Bayesian image reconstruction for improving detection performance of muon tomography.

PubMed

Wang, Guobao; Schultz, Larry J; Qi, Jinyi

2009-05-01

Muon tomography is a novel technology that is being developed for detecting high-Z materials in vehicles or cargo containers. Maximum likelihood methods have been developed for reconstructing the scattering density image from muon measurements. However, the instability of maximum likelihood estimation often results in noisy images and low detectability of high-Z targets. In this paper, we propose using regularization to improve the image quality of muon tomography. We formulate the muon reconstruction problem in a Bayesian framework by introducing a prior distribution on scattering density images. An iterative shrinkage algorithm is derived to maximize the log posterior distribution. At each iteration, the algorithm obtains the maximum a posteriori update by shrinking an unregularized maximum likelihood update. Inverse quadratic shrinkage functions are derived for generalized Laplacian priors and inverse cubic shrinkage functions are derived for generalized Gaussian priors. Receiver operating characteristic studies using simulated data demonstrate that the Bayesian reconstruction can greatly improve the detection performance of muon tomography.

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun

2014-01-01

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Iterative Procedures for Exact Maximum Likelihood Estimation in the First-Order Gaussian Moving Average Model

DTIC Science & Technology

1990-11-01

1 = Q- 1 - 1 QlaaQ- 1.1 + a’Q-1a This is a simple case of a general formula called Woodbury’s formula by some authors; see, for example, Phadke and...1 2. The First-Order Moving Average Model ..... .................. 3. Some Approaches to the Iterative...the approximate likelihood function in some time series models. Useful suggestions have been the Cholesky decomposition of the covariance matrix and

Detection methods for non-Gaussian gravitational wave stochastic backgrounds

NASA Astrophysics Data System (ADS)

Drasco, Steve; Flanagan, Éanna É.

2003-04-01

A gravitational wave stochastic background can be produced by a collection of independent gravitational wave events. There are two classes of such backgrounds, one for which the ratio of the average time between events to the average duration of an event is small (i.e., many events are on at once), and one for which the ratio is large. In the first case the signal is continuous, sounds something like a constant hiss, and has a Gaussian probability distribution. In the second case, the discontinuous or intermittent signal sounds something like popcorn popping, and is described by a non-Gaussian probability distribution. In this paper we address the issue of finding an optimal detection method for such a non-Gaussian background. As a first step, we examine the idealized situation in which the event durations are short compared to the detector sampling time, so that the time structure of the events cannot be resolved, and we assume white, Gaussian noise in two collocated, aligned detectors. For this situation we derive an appropriate version of the maximum likelihood detection statistic. We compare the performance of this statistic to that of the standard cross-correlation statistic both analytically and with Monte Carlo simulations. In general the maximum likelihood statistic performs better than the cross-correlation statistic when the stochastic background is sufficiently non-Gaussian, resulting in a gain factor in the minimum gravitational-wave energy density necessary for detection. This gain factor ranges roughly between 1 and 3, depending on the duty cycle of the background, for realistic observing times and signal strengths for both ground and space based detectors. The computational cost of the statistic, although significantly greater than that of the cross-correlation statistic, is not unreasonable. Before the statistic can be used in practice with real detector data, further work is required to generalize our analysis to accommodate separated, misaligned detectors with realistic, colored, non-Gaussian noise.

Gaussianization for fast and accurate inference from cosmological data

NASA Astrophysics Data System (ADS)

Schuhmann, Robert L.; Joachimi, Benjamin; Peiris, Hiranya V.

2016-06-01

We present a method to transform multivariate unimodal non-Gaussian posterior probability densities into approximately Gaussian ones via non-linear mappings, such as Box-Cox transformations and generalizations thereof. This permits an analytical reconstruction of the posterior from a point sample, like a Markov chain, and simplifies the subsequent joint analysis with other experiments. This way, a multivariate posterior density can be reported efficiently, by compressing the information contained in Markov Chain Monte Carlo samples. Further, the model evidence integral (I.e. the marginal likelihood) can be computed analytically. This method is analogous to the search for normal parameters in the cosmic microwave background, but is more general. The search for the optimally Gaussianizing transformation is performed computationally through a maximum-likelihood formalism; its quality can be judged by how well the credible regions of the posterior are reproduced. We demonstrate that our method outperforms kernel density estimates in this objective. Further, we select marginal posterior samples from Planck data with several distinct strongly non-Gaussian features, and verify the reproduction of the marginal contours. To demonstrate evidence computation, we Gaussianize the joint distribution of data from weak lensing and baryon acoustic oscillations, for different cosmological models, and find a preference for flat Λcold dark matter. Comparing to values computed with the Savage-Dickey density ratio, and Population Monte Carlo, we find good agreement of our method within the spread of the other two.

