistics, ML estimates of 40 nm +/- 4 nm for an axial resolution of 1 μm and an integration time of 5 μs. Finally, the estimator is validated with a digital phantom of tear film dynamics, which reveals estimates of nanometer precision.
Cham, Heining; Reshetnyak, Evgeniya; Rosenfeld, Barry; Breitbart, William
2017-01-01
Researchers have developed missing data handling techniques for estimating interaction effects in multiple regression. Extending to latent variable interactions, we investigated full information maximum likelihood (FIML) estimation to handle incompletely observed indicators for product indicator (PI) and latent moderated structural equations (LMS) methods. Drawing on the analytic work on missing data handling techniques in multiple regression with interaction effects, we compared the performance of FIML for PI and LMS analytically. We performed a simulation study to compare FIML for PI and LMS. We recommend using FIML for LMS when the indicators are missing completely at random (MCAR) or missing at random (MAR) and when they are normally distributed. FIML for LMS produces unbiased parameter estimates with small variances, correct Type I error rates, and high statistical power of interaction effects. We illustrated the use of these methods by analyzing the interaction effect between advanced cancer patients' depression and change of inner peace well-being on future hopelessness levels.
Change point models for cognitive tests using semi-parametric maximum likelihood
van den Hout, Ardo; Muniz-Terrera, Graciela; Matthews, Fiona E.
2013-01-01
Random-effects change point models are formulated for longitudinal data obtained from cognitive tests. The conditional distribution of the response variable in a change point model is often assumed to be normal even if the response variable is discrete and shows ceiling effects. For the sum score of a cognitive test, the binomial and the beta-binomial distributions are presented as alternatives to the normal distribution. Smooth shapes for the change point models are imposed. Estimation is by marginal maximum likelihood where a parametric population distribution for the random change point is combined with a non-parametric mixing distribution for other random effects. An extension to latent class modelling is possible in case some individuals do not experience a change in cognitive ability. The approach is illustrated using data from a longitudinal study of Swedish octogenarians and nonagenarians that began in 1991. Change point models are applied to investigate cognitive change in the years before death. PMID:23471297
Targeted search for continuous gravitational waves: Bayesian versus maximum-likelihood statistics
NASA Astrophysics Data System (ADS)
Prix, Reinhard; Krishnan, Badri
2009-10-01
We investigate the Bayesian framework for detection of continuous gravitational waves (GWs) in the context of targeted searches, where the phase evolution of the GW signal is assumed to be known, while the four amplitude parameters are unknown. We show that the orthodox maximum-likelihood statistic (known as F-statistic) can be rediscovered as a Bayes factor with an unphysical prior in amplitude parameter space. We introduce an alternative detection statistic ('B-statistic') using the Bayes factor with a more natural amplitude prior, namely an isotropic probability distribution for the orientation of GW sources. Monte Carlo simulations of targeted searches show that the resulting Bayesian B-statistic is more powerful in the Neyman-Pearson sense (i.e., has a higher expected detection probability at equal false-alarm probability) than the frequentist F-statistic.
Li, Xinya; Deng, Z. Daniel; USA, Richland Washington; Sun, Yannan; USA, Richland Washington; Martinez, Jayson J.; USA, Richland Washington; Fu, Tao; USA, Richland Washington; McMichael, Geoffrey A.; USA, Richland Washington; Carlson, Thomas J.; USA, Richland Washington
2014-11-27
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
Li, Xinya; Deng, Z. Daniel; USA, Richland Washington; ...
2014-11-27
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developedmore » using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.« less
Determination of instrumentation errors from measured data using maximum likelihood method
NASA Technical Reports Server (NTRS)
Keskar, D. A.; Klein, V.
1980-01-01
The maximum likelihood method is used for estimation of unknown initial conditions, constant bias and scale factor errors in measured flight data. The model for the system to be identified consists of the airplane six-degree-of-freedom kinematic equations, and the output equations specifying the measured variables. The estimation problem is formulated in a general way and then, for practical use, simplified by ignoring the effect of process noise. The algorithm developed is first applied to computer generated data having different levels of process noise for the demonstration of the robustness of the method. Then the real flight data are analyzed and the results compared with those obtained by the extended Kalman filter algorithm.
A comparison of minimum distance and maximum likelihood techniques for proportion estimation
NASA Technical Reports Server (NTRS)
Woodward, W. A.; Schucany, W. R.; Lindsey, H.; Gray, H. L.
1982-01-01
The estimation of mixing proportions P sub 1, P sub 2,...P sub m in the mixture density f(x) = the sum of the series P sub i F sub i(X) with i = 1 to M is often encountered in agricultural remote sensing problems in which case the p sub i's usually represent crop proportions. In these remote sensing applications, component densities f sub i(x) have typically been assumed to be normally distributed, and parameter estimation has been accomplished using maximum likelihood (ML) techniques. Minimum distance (MD) estimation is examined as an alternative to ML where, in this investigation, both procedures are based upon normal components. Results indicate that ML techniques are superior to MD when component distributions actually are normal, while MD estimation provides better estimates than ML under symmetric departures from normality. When component distributions are not symmetric, however, it is seen that neither of these normal based techniques provides satisfactory results.
Maximum-Likelihood Tree Estimation Using Codon Substitution Models with Multiple Partitions
Zoller, Stefan; Boskova, Veronika; Anisimova, Maria
2015-01-01
Many protein sequences have distinct domains that evolve with different rates, different selective pressures, or may differ in codon bias. Instead of modeling these differences by more and more complex models of molecular evolution, we present a multipartition approach that allows maximum-likelihood phylogeny inference using different codon models at predefined partitions in the data. Partition models can, but do not have to, share free parameters in the estimation process. We test this approach with simulated data as well as in a phylogenetic study of the origin of the leucin-rich repeat regions in the type III effector proteins of the pythopathogenic bacteria Ralstonia solanacearum. Our study does not only show that a simple two-partition model resolves the phylogeny better than a one-partition model but also gives more evidence supporting the hypothesis of lateral gene transfer events between the bacterial pathogens and its eukaryotic hosts. PMID:25911229
NASA Astrophysics Data System (ADS)
Kojima, Yohei; Takeda, Kazuaki; Adachi, Fumiyuki
Frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can provide better downlink bit error rate (BER) performance of direct sequence code division multiple access (DS-CDMA) than the conventional rake combining in a frequency-selective fading channel. FDE requires accurate channel estimation. In this paper, we propose a new 2-step maximum likelihood channel estimation (MLCE) for DS-CDMA with FDE in a very slow frequency-selective fading environment. The 1st step uses the conventional pilot-assisted MMSE-CE and the 2nd step carries out the MLCE using decision feedback from the 1st step. The BER performance improvement achieved by 2-step MLCE over pilot assisted MMSE-CE is confirmed by computer simulation.
Haker, Steven; Wells, William M.; Warfield, Simon K.; Talos, Ion-Florin; Bhagwat, Jui G.; Goldberg-Zimring, Daniel; Mian, Asim; Ohno-Machado, Lucila; Zou, Kelly H.
2010-01-01
In any medical domain, it is common to have more than one test (classifier) to diagnose a disease. In image analysis, for example, there is often more than one reader or more than one algorithm applied to a certain data set. Combining of classifiers is often helpful, but determining the way in which classifiers should be combined is not trivial. Standard strategies are based on learning classifier combination functions from data. We describe a simple strategy to combine results from classifiers that have not been applied to a common data set, and therefore can not undergo this type of joint training. The strategy, which assumes conditional independence of classifiers, is based on the calculation of a combined Receiver Operating Characteristic (ROC) curve, using maximum likelihood analysis to determine a combination rule for each ROC operating point. We offer some insights into the use of ROC analysis in the field of medical imaging. PMID:16685884
Emura, Takeshi; Konno, Yoshihiko; Michimae, Hirofumi
2015-07-01
Doubly truncated data consist of samples whose observed values fall between the right- and left- truncation limits. With such samples, the distribution function of interest is estimated using the nonparametric maximum likelihood estimator (NPMLE) that is obtained through a self-consistency algorithm. Owing to the complicated asymptotic distribution of the NPMLE, the bootstrap method has been suggested for statistical inference. This paper proposes a closed-form estimator for the asymptotic covariance function of the NPMLE, which is computationally attractive alternative to bootstrapping. Furthermore, we develop various statistical inference procedures, such as confidence interval, goodness-of-fit tests, and confidence bands to demonstrate the usefulness of the proposed covariance estimator. Simulations are performed to compare the proposed method with both the bootstrap and jackknife methods. The methods are illustrated using the childhood cancer dataset.
BOREAS TE-18 Landsat TM Maximum Likelihood Classification Image of the NSA
NASA Technical Reports Server (NTRS)
Hall, Forrest G. (Editor); Knapp, David
2000-01-01
The BOREAS TE-18 team focused its efforts on using remotely sensed data to characterize the successional and disturbance dynamics of the boreal forest for use in carbon modeling. The objective of this classification is to provide the BOREAS investigators with a data product that characterizes the land cover of the NSA. A Landsat-5 TM image from 20-Aug-1988 was used to derive this classification. A standard supervised maximum likelihood classification approach was used to produce this classification. The data are provided in a binary image format file. The data files are available on a CD-ROM (see document number 20010000884), or from the Oak Ridge National Laboratory (ORNL) Distributed Activity Archive Center (DAAC).
A maximum likelihood analysis of the CoGeNT public dataset
NASA Astrophysics Data System (ADS)
Kelso, Chris
2016-06-01
The CoGeNT detector, located in the Soudan Underground Laboratory in Northern Minnesota, consists of a 475 grams (fiducial mass of 330 grams) target mass of p-type point contact germanium detector that measures the ionization charge created by nuclear recoils. This detector has searched for recoils created by dark matter since December of 2009. We analyze the public dataset from the CoGeNT experiment to search for evidence of dark matter interactions with the detector. We perform an unbinned maximum likelihood fit to the data and compare the significance of different WIMP hypotheses relative to each other and the null hypothesis of no WIMP interactions. This work presents the current status of the analysis.
NASA Astrophysics Data System (ADS)
Simbolon, H. G.; Fithriani, I.; Nurrohmah, S.
2017-07-01
This paper discusses the Maximum Likelihood (ML) and Bayes method for estimating the shape β parameter in Kumaraswamy distribution. Both methods will be compared according to Mean Square Error (MSE) obtained from each estimator. In the Bayes method, two Loss functions will be used, i.e., the Square Error Loss Function (SELF) and Precautionary Loss Function (PLF). Then, the Posterior Risk obtained from both loss functions will be compared. The comparison will be applied to hydrological data as a recommendation for the best method of representing the data. Hydrological data used in this study is a water storage in Shasta Reservoir, obtained from the California Data Exchange Center. By using the Mathematica Software and the formulas from both methods one obtains a statistic which can nicely describe the data and also predict the next observation of a reservoir in a certain time.
A new maximum-likelihood change estimator for two-pass SAR coherent change detection
Wahl, Daniel E.; Yocky, David A.; Jakowatz, Jr., Charles V.; Simonson, Katherine Mary
2016-01-11
In past research, two-pass repeat-geometry synthetic aperture radar (SAR) coherent change detection (CCD) predominantly utilized the sample degree of coherence as a measure of the temporal change occurring between two complex-valued image collects. Previous coherence-based CCD approaches tend to show temporal change when there is none in areas of the image that have a low clutter-to-noise power ratio. Instead of employing the sample coherence magnitude as a change metric, in this paper, we derive a new maximum-likelihood (ML) temporal change estimate—the complex reflectance change detection (CRCD) metric to be used for SAR coherent temporal change detection. The new CRCD estimator is a surprisingly simple expression, easy to implement, and optimal in the ML sense. As a result, this new estimate produces improved results in the coherent pair collects that we have tested.
NASA Astrophysics Data System (ADS)
Sobolev, V. S.; Zhuravel', F. A.; Kashcheeva, G. A.
2016-11-01
This paper presents a comparative analysis of the errors of two alternative methods of estimating the central frequency of signals of laser Doppler systems, one of which is based on the maximum likelihood criterion and the other on the so-called pulse-pair technique. Using computer simulation, the standard deviations of the Doppler signal frequency from its true values are determined for both methods and plots of the ratios of these deviations as a measure of the accuracy gain of one of them are constructed. The results can be used by developers of appropriate systems to choose an optimal algorithm of signal processing based on a compromise between the accuracy and speed of the systems as well as the labor intensity of calculations.
NASA Astrophysics Data System (ADS)
Chou, Heng-Chih; Wang, David
2007-11-01
We investigate the performance of a default risk model based on the barrier option framework with maximum likelihood estimation. We provide empirical validation of the model by showing that implied default barriers are statistically significant for a sample of construction firms in Taiwan over the period 1994-2004. We find that our model dominates the commonly adopted models, Merton model, Z-score model and ZETA model. Moreover, we test the n-year-ahead prediction performance of the model and find evidence that the prediction accuracy of the model improves as the forecast horizon decreases. Finally, we assess the effect of estimated default risk on equity returns and find that default risk is able to explain equity returns and that default risk is a variable worth considering in asset-pricing tests, above and beyond size and book-to-market.
Kvam, P.H.
1994-08-01
We investigate systems designed using redundant component configurations. If external events exist in the working environment that cause two or more components in the system to fail within the same demand period, the designed redundancy in the system can be quickly nullified. In the engineering field, such events are called common cause failures (CCFs), and are primary factors in some risk assessments. If CCFs have positive probability, but are not addressed in the analysis, the assessment may contain a gross overestimation of the system reliability. We apply a discrete, multivariate shock model for a parallel system of two or more components, allowing for positive probability that such external events can occur. The methods derived are motivated by attribute data for emergency diesel generators from various US nuclear power plants. Closed form solutions for maximum likelihood estimators exist in many cases; statistical tests and confidence intervals are discussed for the different test environments considered.
NASA Technical Reports Server (NTRS)
Murphy, P. C.
1984-01-01
An algorithm for maximum likelihood (ML) estimation is developed primarily for multivariable dynamic systems. The algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). The method determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared with integrating the analytically determined sensitivity equations or using a finite-difference method. Different surface-fitting methods are discussed and demonstrated. Aircraft estimation problems are solved by using both simulated and real-flight data to compare MNRES with commonly used methods; in these solutions MNRES is found to be equally accurate and substantially faster. MNRES eliminates the need to derive sensitivity equations, thus producing a more generally applicable algorithm.
NASA Astrophysics Data System (ADS)
Kong, Gyuyeol; Choi, Sooyong
2012-08-01
An effective two-dimensional (2D) partial response maximum likelihood (PRML) detection scheme for holographic data storage (HDS) systems is proposed. The proposed scheme adopts the simplified trellis diagram, uses a priori information, and detects the data in two directions from the previously proposed detection schemes. The simplified trellis diagram which has 4 states and 8 branches yields a dramatic complexity reduction while the simplified 2D PRML detector shows serious performance degradation in the high density HDS channels. To prevent performance degradation, the proposed detector uses a priori information in order to give higher reliability to the branch metric. Furthermore, the proposed scheme detects the data in the vertical and horizontal directions to fully utilize the characteristics of the channel detection with a 2D partial response target. By effective combination of these three techniques, the proposed scheme with a simple structure has more than 2 dB gains compared to the conventional detection schemes.
Modifying high-order aeroelastic math model of a jet transport using maximum likelihood estimation
NASA Technical Reports Server (NTRS)
Anissipour, Amir A.; Benson, Russell A.
1989-01-01
The design of control laws to damp flexible structural modes requires accurate math models. Unlike the design of control laws for rigid body motion (e.g., where robust control is used to compensate for modeling inaccuracies), structural mode damping usually employs narrow band notch filters. In order to obtain the required accuracy in the math model, maximum likelihood estimation technique is employed to improve the accuracy of the math model using flight data. Presented here are all phases of this methodology: (1) pre-flight analysis (i.e., optimal input signal design for flight test, sensor location determination, model reduction technique, etc.), (2) data collection and preprocessing, and (3) post-flight analysis (i.e., estimation technique and model verification). In addition, a discussion is presented of the software tools used and the need for future study in this field.
Equivalence between modularity optimization and maximum likelihood methods for community detection
NASA Astrophysics Data System (ADS)
Newman, M. E. J.
2016-11-01
We demonstrate an equivalence between two widely used methods of community detection in networks, the method of modularity maximization and the method of maximum likelihood applied to the degree-corrected stochastic block model. Specifically, we show an exact equivalence between maximization of the generalized modularity that includes a resolution parameter and the special case of the block model known as the planted partition model, in which all communities in a network are assumed to have statistically similar properties. Among other things, this equivalence provides a mathematically principled derivation of the modularity function, clarifies the conditions and assumptions of its use, and gives an explicit formula for the optimal value of the resolution parameter.
A new maximum-likelihood change estimator for two-pass SAR coherent change detection
Wahl, Daniel E.; Yocky, David A.; Jakowatz, Jr., Charles V.; ...
2016-01-11
In past research, two-pass repeat-geometry synthetic aperture radar (SAR) coherent change detection (CCD) predominantly utilized the sample degree of coherence as a measure of the temporal change occurring between two complex-valued image collects. Previous coherence-based CCD approaches tend to show temporal change when there is none in areas of the image that have a low clutter-to-noise power ratio. Instead of employing the sample coherence magnitude as a change metric, in this paper, we derive a new maximum-likelihood (ML) temporal change estimate—the complex reflectance change detection (CRCD) metric to be used for SAR coherent temporal change detection. The new CRCD estimatormore » is a surprisingly simple expression, easy to implement, and optimal in the ML sense. As a result, this new estimate produces improved results in the coherent pair collects that we have tested.« less
A maximum likelihood analysis of the CoGeNT public dataset
Kelso, Chris
2016-06-21
The CoGeNT detector, located in the Soudan Underground Laboratory in Northern Minnesota, consists of a 475 grams (fiducial mass of 330 grams) target mass of p-type point contact germanium detector that measures the ionization charge created by nuclear recoils. This detector has searched for recoils created by dark matter since December of 2009. We analyze the public dataset from the CoGeNT experiment to search for evidence of dark matter interactions with the detector. We perform an unbinned maximum likelihood fit to the data and compare the significance of different WIMP hypotheses relative to each other and the null hypothesis of no WIMP interactions. This work presents the current status of the analysis.
NASA Astrophysics Data System (ADS)
Kalafut, Bennett; Visscher, Koen
2008-10-01
Optical tweezers experiments allow us to probe the role of force and mechanical work in a variety of biochemical processes. However, observable states do not usually correspond in a one-to-one fashion with the internal state of an enzyme or enzyme-substrate complex. Different kinetic pathways yield different distributions for the dwells in the observable states. Furthermore, the dwell-time distribution will be dependent upon force, and upon where in the biochemical pathway force acts. I will present a maximum-likelihood method for identifying rate constants and the locations of force-dependent transitions in transcription initiation by T7 RNA Polymerase. This method is generalizable to systems with more complicated kinetic pathways in which there are two observable states (e.g. bound and unbound) and an irreversible final transition.
Maximum likelihood estimation for semiparametric transformation models with interval-censored data
Zeng, Donglin; Mao, Lu; Lin, D. Y.
2016-01-01
Interval censoring arises frequently in clinical, epidemiological, financial and sociological studies, where the event or failure of interest is known only to occur within an interval induced by periodic monitoring. We formulate the effects of potentially time-dependent covariates on the interval-censored failure time through a broad class of semiparametric transformation models that encompasses proportional hazards and proportional odds models. We consider nonparametric maximum likelihood estimation for this class of models with an arbitrary number of monitoring times for each subject. We devise an EM-type algorithm that converges stably, even in the presence of time-dependent covariates, and show that the estimators for the regression parameters are consistent, asymptotically normal, and asymptotically efficient with an easily estimated covariance matrix. Finally, we demonstrate the performance of our procedures through simulation studies and application to an HIV/AIDS study conducted in Thailand. PMID:27279656
A Sum-of-Squares and Semidefinite Programming Approach for Maximum Likelihood DOA Estimation
Cai, Shu; Zhou, Quan; Zhu, Hongbo
2016-01-01
Direction of arrival (DOA) estimation using a uniform linear array (ULA) is a classical problem in array signal processing. In this paper, we focus on DOA estimation based on the maximum likelihood (ML) criterion, transform the estimation problem into a novel formulation, named as sum-of-squares (SOS), and then solve it using semidefinite programming (SDP). We first derive the SOS and SDP method for DOA estimation in the scenario of a single source and then extend it under the framework of alternating projection for multiple DOA estimation. The simulations demonstrate that the SOS- and SDP-based algorithms can provide stable and accurate DOA estimation when the number of snapshots is small and the signal-to-noise ratio (SNR) is low. Moveover, it has a higher spatial resolution compared to existing methods based on the ML criterion. PMID:27999397
NASA Astrophysics Data System (ADS)
Zhang, Lu; Wu, Zhiyong; Zhang, Yaoyu; Detian, Huang
2013-01-01
To mitigate the impact of the error between the estimated channel fading coefficient and the perfect fading coefficient on the bit error rate (BER), a priori conditional probability density function averaging the estimation error is proposed. Then, an improved maximum-likelihood (ML) symbol-by-symbol detection is derived for the free-space optical communication systems, which implement pilot symbol assisted modulation. To reduce complexity, a closed-form suboptimal improved ML detection is deduced using distribution approximation. Numerical results confirm that BER performance improvement can be reached by the improved ML detection, and that its suboptimal version performs as well as it does. Therefore, they both outperform classical ML detection, which doses not consider channel estimation error.
NASA Technical Reports Server (NTRS)
Howell, Leonard W.; Whitaker, Ann F. (Technical Monitor)
2001-01-01
The maximum likelihood procedure is developed for estimating the three spectral parameters of an assumed broken power law energy spectrum from simulated detector responses and their statistical properties investigated. The estimation procedure is then generalized for application to real cosmic-ray data. To illustrate the procedure and its utility, analytical methods were developed in conjunction with a Monte Carlo simulation to explore the combination of the expected cosmic-ray environment with a generic space-based detector and its planned life cycle, allowing us to explore various detector features and their subsequent influence on estimating the spectral parameters. This study permits instrument developers to make important trade studies in design parameters as a function of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose rigorous practical limits to the design envelope.