A Maximum-Likelihood Approach to Force-Field Calibration.

PubMed

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); and optimization of the energy-term weights and the coefficients of the torsional and multibody energy terms and use of experimental ensembles at all three temperatures (run 3). The force fields were subsequently tested with a set of 14 α-helical and two α + β proteins. Optimization run 1 resulted in better agreement with the experimental ensemble at T = 280 K compared with optimization run 2 and in comparable performance on the test set but poorer agreement of the calculated folding temperature with the experimental folding temperature. Optimization run 3 resulted in the best fit of the calculated ensembles to the experimental ones for the tryptophan cage but in much poorer performance on the training set, suggesting that use of a small α-helical protein for extensive force-field calibration resulted in overfitting of the data for this protein at the expense of transferability. The optimized force field resulting from run 2 was found to fold 13 of the 14 tested α-helical proteins and one small α + β protein with the correct topologies; the average structures of 10 of them were predicted with accuracies of about 5 Å C(α) root-mean-square deviation or better. Test simulations with an additional set of 12 α-helical proteins demonstrated that this force field performed better on α-helical proteins than the previous parametrizations of UNRES. The proposed approach is applicable to any problem of maximum-likelihood parameter estimation when the contributions to the maximum-likelihood function cannot be evaluated at the experimental points and the dimension of the configurational space is too high to construct histograms of the experimental distributions.

Back to Normal! Gaussianizing posterior distributions for cosmological probes

NASA Astrophysics Data System (ADS)

Schuhmann, Robert L.; Joachimi, Benjamin; Peiris, Hiranya V.

2014-05-01

We present a method to map multivariate non-Gaussian posterior probability densities into Gaussian ones via nonlinear Box-Cox transformations, and generalizations thereof. This is analogous to the search for normal parameters in the CMB, but can in principle be applied to any probability density that is continuous and unimodal. The search for the optimally Gaussianizing transformation amongst the Box-Cox family is performed via a maximum likelihood formalism. We can judge the quality of the found transformation a posteriori: qualitatively via statistical tests of Gaussianity, and more illustratively by how well it reproduces the credible regions. The method permits an analytical reconstruction of the posterior from a sample, e.g. a Markov chain, and simplifies the subsequent joint analysis with other experiments. Furthermore, it permits the characterization of a non-Gaussian posterior in a compact and efficient way. The expression for the non-Gaussian posterior can be employed to find analytic formulae for the Bayesian evidence, and consequently be used for model comparison.

PERIOD ESTIMATION FOR SPARSELY SAMPLED QUASI-PERIODIC LIGHT CURVES APPLIED TO MIRAS

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Shiyuan; Huang, Jianhua Z.; Long, James

2016-12-01

We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequencymore » parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period–luminosity relations.« less

The Extended-Image Tracking Technique Based on the Maximum Likelihood Estimation

NASA Technical Reports Server (NTRS)

Tsou, Haiping; Yan, Tsun-Yee

2000-01-01

This paper describes an extended-image tracking technique based on the maximum likelihood estimation. The target image is assume to have a known profile covering more than one element of a focal plane detector array. It is assumed that the relative position between the imager and the target is changing with time and the received target image has each of its pixels disturbed by an independent additive white Gaussian noise. When a rotation-invariant movement between imager and target is considered, the maximum likelihood based image tracking technique described in this paper is a closed-loop structure capable of providing iterative update of the movement estimate by calculating the loop feedback signals from a weighted correlation between the currently received target image and the previously estimated reference image in the transform domain. The movement estimate is then used to direct the imager to closely follow the moving target. This image tracking technique has many potential applications, including free-space optical communications and astronomy where accurate and stabilized optical pointing is essential.

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.

SMURC: High-Dimension Small-Sample Multivariate Regression With Covariance Estimation.

PubMed

Bayar, Belhassen; Bouaynaya, Nidhal; Shterenberg, Roman

2017-03-01

We consider a high-dimension low sample-size multivariate regression problem that accounts for correlation of the response variables. The system is underdetermined as there are more parameters than samples. We show that the maximum likelihood approach with covariance estimation is senseless because the likelihood diverges. We subsequently propose a normalization of the likelihood function that guarantees convergence. We call this method small-sample multivariate regression with covariance (SMURC) estimation. We derive an optimization problem and its convex approximation to compute SMURC. Simulation results show that the proposed algorithm outperforms the regularized likelihood estimator with known covariance matrix and the sparse conditional Gaussian graphical model. We also apply SMURC to the inference of the wing-muscle gene network of the Drosophila melanogaster (fruit fly).

Human Language Technology: Opportunities and Challenges

DTIC Science & Technology

2005-01-01

because of the connections to and reliance on signal processing. Audio diarization critically includes indexing of speakers [12], since speaker ...to reduce inter- speaker variability in training. Standard techniques include vocal-tract length normalization, adaptation of acoustic models using...maximum likelihood linear regression (MLLR), and speaker -adaptive training based on MLLR. The acoustic models are mixtures of Gaussians, typically with

A Poisson Log-Normal Model for Constructing Gene Covariation Network Using RNA-seq Data.

PubMed

Choi, Yoonha; Coram, Marc; Peng, Jie; Tang, Hua

2017-07-01

Constructing expression networks using transcriptomic data is an effective approach for studying gene regulation. A popular approach for constructing such a network is based on the Gaussian graphical model (GGM), in which an edge between a pair of genes indicates that the expression levels of these two genes are conditionally dependent, given the expression levels of all other genes. However, GGMs are not appropriate for non-Gaussian data, such as those generated in RNA-seq experiments. We propose a novel statistical framework that maximizes a penalized likelihood, in which the observed count data follow a Poisson log-normal distribution. To overcome the computational challenges, we use Laplace's method to approximate the likelihood and its gradients, and apply the alternating directions method of multipliers to find the penalized maximum likelihood estimates. The proposed method is evaluated and compared with GGMs using both simulated and real RNA-seq data. The proposed method shows improved performance in detecting edges that represent covarying pairs of genes, particularly for edges connecting low-abundant genes and edges around regulatory hubs.

Multivariate interactive digital analysis system /MIDAS/ - A new fast multispectral recognition system

NASA Technical Reports Server (NTRS)

Kriegler, F.; Marshall, R.; Lampert, S.; Gordon, M.; Cornell, C.; Kistler, R.

1973-01-01

The MIDAS system is a prototype, multiple-pipeline digital processor mechanizing the multivariate-Gaussian, maximum-likelihood decision algorithm operating at 200,000 pixels/second. It incorporates displays and film printer equipment under control of a general purpose midi-computer and possesses sufficient flexibility that operational versions of the equipment may be subsequently specified as subsets of the system.

Similarity measure and domain adaptation in multiple mixture model clustering: An application to image processing.

PubMed

Leong, Siow Hoo; Ong, Seng Huat

2017-01-01

This paper considers three crucial issues in processing scaled down image, the representation of partial image, similarity measure and domain adaptation. Two Gaussian mixture model based algorithms are proposed to effectively preserve image details and avoids image degradation. Multiple partial images are clustered separately through Gaussian mixture model clustering with a scan and select procedure to enhance the inclusion of small image details. The local image features, represented by maximum likelihood estimates of the mixture components, are classified by using the modified Bayes factor (MBF) as a similarity measure. The detection of novel local features from MBF will suggest domain adaptation, which is changing the number of components of the Gaussian mixture model. The performance of the proposed algorithms are evaluated with simulated data and real images and it is shown to perform much better than existing Gaussian mixture model based algorithms in reproducing images with higher structural similarity index.