NASA Astrophysics Data System (ADS)
Loveday, J.; Norberg, P.; Baldry, I. K.; Bland-Hawthorn, J.; Brough, S.; Brown, M. J. I.; Driver, S. P.; Kelvin, L. S.; Phillipps, S.
2015-08-01
We describe modifications to the joint stepwise maximum-likelihood method of Cole in order to simultaneously fit the Galaxy and Mass Assembly II galaxy luminosity function (LF), corrected for radial density variations, and its evolution with redshift. The whole sample is reasonably well fitted with luminosity (Qe) and density (Pe) evolution parameters Qe, Pe ≈ 1.0, 1.0 but with significant degeneracies characterized by Qe ≈ 1.4 - 0.4Pe. Blue galaxies exhibit larger luminosity density evolution than red galaxies, as expected. We present the evolution-corrected r-band LF for the whole sample and for blue and red subsamples, using both Petrosian and Sérsic magnitudes. Petrosian magnitudes miss a substantial fraction of the flux of de Vaucouleurs profile galaxies: the Sérsic LF is substantially higher than the Petrosian LF at the bright end.
Smolin, John A; Gambetta, Jay M; Smith, Graeme
2012-02-17
We provide an efficient method for computing the maximum-likelihood mixed quantum state (with density matrix ρ) given a set of measurement outcomes in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix μ which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst O(d(4)) for the basis change plus O(d(3)) for finding ρ where d is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only O(d(3)) as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one.
Programmer's manual for MMLE3, a general FORTRAN program for maximum likelihood parameter estimation
NASA Technical Reports Server (NTRS)
Maine, R. E.
1981-01-01
The MMLE3 is a maximum likelihood parameter estimation program capable of handling general bilinear dynamic equations of arbitrary order with measurement noise and/or state noise (process noise). The basic MMLE3 program is quite general and, therefore, applicable to a wide variety of problems. The basic program can interact with a set of user written problem specific routines to simplify the use of the program on specific systems. A set of user routines for the aircraft stability and control derivative estimation problem is provided with the program. The implementation of the program on specific computer systems is discussed. The structure of the program is diagrammed, and the function and operation of individual routines is described. Complete listings and reference maps of the routines are included on microfiche as a supplement. Four test cases are discussed; listings of the input cards and program output for the test cases are included on microfiche as a supplement.
A Sum-of-Squares and Semidefinite Programming Approach for Maximum Likelihood DOA Estimation.
Cai, Shu; Zhou, Quan; Zhu, Hongbo
2016-12-20
Direction of arrival (DOA) estimation using a uniform linear array (ULA) is a classical problem in array signal processing. In this paper, we focus on DOA estimation based on the maximum likelihood (ML) criterion, transform the estimation problem into a novel formulation, named as sum-of-squares (SOS), and then solve it using semidefinite programming (SDP). We first derive the SOS and SDP method for DOA estimation in the scenario of a single source and then extend it under the framework of alternating projection for multiple DOA estimation. The simulations demonstrate that the SOS- and SDP-based algorithms can provide stable and accurate DOA estimation when the number of snapshots is small and the signal-to-noise ratio (SNR) is low. Moveover, it has a higher spatial resolution compared to existing methods based on the ML criterion.
Cohn, T.A.
2005-01-01
This paper presents an adjusted maximum likelihood estimator (AMLE) that can be used to estimate fluvial transport of contaminants, like phosphorus, that are subject to censoring because of analytical detection limits. The AMLE is a generalization of the widely accepted minimum variance unbiased estimator (MVUE), and Monte Carlo experiments confirm that it shares essentially all of the MVUE's desirable properties, including high efficiency and negligible bias. In particular, the AMLE exhibits substantially less bias than alternative censored-data estimators such as the MLE (Tobit) or the MLE followed by a jackknife. As with the MLE and the MVUE the AMLE comes close to achieving the theoretical Frechet-Crame??r-Rao bounds on its variance. This paper also presents a statistical framework, applicable to both censored and complete data, for understanding and estimating the components of uncertainty associated with load estimates. This can serve to lower the cost and improve the efficiency of both traditional and real-time water quality monitoring.
Haker, Steven; Wells, William M; Warfield, Simon K; Talos, Ion-Florin; Bhagwat, Jui G; Goldberg-Zimring, Daniel; Mian, Asim; Ohno-Machado, Lucila; Zou, Kelly H
2005-01-01
In any medical domain, it is common to have more than one test (classifier) to diagnose a disease. In image analysis, for example, there is often more than one reader or more than one algorithm applied to a certain data set. Combining of classifiers is often helpful, but determining the way in which classifiers should be combined is not trivial. Standard strategies are based on learning classifier combination functions from data. We describe a simple strategy to combine results from classifiers that have not been applied to a common data set, and therefore can not undergo this type of joint training. The strategy, which assumes conditional independence of classifiers, is based on the calculation of a combined Receiver Operating Characteristic (ROC) curve, using maximum likelihood analysis to determine a combination rule for each ROC operating point. We offer some insights into the use of ROC analysis in the field of medical imaging.
GFREG: a computer program for maximum likelihood regression using the Generalized F distribution.
Hogg, S A; Ciampi, A
1985-07-01
A FORTRAN program is described for maximum likelihood estimation within the Generalized F family of distributions. It can be used to estimate regression parameters in a log-linear model for censored survival times with covariates, for which the error distribution may have a great variety of shapes, including most distributions of current use in biostatistics. The optimization is performed by an algorithm based on the generalized reduced gradient method. A stepwise variable search algorithm for covariate selection is included in the program. Output features include: model selection criteria, standard errors of parameter estimates, quantile and survival rates with their standard errors, residuals and several plots. An example based on data from Princess Margaret Hospital, Toronto, is discussed to illustrate the program's capabilities.
Maximum likelihood-based analysis of photon arrival trajectories in single-molecule FRET
NASA Astrophysics Data System (ADS)
Waligórska, Marta; Molski, Andrzej
2012-07-01
When two fluorophores (donor and acceptor) are attached to an immobilized biomolecule, anti-correlated fluctuations of the donor and acceptor fluorescence caused by Förster resonance energy transfer (FRET) report on the conformational kinetics of the molecule. Here we assess the maximum likelihood-based analysis of donor and acceptor photon arrival trajectories as a method for extracting the conformational kinetics. Using computer generated data we quantify the accuracy and precision of parameter estimates and the efficiency of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) in selecting the true kinetic model. We find that the number of observed photons is the key parameter determining parameter estimation and model selection. For long trajectories, one can extract mean dwell times that are comparable to inter-photon times.
Real-time Data Acquisition and Maximum-Likelihood Estimation for Gamma Cameras
Furenlid, L.R.; Hesterman, J.Y.; Barrett, H.H.
2015-01-01
We have developed modular gamma-ray cameras for biomedical imaging that acquire data with a raw list-mode acquisition architecture. All observations associated with a gamma-ray event, such as photomultiplier (PMT) signals and time, are assembled into an event packet and added to an ordered list of event entries that comprise the acquired data. In this work we present the design of the data-acquisition system, and discuss algorithms for a specialized computing engine to reside in the data path between the front and back ends of each camera and carry out maximum-likelihood position and energy estimations in real time while data was being acquired.. PMID:27066595
Parsimonious estimation of sex-specific map distances by stepwise maximum likelihood regression
Fann, C.S.J.; Ott, J.
1995-10-10
In human genetic maps, differences between female (x{sub f}) and male (x{sub m}) map distances may be characterized by the ratio, R = x{sub f}/x{sub m}, or the relative difference, Q = (x{sub f} - x{sub m})/(x{sub f} + x{sub m}) = (R - 1)/(R + 1). For a map of genetic markers spread along a chromosome, Q(d) may be viewed as a graph of Q versus the midpoints, d, of the map intervals. To estimate male and female map distances for each interval, a novel method is proposed to evaluate the most parsimonious trend of Q(d) along the chromosome, where Q(d) is expressed as a polynomial in d. Stepwise maximum likelihood polynomial regression of Q is described. The procedure has been implemented in a FORTRAN program package, TREND, and is applied to data on chromosome 18. 11 refs., 2 figs., 3 tabs.
Fast and accurate estimation of the covariance between pairwise maximum likelihood distances
2014-01-01
Pairwise evolutionary distances are a model-based summary statistic for a set of molecular sequences. They represent the leaf-to-leaf path lengths of the underlying phylogenetic tree. Estimates of pairwise distances with overlapping paths covary because of shared mutation events. It is desirable to take these covariance structure into account to increase precision in any process that compares or combines distances. This paper introduces a fast estimator for the covariance of two pairwise maximum likelihood distances, estimated under general Markov models. The estimator is based on a conjecture (going back to Nei & Jin, 1989) which links the covariance to path lengths. It is proven here under a simple symmetric substitution model. A simulation shows that the estimator outperforms previously published ones in terms of the mean squared error. PMID:25279263
Li, Xinya; Deng, Z Daniel; Sun, Yannan; Martinez, Jayson J; Fu, Tao; McMichael, Geoffrey A; Carlson, Thomas J
2014-11-27
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
NASA Astrophysics Data System (ADS)
Li, Xinya; Deng, Z. Daniel; Sun, Yannan; Martinez, Jayson J.; Fu, Tao; McMichael, Geoffrey A.; Carlson, Thomas J.
2014-11-01
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
Li, Xinya; Deng, Z. Daniel; Sun, Yannan; Martinez, Jayson J.; Fu, Tao; McMichael, Geoffrey A.; Carlson, Thomas J.
2014-01-01
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature. PMID:25427517
MADmap: A Massively Parallel Maximum-Likelihood Cosmic Microwave Background Map-Maker
Cantalupo, Christopher; Borrill, Julian; Jaffe, Andrew; Kisner, Theodore; Stompor, Radoslaw
2009-06-09
MADmap is a software application used to produce maximum-likelihood images of the sky from time-ordered data which include correlated noise, such as those gathered by Cosmic Microwave Background (CMB) experiments. It works efficiently on platforms ranging from small workstations to the most massively parallel supercomputers. Map-making is a critical step in the analysis of all CMB data sets, and the maximum-likelihood approach is the most accurate and widely applicable algorithm; however, it is a computationally challenging task. This challenge will only increase with the next generation of ground-based, balloon-borne and satellite CMB polarization experiments. The faintness of the B-mode signal that these experiments seek to measure requires them to gather enormous data sets. MADmap is already being run on up to O(1011) time samples, O(108) pixels and O(104) cores, with ongoing work to scale to the next generation of data sets and supercomputers. We describe MADmap's algorithm based around a preconditioned conjugate gradient solver, fast Fourier transforms and sparse matrix operations. We highlight MADmap's ability to address problems typically encountered in the analysis of realistic CMB data sets and describe its application to simulations of the Planck and EBEX experiments. The massively parallel and distributed implementation is detailed and scaling complexities are given for the resources required. MADmap is capable of analysing the largest data sets now being collected on computing resources currently available, and we argue that, given Moore's Law, MADmap will be capable of reducing the most massive projected data sets.
Joint maximum-likelihood magnitudes of presumed underground nuclear test explosions
NASA Astrophysics Data System (ADS)
Peacock, Sheila; Douglas, Alan; Bowers, David
2017-08-01
Body-wave magnitudes (mb) of 606 seismic disturbances caused by presumed underground nuclear test explosions at specific test sites between 1964 and 1996 have been derived from station amplitudes collected by the International Seismological Centre (ISC), by a joint inversion for mb and station-specific magnitude corrections. A maximum-likelihood method was used to reduce the upward bias of network mean magnitudes caused by data censoring, where arrivals at stations that do not report arrivals are assumed to be hidden by the ambient noise at the time. Threshold noise levels at each station were derived from the ISC amplitudes using the method of Kelly and Lacoss, which fits to the observed magnitude-frequency distribution a Gutenberg-Richter exponential decay truncated at low magnitudes by an error function representing the low-magnitude threshold of the station. The joint maximum-likelihood inversion is applied to arrivals from the sites: Semipalatinsk (Kazakhstan) and Novaya Zemlya, former Soviet Union; Singer (Lop Nor), China; Mururoa and Fangataufa, French Polynesia; and Nevada, USA. At sites where eight or more arrivals could be used to derive magnitudes and station terms for 25 or more explosions (Nevada, Semipalatinsk and Mururoa), the resulting magnitudes and station terms were fixed and a second inversion carried out to derive magnitudes for additional explosions with three or more arrivals. 93 more magnitudes were thus derived. During processing for station thresholds, many stations were rejected for sparsity of data, obvious errors in reported amplitude, or great departure of the reported amplitude-frequency distribution from the expected left-truncated exponential decay. Abrupt changes in monthly mean amplitude at a station apparently coincide with changes in recording equipment and/or analysis method at the station.
IM3SHAPE: a maximum likelihood galaxy shear measurement code for cosmic gravitational lensing
NASA Astrophysics Data System (ADS)
Zuntz, Joe; Kacprzak, Tomasz; Voigt, Lisa; Hirsch, Michael; Rowe, Barnaby; Bridle, Sarah
2013-09-01
We present and describe IM3SHAPE, a new publicly available galaxy shape measurement code for weak gravitational lensing shear. IM3SHAPE performs a maximum likelihood fit of a bulge-plus-disc galaxy model to noisy images, incorporating an applied point spread function. We detail challenges faced and choices made in its design and implementation, and then discuss various limitations that affect this and other maximum likelihood methods. We assess the bias arising from fitting an incorrect galaxy model using simple noise-free images and find that it should not be a concern for current cosmic shear surveys. We test IM3SHAPE on the Gravitational Lensing Accuracy Testing 2008 (GREAT08) challenge image simulations, and meet the requirements for upcoming cosmic shear surveys in the case that the simulations are encompassed by the fitted model, using a simple correction for image noise bias. For the fiducial branch of GREAT08 we obtain a negligible additive shear bias and sub-two per cent level multiplicative bias, which is suitable for analysis of current surveys. We fall short of the sub-per cent level requirement for upcoming surveys, which we attribute to a combination of noise bias and the mismatch between our galaxy model and the model used in the GREAT08 simulations. We meet the requirements for current surveys across all branches of GREAT08, except those with small or high noise galaxies, which we would cut from our analysis. Using the GREAT08 metric we we obtain a score of Q = 717 for the usable branches, relative to the goal of Q = 1000 for future experiments. The code is freely available from https://bitbucket.org/joezuntz/im3shape
TrExML: a maximum-likelihood approach for extensive tree-space exploration.
Wolf, M J; Easteal, S; Kahn, M; McKay, B D; Jermiin, L S
2000-04-01
Maximum-likelihood analysis of nucleotide and amino acid sequences is a powerful approach for inferring phylogenetic relationships and for comparing evolutionary hypotheses. Because it is a computationally demanding and time-consuming process, most algorithms explore only a minute portion of tree-space, with the emphasis on finding the most likely tree while ignoring the less likely, but not significantly worse, trees. However, when such trees exist, it is equally important to identify them to give due consideration to the phylogenetic uncertainty. Consequently, it is necessary to change the focus of these algorithms such that near optimal trees are also identified. This paper presents the Advanced Stepwise Addition Algorithm for exploring tree-space and two algorithms for generating all binary trees on a set of sequences. The Advanced Stepwise Addition Algorithm has been implemented in TrExML, a phylogenetic program for maximum-likelihood analysis of nucleotide sequences. TrExML is shown to be more effective at finding near optimal trees than a similar program, fastDNAml, implying that TrExML offers a better approach to account for phylogenetic uncertainty than has previously been possible. A program, TreeGen, is also described; it generates binary trees on a set of sequences allowing for extensive exploration of tree-space using other programs. TreeGen, TrExML, and the sequence data used to test the programs are available from the following two WWW sites: http://whitetail.bemidji.msus. edu/trexml/and http://jcsmr.anu.edu.au/dmm/humgen.+ ++html.
Application of Maximum Entropy reconstruction to PISEMA spectra.
Jones, D H; Opella, S J
2006-03-01
Maximum Entropy reconstruction is applied to two-dimensional PISEMA spectra of stationary samples of peptide crystals and proteins in magnetically aligned virus particles and membrane bilayers. Improvements in signal-to-noise ratios were observed with minimal distortion of the spectra when Maximum Entropy reconstruction was applied to non-linearly sampled data in the indirect dimension. Maximum Entropy reconstruction was also applied in the direct dimension by selecting sub-sets of data from the free induction decays. Because the noise is uncorrelated in the spectra obtained by Maximum Entropy reconstruction of data with different non-linear sampling schedules, it is possible to improve the signal-to-noise ratios by co-addition of multiple spectra derived from one experimental data set. The combined application of Maximum Entropy to data in the indirect and direct dimensions has the potential to lead to substantial reductions in the total amount of experimental time required for acquisition of data in multidimensional NMR experiments.
NASA Astrophysics Data System (ADS)
Polack, John Kyle
The threat of nuclear warfare is an ongoing global concern. The reduction of this threat is an international effort that is aided by numerous technologies aimed at the detection, localization, and characterization of special nuclear material (SNM). Radiation imaging systems have a distinct advantage over more traditional systems in that they are designed to provide localized information of the observed the radiation field. Accurate characterization of detected sources requires robust reconstruction algorithms with well characterized uncertainties that are capable of delivering consistently reliable information. This work presents a versatile detection system and powerful reconstruction algorithm that, when combined, are well-suited to meeting many present challenges in the nuclear nonproliferation and treaty verification fields. The detection system, known as the Dual-Particle Imager (DPI), is a single device capable of performing both imaging and spectroscopy with photons and fast neutrons. The reconstruction algorithm leverages maximum-likelihood expectation-maximization (MLEM) and a robust system matrix, simulated in MCNPX-PoliMi, to perform image reconstruction and simultaneously unfold localized energy spectra for each pixel in the image. The localized energy spectra make it possible to analyze multiple detected sources simultaneously and the spectrum unfolding capabilities significantly improve the information available for characterizing the sources. Combining this algorithm with the DPI allows for localized spectra to be computed for photons and neutrons, which is particularly useful for the localization and characterization of SNM. The capabilities of this algorithm have been demonstrated through series of experiments and a detailed analysis of the uncertainties associated with the reconstruction process has been performed. The algorithm was used to analyze two complex environments, measured by the DPI, that each contained an SNM sample in a field of
Peyronie's Reconstruction for Maximum Length and Girth Gain: Geometrical Principles
Egydio, Paulo H.; Sansalone, Salvatore
2008-01-01
Peyronie's disease has been associated with penile shortening and some degree of erectile dysfunction. Surgical reconstruction should be based on giving a functional penis, that is, rectifying the penis with rigidity enough to make the sexual intercourse. The procedure should be discussed preoperatively in terms of length and girth reconstruction in order to improve patient satisfaction. The tunical reconstruction for maximum penile length and girth restoration should be based on the maximum length of the dissected neurovascular bundle possible and the application of geometrical principles to define the precise site and size of tunical incision and grafting procedure. As penile rectification and rigidity are required to achieve complete functional restoration of the penis and 20 to 54% of patients experience associated erectile dysfunction, penile straightening alone may not be enough to provide complete functional restoration. Therefore, phosphodiesterase inhibitors, self-injection, or penile prosthesis may need to be added in some cases. PMID:19081785
West, R. Derek; Gunther, Jacob H.; Moon, Todd K.
2016-12-01
In this study, we derive a comprehensive forward model for the data collected by stripmap synthetic aperture radar (SAR) that is linear in the ground reflectivity parameters. It is also shown that if the noise model is additive, then the forward model fits into the linear statistical model framework, and the ground reflectivity parameters can be estimated by statistical methods. We derive the maximum likelihood (ML) estimates for the ground reflectivity parameters in the case of additive white Gaussian noise. Furthermore, we show that obtaining the ML estimates of the ground reflectivity requires two steps. The first step amounts to a cross-correlation of the data with a model of the data acquisition parameters, and it is shown that this step has essentially the same processing as the so-called convolution back-projection algorithm. The second step is a complete system inversion that is capable of mitigating the sidelobes of the spatially variant impulse responses remaining after the correlation processing. We also state the Cramer-Rao lower bound (CRLB) for the ML ground reflectivity estimates.We show that the CRLB is linked to the SAR system parameters, the flight path of the SAR sensor, and the image reconstruction grid.We demonstrate the ML image formation and the CRLB bound for synthetically generated data.
West, R. Derek; Gunther, Jacob H.; Moon, Todd K.