Similarity measure and domain adaptation in multiple mixture model clustering: An application to image processing

PubMed Central

Leong, Siow Hoo

2017-01-01

This paper considers three crucial issues in processing scaled down image, the representation of partial image, similarity measure and domain adaptation. Two Gaussian mixture model based algorithms are proposed to effectively preserve image details and avoids image degradation. Multiple partial images are clustered separately through Gaussian mixture model clustering with a scan and select procedure to enhance the inclusion of small image details. The local image features, represented by maximum likelihood estimates of the mixture components, are classified by using the modified Bayes factor (MBF) as a similarity measure. The detection of novel local features from MBF will suggest domain adaptation, which is changing the number of components of the Gaussian mixture model. The performance of the proposed algorithms are evaluated with simulated data and real images and it is shown to perform much better than existing Gaussian mixture model based algorithms in reproducing images with higher structural similarity index. PMID:28686634

PERIODIC AUTOREGRESSIVE-MOVING AVERAGE (PARMA) MODELING WITH APPLICATIONS TO WATER RESOURCES.

USGS Publications Warehouse

Vecchia, A.V.

1985-01-01

Results involving correlation properties and parameter estimation for autogressive-moving average models with periodic parameters are presented. A multivariate representation of the PARMA model is used to derive parameter space restrictions and difference equations for the periodic autocorrelations. Close approximation to the likelihood function for Gaussian PARMA processes results in efficient maximum-likelihood estimation procedures. Terms in the Fourier expansion of the parameters are sequentially included, and a selection criterion is given for determining the optimal number of harmonics to be included. Application of the techniques is demonstrated through analysis of a monthly streamflow time series.

A general formula for computing maximum proportion correct scores in various psychophysical paradigms with arbitrary probability distributions of stimulus observations.

PubMed

Dai, Huanping; Micheyl, Christophe

2015-05-01

Proportion correct (Pc) is a fundamental measure of task performance in psychophysics. The maximum Pc score that can be achieved by an optimal (maximum-likelihood) observer in a given task is of both theoretical and practical importance, because it sets an upper limit on human performance. Within the framework of signal detection theory, analytical solutions for computing the maximum Pc score have been established for several common experimental paradigms under the assumption of Gaussian additive internal noise. However, as the scope of applications of psychophysical signal detection theory expands, the need is growing for psychophysicists to compute maximum Pc scores for situations involving non-Gaussian (internal or stimulus-induced) noise. In this article, we provide a general formula for computing the maximum Pc in various psychophysical experimental paradigms for arbitrary probability distributions of sensory activity. Moreover, easy-to-use MATLAB code implementing the formula is provided. Practical applications of the formula are illustrated, and its accuracy is evaluated, for two paradigms and two types of probability distributions (uniform and Gaussian). The results demonstrate that Pc scores computed using the formula remain accurate even for continuous probability distributions, as long as the conversion from continuous probability density functions to discrete probability mass functions is supported by a sufficiently high sampling resolution. We hope that the exposition in this article, and the freely available MATLAB code, facilitates calculations of maximum performance for a wider range of experimental situations, as well as explorations of the impact of different assumptions concerning internal-noise distributions on maximum performance in psychophysical experiments.

Cramer-Rao Bound for Gaussian Random Processes and Applications to Radar Processing of Atmospheric Signals

NASA Technical Reports Server (NTRS)

Frehlich, Rod

1993-01-01

Calculations of the exact Cramer-Rao Bound (CRB) for unbiased estimates of the mean frequency, signal power, and spectral width of Doppler radar/lidar signals (a Gaussian random process) are presented. Approximate CRB's are derived using the Discrete Fourier Transform (DFT). These approximate results are equal to the exact CRB when the DFT coefficients are mutually uncorrelated. Previous high SNR limits for CRB's are shown to be inaccurate because the discrete summations cannot be approximated with integration. The performance of an approximate maximum likelihood estimator for mean frequency approaches the exact CRB for moderate signal to noise ratio and moderate spectral width.

Maximum likelihood estimation for periodic autoregressive moving average models

USGS Publications Warehouse

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.

Spatial Prediction and Optimized Sampling Design for Sodium Concentration in Groundwater

PubMed Central

Shabbir, Javid; M. AbdEl-Salam, Nasser; Hussain, Tajammal

2016-01-01

Sodium is an integral part of water, and its excessive amount in drinking water causes high blood pressure and hypertension. In the present paper, spatial distribution of sodium concentration in drinking water is modeled and optimized sampling designs for selecting sampling locations is calculated for three divisions in Punjab, Pakistan. Universal kriging and Bayesian universal kriging are used to predict the sodium concentrations. Spatial simulated annealing is used to generate optimized sampling designs. Different estimation methods (i.e., maximum likelihood, restricted maximum likelihood, ordinary least squares, and weighted least squares) are used to estimate the parameters of the variogram model (i.e, exponential, Gaussian, spherical and cubic). It is concluded that Bayesian universal kriging fits better than universal kriging. It is also observed that the universal kriging predictor provides minimum mean universal kriging variance for both adding and deleting locations during sampling design. PMID:27683016

Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements

DOE PAGES

Wang, Liming; Huang, Jiaji; Yuan, Xin; ...

2015-09-17

The measurement matrix employed in compressive sensing typically cannot be known precisely a priori and must be estimated via calibration. One may take multiple compressive measurements, from which the measurement matrix and underlying signals may be estimated jointly. This is of interest as well when the measurement matrix may change as a function of the details of what is measured. This problem has been considered recently for Gaussian measurement noise, and here we develop this idea with application to Poisson systems. A collaborative maximum likelihood algorithm and alternating proximal gradient algorithm are proposed, and associated theoretical performance guarantees are establishedmore » based on newly derived concentration-of-measure results. A Bayesian model is then introduced, to improve flexibility and generality. Connections between the maximum likelihood methods and the Bayesian model are developed, and example results are presented for a real compressive X-ray imaging system.« less

Simulating the effect of non-linear mode coupling in cosmological parameter estimation

NASA Astrophysics Data System (ADS)

Kiessling, A.; Taylor, A. N.; Heavens, A. F.

2011-09-01

Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment and to optimize the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimization it is usually assumed that the power-spectrum covariance matrix is diagonal in Fourier space. However, in the low-redshift Universe, non-linear mode coupling will tend to correlate small-scale power, moving information from lower to higher order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naïve Gaussian Fisher matrix forecasts with a maximum likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2D and tomographic shear analysis of a Euclid-like survey. In both cases, we find that the 68 per cent confidence area of the Ωm-σ8 plane increases by a factor of 5. However, the marginal errors increase by just 20-40 per cent. We propose a new method to model the effects of non-linear shear-power mode coupling in the Fisher matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. We find that this approximation can reproduce the 68 per cent confidence regions of the full maximum likelihood analysis in the Ωm-σ8 plane to high accuracy for both 2D and tomographic weak lensing surveys. Finally, we perform a multiparameter analysis of Ωm, σ8, h, ns, w0 and wa to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. The 6D volume of the 1σ error contours for the non-linear Fisher analysis is a factor of 3 larger than for the Gaussian case, and the shape of the 68 per cent confidence volume is modified. We propose that future Fisher matrix estimates of cosmological parameter accuracies should include mode-coupling effects.

Survival analysis of clinical mastitis data using a nested frailty Cox model fit as a mixed-effects Poisson model.

PubMed

Elghafghuf, Adel; Dufour, Simon; Reyher, Kristen; Dohoo, Ian; Stryhn, Henrik

2014-12-01

Mastitis is a complex disease affecting dairy cows and is considered to be the most costly disease of dairy herds. The hazard of mastitis is a function of many factors, both managerial and environmental, making its control a difficult issue to milk producers. Observational studies of clinical mastitis (CM) often generate datasets with a number of characteristics which influence the analysis of those data: the outcome of interest may be the time to occurrence of a case of mastitis, predictors may change over time (time-dependent predictors), the effects of factors may change over time (time-dependent effects), there are usually multiple hierarchical levels, and datasets may be very large. Analysis of such data often requires expansion of the data into the counting-process format - leading to larger datasets - thus complicating the analysis and requiring excessive computing time. In this study, a nested frailty Cox model with time-dependent predictors and effects was applied to Canadian Bovine Mastitis Research Network data in which 10,831 lactations of 8035 cows from 69 herds were followed through lactation until the first occurrence of CM. The model was fit to the data as a Poisson model with nested normally distributed random effects at the cow and herd levels. Risk factors associated with the hazard of CM during the lactation were identified, such as parity, calving season, herd somatic cell score, pasture access, fore-stripping, and proportion of treated cases of CM in a herd. The analysis showed that most of the predictors had a strong effect early in lactation and also demonstrated substantial variation in the baseline hazard among cows and between herds. A small simulation study for a setting similar to the real data was conducted to evaluate the Poisson maximum likelihood estimation approach with both Gaussian quadrature method and Laplace approximation. Further, the performance of the two methods was compared with the performance of a widely used estimation approach for frailty Cox models based on the penalized partial likelihood. The simulation study showed good performance for the Poisson maximum likelihood approach with Gaussian quadrature and biased variance component estimates for both the Poisson maximum likelihood with Laplace approximation and penalized partial likelihood approaches. Copyright © 2014. Published by Elsevier B.V.