2016-12-01
In this study, we derive a comprehensive forward model for the data collected by stripmap synthetic aperture radar (SAR) that is linear in the ground reflectivity parameters. It is also shown that if the noise model is additive, then the forward model fits into the linear statistical model framework, and the ground reflectivity parameters can be estimated by statistical methods. We derive the maximum likelihood (ML) estimates for the ground reflectivity parameters in the case of additive white Gaussian noise. Furthermore, we show that obtaining the ML estimates of the ground reflectivity requires two steps. The first step amounts tomore » a cross-correlation of the data with a model of the data acquisition parameters, and it is shown that this step has essentially the same processing as the so-called convolution back-projection algorithm. The second step is a complete system inversion that is capable of mitigating the sidelobes of the spatially variant impulse responses remaining after the correlation processing. We also state the Cramer-Rao lower bound (CRLB) for the ML ground reflectivity estimates.We show that the CRLB is linked to the SAR system parameters, the flight path of the SAR sensor, and the image reconstruction grid.We demonstrate the ML image formation and the CRLB bound for synthetically generated data.« less
Curiale, Ariel H; Vegas-Sánchez-Ferrero, Gonzalo; Bosch, Johan G; Aja-Fernández, Santiago
2015-08-01
The strain and strain-rate measures are commonly used for the analysis and assessment of regional myocardial function. In echocardiography (EC), the strain analysis became possible using Tissue Doppler Imaging (TDI). Unfortunately, this modality shows an important limitation: the angle between the myocardial movement and the ultrasound beam should be small to provide reliable measures. This constraint makes it difficult to provide strain measures of the entire myocardium. Alternative non-Doppler techniques such as Speckle Tracking (ST) can provide strain measures without angle constraints. However, the spatial resolution and the noisy appearance of speckle still make the strain estimation a challenging task in EC. Several maximum likelihood approaches have been proposed to statistically characterize the behavior of speckle, which results in a better performance of speckle tracking. However, those models do not consider common transformations to achieve the final B-mode image (e.g. interpolation). This paper proposes a new maximum likelihood approach for speckle tracking which effectively characterizes speckle of the final B-mode image. Its formulation provides a diffeomorphic scheme than can be efficiently optimized with a second-order method. The novelty of the method is threefold: First, the statistical characterization of speckle generalizes conventional speckle models (Rayleigh, Nakagami and Gamma) to a more versatile model for real data. Second, the formulation includes local correlation to increase the efficiency of frame-to-frame speckle tracking. Third, a probabilistic myocardial tissue characterization is used to automatically identify more reliable myocardial motions. The accuracy and agreement assessment was evaluated on a set of 16 synthetic image sequences for three different scenarios: normal, acute ischemia and acute dyssynchrony. The proposed method was compared to six speckle tracking methods. Results revealed that the proposed method is the most
Integrating functional genomics data using maximum likelihood based simultaneous component analysis
van den Berg, Robert A; Van Mechelen, Iven; Wilderjans, Tom F; Van Deun, Katrijn; Kiers, Henk AL; Smilde, Age K
2009-01-01
Background In contemporary biology, complex biological processes are increasingly studied by collecting and analyzing measurements of the same entities that are collected with different analytical platforms. Such data comprise a number of data blocks that are coupled via a common mode. The goal of collecting this type of data is to discover biological mechanisms that underlie the behavior of the variables in the different data blocks. The simultaneous component analysis (SCA) family of data analysis methods is suited for this task. However, a SCA may be hampered by the data blocks being subjected to different amounts of measurement error, or noise. To unveil the true mechanisms underlying the data, it could be fruitful to take noise heterogeneity into consideration in the data analysis. Maximum likelihood based SCA (MxLSCA-P) was developed for this purpose. In a previous simulation study it outperformed normal SCA-P. This previous study, however, did not mimic in many respects typical functional genomics data sets, such as, data blocks coupled via the experimental mode, more variables than experimental units, and medium to high correlations between variables. Here, we present a new simulation study in which the usefulness of MxLSCA-P compared to ordinary SCA-P is evaluated within a typical functional genomics setting. Subsequently, the performance of the two methods is evaluated by analysis of a real life Escherichia coli metabolomics data set. Results In the simulation study, MxLSCA-P outperforms SCA-P in terms of recovery of the true underlying scores of the common mode and of the true values underlying the data entries. MxLSCA-P further performed especially better when the simulated data blocks were subject to different noise levels. In the analysis of an E. coli metabolomics data set, MxLSCA-P provided a slightly better and more consistent interpretation. Conclusion MxLSCA-P is a promising addition to the SCA family. The analysis of coupled functional genomics
NASA Astrophysics Data System (ADS)
Emanuele Rizzo, Roberto; Healy, David; De Siena, Luca
2016-04-01
The success of any predictive model is largely dependent on the accuracy with which its parameters are known. When characterising fracture networks in fractured rock, one of the main issues is accurately scaling the parameters governing the distribution of fracture attributes. Optimal characterisation and analysis of fracture attributes (lengths, apertures, orientations and densities) is fundamental to the estimation of permeability and fluid flow, which are of primary importance in a number of contexts including: hydrocarbon production from fractured reservoirs; geothermal energy extraction; and deeper Earth systems, such as earthquakes and ocean floor hydrothermal venting. Our work links outcrop fracture data to modelled fracture networks in order to numerically predict bulk permeability. We collected outcrop data from a highly fractured upper Miocene biosiliceous mudstone formation, cropping out along the coastline north of Santa Cruz (California, USA). Using outcrop fracture networks as analogues for subsurface fracture systems has several advantages, because key fracture attributes such as spatial arrangements and lengths can be effectively measured only on outcrops [1]. However, a limitation when dealing with outcrop data is the relative sparseness of natural data due to the intrinsic finite size of the outcrops. We make use of a statistical approach for the overall workflow, starting from data collection with the Circular Windows Method [2]. Then we analyse the data statistically using Maximum Likelihood Estimators, which provide greater accuracy compared to the more commonly used Least Squares linear regression when investigating distribution of fracture attributes. Finally, we estimate the bulk permeability of the fractured rock mass using Oda's tensorial approach [3]. The higher quality of this statistical analysis is fundamental: better statistics of the fracture attributes means more accurate permeability estimation, since the fracture attributes feed
Soil mapping in northern Thailand based on an radiometrically calibrated Maximum likelihood approach
NASA Astrophysics Data System (ADS)
Schuler, U.; Herrmann, L.; Rangnugpit, W.; Stahr, K.
2009-04-01
The highlands of northern Thailand are dominated by the soil reference groups Acrisols and Alisols. The occurrence of these depends mainly on petrography and local climate gradients. The probabilistic Maximum likelihood method locally proved the potential to predict these reference soil groups. However, the available soil information is mostly nested around research stations with vast blank areas in between. Therefore more training data are required. The collection of further soil information is costly and time consuming as the access is often difficult and the determination of the reference soil groups is based on clay content, cation exchange capacity and the organic matter content, which can hardly be determined in the field. Groundbased radiometric data have shown the potential to distinguish Acrisols and Alisols. Therefore, airborne radiometric data, which are available for whole Thailand, might have the potential for regional distinction of those. The airborne data were collected in 1984-89. The sensor was mounted on an airplane flying at approximately 120m altitude, with a distance between the flight lines of approximately 1km and measurements in the flight line of approximately 50m. After orthographic correction a low pass filter (Savitzky Golay) was used for smoothing the data. Corrected output data (grey values) were calibrated and thus transferred to concentration values (K %; Th ppm, U ppm). The standard procedure for interpolation between the flight lines was bidirectional latticing (spline). After interpolation, the data can be presented as a 2D map either as single channel, binary, or ternary presentation. Initial comparisons between the petrography in the field and those ternary maps showed a potential for further subdivision of the existing geological maps. However, smoothing and data interpolation caused numerous artefacts. Therefore it is intended to focus on the primary measuring points. At least, ground measurements of gamma-ray in a limestone
Beyond maximum entropy: Fractal Pixon-based image reconstruction
NASA Technical Reports Server (NTRS)
Puetter, Richard C.; Pina, R. K.
1994-01-01
We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other competing methods, including Goodness-of-Fit methods such as Least-Squares fitting and Lucy-Richardson reconstruction, as well as Maximum Entropy (ME) methods such as those embodied in the MEMSYS algorithms. Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME. Our past work has shown how uniform information content pixons can be used to develop a 'Super-ME' method in which entropy is maximized exactly. Recently, however, we have developed a superior pixon basis for the image, the Fractal Pixon Basis (FPB). Unlike the Uniform Pixon Basis (UPB) of our 'Super-ME' method, the FPB basis is selected by employing fractal dimensional concepts to assess the inherent structure in the image. The Fractal Pixon Basis results in the best image reconstructions to date, superior to both UPB and the best ME reconstructions. In this paper, we review the theory of the UPB and FPB pixon and apply our methodology to the reconstruction of far-infrared imaging of the galaxy M51. The results of our reconstruction are compared to published reconstructions of the same data using the Lucy-Richardson algorithm, the Maximum Correlation Method developed at IPAC, and the MEMSYS ME algorithms. The results show that our reconstructed image has a spatial resolution a factor of two better than best previous methods (and a factor of 20 finer than the width of the point response function), and detects sources two orders of magnitude fainter than other methods.
Maximum-likelihood scintillation detection for EM-CCD based gamma cameras.
Korevaar, Marc A N; Goorden, Marlies C; Heemskerk, Jan W T; Beekman, Freek J
2011-08-07
Gamma cameras based on charge-coupled devices (CCDs) coupled to continuous scintillation crystals can combine a good detection efficiency with high spatial resolutions with the aid of advanced scintillation detection algorithms. A previously developed analytical multi-scale algorithm (MSA) models the depth-dependent light distribution but does not take statistics into account. Here we present and validate a novel statistical maximum-likelihood algorithm (MLA) that combines a realistic light distribution model with an experimentally validated statistical model. The MLA was tested for an electron multiplying CCD optically coupled to CsI(Tl) scintillators of different thicknesses. For (99m)Tc imaging, the spatial resolution (for perpendicular and oblique incidence), energy resolution and signal-to-background counts ratio (SBR) obtained with the MLA were compared with those of the MSA. Compared to the MSA, the MLA improves the energy resolution by more than a factor of 1.6 and the SBR is enhanced by more than a factor of 1.3. For oblique incidence (approximately 45°), the depth-of-interaction corrected spatial resolution is improved by a factor of at least 1.1, while for perpendicular incidence the MLA resolution does not consistently differ significantly from the MSA result for all tested scintillator thicknesses. For the thickest scintillator (3 mm, interaction probability 66% at 141 keV) a spatial resolution (perpendicular incidence) of 147 µm full width at half maximum (FWHM) was obtained with an energy resolution of 35.2% FWHM. These results of the MLA were achieved without prior calibration of scintillations as is needed for many statistical scintillation detection algorithms. We conclude that the MLA significantly improves the gamma camera performance compared to the MSA.
Detection of faint companions in multi-spectral data using a maximum likelihood approach
NASA Astrophysics Data System (ADS)
Hanley, Kenneth; Devaney, Nicholas; Thiébaut, Éric
2016-07-01
Direct, ground-based exoplanet detection is an extremely challenging task requiring extreme adaptive optics (AO) systems and very high contrast. Dedicated planet hunters, such as SPHERE and GPI have been designed with these requirements in mind. Despite this, direct detection is still limited due to the presence of residual speckles. Smith et al.1 described a maximum likelihood estimation technique for the detection of exoplanets in speckle data in which the planet appears to rotate about a host star when observing with an alt-az telescope. We propose the adaptation of this technique to operate on multi-spectral data, such as produced by the integral field spectrographs present on both SPHERE2 or GPI.3 As the speckle pattern approximately scales smoothly with wavelength, it is possible to resample data to a single reference wavelength in which speckles will remain fixed in the wavelength dimension while any companions that are present will exhibit radial motion in a predictable manner. We simulate data comparable to SPHERE and with this we compare the performance of our algorithm with another multi-spectral detection technique; spectral deconvolution. We compare the techniques using a ROC (Receiver Operating Characteristic) analysis.
Rall, Björn C; Latz, Ellen
2016-01-01
The potential of soils to naturally suppress inherent plant pathogens is an important ecosystem function. Usually, pathogen infection assays are used for estimating the suppressive potential of soils. In natural soils, however, co-occurring pathogens might simultaneously infect plants complicating the estimation of a focal pathogen's infection rate (initial slope of the infection-curve) as a measure of soil suppressiveness. Here, we present a method in R correcting for these unwanted effects by developing a two pathogen mono-molecular infection model. We fit the two pathogen mono-molecular infection model to data by using an integrative approach combining a numerical simulation of the model with an iterative maximum likelihood fit. We show that in presence of co-occurring pathogens using uncorrected data leads to a critical under- or overestimation of soil suppressiveness measures. In contrast, our new approach enables to precisely estimate soil suppressiveness measures such as plant infection rate and plant resistance time. Our method allows a correction of measured infection parameters that is necessary in case different pathogens are present. Moreover, our model can be (1) adapted to use other models such as the logistic or the Gompertz model; and (2) it could be extended by a facilitation parameter if infections in plants increase the susceptibility to new infections. We propose our method to be particularly useful for exploring soil suppressiveness of natural soils from different sites (e.g., in biodiversity experiments).
Maximum-Likelihood Estimation With a Contracting-Grid Search Algorithm
Hesterman, Jacob Y.; Caucci, Luca; Kupinski, Matthew A.; Barrett, Harrison H.; Furenlid, Lars R.
2010-01-01
A fast search algorithm capable of operating in multi-dimensional spaces is introduced. As a sample application, we demonstrate its utility in the 2D and 3D maximum-likelihood position-estimation problem that arises in the processing of PMT signals to derive interaction locations in compact gamma cameras. We demonstrate that the algorithm can be parallelized in pipelines, and thereby efficiently implemented in specialized hardware, such as field-programmable gate arrays (FPGAs). A 2D implementation of the algorithm is achieved in Cell/BE processors, resulting in processing speeds above one million events per second, which is a 20× increase in speed over a conventional desktop machine. Graphics processing units (GPUs) are used for a 3D application of the algorithm, resulting in processing speeds of nearly 250,000 events per second which is a 250× increase in speed over a conventional desktop machine. These implementations indicate the viability of the algorithm for use in real-time imaging applications. PMID:20824155
Maximum-likelihood q-estimator uncovers the role of potassium at neuromuscular junctions.
da Silva, A J; Trindade, M A S; Santos, D O C; Lima, R F
2016-02-01
Recently, we demonstrated the existence of nonextensive behavior in neuromuscular transmission (da Silva et al. in Phys Rev E 84:041925, 2011). In this letter, we first obtain a maximum-likelihood q-estimator to calculate the scale factor ([Formula: see text]) and the q-index of q-Gaussian distributions. Next, we use the indexes to analyze spontaneous miniature end plate potentials in electrophysiological recordings from neuromuscular junctions. These calculations were performed assuming both normal and high extracellular potassium concentrations [Formula: see text]. This protocol was used to test the validity of Tsallis statistics under electrophysiological conditions closely resembling physiological stimuli. The analysis shows that q-indexes are distinct depending on the extracellular potassium concentration. Our letter provides a general way to obtain the best estimate of parameters from a q-Gaussian distribution function. It also expands the validity of Tsallis statistics in realistic physiological stimulus conditions. In addition, we discuss the physical and physiological implications of these findings.
NASA Astrophysics Data System (ADS)
Saatci, Esra; Akan, Aydin
2010-12-01
We propose a procedure to estimate the model parameters of presented nonlinear Resistance-Capacitance (RC) and the widely used linear Resistance-Inductance-Capacitance (RIC) models of the respiratory system by Maximum Likelihood Estimator (MLE). The measurement noise is assumed to be Generalized Gaussian Distributed (GGD), and the variance and the shape factor of the measurement noise are estimated by MLE and Kurtosis method, respectively. The performance of the MLE algorithm is also demonstrated by the Cramer-Rao Lower Bound (CRLB) with artificially produced respiratory signals. Airway flow, mask pressure, and lung volume are measured from patients with Chronic Obstructive Pulmonary Disease (COPD) under the noninvasive ventilation and from healthy subjects. Simulations show that respiratory signals from healthy subjects are better represented by the RIC model compared to the nonlinear RC model. On the other hand, the Patient group respiratory signals are fitted to the nonlinear RC model with lower measurement noise variance, better converged measurement noise shape factor, and model parameter tracks. Also, it is observed that for the Patient group the shape factor of the measurement noise converges to values between 1 and 2 whereas for the Control group shape factor values are estimated in the super-Gaussian area.
Maximum-likelihood approaches reveal signatures of positive selection in IL genes in mammals.
Neves, Fabiana; Abrantes, Joana; Steinke, John W; Esteves, Pedro J
2014-02-01
ILs are part of the immune system and are involved in multiple biological activities. ILs have been shown to evolve under positive selection; however, little information exists regarding which codons are specifically selected. By using different codon-based maximum-likelihood (ML) approaches, signatures of positive selection in mammalian ILs were searched for. Sequences of 46 ILs were retrieved from publicly available databases of mammalian genomes to detect signatures of positive selection in individual codons. Evolutionary analyses were conducted under two ML frameworks, the HyPhy package implemented in the Data Monkey Web Server and CODEML implemented in PAML. Signatures of positive selection were found in 28 ILs: IL-1A and B; IL-2, IL-4 to IL-10, IL-12A and B; IL-14 to IL-17A and C; IL-18, IL-20 to IL-22, IL-25, IL-26, IL-27B, IL-31, IL-34, IL-36A; and G. Codons under positive selection varied between 1 and 15. No evidence of positive selection was detected in IL-13; IL-17B and F; IL-19, IL-23, IL-24, IL-27A; or IL-29. Most mammalian ILs have sites evolving under positive selection, which may be explained by the multitude of biological processes in which ILs are enrolled. The results obtained raise hypotheses concerning the ILs functions, which should be pursued by using mutagenesis and crystallographic approaches.
Gutenberg-Richter b-value maximum likelihood estimation and sample size
NASA Astrophysics Data System (ADS)
Nava, F. A.; Márquez-Ramírez, V. H.; Zúñiga, F. R.; Ávila-Barrientos, L.; Quinteros, C. B.
2017-01-01
The Aki-Utsu maximum likelihood method is widely used for estimation of the Gutenberg-Richter b-value, but not all authors are conscious of the method's limitations and implicit requirements. The Aki/Utsu method requires a representative estimate of the population mean magnitude; a requirement seldom satisfied in b-value studies, particularly in those that use data from small geographic and/or time windows, such as b-mapping and b-vs-time studies. Monte Carlo simulation methods are used to determine how large a sample is necessary to achieve representativity, particularly for rounded magnitudes. The size of a representative sample weakly depends on the actual b-value. It is shown that, for commonly used precisions, small samples give meaningless estimations of b. Our results give estimates on the probabilities of getting correct estimates of b for a given desired precision for samples of different sizes. We submit that all published studies reporting b-value estimations should include information about the size of the samples used.
Pearson-type goodness-of-fit test with bootstrap maximum likelihood estimation.
Yin, Guosheng; Ma, Yanyuan
2013-01-01
The Pearson test statistic is constructed by partitioning the data into bins and computing the difference between the observed and expected counts in these bins. If the maximum likelihood estimator (MLE) of the original data is used, the statistic generally does not follow a chi-squared distribution or any explicit distribution. We propose a bootstrap-based modification of the Pearson test statistic to recover the chi-squared distribution. We compute the observed and expected counts in the partitioned bins by using the MLE obtained from a bootstrap sample. This bootstrap-sample MLE adjusts exactly the right amount of randomness to the test statistic, and recovers the chi-squared distribution. The bootstrap chi-squared test is easy to implement, as it only requires fitting exactly the same model to the bootstrap data to obtain the corresponding MLE, and then constructs the bin counts based on the original data. We examine the test size and power of the new model diagnostic procedure using simulation studies and illustrate it with a real data set.
Pearson-type goodness-of-fit test with bootstrap maximum likelihood estimation
Yin, Guosheng; Ma, Yanyuan
2013-01-01
The Pearson test statistic is constructed by partitioning the data into bins and computing the difference between the observed and expected counts in these bins. If the maximum likelihood estimator (MLE) of the original data is used, the statistic generally does not follow a chi-squared distribution or any explicit distribution. We propose a bootstrap-based modification of the Pearson test statistic to recover the chi-squared distribution. We compute the observed and expected counts in the partitioned bins by using the MLE obtained from a bootstrap sample. This bootstrap-sample MLE adjusts exactly the right amount of randomness to the test statistic, and recovers the chi-squared distribution. The bootstrap chi-squared test is easy to implement, as it only requires fitting exactly the same model to the bootstrap data to obtain the corresponding MLE, and then constructs the bin counts based on the original data. We examine the test size and power of the new model diagnostic procedure using simulation studies and illustrate it with a real data set. PMID:23720703
NASA Technical Reports Server (NTRS)
Molusis, J. A.
1982-01-01
An on line technique is presented for the identification of rotor blade modal damping and frequency from rotorcraft random response test data. The identification technique is based upon a recursive maximum likelihood (RML) algorithm, which is demonstrated to have excellent convergence characteristics in the presence of random measurement noise and random excitation. The RML technique requires virtually no user interaction, provides accurate confidence bands on the parameter estimates, and can be used for continuous monitoring of modal damping during wind tunnel or flight testing. Results are presented from simulation random response data which quantify the identified parameter convergence behavior for various levels of random excitation. The data length required for acceptable parameter accuracy is shown to depend upon the amplitude of random response and the modal damping level. Random response amplitudes of 1.25 degrees to .05 degrees are investigated. The RML technique is applied to hingeless rotor test data. The inplane lag regressing mode is identified at different rotor speeds. The identification from the test data is compared with the simulation results and with other available estimates of frequency and damping.
MAGPI: A Framework for Maximum Likelihood MR Phase Imaging Using Multiple Receive Coils
Dagher, Joseph; Nael, Kambiz
2015-01-01
Purpose Combining MR phase images from multiple receive coils is a challenging problem, complicated by ambiguities introduced by phase wrapping, noise and the unknown phase-offset between the coils. Various techniques have been proposed to mitigate the effect of these ambiguities but most of the existing methods require additional reference scans and/or use ad-hoc post-processing techniques that do not guarantee any optimality. Theory and Methods Here, the phase estimation problem is formulated rigorously using a Maximum-Likelihood (ML) approach. The proposed framework jointly designs the acquisition-processing chain: the optimized pulse sequence is a single Multi-Echo Gradient Echo scan and the corresponding post-processing algorithm is a voxel-per-voxel ML estimator of the underlying tissue phase. Results Our proposed framework (MAGPI) achieves substantial improvements in the phase estimate, resulting in phase SNR gains by up to an order of magnitude compared to existing methods. Conclusion The advantages of MAGPI are: (1) ML-optimal combination of phase data from multiple receive coils, without a reference scan; (2) ML-optimal estimation of the underlying tissue phase, without the need for spatial processing; and (3) robust dynamic estimation of channel-dependent phase-offsets. PMID:25946426
Evolutionary analysis of apolipoprotein E by Maximum Likelihood and complex network methods
Benevides, Leandro de Jesus; de Carvalho, Daniel Santana; Andrade, Roberto Fernandes Silva; Bomfim, Gilberto Cafezeiro; Fernandes, Flora Maria de Campos
2016-01-01
Abstract Apolipoprotein E (apo E) is a human glycoprotein with 299 amino acids, and it is a major component of very low density lipoproteins (VLDL) and a group of high-density lipoproteins (HDL). Phylogenetic studies are important to clarify how various apo E proteins are related in groups of organisms and whether they evolved from a common ancestor. Here, we aimed at performing a phylogenetic study on apo E carrying organisms. We employed a classical and robust method, such as Maximum Likelihood (ML), and compared the results using a more recent approach based on complex networks. Thirty-two apo E amino acid sequences were downloaded from NCBI. A clear separation could be observed among three major groups: mammals, fish and amphibians. The results obtained from ML method, as well as from the constructed networks showed two different groups: one with mammals only (C1) and another with fish (C2), and a single node with the single sequence available for an amphibian. The accordance in results from the different methods shows that the complex networks approach is effective in phylogenetic studies. Furthermore, our results revealed the conservation of apo E among animal groups. PMID:27560837
Bit Error Probability for Maximum Likelihood Decoding of Linear Block Codes
NASA Technical Reports Server (NTRS)
Lin, Shu; Fossorier, Marc P. C.; Rhee, Dojun
1996-01-01
In this paper, the bit error probability P(sub b) for maximum likelihood decoding of binary linear codes is investigated. The contribution of each information bit to P(sub b) is considered. For randomly generated codes, it is shown that the conventional approximation at high SNR P(sub b) is approximately equal to (d(sub H)/N)P(sub s), where P(sub s) represents the block error probability, holds for systematic encoding only. Also systematic encoding provides the minimum P(sub b) when the inverse mapping corresponding to the generator matrix of the code is used to retrieve the information sequence. The bit error performances corresponding to other generator matrix forms are also evaluated. Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for decoding methods which require a generator matrix with a particular structure such as trellis decoding or algebraic-based soft decision decoding, equivalent schemes that reduce the bit error probability are discussed.