White Gaussian Noise - Models for Engineers

NASA Astrophysics Data System (ADS)

Jondral, Friedrich K.

2018-04-01

This paper assembles some information about white Gaussian noise (WGN) and its applications. It starts from a description of thermal noise, i. e. the irregular motion of free charge carriers in electronic devices. In a second step, mathematical models of WGN processes and their most important parameters, especially autocorrelation functions and power spectrum densities, are introduced. In order to proceed from mathematical models to simulations, we discuss the generation of normally distributed random numbers. The signal-to-noise ratio as the most important quality measure used in communications, control or measurement technology is accurately introduced. As a practical application of WGN, the transmission of quadrature amplitude modulated (QAM) signals over additive WGN channels together with the optimum maximum likelihood (ML) detector is considered in a demonstrative and intuitive way.

A decision directed detector for the phase incoherent Gaussian channel

NASA Technical Reports Server (NTRS)

Kazakos, D.

1975-01-01

A vector digital signalling scheme is proposed for simultaneous adaptive data transmission and phase estimation. The use of maximum likelihood estimation methods predicts a better performance than the phase-locked loop. The phase estimate is shown to converge to the true value, so that the adaptive nature of the detector effectively achieves phase acquisition and improvement in performance. No separate synchronization interval is required and phase fluctuations can be tracked simultaneously with the transmission of information.

An introduction of component fusion extend Kalman filtering method

NASA Astrophysics Data System (ADS)

Geng, Yue; Lei, Xusheng

2018-05-01

In this paper, the Component Fusion Extend Kalman Filtering (CFEKF) algorithm is proposed. Assuming each component of error propagation are independent with Gaussian distribution. The CFEKF can be obtained through the maximum likelihood of propagation error, which can adjust the state transition matrix and the measured matrix adaptively. With minimize linearization error, CFEKF can an effectively improve the estimation accuracy of nonlinear system state. The computation of CFEKF is similar to EKF which is easy for application.

The use of LANDSAT data to monitor the urban growth of Sao Paulo Metropolitan area

NASA Technical Reports Server (NTRS)

Dejesusparada, N. (Principal Investigator); Niero, M.; Lombardo, M. A.; Foresti, C.

1982-01-01

Urban growth from 1977 to 1979 of the region between Billings and the Guarapiranga reservoir was mapped and the problematic urban areas identified using several LANDSAT products. Visual and automatic interpretation techniques were applied to the data. Computer compatible tapes of LANDSAT multispectral scanner data were analyzed through the maximum likelihood Gaussian algorithm. The feasibility of monitoring fast urban growth by remote sensing techniques for efficient urban planning and control is demonstrated.

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.

Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian

NASA Astrophysics Data System (ADS)

Teneng, Dean

2013-09-01

We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.

Skew-t fits to mortality data--can a Gaussian-related distribution replace the Gompertz-Makeham as the basis for mortality studies?

PubMed

Clark, Jeremy S C; Kaczmarczyk, Mariusz; Mongiało, Zbigniew; Ignaczak, Paweł; Czajkowski, Andrzej A; Klęsk, Przemysław; Ciechanowicz, Andrzej

2013-08-01

Gompertz-related distributions have dominated mortality studies for 187 years. However, nonrelated distributions also fit well to mortality data. These compete with the Gompertz and Gompertz-Makeham data when applied to data with varying extents of truncation, with no consensus as to preference. In contrast, Gaussian-related distributions are rarely applied, despite the fact that Lexis in 1879 suggested that the normal distribution itself fits well to the right of the mode. Study aims were therefore to compare skew-t fits to Human Mortality Database data, with Gompertz-nested distributions, by implementing maximum likelihood estimation functions (mle2, R package bbmle; coding given). Results showed skew-t fits obtained lower Bayesian information criterion values than Gompertz-nested distributions, applied to low-mortality country data, including 1711 and 1810 cohorts. As Gaussian-related distributions have now been found to have almost universal application to error theory, one conclusion could be that a Gaussian-related distribution might replace Gompertz-related distributions as the basis for mortality studies.