Latz, Ellen
2016-01-01
The potential of soils to naturally suppress inherent plant pathogens is an important ecosystem function. Usually, pathogen infection assays are used for estimating the suppressive potential of soils. In natural soils, however, co-occurring pathogens might simultaneously infect plants complicating the estimation of a focal pathogen’s infection rate (initial slope of the infection-curve) as a measure of soil suppressiveness. Here, we present a method in R correcting for these unwanted effects by developing a two pathogen mono-molecular infection model. We fit the two pathogen mono-molecular infection model to data by using an integrative approach combining a numerical simulation of the model with an iterative maximum likelihood fit. We show that in presence of co-occurring pathogens using uncorrected data leads to a critical under- or overestimation of soil suppressiveness measures. In contrast, our new approach enables to precisely estimate soil suppressiveness measures such as plant infection rate and plant resistance time. Our method allows a correction of measured infection parameters that is necessary in case different pathogens are present. Moreover, our model can be (1) adapted to use other models such as the logistic or the Gompertz model; and (2) it could be extended by a facilitation parameter if infections in plants increase the susceptibility to new infections. We propose our method to be particularly useful for exploring soil suppressiveness of natural soils from different sites (e.g., in biodiversity experiments). PMID:27833800
NASA Technical Reports Server (NTRS)
Murphy, P. C.; Klein, V.
1984-01-01
Improved techniques for estimating airplane stability and control derivatives and their standard errors are presented. A maximum likelihood estimation algorithm is developed which relies on an optimization scheme referred to as a modified Newton-Raphson scheme with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared to integrating the analytically-determined sensitivity equations or using a finite difference scheme. An aircraft estimation problem is solved using real flight data to compare MNRES with the commonly used modified Newton-Raphson technique; MNRES is found to be faster and more generally applicable. Parameter standard errors are determined using a random search technique. The confidence intervals obtained are compared with Cramer-Rao lower bounds at the same confidence level. It is observed that the nonlinearity of the cost function is an important factor in the relationship between Cramer-Rao bounds and the error bounds determined by the search technique.
NASA Astrophysics Data System (ADS)
McNicholl, Patrick J.; Crabtree, Peter N.
2014-09-01
Applications of stellar occultation by solar system objects have a long history for determining universal time, detecting binary stars, and providing estimates of sizes of asteroids and minor planets. More recently, extension of this last application has been proposed as a technique to provide information (if not complete shadow images) of geosynchronous satellites. Diffraction has long been recognized as a source of distortion for such occultation measurements, and models subsequently developed to compensate for this degradation. Typically these models employ a knife-edge assumption for the obscuring body. In this preliminary study, we report on the fundamental limitations of knife-edge position estimates due to shot noise in an otherwise idealized measurement. In particular, we address the statistical bounds, both Cramér- Rao and Hammersley-Chapman-Robbins, on the uncertainty in the knife-edge position measurement, as well as the performance of the maximum-likelihood estimator. Results are presented as a function of both stellar magnitude and sensor passband; the limiting case of infinite resolving power is also explored.
NASA Astrophysics Data System (ADS)
Kim, Sunghee; Seo, Dong-Jun; Riazi, Hamideh; Shin, Changmin
2014-11-01
An ensemble data assimilation (DA) procedure is developed and evaluated for the Hydrologic Simulation Program - Fortran (HSPF), a widely used watershed water quality model. The procedure aims at improving the accuracy of short-range water quality prediction by updating the model initial conditions (IC) based on real-time observations of hydrologic and water quality variables. The observations assimilated include streamflow, biochemical oxygen demand (BOD), dissolved oxygen (DO), chlorophyll a (CHL-a), nitrate (NO3), phosphate (PO4) and water temperature (TW). The DA procedure uses the maximum likelihood ensemble filter (MLEF), which is capable of handling both nonlinear model dynamics and nonlinear observation equations, in a fixed-lag smoother formulation. For evaluation, the DA procedure was applied to the Kumho Catchment of the Nakdong River Basin in the Republic of Korea. A set of performance measures was used to evaluate analysis and prediction of streamflow and water quality variables. To remove systematic errors in the model simulation originating from structural and parametric errors, a parsimonious bias correction procedure is incorporated into the observation equation. The results show that the DA procedure substantially improves predictive skill for most variables; reduction in root mean square error ranges from 11% to 60% for Day-1 through 3 predictions for all observed variables except DO. It is seen that MLEF handles highly nonlinear hydrologic and biochemical observation equations very well, and that it is an effective DA technique for water quality forecasting.
NASA Astrophysics Data System (ADS)
Kim, S.; Riazi, H.; Shin, C.; Seo, D.
2013-12-01
Due to the large dimensionality of the state vector and sparsity of observations, the initial conditions (IC) of water quality models are subject to large uncertainties. To reduce the IC uncertainties in operational water quality forecasting, an ensemble data assimilation (DA) procedure for the Hydrologic Simulation Program - Fortran (HSPF) model has been developed and evaluated for the Kumho River Subcatchment of the Nakdong River Basin in Korea. The procedure, referred to herein as MLEF-HSPF, uses maximum likelihood ensemble filter (MLEF) which combines strengths of variational assimilation (VAR) and ensemble Kalman filter (EnKF). The Control variables involved in the DA procedure include the bias correction factors for mean areal precipitation and mean areal potential evaporation, the hydrologic state variables, and the water quality state variables such as water temperature, dissolved oxygen (DO), biochemical oxygen demand (BOD), ammonium (NH4), nitrate (NO3), phosphate (PO4) and chlorophyll a (CHL-a). Due to the very large dimensionality of the inverse problem, accurately specifying the parameters for the DA procdedure is a challenge. Systematic sensitivity analysis is carried out for identifying the optimal parameter settings. To evaluate the robustness of MLEF-HSPF, we use multiple subcatchments of the Nakdong River Basin. In evaluation, we focus on the performance of MLEF-HSPF on prediction of extreme water quality events.
NASA Technical Reports Server (NTRS)
Howell, Leonard W., Jr.; Six, N. Frank (Technical Monitor)
2002-01-01
The Maximum Likelihood (ML) statistical theory required to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments is developed in this paper. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral information based on the combination of data sets. The procedure is of significant value to both existing data sets and those to be produced by future astrophysics missions consisting of two or more detectors by allowing instrument developers to optimize each detector's design parameters through simulation studies in order to design and build complementary detectors that will maximize the precision with which the science objectives may be obtained. The benefits of this ML theory and its application is measured in terms of the reduction of the statistical errors (standard deviations) of the spectra information using the multiple data sets in concert as compared to the statistical errors of the spectra information when the data sets are considered separately, as well as any biases resulting from poor statistics in one or more of the individual data sets that might be reduced when the data sets are combined.
Bao, C.; Hanany, S.; Baccigalupi, C.; Gold, B.; Jaffe, A.; Stompor, R.
2016-03-01
We extend a general maximum likelihood foreground estimation for cosmic microwave background (CMB) polarization data to include estimation of instrumental systematic effects. We focus on two particular effects: frequency band measurement uncertainty and instrumentally induced frequency dependent polarization rotation. We assess the bias induced on the estimation of the B-mode polarization signal by these two systematic effects in the presence of instrumental noise and uncertainties in the polarization and spectral index of Galactic dust. Degeneracies between uncertainties in the band and polarization angle calibration measurements and in the dust spectral index and polarization increase the uncertainty in the extracted CMB B-mode power, and may give rise to a biased estimate. We provide a quantitative assessment of the potential bias and increased uncertainty in an example experimental configuration. For example, we find that with 10% polarized dust, a tensor to scalar ratio of r = 0.05, and the instrumental configuration of the E and B experiment balloon payload, the estimated CMB B-mode power spectrum is recovered without bias when the frequency band measurement has 5% uncertainty or less, and the polarization angle calibration has an uncertainty of up to 4°.
Maximum-Likelihood Adaptive Filter for Partially Observed Boolean Dynamical Systems
NASA Astrophysics Data System (ADS)
Imani, Mahdi; Braga-Neto, Ulisses M.
2017-01-01
Partially-observed Boolean dynamical systems (POBDS) are a general class of nonlinear models with application in estimation and control of Boolean processes based on noisy and incomplete measurements. The optimal minimum mean square error (MMSE) algorithms for POBDS state estimation, namely, the Boolean Kalman filter (BKF) and Boolean Kalman smoother (BKS), are intractable in the case of large systems, due to computational and memory requirements. To address this, we propose approximate MMSE filtering and smoothing algorithms based on the auxiliary particle filter (APF) method from sequential Monte-Carlo theory. These algorithms are used jointly with maximum-likelihood (ML) methods for simultaneous state and parameter estimation in POBDS models. In the presence of continuous parameters, ML estimation is performed using the expectation-maximization (EM) algorithm; we develop for this purpose a special smoother which reduces the computational complexity of the EM algorithm. The resulting particle-based adaptive filter is applied to a POBDS model of Boolean gene regulatory networks observed through noisy RNA-Seq time series data, and performance is assessed through a series of numerical experiments using the well-known cell cycle gene regulatory model.
Chan, Aaron C.; Srinivasan, Vivek J.
2013-01-01
In optical coherence tomography (OCT) and ultrasound, unbiased Doppler frequency estimators with low variance are desirable for blood velocity estimation. Hardware improvements in OCT mean that ever higher acquisition rates are possible, which should also, in principle, improve estimation performance. Paradoxically, however, the widely used Kasai autocorrelation estimator’s performance worsens with increasing acquisition rate. We propose that parametric estimators based on accurate models of noise statistics can offer better performance. We derive a maximum likelihood estimator (MLE) based on a simple additive white Gaussian noise model, and show that it can outperform the Kasai autocorrelation estimator. In addition, we also derive the Cramer Rao lower bound (CRLB), and show that the variance of the MLE approaches the CRLB for moderate data lengths and noise levels. We note that the MLE performance improves with longer acquisition time, and remains constant or improves with higher acquisition rates. These qualities may make it a preferred technique as OCT imaging speed continues to improve. Finally, our work motivates the development of more general parametric estimators based on statistical models of decorrelation noise. PMID:23446044
NASA Astrophysics Data System (ADS)
Huang, Jinxin; Yuan, Qun; Tankam, Patrice; Clarkson, Eric; Kupinski, Matthew; Hindman, Holly B.; Aquavella, James V.; Rolland, Jannick P.
2015-03-01
In biophotonics imaging, one important and quantitative task is layer-thickness estimation. In this study, we investigate the approach of combining optical coherence tomography and a maximum-likelihood (ML) estimator for layer thickness estimation in the context of tear film imaging. The motivation of this study is to extend our understanding of tear film dynamics, which is the prerequisite to advance the management of Dry Eye Disease, through the simultaneous estimation of the thickness of the tear film lipid and aqueous layers. The estimator takes into account the different statistical processes associated with the imaging chain. We theoretically investigated the impact of key system parameters, such as the axial point spread functions (PSF) and various sources of noise on measurement uncertainty. Simulations show that an OCT system with a 1 μm axial PSF (FWHM) allows unbiased estimates down to nanometers with nanometer precision. In implementation, we built a customized Fourier domain OCT system that operates in the 600 to 1000 nm spectral window and achieves 0.93 micron axial PSF in corneal epithelium. We then validated the theoretical framework with physical phantoms made of custom optical coatings, with layer thicknesses from tens of nanometers to microns. Results demonstrate unbiased nanometer-class thickness estimates in three different physical phantoms.
Maximum likelihood estimation of proton irradiated field and deposited dose distribution.
Inaniwa, Taku; Kohno, Toshiyuki; Yamagata, Fumiko; Tomitani, Takehiro; Sato, Shinji; Kanazawa, Mitsutaka; Kanai, Tatsuaki; Urakabe, Eriko
2007-05-01
In proton therapy, it is important to evaluate the field irradiated with protons and the deposited dose distribution in a patient's body. Positron emitters generated through fragmentation reactions of target nuclei can be used for this purpose. By detecting the annihilation gamma rays from the positron emitters, the annihilation gamma ray distribution can be obtained which has information about the quantities essential to proton therapy. In this study, we performed irradiation experiments with mono-energetic proton beams of 160 MeV and the spread-out Bragg peak beams to three kinds of targets. The annihilation events were detected with a positron camera for 500 s after the irradiation and the annihilation gamma ray distributions were obtained. In order to evaluate the range and the position of distal and proximal edges of the SOBP, the maximum likelihood estimation (MLE) method was applied to the detected distributions. The evaluated values with the MLE method were compared with those estimated from the measured dose distributions. As a result, the ranges were determined with the difference between the MLE range and the experimental range less than 1.0 mm for all targets. For the SOBP beams, the positions of distal edges were determined with the difference less than 1.0 mm. On the other hand, the difference amounted to 7.9 mm for proximal edges.
Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors
NASA Technical Reports Server (NTRS)
Erkmen, Baris I.; Moision, Bruce E.
2010-01-01
Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.
Ibraheem, I
2015-02-01
Melanoma is a leading fatal illness responsible for 80% of deaths from skin cancer. It originates in the pigment-producing melanocytes in the basal layer of the epidermis. Melanocytes produce the melanin (the dark pigment), which is responsible for the color of skin. As all cancers, melanoma is caused by damage to the DNA of the cells, which causes the cell to grow out of control, leading to a tumor, which is much more dangerous if it cannot be found or detected early. Only biopsy can determine exact malformation diagnosis, although it can rise metastasizing. When a melanoma is suspected, the usual standard procedure is to perform a biopsy and to subsequently analyze the suspicious tissue under the microscope. In this paper, we provide a new approach using methods known as 'imaging spectroscopy' or 'spectral imaging' for early detection of melanoma using two different supervised classifier algorithms, maximum likelihood (ML) and spectral angle mapper (SAM). SAM rests on the spectral 'angular distances' and the conventional classifier ML rests on the spectral distance concept. The results show that the ML classifier was more efficient for pixel classification than SAM. However, SAM was more suitable for object classification. © 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Extended maximum likelihood halo-independent analysis of dark matter direct detection data
Gelmini, Graciela B.; Georgescu, Andreea; Huh, Ji-Haeng; Gondolo, Paolo E-mail: a.georgescu@physics.ucla.edu E-mail: jhhuh@physics.ucla.edu
2015-11-01
We extend and correct a recently proposed maximum-likelihood halo-independent method to analyze unbinned direct dark matter detection data. Instead of the recoil energy as independent variable we use the minimum speed a dark matter particle must have to impart a given recoil energy to a nucleus. This has the advantage of allowing us to apply the method to any type of target composition and interaction, e.g. with general momentum and velocity dependence, and with elastic or inelastic scattering. We prove the method and provide a rigorous statistical interpretation of the results. As first applications, we find that for dark matter particles with elastic spin-independent interactions and neutron to proton coupling ratio f{sub n}/f{sub p}=−0.7, the WIMP interpretation of the signal observed by CDMS-II-Si is compatible with the constraints imposed by all other experiments with null results. We also find a similar compatibility for exothermic inelastic spin-independent interactions with f{sub n}/f{sub p}=−0.8.
Sparse array 3-D ISAR imaging based on maximum likelihood estimation and CLEAN technique.
Ma, Changzheng; Yeo, Tat Soon; Tan, Chee Seng; Tan, Hwee Siang
2010-08-01
Large 2-D sparse array provides high angular resolution microwave images but artifacts are also induced by the high sidelobes of the beam pattern, thus, limiting its dynamic range. CLEAN technique has been used in the literature to extract strong scatterers for use in subsequent signal cancelation (artifacts removal). However, the performance of DFT parameters estimation based CLEAN algorithm for the estimation of the signal amplitudes is known to be poor, and this affects the signal cancelation. In this paper, DFT is used only to provide the initial estimates, and the maximum likelihood parameters estimation method with steepest descent implementation is then used to improve the precision of the calculated scatterers positions and amplitudes. Time domain information is also used to reduce the sidelobe levels. As a result, clear, artifact-free images could be obtained. The effects of multiple reflections and rotation speed estimation error are also discussed. The proposed method has been verified using numerical simulations and it has been shown to be effective.
Maximum likelihood estimation of proton irradiated field and deposited dose distribution
Inaniwa, Taku; Kohno, Toshiyuki; Yamagata, Fumiko; Tomitani, Takehiro; Sato, Shinji; Kanazawa, Mitsutaka; Kanai, Tatsuaki; Urakabe, Eriko
2007-05-15
In proton therapy, it is important to evaluate the field irradiated with protons and the deposited dose distribution in a patient's body. Positron emitters generated through fragmentation reactions of target nuclei can be used for this purpose. By detecting the annihilation gamma rays from the positron emitters, the annihilation gamma ray distribution can be obtained which has information about the quantities essential to proton therapy. In this study, we performed irradiation experiments with mono-energetic proton beams of 160 MeV and the spread-out Bragg peak beams to three kinds of targets. The annihilation events were detected with a positron camera for 500 s after the irradiation and the annihilation gamma ray distributions were obtained. In order to evaluate the range and the position of distal and proximal edges of the SOBP, the maximum likelihood estimation (MLE) method was applied to the detected distributions. The evaluated values with the MLE method were compared with those estimated from the measured dose distributions. As a result, the ranges were determined with the difference between the MLE range and the experimental range less than 1.0 mm for all targets. For the SOBP beams, the positions of distal edges were determined with the difference less than 1.0 mm. On the other hand, the difference amounted to 7.9 mm for proximal edges.
Mazza, Gina L; Enders, Craig K; Ruehlman, Linda S
2015-01-01
Often when participants have missing scores on one or more of the items comprising a scale, researchers compute prorated scale scores by averaging the available items. Methodologists have cautioned that proration may make strict assumptions about the mean and covariance structures of the items comprising the scale (Schafer & Graham, 2002 ; Graham, 2009 ; Enders, 2010 ). We investigated proration empirically and found that it resulted in bias even under a missing completely at random (MCAR) mechanism. To encourage researchers to forgo proration, we describe a full information maximum likelihood (FIML) approach to item-level missing data handling that mitigates the loss in power due to missing scale scores and utilizes the available item-level data without altering the substantive analysis. Specifically, we propose treating the scale score as missing whenever one or more of the items are missing and incorporating items as auxiliary variables. Our simulations suggest that item-level missing data handling drastically increases power relative to scale-level missing data handling. These results have important practical implications, especially when recruiting more participants is prohibitively difficult or expensive. Finally, we illustrate the proposed method with data from an online chronic pain management program.
Joint maximum likelihood estimation of activation and Hemodynamic Response Function for fMRI.
Bazargani, Negar; Nosratinia, Aria
2014-07-01
Blood Oxygen Level Dependent (BOLD) functional magnetic resonance imaging (fMRI) maps the brain activity by measuring blood oxygenation level, which is related to brain activity via a temporal impulse response function known as the Hemodynamic Response Function (HRF). The HRF varies from subject to subject and within areas of the brain, therefore a knowledge of HRF is necessary for accurately computing voxel activations. Conversely a knowledge of active voxels is highly beneficial for estimating the HRF. This work presents a joint maximum likelihood estimation of HRF and activation based on low-rank matrix approximations operating on regions of interest (ROI). Since each ROI has limited data, a smoothing constraint on the HRF is employed via Tikhonov regularization. The method is analyzed under both white noise and colored noise. Experiments with synthetic data show that accurate estimation of the HRF is possible with this method without prior assumptions on the exact shape of the HRF. Further experiments involving real fMRI experiments with auditory stimuli are used to validate the proposed method.
A New Maximum Likelihood Approach for Free Energy Profile Construction from Molecular Simulations
Lee, Tai-Sung; Radak, Brian K.; Pabis, Anna; York, Darrin M.
2013-01-01
A novel variational method for construction of free energy profiles from molecular simulation data is presented. The variational free energy profile (VFEP) method uses the maximum likelihood principle applied to the global free energy profile based on the entire set of simulation data (e.g from multiple biased simulations) that spans the free energy surface. The new method addresses common obstacles in two major problems usually observed in traditional methods for estimating free energy surfaces: the need for overlap in the re-weighting procedure and the problem of data representation. Test cases demonstrate that VFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct the overall free energy profiles. For typical chemical reactions, only ~5 windows and ~20-35 independent data points per window are sufficient to obtain an overall qualitatively correct free energy profile with sampling errors an order of magnitude smaller than the free energy barrier. The proposed approach thus provides a feasible mechanism to quickly construct the global free energy profile and identify free energy barriers and basins in free energy simulations via a robust, variational procedure that determines an analytic representation of the free energy profile without the requirement of numerically unstable histograms or binning procedures. It can serve as a new framework for biased simulations and is suitable to be used together with other methods to tackle with the free energy estimation problem. PMID:23457427
NASA Astrophysics Data System (ADS)
Zhao, Xiang; Lin, Jiming
2016-04-01
Image sensor-based visible light positioning can be applied not only to indoor environments but also to outdoor environments. To determine the performance bounds of the positioning accuracy from the view of statistical optimization for an outdoor image sensor-based visible light positioning system, we analyze and derive the maximum likelihood estimation and corresponding Cramér-Rao lower bounds of vehicle position, under the condition that the observation values of the light-emitting diode (LED) imaging points are affected by white Gaussian noise. For typical parameters of an LED traffic light and in-vehicle camera image sensor, simulation results show that accurate estimates are available, with positioning error generally less than 0.1 m at a communication distance of 30 m between the LED array transmitter and the camera receiver. With the communication distance being constant, the positioning accuracy depends on the number of LEDs used, the focal length of the lens, the pixel size, and the frame rate of the camera receiver.
Extended maximum likelihood halo-independent analysis of dark matter direct detection data
Gelmini, Graciela B.; Georgescu, Andreea; Gondolo, Paolo; Huh, Ji-Haeng
2015-11-24
We extend and correct a recently proposed maximum-likelihood halo-independent method to analyze unbinned direct dark matter detection data. Instead of the recoil energy as independent variable we use the minimum speed a dark matter particle must have to impart a given recoil energy to a nucleus. This has the advantage of allowing us to apply the method to any type of target composition and interaction, e.g. with general momentum and velocity dependence, and with elastic or inelastic scattering. We prove the method and provide a rigorous statistical interpretation of the results. As first applications, we find that for dark matter particles with elastic spin-independent interactions and neutron to proton coupling ratio f{sub n}/f{sub p}=−0.7, the WIMP interpretation of the signal observed by CDMS-II-Si is compatible with the constraints imposed by all other experiments with null results. We also find a similar compatibility for exothermic inelastic spin-independent interactions with f{sub n}/f{sub p}=−0.8.
NASA Technical Reports Server (NTRS)
Howell, Leonard W.
2002-01-01
The method of Maximum Likelihood (ML) is used to estimate the spectral parameters of an assumed broken power law energy spectrum from simulated detector responses. This methodology, which requires the complete specificity of all cosmic-ray detector design parameters, is shown to provide approximately unbiased, minimum variance, and normally distributed spectra information for events detected by an instrument having a wide range of commonly used detector response functions. The ML procedure, coupled with the simulated performance of a proposed space-based detector and its planned life cycle, has proved to be of significant value in the design phase of a new science instrument. The procedure helped make important trade studies in design parameters as a function of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose rigorous practical limits to the design envelope. This ML methodology is then generalized to estimate broken power law spectral parameters from real cosmic-ray data sets.
NASA Technical Reports Server (NTRS)
Murphy, P. C.; Klein, V.
1984-01-01
Improved techniques for estimating airplane stability and control derivatives and their standard errors are presented. A maximum likelihood estimation algorithm is developed which relies on an optimization scheme referred to as a modified Newton-Raphson scheme with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared to integrating the analytically-determined sensitivity equations or using a finite difference scheme. An aircraft estimation problem is solved using real flight data to compare MNRES with the commonly used modified Newton-Raphson technique; MNRES is found to be faster and more generally applicable. Parameter standard errors are determined using a random search technique. The confidence intervals obtained are compared with Cramer-Rao lower bounds at the same confidence level. It is observed that the nonlinearity of the cost function is an important factor in the relationship between Cramer-Rao bounds and the error bounds determined by the search technique.
NASA Astrophysics Data System (ADS)
Hung, Kwok-Wai; Siu, Wan-Chi
2013-10-01
Computationally scalable image interpolation algorithm is always desirable for software and hardware implementations on center processing unit (CPU), digital signal processor, field-programmable gate array, and low-cost hardware. A low-complexity, computationally scalable, and data-adaptive image interpolation algorithm that has a simple and homogeneous structure to efficiently scale the computation is proposed. Specifically, the image interpolation as a denoising problem is formulated by proposing a new image model to relate the observed low-resolution pixels and missing high-resolution pixels. Applying the maximum-likelihood estimation using the new image model results in an adaptive linear filter, where the filter coefficients depend on the local noise covariance matrix, which is estimated by local noise samples. Due to low overhead of the proposed interpolator, the overall computation efficiently scales with the number of noise samples. Experimental results show that the proposed scalable algorithm outperforms the state-of-the-art fast algorithms and achieves more than 36 frames per second for upscaling a 540 p (960×540) video to a 1080 p (1920×1080) video using multithreaded C++ software implementation on a PC system with Intel i7 950 3 GHz CPU.
Maximum penalized likelihood estimation in semiparametric mark-recapture-recovery models.
Michelot, Théo; Langrock, Roland; Kneib, Thomas; King, Ruth
2016-01-01
We discuss the semiparametric modeling of mark-recapture-recovery data where the temporal and/or individual variation of model parameters is explained via covariates. Typically, in such analyses a fixed (or mixed) effects parametric model is specified for the relationship between the model parameters and the covariates of interest. In this paper, we discuss the modeling of the relationship via the use of penalized splines, to allow for considerably more flexible functional forms. Corresponding models can be fitted via numerical maximum penalized likelihood estimation, employing cross-validation to choose the smoothing parameters in a data-driven way. Our contribution builds on and extends the existing literature, providing a unified inferential framework for semiparametric mark-recapture-recovery models for open populations, where the interest typically lies in the estimation of survival probabilities. The approach is applied to two real datasets, corresponding to gray herons (Ardea cinerea), where we model the survival probability as a function of environmental condition (a time-varying global covariate), and Soay sheep (Ovis aries), where we model the survival probability as a function of individual weight (a time-varying individual-specific covariate). The proposed semiparametric approach is compared to a standard parametric (logistic) regression and new interesting underlying dynamics are observed in both cases.
Object recognition and localization from 3D point clouds by maximum-likelihood estimation.
Dantanarayana, Harshana G; Huntley, Jonathan M
2017-08-01
We present an algorithm based on maximum-likelihood analysis for the automated recognition of objects, and estimation of their pose, from 3D point clouds. Surfaces segmented from depth images are used as the features, unlike 'interest point'-based algorithms which normally discard such data. Compared to the 6D Hough transform, it has negligible memory requirements, and is computationally efficient compared to iterative closest point algorithms. The same method is applicable to both the initial recognition/pose estimation problem as well as subsequent pose refinement through appropriate choice of the dispersion of the probability density functions. This single unified approach therefore avoids the usual requirement for different algorithms for these two tasks. In addition to the theoretical description, a simple 2 degrees of freedom (d.f.) example is given, followed by a full 6 d.f. analysis of 3D point cloud data from a cluttered scene acquired by a projected fringe-based scanner, which demonstrated an RMS alignment error as low as 0.3 mm.
Pražnikar, Jure; Turk, Dušan
2014-12-01
The refinement of a molecular model is a computational procedure by which the atomic model is fitted to the diffraction data. The commonly used target in the refinement of macromolecular structures is the maximum-likelihood (ML) function, which relies on the assessment of model errors. The current ML functions rely on cross-validation. They utilize phase-error estimates that are calculated from a small fraction of diffraction data, called the test set, that are not used to fit the model. An approach has been developed that uses the work set to calculate the phase-error estimates in the ML refinement from simulating the model errors via the random displacement of atomic coordinates. It is called ML free-kick refinement as it uses the ML formulation of the target function and is based on the idea of freeing the model from the model bias imposed by the chemical energy restraints used in refinement. This approach for the calculation of error estimates is superior to the cross-validation approach: it reduces the phase error and increases the accuracy of molecular models, is more robust, provides clearer maps and may use a smaller portion of data for the test set for the calculation of Rfree or may leave it out completely.
Pražnikar, Jure; Turk, Dušan
2014-01-01
The refinement of a molecular model is a computational procedure by which the atomic model is fitted to the diffraction data. The commonly used target in the refinement of macromolecular structures is the maximum-likelihood (ML) function, which relies on the assessment of model errors. The current ML functions rely on cross-validation. They utilize phase-error estimates that are calculated from a small fraction of diffraction data, called the test set, that are not used to fit the model. An approach has been developed that uses the work set to calculate the phase-error estimates in the ML refinement from simulating the model errors via the random displacement of atomic coordinates. It is called ML free-kick refinement as it uses the ML formulation of the target function and is based on the idea of freeing the model from the model bias imposed by the chemical energy restraints used in refinement. This approach for the calculation of error estimates is superior to the cross-validation approach: it reduces the phase error and increases the accuracy of molecular models, is more robust, provides clearer maps and may use a smaller portion of data for the test set for the calculation of R free or may leave it out completely. PMID:25478831
Berger, Simon A.; Krompass, Denis; Stamatakis, Alexandros
2011-01-01
We present an evolutionary placement algorithm (EPA) and a Web server for the rapid assignment of sequence fragments (short reads) to edges of a given phylogenetic tree under the maximum-likelihood model. The accuracy of the algorithm is evaluated on several real-world data sets and compared with placement by pair-wise sequence comparison, using edit distances and BLAST. We introduce a slow and accurate as well as a fast and less accurate placement algorithm. For the slow algorithm, we develop additional heuristic techniques that yield almost the same run times as the fast version with only a small loss of accuracy. When those additional heuristics are employed, the run time of the more accurate algorithm is comparable with that of a simple BLAST search for data sets with a high number of short query sequences. Moreover, the accuracy of the EPA is significantly higher, in particular when the sample of taxa in the reference topology is sparse or inadequate. Our algorithm, which has been integrated into RAxML, therefore provides an equally fast but more accurate alternative to BLAST for tree-based inference of the evolutionary origin and composition of short sequence reads. We are also actively developing a Web server that offers a freely available service for computing read placements on trees using the EPA. PMID:21436105
Gianfrancesco, Milena A.; Balzer, Laura; Taylor, Kimberly E.; Trupin, Laura; Nititham, Joanne; Seldin, Michael F.; Singer, Amanda Wheeler; Criswell, Lindsey A.; Barcellos, Lisa F.
2016-01-01
Systemic lupus erythematous (SLE) is a chronic autoimmune disease associated with genetic and environmental risk factors. However, the extent to which genetic risk is causally associated with disease activity is unknown. We utilized longitudinal targeted maximum likelihood estimation to estimate the causal association between a genetic risk score (GRS) comprised of 41 established SLE variants and clinically important disease activity as measured by the validated systemic lupus activity questionnaire (SLAQ) in a multi-ethnic cohort of 942 individuals with SLE. We did not find evidence of a clinically important SLAQ score difference (> 4.0) for individuals with a high GRS compared to those with a low GRS across nine timepoints after controlling for sex, ancestry, renal status, dialysis, disease duration, treatment, depression, smoking, and education, as well as time-dependent confounding of missing visits. Individual SNP analyses revealed that 12 of the 41 variants were significantly associated with clinically relevant changes in SLAQ scores across timepoints 8 and 9 after controlling for multiple testing. Results based on sophisticated causal modeling of longitudinal data in a large patient cohort suggest that individual SLE risk variants may influence disease activity over time. Our findings also emphasize a role for other biological or environmental factors. PMID:27467283
Gianfrancesco, M A; Balzer, L; Taylor, K E; Trupin, L; Nititham, J; Seldin, M F; Singer, A W; Criswell, L A; Barcellos, L F
2016-09-01
Systemic lupus erythematous (SLE) is a chronic autoimmune disease associated with genetic and environmental risk factors. However, the extent to which genetic risk is causally associated with disease activity is unknown. We utilized longitudinal-targeted maximum likelihood estimation to estimate the causal association between a genetic risk score (GRS) comprising 41 established SLE variants and clinically important disease activity as measured by the validated Systemic Lupus Activity Questionnaire (SLAQ) in a multiethnic cohort of 942 individuals with SLE. We did not find evidence of a clinically important SLAQ score difference (>4.0) for individuals with a high GRS compared with those with a low GRS across nine time points after controlling for sex, ancestry, renal status, dialysis, disease duration, treatment, depression, smoking and education, as well as time-dependent confounding of missing visits. Individual single-nucleotide polymorphism (SNP) analyses revealed that 12 of the 41 variants were significantly associated with clinically relevant changes in SLAQ scores across time points eight and nine after controlling for multiple testing. Results based on sophisticated causal modeling of longitudinal data in a large patient cohort suggest that individual SLE risk variants may influence disease activity over time. Our findings also emphasize a role for other biological or environmental factors.
Maximum likelihood-based analysis of single-molecule photon arrival trajectories
NASA Astrophysics Data System (ADS)
Hajdziona, Marta; Molski, Andrzej
2011-02-01
In this work we explore the statistical properties of the maximum likelihood-based analysis of one-color photon arrival trajectories. This approach does not involve binning and, therefore, all of the information contained in an observed photon strajectory is used. We study the accuracy and precision of parameter estimates and the efficiency of the Akaike information criterion and the Bayesian information criterion (BIC) in selecting the true kinetic model. We focus on the low excitation regime where photon trajectories can be modeled as realizations of Markov modulated Poisson processes. The number of observed photons is the key parameter in determining model selection and parameter estimation. For example, the BIC can select the true three-state model from competing two-, three-, and four-state kinetic models even for relatively short trajectories made up of 2 × 103 photons. When the intensity levels are well-separated and 104 photons are observed, the two-state model parameters can be estimated with about 10% precision and those for a three-state model with about 20% precision.
NASA Astrophysics Data System (ADS)
Gupta, Kinjal Dhar; Vilalta, Ricardo; Asadourian, Vicken; Macri, Lucas
2014-05-01
We describe an approach to automate the classification of Cepheid variable stars into two subtypes according to their pulsation mode. Automating such classification is relevant to obtain a precise determination of distances to nearby galaxies, which in addition helps reduce the uncertainty in the current expansion of the universe. One main difficulty lies in the compatibility of models trained using different galaxy datasets; a model trained using a training dataset may be ineffectual on a testing set. A solution to such difficulty is to adapt predictive models across domains; this is necessary when the training and testing sets do not follow the same distribution. The gist of our methodology is to train a predictive model on a nearby galaxy (e.g., Large Magellanic Cloud), followed by a model-adaptation step to make the model operable on other nearby galaxies. We follow a parametric approach to density estimation by modeling the training data (anchor galaxy) using a mixture of linear models. We then use maximum likelihood to compute the right amount of variable displacement, until the testing data closely overlaps the training data. At that point, the model can be directly used in the testing data (target galaxy).
A New Maximum Likelihood Approach for Free Energy Profile Construction from Molecular Simulations.
Lee, Tai-Sung; Radak, Brian K; Pabis, Anna; York, Darrin M
2013-01-08
A novel variational method for construction of free energy profiles from molecular simulation data is presented. The variational free energy profile (VFEP) method uses the maximum likelihood principle applied to the global free energy profile based on the entire set of simulation data (e.g from multiple biased simulations) that spans the free energy surface. The new method addresses common obstacles in two major problems usually observed in traditional methods for estimating free energy surfaces: the need for overlap in the re-weighting procedure and the problem of data representation. Test cases demonstrate that VFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct the overall free energy profiles. For typical chemical reactions, only ~5 windows and ~20-35 independent data points per window are sufficient to obtain an overall qualitatively correct free energy profile with sampling errors an order of magnitude smaller than the free energy barrier. The proposed approach thus provides a feasible mechanism to quickly construct the global free energy profile and identify free energy barriers and basins in free energy simulations via a robust, variational procedure that determines an analytic representation of the free energy profile without the requirement of numerically unstable histograms or binning procedures. It can serve as a new framework for biased simulations and is suitable to be used together with other methods to tackle with the free energy estimation problem.
Maximum likelihood estimation of parameterized 3-D surfaces using a moving camera
NASA Technical Reports Server (NTRS)
Hung, Y.; Cernuschi-Frias, B.; Cooper, D. B.
1987-01-01
A new approach is introduced to estimating object surfaces in three-dimensional space from a sequence of images. A surface of interest here is modeled as a 3-D function known up to the values of a few parameters. The approach will work with any parameterization. However, in work to date researchers have modeled objects as patches of spheres, cylinders, and planes - primitive objects. These primitive surfaces are special cases of 3-D quadric surfaces. Primitive surface estimation is treated as the general problem of maximum likelihood parameter estimation based on two or more functionally related data sets. In the present case, these data sets constitute a sequence of images taken at different locations and orientations. A simple geometric explanation is given for the estimation algorithm. Though various techniques can be used to implement this nonlinear estimation, researches discuss the use of gradient descent. Experiments are run and discussed for the case of a sphere of unknown location. These experiments graphically illustrate the various advantages of using as many images as possible in the estimation and of distributing camera positions from first to last over as large a baseline as possible. Researchers introduce the use of asymptotic Bayesian approximations in order to summarize the useful information in a sequence of images, thereby drastically reducing both the storage and amount of processing required.
Efficient Levenberg-Marquardt minimization of the maximum likelihood estimator for Poisson deviates
Laurence, T; Chromy, B
2009-11-10
Histograms of counted events are Poisson distributed, but are typically fitted without justification using nonlinear least squares fitting. The more appropriate maximum likelihood estimator (MLE) for Poisson distributed data is seldom used. We extend the use of the Levenberg-Marquardt algorithm commonly used for nonlinear least squares minimization for use with the MLE for Poisson distributed data. In so doing, we remove any excuse for not using this more appropriate MLE. We demonstrate the use of the algorithm and the superior performance of the MLE using simulations and experiments in the context of fluorescence lifetime imaging. Scientists commonly form histograms of counted events from their data, and extract parameters by fitting to a specified model. Assuming that the probability of occurrence for each bin is small, event counts in the histogram bins will be distributed according to the Poisson distribution. We develop here an efficient algorithm for fitting event counting histograms using the maximum likelihood estimator (MLE) for Poisson distributed data, rather than the non-linear least squares measure. This algorithm is a simple extension of the common Levenberg-Marquardt (L-M) algorithm, is simple to implement, quick and robust. Fitting using a least squares measure is most common, but it is the maximum likelihood estimator only for Gaussian-distributed data. Non-linear least squares methods may be applied to event counting histograms in cases where the number of events is very large, so that the Poisson distribution is well approximated by a Gaussian. However, it is not easy to satisfy this criterion in practice - which requires a large number of events. It has been well-known for years that least squares procedures lead to biased results when applied to Poisson-distributed data; a recent paper providing extensive characterization of these biases in exponential fitting is given. The more appropriate measure based on the maximum likelihood estimator (MLE
NASA Technical Reports Server (NTRS)
Stepner, D. E.; Mehra, R. K.
1973-01-01
A new method of extracting aircraft stability and control derivatives from flight test data is developed based on the maximum likelihood cirterion. It is shown that this new method is capable of processing data from both linear and nonlinear models, both with and without process noise and includes output error and equation error methods as special cases. The first application of this method to flight test data is reported for lateral maneuvers of the HL-10 and M2/F3 lifting bodies, including the extraction of stability and control derivatives in the presence of wind gusts. All the problems encountered in this identification study are discussed. Several different methods (including a priori weighting, parameter fixing and constrained parameter values) for dealing with identifiability and uniqueness problems are introduced and the results given. The method for the design of optimal inputs for identifying the parameters of linear dynamic systems is also given. The criterion used for the optimization is the sensitivity of the system output to the unknown parameters. Several simple examples are first given and then the results of an extensive stability and control dervative identification simulation for a C-8 aircraft are detailed.
NASA Technical Reports Server (NTRS)
Howell, Leonard W., Jr.; Six, N. Frank (Technical Monitor)
2002-01-01
The Maximum Likelihood (ML) statistical theory required to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments is developed in this paper. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral information based on the combination of data sets. The procedure is of significant value to both existing data sets and those to be produced by future astrophysics missions consisting of two or more detectors by allowing instrument developers to optimize each detector's design parameters through simulation studies in order to design and build complementary detectors that will maximize the precision with which the science objectives may be obtained. The benefits of this ML theory and its application is measured in terms of the reduction of the statistical errors (standard deviations) of the spectra information using the multiple data sets in concert as compared to the statistical errors of the spectra information when the data sets are considered separately, as well as any biases resulting from poor statistics in one or more of the individual data sets that might be reduced when the data sets are combined.
Maximum Likelihood Implementation of an Isolation-with-Migration Model for Three Species.
Dalquen, Daniel A; Zhu, Tianqi; Yang, Ziheng
2017-05-01
We develop a maximum likelihood (ML) method for estimating migration rates between species using genomic sequence data. A species tree is used to accommodate the phylogenetic relationships among three species, allowing for migration between the two sister species, while the third species is used as an out-group. A Markov chain characterization of the genealogical process of coalescence and migration is used to integrate out the migration histories at each locus analytically, whereas Gaussian quadrature is used to integrate over the coalescent times on each genealogical tree numerically. This is an extension of our early implementation of the symmetrical isolation-with-migration model for three species to accommodate arbitrary loci with two or three sequences per locus and to allow asymmetrical migration rates. Our implementation can accommodate tens of thousands of loci, making it feasible to analyze genome-scale data sets to test for gene flow. We calculate the posterior probabilities of gene trees at individual loci to identify genomic regions that are likely to have been transferred between species due to gene flow. We conduct a simulation study to examine the statistical properties of the likelihood ratio test for gene flow between the two in-group species and of the ML estimates of model parameters such as the migration rate. Inclusion of data from a third out-group species is found to increase dramatically the power of the test and the precision of parameter estimation. We compiled and analyzed several genomic data sets from the Drosophila fruit flies. Our analyses suggest no migration from D. melanogaster to D. simulans, and a significant amount of gene flow from D. simulans to D. melanogaster, at the rate of ~0.02 migrant individuals per generation. We discuss the utility of the multispecies coalescent model for species tree estimation, accounting for incomplete lineage sorting and migration. © The Author(s) 2016. Published by Oxford University Press, on
Rius, Jordi
2006-09-01
The maximum-likelihood method is applied to direct methods to derive a more general probability density function of the triple-phase sums which is capable of predicting negative values. This study also proves that maximization of the origin-free modulus sum function S yields, within the limitations imposed by the assumed approximations, the maximum-likelihood estimates of the phases. It thus represents the formal theoretical justification of the S function that was initially derived from Patterson-function arguments [Rius (1993). Acta Cryst. A49, 406-409].