Dynamical analysis of contrastive divergence learning: Restricted Boltzmann machines with Gaussian visible units.

PubMed

Karakida, Ryo; Okada, Masato; Amari, Shun-Ichi

2016-07-01

The restricted Boltzmann machine (RBM) is an essential constituent of deep learning, but it is hard to train by using maximum likelihood (ML) learning, which minimizes the Kullback-Leibler (KL) divergence. Instead, contrastive divergence (CD) learning has been developed as an approximation of ML learning and widely used in practice. To clarify the performance of CD learning, in this paper, we analytically derive the fixed points where ML and CDn learning rules converge in two types of RBMs: one with Gaussian visible and Gaussian hidden units and the other with Gaussian visible and Bernoulli hidden units. In addition, we analyze the stability of the fixed points. As a result, we find that the stable points of CDn learning rule coincide with those of ML learning rule in a Gaussian-Gaussian RBM. We also reveal that larger principal components of the input data are extracted at the stable points. Moreover, in a Gaussian-Bernoulli RBM, we find that both ML and CDn learning can extract independent components at one of stable points. Our analysis demonstrates that the same feature components as those extracted by ML learning are extracted simply by performing CD1 learning. Expanding this study should elucidate the specific solutions obtained by CD learning in other types of RBMs or in deep networks. Copyright © 2016 Elsevier Ltd. All rights reserved.

Statistics of Sxy estimates

NASA Technical Reports Server (NTRS)

Freilich, M. H.; Pawka, S. S.

1987-01-01

The statistics of Sxy estimates derived from orthogonal-component measurements are examined. Based on results of Goodman (1957), the probability density function (pdf) for Sxy(f) estimates is derived, and a closed-form solution for arbitrary moments of the distribution is obtained. Characteristic functions are used to derive the exact pdf of Sxy(tot). In practice, a simple Gaussian approximation is found to be highly accurate even for relatively few degrees of freedom. Implications for experiment design are discussed, and a maximum-likelihood estimator for a posterior estimation is outlined.

A novel latent gaussian copula framework for modeling spatial correlation in quantized SAR imagery with applications to ATR

NASA Astrophysics Data System (ADS)

Thelen, Brian T.; Xique, Ismael J.; Burns, Joseph W.; Goley, G. Steven; Nolan, Adam R.; Benson, Jonathan W.

2017-04-01

With all of the new remote sensing modalities available, and with ever increasing capabilities and frequency of collection, there is a desire to fundamentally understand/quantify the information content in the collected image data relative to various exploitation goals, such as detection/classification. A fundamental approach for this is the framework of Bayesian decision theory, but a daunting challenge is to have significantly flexible and accurate multivariate models for the features and/or pixels that capture a wide assortment of distributions and dependen- cies. In addition, data can come in the form of both continuous and discrete representations, where the latter is often generated based on considerations of robustness to imaging conditions and occlusions/degradations. In this paper we propose a novel suite of "latent" models fundamentally based on multivariate Gaussian copula models that can be used for quantized data from SAR imagery. For this Latent Gaussian Copula (LGC) model, we derive an approximate, maximum-likelihood estimation algorithm and demonstrate very reasonable estimation performance even for the larger images with many pixels. However applying these LGC models to large dimen- sions/images within a Bayesian decision/classification theory is infeasible due to the computational/numerical issues in evaluating the true full likelihood, and we propose an alternative class of novel pseudo-likelihoood detection statistics that are computationally feasible. We show in a few simple examples that these statistics have the potential to provide very good and robust detection/classification performance. All of this framework is demonstrated on a simulated SLICY data set, and the results show the importance of modeling the dependencies, and of utilizing the pseudo-likelihood methods.

Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient.

PubMed

Bian, Liheng; Suo, Jinli; Chung, Jaebum; Ou, Xiaoze; Yang, Changhuei; Chen, Feng; Dai, Qionghai

2016-06-10

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.

Evaluation of the maximum-likelihood adaptive neural system (MLANS) applications to noncooperative IFF

NASA Astrophysics Data System (ADS)

Chernick, Julian A.; Perlovsky, Leonid I.; Tye, David M.