NASA Technical Reports Server (NTRS)
Mccallister, R. D.; Crawford, J. J.
1981-01-01
It is pointed out that the NASA 30/20 GHz program will place in geosynchronous orbit a technically advanced communication satellite which can process time-division multiple access (TDMA) information bursts with a data throughput in excess of 4 GBPS. To guarantee acceptable data quality during periods of signal attenuation it will be necessary to provide a significant forward error correction (FEC) capability. Convolutional decoding (utilizing the maximum-likelihood techniques) was identified as the most attractive FEC strategy. Design trade-offs regarding a maximum-likelihood convolutional decoder (MCD) in a single-chip CMOS implementation are discussed.
Beyond maximum entropy: Fractal pixon-based image reconstruction
NASA Technical Reports Server (NTRS)
Puetter, R. C.; Pina, R. K.
1994-01-01
We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other methods, including Goodness-of-Fit (e.g. Least-Squares and Lucy-Richardson) and Maximum Entropy (ME). Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME.
Beyond maximum entropy: Fractal pixon-based image reconstruction
NASA Technical Reports Server (NTRS)
Puetter, R. C.; Pina, R. K.
1994-01-01
We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other methods, including Goodness-of-Fit (e.g. Least-Squares and Lucy-Richardson) and Maximum Entropy (ME). Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME.
Estimating the Effect of Competition on Trait Evolution Using Maximum Likelihood Inference.
Drury, Jonathan; Clavel, Julien; Manceau, Marc; Morlon, Hélène
2016-07-01
Many classical ecological and evolutionary theoretical frameworks posit that competition between species is an important selective force. For example, in adaptive radiations, resource competition between evolving lineages plays a role in driving phenotypic diversification and exploration of novel ecological space. Nevertheless, current models of trait evolution fit to phylogenies and comparative data sets are not designed to incorporate the effect of competition. The most advanced models in this direction are diversity-dependent models where evolutionary rates depend on lineage diversity. However, these models still treat changes in traits in one branch as independent of the value of traits on other branches, thus ignoring the effect of species similarity on trait evolution. Here, we consider a model where the evolutionary dynamics of traits involved in interspecific interactions are influenced by species similarity in trait values and where we can specify which lineages are in sympatry. We develop a maximum likelihood based approach to fit this model to combined phylogenetic and phenotypic data. Using simulations, we demonstrate that the approach accurately estimates the simulated parameter values across a broad range of parameter space. Additionally, we develop tools for specifying the biogeographic context in which trait evolution occurs. In order to compare models, we also apply these biogeographic methods to specify which lineages interact sympatrically for two diversity-dependent models. Finally, we fit these various models to morphological data from a classical adaptive radiation (Greater Antillean Anolis lizards). We show that models that account for competition and geography perform better than other models. The matching competition model is an important new tool for studying the influence of interspecific interactions, in particular competition, on phenotypic evolution. More generally, it constitutes a step toward a better integration of interspecific
Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information
NASA Technical Reports Server (NTRS)
Howell, L. W., Jr.
2003-01-01
A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.
Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors
NASA Astrophysics Data System (ADS)
Langbein, John
2017-08-01
Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1/f^{α } with frequency, f. With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013. doi: 10.1007/s00190-012-0605-0) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.
Curtis, Gary P.; Lu, Dan; Ye, Ming
2015-01-01
While Bayesian model averaging (BMA) has been widely used in groundwater modeling, it is infrequently applied to groundwater reactive transport modeling because of multiple sources of uncertainty in the coupled hydrogeochemical processes and because of the long execution time of each model run. To resolve these problems, this study analyzed different levels of uncertainty in a hierarchical way, and used the maximum likelihood version of BMA, i.e., MLBMA, to improve the computational efficiency. This study demonstrates the applicability of MLBMA to groundwater reactive transport modeling in a synthetic case in which twenty-seven reactive transport models were designed to predict the reactive transport of hexavalent uranium (U(VI)) based on observations at a former uranium mill site near Naturita, CO. These reactive transport models contain three uncertain model components, i.e., parameterization of hydraulic conductivity, configuration of model boundary, and surface complexation reactions that simulate U(VI) adsorption. These uncertain model components were aggregated into the alternative models by integrating a hierarchical structure into MLBMA. The modeling results of the individual models and MLBMA were analyzed to investigate their predictive performance. The predictive logscore results show that MLBMA generally outperforms the best model, suggesting that using MLBMA is a sound strategy to achieve more robust model predictions relative to a single model. MLBMA works best when the alternative models are structurally distinct and have diverse model predictions. When correlation in model structure exists, two strategies were used to improve predictive performance by retaining structurally distinct models or assigning smaller prior model probabilities to correlated models. Since the synthetic models were designed using data from the Naturita site, the results of this study are expected to provide guidance for real-world modeling. Limitations of applying MLBMA to the
NASA Astrophysics Data System (ADS)
Rizzo, R. E.; Healy, D.; De Siena, L.
2015-12-01
The success of any model prediction is largely dependent on the accuracy with which its parameters are known. In characterising fracture networks in naturally fractured rocks, the main issues are related with the difficulties in accurately up- and down-scaling the parameters governing the distribution of fracture attributes. Optimal characterisation and analysis of fracture attributes (fracture lengths, apertures, orientations and densities) represents a fundamental step which can aid the estimation of permeability and fluid flow, which are of primary importance in a number of contexts ranging from hydrocarbon production in fractured reservoirs and reservoir stimulation by hydrofracturing, to geothermal energy extraction and deeper Earth systems, such as earthquakes and ocean floor hydrothermal venting. This work focuses on linking fracture data collected directly from outcrops to permeability estimation and fracture network modelling. Outcrop studies can supplement the limited data inherent to natural fractured systems in the subsurface. The study area is a highly fractured upper Miocene biosiliceous mudstone formation cropping out along the coastline north of Santa Cruz (California, USA). These unique outcrops exposes a recently active bitumen-bearing formation representing a geological analogue of a fractured top seal. In order to validate field observations as useful analogues of subsurface reservoirs, we describe a methodology of statistical analysis for more accurate probability distribution of fracture attributes, using Maximum Likelihood Estimators. These procedures aim to understand whether the average permeability of a fracture network can be predicted reducing its uncertainties, and if outcrop measurements of fracture attributes can be used directly to generate statistically identical fracture network models.
Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors
NASA Astrophysics Data System (ADS)
Langbein, John
2017-02-01
Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1/f^{α } with frequency, f. With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013. doi: 10.1007/s00190-012-0605-0) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.
Fusion of hyperspectral and lidar data based on dimension reduction and maximum likelihood
NASA Astrophysics Data System (ADS)
Abbasi, B.; Arefi, H.; Bigdeli, B.; Motagh, M.; Roessner, S.
2015-04-01
Limitations and deficiencies of different remote sensing sensors in extraction of different objects caused fusion of data from different sensors to become more widespread for improving classification results. Using a variety of data which are provided from different sensors, increase the spatial and the spectral accuracy. Lidar (Light Detection and Ranging) data fused together with hyperspectral images (HSI) provide rich data for classification of the surface objects. Lidar data representing high quality geometric information plays a key role for segmentation and classification of elevated features such as buildings and trees. On the other hand, hyperspectral data containing high spectral resolution would support high distinction between the objects having different spectral information such as soil, water, and grass. This paper presents a fusion methodology on Lidar and hyperspectral data for improving classification accuracy in urban areas. In first step, we applied feature extraction strategies on each data separately. In this step, texture features based on GLCM (Grey Level Co-occurrence Matrix) from Lidar data and PCA (Principal Component Analysis) and MNF (Minimum Noise Fraction) based dimension reduction methods for HSI are generated. In second step, a Maximum Likelihood (ML) based classification method is applied on each feature spaces. Finally, a fusion method is applied to fuse the results of classification. A co-registered hyperspectral and Lidar data from University of Houston was utilized to examine the result of the proposed method. This data contains nine classes: Building, Tree, Grass, Soil, Water, Road, Parking, Tennis Court and Running Track. Experimental investigation proves the improvement of classification accuracy to 88%.
Schwab, Joshua; Gruber, Susan; Blaser, Nello; Schomaker, Michael; van der Laan, Mark
2015-01-01
This paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates, and a possibly time-dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention-specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because the true shape of this function is rarely known, the marginal structural model is used as a working model. The causal quantity of interest is defined as the projection of the true function onto this working model. Iterated conditional expectation double robust estimators for marginal structural model parameters were previously proposed by Robins (2000, 2002) and Bang and Robins (2005). Here we build on this work and present a pooled TMLE for the parameters of marginal structural working models. We compare this pooled estimator to a stratified TMLE (Schnitzer et al. 2014) that is based on estimating the intervention-specific mean separately for each intervention of interest. The performance of the pooled TMLE is compared to the performance of the stratified TMLE and the performance of inverse probability weighted (IPW) estimators using simulations. Concepts are illustrated using an example in which the aim is to estimate the causal effect of delayed switch following immunological failure of first line antiretroviral therapy among HIV-infected patients. Data from the International Epidemiological Databases to Evaluate AIDS, Southern Africa are analyzed to investigate this question using both TML and IPW estimators. Our results demonstrate practical advantages of the
Lu, Dan; Ye, Ming; Curtis, Gary P.
2015-08-01
While Bayesian model averaging (BMA) has been widely used in groundwater modeling, it is infrequently applied to groundwater reactive transport modeling because of multiple sources of uncertainty in the coupled hydrogeochemical processes and because of the long execution time of each model run. To resolve these problems, this study analyzed different levels of uncertainty in a hierarchical way, and used the maximum likelihood version of BMA, i.e., MLBMA, to improve the computational efficiency. Our study demonstrates the applicability of MLBMA to groundwater reactive transport modeling in a synthetic case in which twenty-seven reactive transport models were designed to predict the reactive transport of hexavalent uranium (U(VI)) based on observations at a former uranium mill site near Naturita, CO. Moreover, these reactive transport models contain three uncertain model components, i.e., parameterization of hydraulic conductivity, configuration of model boundary, and surface complexation reactions that simulate U(VI) adsorption. These uncertain model components were aggregated into the alternative models by integrating a hierarchical structure into MLBMA. The modeling results of the individual models and MLBMA were analyzed to investigate their predictive performance. The predictive logscore results show that MLBMA generally outperforms the best model, suggesting that using MLBMA is a sound strategy to achieve more robust model predictions relative to a single model. MLBMA works best when the alternative models are structurally distinct and have diverse model predictions. When correlation in model structure exists, two strategies were used to improve predictive performance by retaining structurally distinct models or assigning smaller prior model probabilities to correlated models. Since the synthetic models were designed using data from the Naturita site, the results of this study are expected to provide guidance for real-world modeling. Finally, limitations of
NASA Astrophysics Data System (ADS)
Keenan, Michael R.
2005-07-01
Many modern surface analytical instruments are able to acquire huge amounts of data in the form of spectral images. Time-of-flight secondary ion mass spectrometry (TOF-SIMS), for instance, can easily generate a complete mass spectrum at each point in a two-dimensional or three-dimensional spatial array. The challenge for the data analyst, then, is to garner the analytically useful information from the overwhelming quantity of raw spectral data. Factor analysis techniques such as principal component analysis (PCA) have proven quite useful in this endeavor. Standard PCA, however, assumes that noise in the data is uniform, that is, that it does not depend on the magnitude of signal. This is clearly not correct for methods that rely on particle counting where the noise is governed by Poisson statistics. In this case, properly accounting for heteroscedasticity is essential to extracting the chemical information into a minimum number of factors while optimally excluding noise. Maximum likelihood PCA (MLPCA) is one approach to addressing this issue. MLPCA can, in principle, incorporate a separate uncertainty estimate for each individual observation in a data set. This article will present a MLPCA analysis of a simple and intuitive TOF-SIMS spectral image. The results show that there is a trade-off between the number of uncertainty parameters included in the model and the quality of each and, in fact, using poor estimates may be worse than ignoring the noise characteristics altogether. The best results were obtained by using a low-rank approximation to the noise rather than individual estimates. MLPCA will also be compared with an optimal scaling approach. For the particular example given, the added benefits of MLPCA do not outweigh the greatly increased computational demands of the technique.
Analysis of Rayleigh waves with circular wavefront: a maximum likelihood approach
NASA Astrophysics Data System (ADS)
Maranò, Stefano; Hobiger, Manuel; Bergamo, Paolo; Fäh, Donat
2017-09-01
Analysis of Rayleigh waves is an important task in seismology and geotechnical investigations. In fact, properties of Rayleigh waves such as velocity and polarization are important observables that carry information about the structure of the subsoil. Applications analysing Rayleigh waves include active and passive seismic surveys. In active surveys, there is a controlled source of seismic energy and the sensors are typically placed near the source. In passive surveys, there is not a controlled source, rather, seismic waves from ambient vibrations are analysed and the sources are assumed to be far outside the array, simplifying the analysis by the assumption of plane waves. Whenever the source is in the proximity of the array of sensors or even within the array it is necessary to model the wave propagation accounting for the circular wavefront. In addition, it is also necessary to model the amplitude decay due to geometrical spreading. This is the case of active seismic surveys in which sensors are located near the seismic source. In this work, we propose a maximum likelihood (ML) approach for the analysis of Rayleigh waves generated at a near source. Our statistical model accounts for the curvature of the wavefront and amplitude decay due to geometrical spreading. Using our method, we show applications on real data of the retrieval of Rayleigh wave dispersion and ellipticity. We employ arrays with arbitrary geometry. Furthermore, we show how it is possible to combine active and passive surveys. This enables us to enlarge the analysable frequency range and therefore the depths investigated. We retrieve properties of Rayleigh waves from both active and passive surveys and show the excellent agreement of the results from the two surveys. In our approach we use the same array of sensors for both the passive and the active survey. This greatly simplifies the logistics necessary to perform a survey.
Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors
Langbein, John O.
2017-01-01
Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1/fα">1/fα1/fα with frequency, f. With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013. doi:10.1007/s00190-012-0605-0) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.
Fast maximum likelihood estimation using continuous-time neural point process models.
Lepage, Kyle Q; MacDonald, Christopher J
2015-06-01
A recent report estimates that the number of simultaneously recorded neurons is growing exponentially. A commonly employed statistical paradigm using discrete-time point process models of neural activity involves the computation of a maximum-likelihood estimate. The time to computate this estimate, per neuron, is proportional to the number of bins in a finely spaced discretization of time. By using continuous-time models of neural activity and the optimally efficient Gaussian quadrature, memory requirements and computation times are dramatically decreased in the commonly encountered situation where the number of parameters p is much less than the number of time-bins n. In this regime, with q equal to the quadrature order, memory requirements are decreased from O(np) to O(qp), and the number of floating-point operations are decreased from O(np(2)) to O(qp(2)). Accuracy of the proposed estimates is assessed based upon physiological consideration, error bounds, and mathematical results describing the relation between numerical integration error and numerical error affecting both parameter estimates and the observed Fisher information. A check is provided which is used to adapt the order of numerical integration. The procedure is verified in simulation and for hippocampal recordings. It is found that in 95 % of hippocampal recordings a q of 60 yields numerical error negligible with respect to parameter estimate standard error. Statistical inference using the proposed methodology is a fast and convenient alternative to statistical inference performed using a discrete-time point process model of neural activity. It enables the employment of the statistical methodology available with discrete-time inference, but is faster, uses less memory, and avoids any error due to discretization.
Concept for estimating mitochondrial DNA haplogroups using a maximum likelihood approach (EMMA).
Röck, Alexander W; Dür, Arne; van Oven, Mannis; Parson, Walther
2013-12-01
The assignment of haplogroups to mitochondrial DNA haplotypes contributes substantial value for quality control, not only in forensic genetics but also in population and medical genetics. The availability of Phylotree, a widely accepted phylogenetic tree of human mitochondrial DNA lineages, led to the development of several (semi-)automated software solutions for haplogrouping. However, currently existing haplogrouping tools only make use of haplogroup-defining mutations, whereas private mutations (beyond the haplogroup level) can be additionally informative allowing for enhanced haplogroup assignment. This is especially relevant in the case of (partial) control region sequences, which are mainly used in forensics. The present study makes three major contributions toward a more reliable, semi-automated estimation of mitochondrial haplogroups. First, a quality-controlled database consisting of 14,990 full mtGenomes downloaded from GenBank was compiled. Together with Phylotree, these mtGenomes serve as a reference database for haplogroup estimates. Second, the concept of fluctuation rates, i.e. a maximum likelihood estimation of the stability of mutations based on 19,171 full control region haplotypes for which raw lane data is available, is presented. Finally, an algorithm for estimating the haplogroup of an mtDNA sequence based on the combined database of full mtGenomes and Phylotree, which also incorporates the empirically determined fluctuation rates, is brought forward. On the basis of examples from the literature and EMPOP, the algorithm is not only validated, but both the strength of this approach and its utility for quality control of mitochondrial haplotypes is also demonstrated. Copyright © 2013 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.
Concept for estimating mitochondrial DNA haplogroups using a maximum likelihood approach (EMMA)☆
Röck, Alexander W.; Dür, Arne; van Oven, Mannis; Parson, Walther
2013-01-01
The assignment of haplogroups to mitochondrial DNA haplotypes contributes substantial value for quality control, not only in forensic genetics but also in population and medical genetics. The availability of Phylotree, a widely accepted phylogenetic tree of human mitochondrial DNA lineages, led to the development of several (semi-)automated software solutions for haplogrouping. However, currently existing haplogrouping tools only make use of haplogroup-defining mutations, whereas private mutations (beyond the haplogroup level) can be additionally informative allowing for enhanced haplogroup assignment. This is especially relevant in the case of (partial) control region sequences, which are mainly used in forensics. The present study makes three major contributions toward a more reliable, semi-automated estimation of mitochondrial haplogroups. First, a quality-controlled database consisting of 14,990 full mtGenomes downloaded from GenBank was compiled. Together with Phylotree, these mtGenomes serve as a reference database for haplogroup estimates. Second, the concept of fluctuation rates, i.e. a maximum likelihood estimation of the stability of mutations based on 19,171 full control region haplotypes for which raw lane data is available, is presented. Finally, an algorithm for estimating the haplogroup of an mtDNA sequence based on the combined database of full mtGenomes and Phylotree, which also incorporates the empirically determined fluctuation rates, is brought forward. On the basis of examples from the literature and EMPOP, the algorithm is not only validated, but both the strength of this approach and its utility for quality control of mitochondrial haplotypes is also demonstrated. PMID:23948335
NASA Technical Reports Server (NTRS)
Murphy, Patrick Charles
1985-01-01
An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.
Maximum likelihood estimation of linkage disequilibrium in half-sib families.
Gomez-Raya, L
2012-05-01
Maximum likelihood methods for the estimation of linkage disequilibrium between biallelic DNA-markers in half-sib families (half-sib method) are developed for single and multifamily situations. Monte Carlo computer simulations were carried out for a variety of scenarios regarding sire genotypes, linkage disequilibrium, recombination fraction, family size, and number of families. A double heterozygote sire was simulated with recombination fraction of 0.00, linkage disequilibrium among dams of δ=0.10, and alleles at both markers segregating at intermediate frequencies for a family size of 500. The average estimates of δ were 0.17, 0.25, and 0.10 for Excoffier and Slatkin (1995), maternal informative haplotypes, and the half-sib method, respectively. A multifamily EM algorithm was tested at intermediate frequencies by computer simulation. The range of the absolute difference between estimated and simulated δ was between 0.000 and 0.008. A cattle half-sib family was genotyped with the Illumina 50K BeadChip. There were 314,730 SNP pairs for which the sire was a homo-heterozygote with average estimates of r2 of 0.115, 0.067, and 0.111 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. There were 208,872 SNP pairs for which the sire was double heterozygote with average estimates of r2 across the genome of 0.100, 0.267, and 0.925 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. Genome analyses for all possible sire genotypes with 829,042 tests showed that ignoring half-sib family structure leads to upward biased estimates of linkage disequilibrium. Published inferences on population structure and evolution of cattle should be revisited after accommodating existing half-sib family structure in the estimation of linkage disequilibrium.
Maximum Likelihood Estimation of Linkage Disequilibrium in Half-Sib Families
Gomez-Raya, L.
2012-01-01
Maximum likelihood methods for the estimation of linkage disequilibrium between biallelic DNA-markers in half-sib families (half-sib method) are developed for single and multifamily situations. Monte Carlo computer simulations were carried out for a variety of scenarios regarding sire genotypes, linkage disequilibrium, recombination fraction, family size, and number of families. A double heterozygote sire was simulated with recombination fraction of 0.00, linkage disequilibrium among dams of δ = 0.10, and alleles at both markers segregating at intermediate frequencies for a family size of 500. The average estimates of δ were 0.17, 0.25, and 0.10 for Excoffier and Slatkin (1995), maternal informative haplotypes, and the half-sib method, respectively. A multifamily EM algorithm was tested at intermediate frequencies by computer simulation. The range of the absolute difference between estimated and simulated δ was between 0.000 and 0.008. A cattle half-sib family was genotyped with the Illumina 50K BeadChip. There were 314,730 SNP pairs for which the sire was a homo-heterozygote with average estimates of r2 of 0.115, 0.067, and 0.111 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. There were 208,872 SNP pairs for which the sire was double heterozygote with average estimates of r2 across the genome of 0.100, 0.267, and 0.925 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. Genome analyses for all possible sire genotypes with 829,042 tests showed that ignoring half-sib family structure leads to upward biased estimates of linkage disequilibrium. Published inferences on population structure and evolution of cattle should be revisited after accommodating existing half-sib family structure in the estimation of linkage disequilibrium. PMID:22377635
Lu, Dan; Ye, Ming; Curtis, Gary P.
2015-08-01
While Bayesian model averaging (BMA) has been widely used in groundwater modeling, it is infrequently applied to groundwater reactive transport modeling because of multiple sources of uncertainty in the coupled hydrogeochemical processes and because of the long execution time of each model run. To resolve these problems, this study analyzed different levels of uncertainty in a hierarchical way, and used the maximum likelihood version of BMA, i.e., MLBMA, to improve the computational efficiency. Our study demonstrates the applicability of MLBMA to groundwater reactive transport modeling in a synthetic case in which twenty-seven reactive transport models were designed to predict themore » reactive transport of hexavalent uranium (U(VI)) based on observations at a former uranium mill site near Naturita, CO. Moreover, these reactive transport models contain three uncertain model components, i.e., parameterization of hydraulic conductivity, configuration of model boundary, and surface complexation reactions that simulate U(VI) adsorption. These uncertain model components were aggregated into the alternative models by integrating a hierarchical structure into MLBMA. The modeling results of the individual models and MLBMA were analyzed to investigate their predictive performance. The predictive logscore results show that MLBMA generally outperforms the best model, suggesting that using MLBMA is a sound strategy to achieve more robust model predictions relative to a single model. MLBMA works best when the alternative models are structurally distinct and have diverse model predictions. When correlation in model structure exists, two strategies were used to improve predictive performance by retaining structurally distinct models or assigning smaller prior model probabilities to correlated models. Since the synthetic models were designed using data from the Naturita site, the results of this study are expected to provide guidance for real-world modeling. Finally
Limit Distribution Theory for Maximum Likelihood Estimation of a Log-Concave Density.
Balabdaoui, Fadoua; Rufibach, Kaspar; Wellner, Jon A
2009-06-01
We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, i.e. a density of the form f(0) = exp varphi(0) where varphi(0) is a concave function on R. Existence, form, characterizations and uniform rates of convergence of the MLE are given by Rufibach (2006) and Dümbgen and Rufibach (2007). The characterization of the log-concave MLE in terms of distribution functions is the same (up to sign) as the characterization of the least squares estimator of a convex density on [0, infinity) as studied by Groeneboom, Jongbloed and Wellner (2001b). We use this connection to show that the limiting distributions of the MLE and its derivative are, under comparable smoothness assumptions, the same (up to sign) as in the convex density estimation problem. In particular, changing the smoothness assumptions of Groeneboom, Jongbloed and Wellner (2001b) slightly by allowing some higher derivatives to vanish at the point of interest, we find that the pointwise limiting distributions depend on the second and third derivatives at 0 of H(k), the "lower invelope" of an integrated Brownian motion process minus a drift term depending on the number of vanishing derivatives of varphi(0) = log f(0) at the point of interest. We also establish the limiting distribution of the resulting estimator of the mode M(f(0)) and establish a new local asymptotic minimax lower bound which shows the optimality of our mode estimator in terms of both rate of convergence and dependence of constants on population values.
Maximum likelihood fitting of tidal streams with application to the Sagittarius dwarf tidal tails
NASA Astrophysics Data System (ADS)
Cole, Nathan
2009-06-01
A maximum likelihood method for determining the spatial properties of tidal debris and of the Galactic spheroid is presented. Over small spatial extent, the tidal debris is modeled as a cylinder with density that falls off as a Gaussian with distance from its axis while the smooth component of the stellar spheroid is modeled as a Hernquist profile. The method is designed to use 2.5° wide stripes of data that follow great circles across the sky in which the tidal debris within each stripe is fit separately. A probabilistic separation technique which allows for the extraction of the optimized tidal streams from the input data set is presented. This technique allows for the creation of separate catalogs for each component fit in the stellar spheroid: one catalog for each piece of tidal debris that fits the density profile of the debris and a single catalog which fits the density profile of the smooth stellar spheroid component. This separation technique is proven to be effective by extracting the simulated tidal debris from the simulated datasets. A method to determine the statistical errors is also developed which utilizes a Hessian matrix to determine the width of the peak at the maximum of the likelihood surface. This error analysis method serves as a means of testing the the algorithm with regard to the simulated datasets as well as determining the statistical errors of the optimizations over observational data. An heuristic method is also defined for determining the numerical error in the optimizations. The maximum likelihood algorithm is then used to optimize spatial data taken from the Sloan Digital Sky Survey. Stars having the color of blue F turnoff stars 0.1 < ( g - r ) 0 < 0.3 and ( u - g ) 0 > 0.4 are extracted from the Sloan Digital Sky Survey database. In the algorithm, the absolute magnitude distribution of F turnoff stars is modeled as a Gaussian distribution, which is an improvement over previous methods which utilize a fixed absolute magnitude M g 0
Regularization parameter selection for penalized-likelihood list-mode image reconstruction in PET
NASA Astrophysics Data System (ADS)
Zhang, Mengxi; Zhou, Jian; Niu, Xiaofeng; Asma, Evren; Wang, Wenli; Qi, Jinyi
2017-06-01
Penalized likelihood (PL) reconstruction has demonstrated potential to improve image quality of positron emission tomography (PET) over unregularized ordered-subsets expectation-maximization (OSEM) algorithm. However, selecting proper regularization parameters in PL reconstruction has been challenging due to the lack of ground truth and variation of penalty functions. Here we present a method to choose regularization parameters using a cross-validation log-likelihood (CVLL) function. This new method does not require any knowledge of the true image and is directly applicable to list-mode PET data. We performed statistical analysis of the mean and variance of the CVLL. The results show that the CVLL provides an unbiased estimate of the log-likelihood function calculated using the noise free data. The predicted variance can be used to verify the statistical significance of the difference between CVLL values. The proposed method was validated using simulation studies and also applied to real patient data. The reconstructed images using optimum parameters selected by the proposed method show good image quality visually.
Regularization parameter selection for penalized-likelihood list-mode image reconstruction in PET.
Zhang, Mengxi; Zhou, Jian; Niu, Xiaofeng; Asma, Evren; Wang, Wenli; Qi, Jinyi
2017-06-21
Penalized likelihood (PL) reconstruction has demonstrated potential to improve image quality of positron emission tomography (PET) over unregularized ordered-subsets expectation-maximization (OSEM) algorithm. However, selecting proper regularization parameters in PL reconstruction has been challenging due to the lack of ground truth and variation of penalty functions. Here we present a method to choose regularization parameters using a cross-validation log-likelihood (CVLL) function. This new method does not require any knowledge of the true image and is directly applicable to list-mode PET data. We performed statistical analysis of the mean and variance of the CVLL. The results show that the CVLL provides an unbiased estimate of the log-likelihood function calculated using the noise free data. The predicted variance can be used to verify the statistical significance of the difference between CVLL values. The proposed method was validated using simulation studies and also applied to real patient data. The reconstructed images using optimum parameters selected by the proposed method show good image quality visually.
NASA Technical Reports Server (NTRS)
Walker, H. F.
1976-01-01
Likelihood equations determined by the two types of samples which are necessary conditions for a maximum-likelihood estimate were considered. These equations suggest certain successive approximations iterative procedures for obtaining maximum likelihood estimates. The procedures, which are generalized steepest ascent (deflected gradient) procedures, contain those of Hosmer as a special case.
ERIC Educational Resources Information Center
Rijmen, Frank
2009-01-01
Maximum marginal likelihood estimation of multidimensional item response theory (IRT) models has been hampered by the calculation of the multidimensional integral over the ability distribution. However, the researcher often has a specific hypothesis about the conditional (in)dependence relations among the latent variables. Exploiting these…
ERIC Educational Resources Information Center
Beauducel, Andre; Herzberg, Philipp Yorck
2006-01-01
This simulation study compared maximum likelihood (ML) estimation with weighted least squares means and variance adjusted (WLSMV) estimation. The study was based on confirmatory factor analyses with 1, 2, 4, and 8 factors, based on 250, 500, 750, and 1,000 cases, and on 5, 10, 20, and 40 variables with 2, 3, 4, 5, and 6 categories. There was no…
ERIC Educational Resources Information Center
Kieftenbeld, Vincent; Natesan, Prathiba
2012-01-01
Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…
Zhaxybayeva, Olga; Gogarten, J Peter
2002-01-01
Background Horizontal gene transfer (HGT) played an important role in shaping microbial genomes. In addition to genes under sporadic selection, HGT also affects housekeeping genes and those involved in information processing, even ribosomal RNA encoding genes. Here we describe tools that provide an assessment and graphic illustration of the mosaic nature of microbial genomes. Results We adapted the Maximum Likelihood (ML) mapping to the analyses of all detected quartets of orthologous genes found in four genomes. We have automated the assembly and analyses of these quartets of orthologs given the selection of four genomes. We compared the ML-mapping approach to more rigorous Bayesian probability and Bootstrap mapping techniques. The latter two approaches appear to be more conservative than the ML-mapping approach, but qualitatively all three approaches give equivalent results. All three tools were tested on mitochondrial genomes, which presumably were inherited as a single linkage group. Conclusions In some instances of interphylum relationships we find nearly equal numbers of quartets strongly supporting the three possible topologies. In contrast, our analyses of genome quartets containing the cyanobacterium Synechocystis sp. indicate that a large part of the cyanobacterial genome is related to that of low GC Gram positives. Other groups that had been suggested as sister groups to the cyanobacteria contain many fewer genes that group with the Synechocystis orthologs. Interdomain comparisons of genome quartets containing the archaeon Halobacterium sp. revealed that Halobacterium sp. shares more genes with Bacteria that live in the same environment than with Bacteria that are more closely related based on rRNA phylogeny . Many of these genes encode proteins involved in substrate transport and metabolism and in information storage and processing. The performed analyses demonstrate that relationships among prokaryotes cannot be accurately depicted by or inferred from
Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information
NASA Technical Reports Server (NTRS)
Howell, L. W.
2002-01-01
A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from
Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction
NASA Astrophysics Data System (ADS)
Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng
2012-11-01
We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constraint involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the PAPA. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality.
Williams, O. R.; Bennett, K.; Much, R.; Schoenfelder, V.; Blom, J. J.; Ryan, J.
1997-05-10
The maximum likelihood-ratio method is frequently used in COMPTEL analysis to determine the significance of a point source at a given location. In this paper we do not consider whether the likelihood-ratio at a particular location indicates a detection, but rather whether distributions of likelihood-ratios derived from many locations depart from that expected for source free data. We have constructed distributions of likelihood-ratios by reading values from standard COMPTEL maximum-likelihood ratio maps at positions corresponding to the locations of different categories of AGN. Distributions derived from the locations of Seyfert galaxies are indistinguishable, according to a Kolmogorov-Smirnov test, from those obtained from ''random'' locations, but differ slightly from those obtained from the locations of flat spectrum radio loud quasars, OVVs, and BL Lac objects. This difference is not due to known COMPTEL sources, since regions near these sources are excluded from the analysis. We suggest that it might arise from a number of sources with fluxes below the COMPTEL detection threshold.
A maximum entropy reconstruction technique for tomographic particle image velocimetry
NASA Astrophysics Data System (ADS)
Bilsky, A. V.; Lozhkin, V. A.; Markovich, D. M.; Tokarev, M. P.
2013-04-01
This paper studies a novel approach for reducing tomographic PIV computational complexity. The proposed approach is an algebraic reconstruction technique, termed MENT (maximum entropy). This technique computes the three-dimensional light intensity distribution several times faster than SMART, using at least ten times less memory. Additionally, the reconstruction quality remains nearly the same as with SMART. This paper presents the theoretical computation performance comparison for MENT, SMART and MART, followed by validation using synthetic particle images. Both the theoretical assessment and validation of synthetic images demonstrate significant computational time reduction. The data processing accuracy of MENT was compared to that of SMART in a slot jet experiment. A comparison of the average velocity profiles shows a high level of agreement between the results obtained with MENT and those obtained with SMART.
Inverting ion images without Abel inversion: maximum entropy reconstruction of velocity maps.
Dick, Bernhard
2014-01-14
A new method for the reconstruction of velocity maps from ion images is presented, which is based on the maximum entropy concept. In contrast to other methods used for Abel inversion the new method never applies an inversion or smoothing to the data. Instead, it iteratively finds the map which is the most likely cause for the observed data, using the correct likelihood criterion for data sampled from a Poissonian distribution. The entropy criterion minimizes the information content in this map, which hence contains no information for which there is no evidence in the data. Two implementations are proposed, and their performance is demonstrated with simulated and experimental data: Maximum Entropy Velocity Image Reconstruction (MEVIR) obtains a two-dimensional slice through the velocity distribution and can be compared directly to Abel inversion. Maximum Entropy Velocity Legendre Reconstruction (MEVELER) finds one-dimensional distribution functions Q(l)(v) in an expansion of the velocity distribution in Legendre polynomials P((cos θ) for the angular dependence. Both MEVIR and MEVELER can be used for the analysis of ion images with intensities as low as 0.01 counts per pixel, with MEVELER performing significantly better than MEVIR for images with low intensity. Both methods perform better than pBASEX, in particular for images with less than one average count per pixel.
Comparison of sinogram- and image-domain penalized-likelihood image reconstruction estimators.
Vargas, Phillip A; La Rivière, Patrick J
2011-08-01
In recent years, the authors and others have been exploring the use of penalized-likelihood sinogram-domain smoothing and restoration approaches for emission and transmission tomography. The motivation for this strategy was initially pragmatic: to provide a more computationally feasible alternative to fully iterative penalized-likelihood image reconstruction involving expensive backprojections and reprojections, while still obtaining some of the benefits of the statistical modeling employed in penalized-likelihood approaches. In this work, the authors seek to compare the two approaches in greater detail. The sinogram-domain strategy entails estimating the "ideal" line integrals needed for reconstruction of an activity or attenuation distribution from the set of noisy, potentially degraded tomographic measurements by maximizing a penalized-likelihood objective function. The objective function models the data statistics as well as any degradation that can be represented in the sinogram domain. The estimated line integrals can then be input to analytic reconstruction algorithms such as filtered backprojection (FBP). The authors compare this to fully iterative approaches maximizing similar objective functions. The authors present mathematical analyses based on so-called equivalent optimization problems that establish that the approaches can be made precisely equivalent under certain restrictive conditions. More significantly, by use of resolution-variance tradeoff studies, the authors show that they can yield very similar performance under more relaxed, realistic conditions. The sinogram- and image-domain approaches are equivalent under certain restrictive conditions and can perform very similarly under more relaxed conditions. The match is particularly good for fully sampled, high-resolution CT geometries. One limitation of the sinogram-domain approach relative to the image-domain approach is the difficulty of imposing additional constraints, such as image non-negativity.
Harbert, Robert S; Nixon, Kevin C
2015-08-01
• Plant distributions have long been understood to be correlated with the environmental conditions to which species are adapted. Climate is one of the major components driving species distributions. Therefore, it is expected that the plants coexisting in a community are reflective of the local environment, particularly climate.• Presented here is a method for the estimation of climate from local plant species coexistence data. The method, Climate Reconstruction Analysis using Coexistence Likelihood Estimation (CRACLE), is a likelihood-based method that employs specimen collection data at a global scale for the inference of species climate tolerance. CRACLE calculates the maximum joint likelihood of coexistence given individual species climate tolerance characterization to estimate the expected climate.• Plant distribution data for more than 4000 species were used to show that this method accurately infers expected climate profiles for 165 sites with diverse climatic conditions. Estimates differ from the WorldClim global climate model by less than 1.5°C on average for mean annual temperature and less than ∼250 mm for mean annual precipitation. This is a significant improvement upon other plant-based climate-proxy methods.• CRACLE validates long hypothesized interactions between climate and local associations of plant species. Furthermore, CRACLE successfully estimates climate that is consistent with the widely used WorldClim model and therefore may be applied to the quantitative estimation of paleoclimate in future studies. © 2015 Botanical Society of America, Inc.
Chen, Y
2015-06-15
Purpose: To improve the quality of kV X-ray cone beam CT (CBCT) for use in radiotherapy delivery assessment and re-planning by using penalized likelihood (PL) iterative reconstruction and auto-segmentation accuracy of the resulting CBCTs as an image quality metric. Methods: Present filtered backprojection (FBP) CBCT reconstructions can be improved upon by PL reconstruction with image formation models and appropriate regularization constraints. We use two constraints: 1) image smoothing via an edge preserving filter, and 2) a constraint minimizing the differences between the reconstruction and a registered prior image. Reconstructions of prostate therapy CBCTs were computed with constraint 1 alone and with both constraints. The prior images were planning CTs(pCT) deformable-registered to the FBP reconstructions. Anatomy segmentations were done using atlas-based auto-segmentation (Elekta ADMIRE). Results: We observed small but consistent improvements in the Dice similarity coefficients of PL reconstructions over the FBP results, and additional small improvements with the added prior image constraint. For a CBCT with anatomy very similar in appearance to the pCT, we observed these changes in the Dice metric: +2.9% (prostate), +8.6% (rectum), −1.9% (bladder). For a second CBCT with a very different rectum configuration, we observed +0.8% (prostate), +8.9% (rectum), −1.2% (bladder). For a third case with significant lateral truncation of the field of view, we observed: +0.8% (prostate), +8.9% (rectum), −1.2% (bladder). Adding the prior image constraint raised Dice measures by about 1%. Conclusion: Efficient and practical adaptive radiotherapy requires accurate deformable registration and accurate anatomy delineation. We show here small and consistent patterns of improved contour accuracy using PL iterative reconstruction compared with FBP reconstruction. However, the modest extent of these results and the pattern of differences across CBCT cases suggest that
NASA Technical Reports Server (NTRS)
Peters, B. C., Jr.; Walker, H. F.
1978-01-01
This paper addresses the problem of obtaining numerically maximum-likelihood estimates of the parameters for a mixture of normal distributions. In recent literature, a certain successive-approximations procedure, based on the likelihood equations, was shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, we introduce a general iterative procedure, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. We show that, with probability 1 as the sample size grows large, this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. We also show that the step-size which yields optimal local convergence rates for large samples is determined in a sense by the 'separation' of the component normal densities and is bounded below by a number between 1 and 2.
NASA Technical Reports Server (NTRS)
Peters, B. C., Jr.; Walker, H. F.
1976-01-01
The problem of obtaining numerically maximum likelihood estimates of the parameters for a mixture of normal distributions is addressed. In recent literature, a certain successive approximations procedure, based on the likelihood equations, is shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, a general iterative procedure is introduced, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. With probability 1 as the sample size grows large, it is shown that this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. The step-size which yields optimal local convergence rates for large samples is determined in a sense by the separation of the component normal densities and is bounded below by a number between 1 and 2.
NASA Astrophysics Data System (ADS)
Marra, M. J.; Smith, E. G. C.; Shulmeister, J.; Leschen, R.
2004-07-01
We present a new climatic reconstruction method appropriate for biological proxies where modern distributions are poorly defined and data sets are small. The technique uses a sine function in conjunction with maximum likelihood estimates of best high and best low values for the distribution of each species. To demonstrate the model we present temperature reconstructions for the Last Glacial Maximum (LGM) and Holocene from beetle fossil assemblages from the Awatere Valley, New Zealand. The temperature estimates are determined by the mutual overlap of the climate range for all the species in the assemblage. The overlap is then compared with modern physio-chemical conditions. For our example, we estimate the LGM summer (February) mean temperature was about 3.5-4°C cooler, and July (winter) mean daily minimum temperature was about 4-5°C cooler than present day temperatures. The maximum likelihood estimates broaden the reconstructed temperature ranges to 2.5-5°C cooler for February temperatures and 3.5-6.0°C cooler for mean minimum daily temperature of the coldest month (July). These estimates are consistent with LGM temperature estimates of 4-7°C from other climate proxy indicators. Estimates of Holocene temperatures are very similar to modern. Estimates are compared with results from the established mutual climatic range (MCR) technique and the results are compatible. MCR is less robust than the sine model approach for these data because it requires the pre-determination of the critical physio-chemical controls and assumes Gaussian distributions in climate space. The sine model is conceptually superior to traditional BIOCLIM modelling, with which it shares many features, because BIOCLIM also assumes Gaussian distributions and the sine model allows attribute testing of the data sets which are not possible with BIOCLIM.
Maximum Likelihood Comparison of Tully-Fisher and Redshift Data. II. Results from an Expanded Sample
NASA Astrophysics Data System (ADS)
Willick, Jeffrey A.; Strauss, Michael A.
1998-11-01
This is the second in a series of papers in which we compare Tully-Fisher (TF) data from the Mark III Catalog with predicted peculiar velocities based on the IRAS galaxy redshift survey and gravitational instability theory, using a rigorous maximum likelihood method called VELMOD. In the first paper in this series, we applied the method to a czLG <= 3000 km s-1, 838 galaxy TF sample and found βI = 0.49 +/- 0.07, where βI ≡ Ω0.6/bI and bI is the linear biasing parameter for IRAS galaxies. In this paper we increase the redshift limit to czLG = 7500 km s-1, thereby enlarging the sample to 1876 galaxies. The expanded sample now includes the Willick Pisces-Perseus (W91PP) and Courteau-Faber (CF) subsamples of the Mark III Catalog, in addition to the Aaronson et al. (A82) and Mathewson et al. (MAT) subsamples already considered in the first paper in this series. We implement VELMOD using both the forward and inverse forms of the TF relation and allow for a more general form of the quadrupole velocity residual than considered in the first paper in this series. We find βI = 0.50 +/- 0.04 (1 σ error) at 300 km s-1 smoothing of the IRAS-predicted velocity field. The fit residuals are spatially incoherent for βI = 0.5, which indicates that the IRAS plus quadrupole velocity field is a good fit to the TF data. If we eliminate the quadrupole we obtain a worse fit but a similar value for βI of 0.54 +/- 0.04. Changing the IRAS smoothing scale to 500 km s-1 has almost no effect on the best βI. Thus the data are consistent with a model in which the cosmological density parameter Ω ~ 0.3, and IRAS galaxies are unbiased, bI = 1. We find evidence for a density dependence of the small-scale velocity dispersion, σv(δg) ~= (100 + 35δg) km s-1. One of the byproducts of the VELMOD method is a self-consistent calibration of the TF relation. We confirm our result from the first paper in this series that the TF relations for the A82 and MAT samples found by VELMOD are consistent
Nguyen, Hien D; Wood, Ian A
2016-03-01
Maximum pseudo-likelihood estimation (MPLE) is an attractive method for training fully visible Boltzmann machines (FVBMs) due to its computational scalability and the desirable statistical properties of the MPLE. No published algorithms for MPLE have been proven to be convergent or monotonic. In this note, we present an algorithm for the MPLE of FVBMs based on the block successive lower-bound maximization (BSLM) principle. We show that the BSLM algorithm monotonically increases the pseudo-likelihood values and that the sequence of BSLM estimates converges to the unique global maximizer of the pseudo-likelihood function. The relationship between the BSLM algorithm and the gradient ascent (GA) algorithm for MPLE of FVBMs is also discussed, and a convergence criterion for the GA algorithm is given.
Preconditioned Alternating Projection Algorithms for Maximum a Posteriori ECT Reconstruction
Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng
2012-01-01
We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constrain involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the preconditioned alternating projection algorithm. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality. PMID:23271835
Estimating probability densities from short samples: A parametric maximum likelihood approach
NASA Astrophysics Data System (ADS)
Dudok de Wit, T.; Floriani, E.
1998-10-01
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (PDF) of a random set. The method proceeds by maximizing the likelihood of the PDF, yielding estimates that perform equally well in the tails as in the bulk of the distribution. It is therefore well suited for the analysis of short sets drawn from smooth PDF's and stands out by the simplicity of its computational scheme. Its advantages and limitations are discussed.
Nagelkerke, Nico; Fidler, Vaclav
2015-01-01
The problem of discrimination and classification is central to much of epidemiology. Here we consider the estimation of a logistic regression/discrimination function from training samples, when one of the training samples is subject to misclassification or mislabeling, e.g. diseased individuals are incorrectly classified/labeled as healthy controls. We show that this leads to zero-inflated binomial model with a defective logistic regression or discrimination function, whose parameters can be estimated using standard statistical methods such as maximum likelihood. These parameters can be used to estimate the probability of true group membership among those, possibly erroneously, classified as controls. Two examples are analyzed and discussed. A simulation study explores properties of the maximum likelihood parameter estimates and the estimates of the number of mislabeled observations. PMID:26474313
Lele, Subhash R; Dennis, Brian; Lutscher, Frithjof
2007-07-01
We introduce a new statistical computing method, called data cloning, to calculate maximum likelihood estimates and their standard errors for complex ecological models. Although the method uses the Bayesian framework and exploits the computational simplicity of the Markov chain Monte Carlo (MCMC) algorithms, it provides valid frequentist inferences such as the maximum likelihood estimates and their standard errors. The inferences are completely invariant to the choice of the prior distributions and therefore avoid the inherent subjectivity of the Bayesian approach. The data cloning method is easily implemented using standard MCMC software. Data cloning is particularly useful for analysing ecological situations in which hierarchical statistical models, such as state-space models and mixed effects models, are appropriate. We illustrate the method by fitting two nonlinear population dynamics models to data in the presence of process and observation noise.
NASA Astrophysics Data System (ADS)
Dang, Cong-Thuat; Le, Thien-Phu; Ray, Pascal
2017-10-01
Seismic fragility curves presenting some probability of failure or of a damage state exceedance versus seismic intensity can be established by engineering judgment, empirical or numerical approaches. This paper focuses on the latter issue. In recent studies, three popular methods based on numerical simulations, comprising scaled seismic intensity, maximum likelihood estimation and probabilistic seismic demand/capacity models, have been studied and compared. The results obtained show that the maximum likelihood estimation (MLE) method is in general better than other ones. However, previous publications also indicated the dependence of the MLE method on the ground excitation input. The objective of this paper is thus to propose a novel method improving the existing MLE one. Improvements are based on probabilistic ground motion information, which is taken into account in the proposed procedure. The validity of this new approach is verified by analytical tests and numerical examples.
A comparison of feed-forward networks and maximum likelihood on a point-source location problem
NASA Astrophysics Data System (ADS)
Webb, Andrew R.
1991-04-01
The problem of point source location using a multibeam focal plane staring array radar is considered. It is viewed as one in functional approximation in which the position of the source is regarded as a nonlinear function of the sampled radar image. An approximant is constructed, using a training set, which minimizes the mean square error in the position estimate. The problem of generalization is discussed. Two feed forward network architectures are considered: a particular radial basis function network which arises as a consequence of the minimum mean square error solution and is appropriate when the signal to noise ratio is 'small', and a multilayer perceptron, chosen for high signal to noise ratio approximation. The errors in the position estimates for each of these approaches are compared with a maximum likelihood position estimation method. The maximum likelihood method gives better overall performance and has the advantage that it is not dependent on the signal to noise ratio.
Ferro, Mark A
2014-01-01
The aim of this research was to examine, in an exploratory manner, whether cross-sectional multiple imputation generates valid parameter estimates for a latent growth curve model in a longitudinal data set with nonmonotone missingness. A simulated longitudinal data set of N = 5000 was generated and consisted of a continuous dependent variable, assessed at three measurement occasions and a categorical time-invariant independent variable. Missing data had a nonmonotone pattern and the proportion of missingness increased from the initial to the final measurement occasion (5%-20%). Three methods were considered to deal with missing data: listwise deletion, full-information maximum likelihood, and multiple imputation. A latent growth curve model was specified and analysis of variance was used to compare parameter estimates between the full data set and missing data approaches. Multiple imputation resulted in significantly lower slope variance compared with the full data set. There were no differences in any parameter estimates between the multiple imputation and full-information maximum likelihood approaches. This study suggested that in longitudinal studies with nonmonotone missingness, cross-sectional imputation at each time point may be viable and produces estimates comparable with those obtained with full-information maximum likelihood. Future research pursuing the validity of this method is warranted. Copyright © 2014 Elsevier Inc. All rights reserved.
Bouhrara, Mustapha; Bonny, Jean-Marie; Ashinsky, Beth G; Maring, Michael C; Spencer, Richard G
2017-01-01
Denoising of magnetic resonance (MR) images enhances diagnostic accuracy, the quality of image manipulations such as registration and segmentation, and parameter estimation. The first objective of this paper is to introduce a new, high-performance, nonlocal filter for noise reduction in MR image sets consisting of progressively-weighted, that is, multispectral, images. This filter is a multispectral extension of the nonlocal maximum likelihood filter (NLML). Performance was evaluated on synthetic and in-vivo T2 - and T1 -weighted brain imaging data, and compared to the nonlocal-means (NLM) and its multispectral version, that is, MS-NLM, and the nonlocal maximum likelihood (NLML) filters. Visual inspection of filtered images and quantitative analyses showed that all filters provided substantial reduction of noise. Further, as expected, the use of multispectral information improves filtering quality. In addition, numerical and experimental analyses indicated that the new multispectral NLML filter, MS-NLML, demonstrated markedly less blurring and loss of image detail than seen with the other filters evaluated. In addition, since noise standard deviation (SD) is an important parameter for all of these nonlocal filters, a multispectral extension of the method of maximum likelihood estimation (MLE) of noise amplitude is presented and compared to both local and nonlocal MLE methods. Numerical and experimental analyses indicated the superior performance of this multispectral method for estimation of noise SD.
Jin, Shaobo; Yang-Wallentin, Fan; Christoffersson, Anders
2015-05-15
A multi-group factor model is suitable for data originating from different strata. However, it often requires a relatively large sample size to avoid numerical issues such as non-convergence and non-positive definite covariance matrices. An alternative is to pool data from different groups in which a single-group factor model is fitted to the pooled data using maximum likelihood. In this paper, properties of pseudo-maximum likelihood (PML) estimators for pooled data are studied. The pooled data are assumed to be normally distributed from a single group. The resulting asymptotic efficiency of the PML estimators of factor loadings is compared with that of the multi-group maximum likelihood estimators. The effect of pooling is investigated through a two-group factor model. The variances of factor loadings for the pooled data are underestimated under the normal theory when error variances in the smaller group are larger. Underestimation is due to dependence between the pooled factors and pooled error terms. Small-sample properties of the PML estimators are also investigated using a Monte Carlo study.
NASA Technical Reports Server (NTRS)
Deckert, J. C.; Deyst, J. J.
1975-01-01
A technique for on-board detection and identification of hard failures and leaks of the shuttle orbiter reaction control subsystem jets, during the orbital flight phase, is presented. The method uses gimbal angle and linear accelerometer measurements from the orbiter inertial measurement unit and requires no additional hardware. Extended Kalman filters with residual traps are employed for state estimation, and generalized likelihood ratio tests for jet failure identification. Rigid body simulation results indicate identification times of less than 2 seconds for hard jet failures and less than 70 seconds for jet leaks.
Improving lesion detectability in PET imaging with a penalized likelihood reconstruction algorithm
NASA Astrophysics Data System (ADS)
Wangerin, Kristen A.; Ahn, Sangtae; Ross, Steven G.; Kinahan, Paul E.; Manjeshwar, Ravindra M.
2015-03-01
Ordered Subset Expectation Maximization (OSEM) is currently the most widely used image reconstruction algorithm for clinical PET. However, OSEM does not necessarily provide optimal image quality, and a number of alternative algorithms have been explored. We have recently shown that a penalized likelihood image reconstruction algorithm using the relative difference penalty, block sequential regularized expectation maximization (BSREM), achieves more accurate lesion quantitation than OSEM, and importantly, maintains acceptable visual image quality in clinical wholebody PET. The goal of this work was to evaluate lesion detectability with BSREM versus OSEM. We performed a twoalternative forced choice study using 81 patient datasets with lesions of varying contrast inserted into the liver and lung. At matched imaging noise, BSREM and OSEM showed equivalent detectability in the lungs, and BSREM outperformed OSEM in the liver. These results suggest that BSREM provides not only improved quantitation and clinically acceptable visual image quality as previously shown but also improved lesion detectability compared to OSEM. We then modeled this detectability study, applying both nonprewhitening (NPW) and channelized Hotelling (CHO) model observers to the reconstructed images. The CHO model observer showed good agreement with the human observers, suggesting that we can apply this model to future studies with varying simulation and reconstruction parameters.
NASA Astrophysics Data System (ADS)
Ren, Xue; Lee, Soo-Jin
2016-03-01
Patch-based regularization methods, which have proven useful not only for image denoising, but also for tomographic reconstruction, penalize image roughness based on the intensity differences between two nearby patches. However, when two patches are not considered to be similar in the general sense of similarity but still have similar features in a scaled domain after normalizing the two patches, the difference between the two patches in the scaled domain is smaller than the intensity difference measured in the standard method. Standard patch-based methods tend to ignore such similarities due to the large intensity differences between the two patches. In this work, for patch-based penalized likelihood tomographic reconstruction, we propose a new approach to the similarity measure using the normalized patch differences as well as the intensity-based patch differences. A normalized patch difference is obtained by normalizing and scaling the intensity-based patch difference. To selectively take advantage of the standard patch (SP) and normalized patch (NP), we use switching schemes that can select either SP or NP based on the gradient of a reconstructed image. In this case the SP is selected for restoring large-scaled piecewise-smooth regions, while the NP is selected for preserving the contrast of fine details. The numerical experiments using software phantom demonstrate that our proposed methods not only improve overall reconstruction accuracy in terms of the percentage error, but also reveal better recovery of fine details in terms of the contrast recovery coefficient.
McGuire, Jimmy A; Witt, Christopher C; Altshuler, Douglas L; Remsen, J V
2007-10-01
Hummingbirds are an important model system in avian biology, but to date the group has been the subject of remarkably few phylogenetic investigations. Here we present partitioned Bayesian and maximum likelihood phylogenetic analyses for 151 of approximately 330 species of hummingbirds and 12 outgroup taxa based on two protein-coding mitochondrial genes (ND2 and ND4), flanking tRNAs, and two nuclear introns (AK1 and BFib). We analyzed these data under several partitioning strategies ranging between unpartitioned and a maximum of nine partitions. In order to select a statistically justified partitioning strategy following partitioned Bayesian analysis, we considered four alternative criteria including Bayes factors, modified versions of the Akaike information criterion for small sample sizes (AIC(c)), Bayesian information criterion (BIC), and a decision-theoretic methodology (DT). Following partitioned maximum likelihood analyses, we selected a best-fitting strategy using hierarchical likelihood ratio tests (hLRTS), the conventional AICc, BIC, and DT, concluding that the most stringent criterion, the performance-based DT, was the most appropriate methodology for selecting amongst partitioning strategies. In the context of our well-resolved and well-supported phylogenetic estimate, we consider the historical biogeography of hummingbirds using ancestral state reconstructions of (1) primary geographic region of occurrence (i.e., South America, Central America, North America, Greater Antilles, Lesser Antilles), (2) Andean or non-Andean geographic distribution, and (3) minimum elevational occurrence. These analyses indicate that the basal hummingbird assemblages originated in the lowlands of South America, that most of the principle clades of hummingbirds (all but Mountain Gems and possibly Bees) originated on this continent, and that there have been many (at least 30) independent invasions of other primary landmasses, especially Central America.
Gu, Fei; Wu, Hao
2016-09-01
The specifications of state space model for some principal component-related models are described, including the independent-group common principal component (CPC) model, the dependent-group CPC model, and principal component-based multivariate analysis of variance. Some derivations are provided to show the equivalence of the state space approach and the existing Wishart-likelihood approach. For each model, a numeric example is used to illustrate the state space approach. In addition, a simulation study is conducted to evaluate the standard error estimates under the normality and nonnormality conditions. In order to cope with the nonnormality conditions, the robust standard errors are also computed. Finally, other possible applications of the state space approach are discussed at the end.
Efficient and exact maximum likelihood quantisation of genomic features using dynamic programming.
Song, Mingzhou; Haralick, Robert M; Boissinot, Stéphane
2010-01-01
An efficient and exact dynamic programming algorithm is introduced to quantise a continuous random variable into a discrete random variable that maximises the likelihood of the quantised probability distribution for the original continuous random variable. Quantisation is often useful before statistical analysis and modelling of large discrete network models from observations of multiple continuous random variables. The quantisation algorithm is applied to genomic features including the recombination rate distribution across the chromosomes and the non-coding transposable element LINE-1 in the human genome. The association pattern is studied between the recombination rate, obtained by quantisation at genomic locations around LINE-1 elements, and the length groups of LINE-1 elements, also obtained by quantisation on LINE-1 length. The exact and density-preserving quantisation approach provides an alternative superior to the inexact and distance-based univariate iterative k-means clustering algorithm for discretisation.
1984-10-01
and second Fr~ chet derivatives of 3(v) 1 n L(v) are given by (Tapia, 1971) n d I n(xi) n (1- d )I X I iv MxZ) ’-t)dt -2 < v,rn and n d 2. (X-n j~i (v)i...8217 first APLE; SurvivaZ e.t..a- tion; Random censor-hip; Nonparaet"c density estimation; Reliability. AB STRACT D Based on arbitrarily right-censored...functional 0: H(n) -I R. Given the arbitrarily right-censored sample (xi,dt), i11,2,... ,n, the #-penalized likelihood of v c H(n) is defined by %I n d
Laval, Guillaume; SanCristobal, Magali; Chevalet, Claude
2003-01-01
Maximum-likelihood and Bayesian (MCMC algorithm) estimates of the increase of the Wright-Malécot inbreeding coefficient, F(t), between two temporally spaced samples, were developed from the Dirichlet approximation of allelic frequency distribution (model MD) and from the admixture of the Dirichlet approximation and the probabilities of fixation and loss of alleles (model MDL). Their accuracy was tested using computer simulations in which F(t) = 10% or less. The maximum-likelihood method based on the model MDL was found to be the best estimate of F(t) provided that initial frequencies are known exactly. When founder frequencies are estimated from a limited set of founder animals, only the estimates based on the model MD can be used for the moment. In this case no method was found to be the best in all situations investigated. The likelihood and Bayesian approaches give better results than the classical F-statistics when markers exhibiting a low polymorphism (such as the SNP markers) are used. Concerning the estimations of the effective population size all the new estimates presented here were found to be better than the F-statistics classically used. PMID:12871924
Guindon, Stéphane; Dufayard, Jean-François; Lefort, Vincent; Anisimova, Maria; Hordijk, Wim; Gascuel, Olivier
2010-05-01
PhyML is a phylogeny software based on the maximum-likelihood principle. Early PhyML versions used a fast algorithm performing nearest neighbor interchanges to improve a reasonable starting tree topology. Since the original publication (Guindon S., Gascuel O. 2003. A simple, fast and accurate algorithm to estimate large phylogenies by maximum likelihood. Syst. Biol. 52:696-704), PhyML has been widely used (>2500 citations in ISI Web of Science) because of its simplicity and a fair compromise between accuracy and speed. In the meantime, research around PhyML has continued, and this article describes the new algorithms and methods implemented in the program. First, we introduce a new algorithm to search the tree space with user-defined intensity using subtree pruning and regrafting topological moves. The parsimony criterion is used here to filter out the least promising topology modifications with respect to the likelihood function. The analysis of a large collection of real nucleotide and amino acid data sets of various sizes demonstrates the good performance of this method. Second, we describe a new test to assess the support of the data for internal branches of a phylogeny. This approach extends the recently proposed approximate likelihood-ratio test and relies on a nonparametric, Shimodaira-Hasegawa-like procedure. A detailed analysis of real alignments sheds light on the links between this new approach and the more classical nonparametric bootstrap method. Overall, our tests show that the last version (3.0) of PhyML is fast, accurate, stable, and ready to use. A Web server and binary files are available from http://www.atgc-montpellier.fr/phyml/.
NASA Astrophysics Data System (ADS)
Ahn, Sangtae; Ross, Steven G.; Asma, Evren; Miao, Jun; Jin, Xiao; Cheng, Lishui; Wollenweber, Scott D.; Manjeshwar, Ravindra M.
2015-08-01
Ordered subset expectation maximization (OSEM) is the most widely used algorithm for clinical PET image reconstruction. OSEM is usually stopped early and post-filtered to control image noise and does not necessarily achieve optimal quantitation accuracy. As an alternative to OSEM, we have recently implemented a penalized likelihood (PL) image reconstruction algorithm for clinical PET using the relative difference penalty with the aim of improving quantitation accuracy without compromising visual image quality. Preliminary clinical studies have demonstrated visual image quality including lesion conspicuity in images reconstructed by the PL algorithm is better than or at least as good as that in OSEM images. In this paper we evaluate lesion quantitation accuracy of the PL algorithm with the relative difference penalty compared to OSEM by using various data sets including phantom data acquired with an anthropomorphic torso phantom, an extended oval phantom and the NEMA image quality phantom; clinical data; and hybrid clinical data generated by adding simulated lesion data to clinical data. We focus on mean standardized uptake values and compare them for PL and OSEM using both time-of-flight (TOF) and non-TOF data. The results demonstrate improvements of PL in lesion quantitation accuracy compared to OSEM with a particular improvement in cold background regions such as lungs.
Gruber, Susan; van der Laan, Mark J
2010-01-01
A concrete example of the collaborative double-robust targeted likelihood estimator (C-TMLE) introduced in a companion article in this issue is presented, and applied to the estimation of causal effects and variable importance parameters in genomic data. The focus is on non-parametric estimation in a point treatment data structure. Simulations illustrate the performance of C-TMLE relative to current competitors such as the augmented inverse probability of treatment weighted estimator that relies on an external non-collaborative estimator of the treatment mechanism, and inefficient estimation procedures including propensity score matching and standard inverse probability of treatment weighting. C-TMLE is also applied to the estimation of the covariate-adjusted marginal effect of individual HIV mutations on resistance to the anti-retroviral drug lopinavir. The influence curve of the C-TMLE is used to establish asymptotically valid statistical inference. The list of mutations found to have a statistically significant association with resistance is in excellent agreement with mutation scores provided by the Stanford HIVdb mutation scores database.
Lee, Wonyul; Liu, Yufeng
2012-10-01
Multivariate regression is a common statistical tool for practical problems. Many multivariate regression techniques are designed for univariate response cases. For problems with multiple response variables available, one common approach is to apply the univariate response regression technique separately on each response variable. Although it is simple and popular, the univariate response approach ignores the joint information among response variables. In this paper, we propose three new methods for utilizing joint information among response variables. All methods are in a penalized likelihood framework with weighted L(1) regularization. The proposed methods provide sparse estimators of conditional inverse co-variance matrix of response vector given explanatory variables as well as sparse estimators of regression parameters. Our first approach is to estimate the regression coefficients with plug-in estimated inverse covariance matrices, and our second approach is to estimate the inverse covariance matrix with plug-in estimated regression parameters. Our third approach is to estimate both simultaneously. Asymptotic properties of these methods are explored. Our numerical examples demonstrate that the proposed methods perform competitively in terms of prediction, variable selection, as well as inverse covariance matrix estimation.
Mavrodiev, Evgeny V; Laktionov, Alexy P; Cellinese, Nico
2012-01-01
The evolution of the diverse flora in the Lower Volga Valley (LVV) (southwest Russia) is complex due to the composite geomorphology and tectonic history of the Caspian Sea and adjacent areas. In the absence of phylogenetic studies and temporal information, we implemented a maximum likelihood (ML) approach and stochastic character mapping reconstruction aiming at recovering historical signals from species occurrence data. A taxon-area matrix of 13 floristic areas and 1018 extant species was constructed and analyzed with RAxML and Mesquite. Additionally, we simulated scenarios with numbers of hypothetical extinct taxa from an unknown palaeoflora that occupied the areas before the dramatic transgression and regression events that have occurred from the Pleistocene to the present day. The flora occurring strictly along the river valley and delta appear to be younger than that of adjacent steppes and desert-like regions, regardless of the chronology of transgression and regression events that led to the geomorphological formation of the LVV. This result is also supported when hypothetical extinct taxa are included in the analyses. The history of each species was inferred by using a stochastic character mapping reconstruction method as implemented in Mesquite. Individual histories appear to be independent from one another and have been shaped by repeated dispersal and extinction events. These reconstructions provide testable hypotheses for more in-depth investigations of their population structure and dynamics. PMID:22957179