1994-06-01

This paper describes applications of maximum likelihood adaptive neural system (MLANS) to the characterization of clutter in IR images and to the identification of targets. The characterization of image clutter is needed to improve target detection and to enhance the ability to compare performance of different algorithms using diverse imagery data. Enhanced unambiguous IFF is important for fratricide reduction while automatic cueing and targeting is becoming an ever increasing part of operations. We utilized MLANS which is a parametric neural network that combines optimal statistical techniques with a model-based approach. This paper shows that MLANS outperforms classical classifiers, the quadratic classifier and the nearest neighbor classifier, because on the one hand it is not limited to the usual Gaussian distribution assumption and can adapt in real time to the image clutter distribution; on the other hand MLANS learns from fewer samples and is more robust than the nearest neighbor classifiers. Future research will address uncooperative IFF using fused IR and MMW data.

On the insufficiency of arbitrarily precise covariance matrices: non-Gaussian weak-lensing likelihoods

NASA Astrophysics Data System (ADS)

Sellentin, Elena; Heavens, Alan F.

2018-01-01

We investigate whether a Gaussian likelihood, as routinely assumed in the analysis of cosmological data, is supported by simulated survey data. We define test statistics, based on a novel method that first destroys Gaussian correlations in a data set, and then measures the non-Gaussian correlations that remain. This procedure flags pairs of data points that depend on each other in a non-Gaussian fashion, and thereby identifies where the assumption of a Gaussian likelihood breaks down. Using this diagnosis, we find that non-Gaussian correlations in the CFHTLenS cosmic shear correlation functions are significant. With a simple exclusion of the most contaminated data points, the posterior for s8 is shifted without broadening, but we find no significant reduction in the tension with s8 derived from Planck cosmic microwave background data. However, we also show that the one-point distributions of the correlation statistics are noticeably skewed, such that sound weak-lensing data sets are intrinsically likely to lead to a systematically low lensing amplitude being inferred. The detected non-Gaussianities get larger with increasing angular scale such that for future wide-angle surveys such as Euclid or LSST, with their very small statistical errors, the large-scale modes are expected to be increasingly affected. The shifts in posteriors may then not be negligible and we recommend that these diagnostic tests be run as part of future analyses.

Signal detection theory and vestibular perception: III. Estimating unbiased fit parameters for psychometric functions.

PubMed

Chaudhuri, Shomesh E; Merfeld, Daniel M

2013-03-01

Psychophysics generally relies on estimating a subject's ability to perform a specific task as a function of an observed stimulus. For threshold studies, the fitted functions are called psychometric functions. While fitting psychometric functions to data acquired using adaptive sampling procedures (e.g., "staircase" procedures), investigators have encountered a bias in the spread ("slope" or "threshold") parameter that has been attributed to the serial dependency of the adaptive data. Using simulations, we confirm this bias for cumulative Gaussian parametric maximum likelihood fits on data collected via adaptive sampling procedures, and then present a bias-reduced maximum likelihood fit that substantially reduces the bias without reducing the precision of the spread parameter estimate and without reducing the accuracy or precision of the other fit parameters. As a separate topic, we explain how to implement this bias reduction technique using generalized linear model fits as well as other numeric maximum likelihood techniques such as the Nelder-Mead simplex. We then provide a comparison of the iterative bootstrap and observed information matrix techniques for estimating parameter fit variance from adaptive sampling procedure data sets. The iterative bootstrap technique is shown to be slightly more accurate; however, the observed information technique executes in a small fraction (0.005 %) of the time required by the iterative bootstrap technique, which is an advantage when a real-time estimate of parameter fit variance is required.

Inverse problems-based maximum likelihood estimation of ground reflectivity for selected regions of interest from stripmap SAR data [Regularized maximum likelihood estimation of ground reflectivity from stripmap SAR data

DOE Office of Scientific and Technical Information (OSTI.GOV)

West, R. Derek; Gunther, Jacob H.; Moon, Todd K.

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

Inverse problems-based maximum likelihood estimation of ground reflectivity for selected regions of interest from stripmap SAR data [Regularized maximum likelihood estimation of ground reflectivity from stripmap SAR data

DOE PAGES

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

Detecting spatial structures in throughfall data: the effect of extent, sample size, sampling design, and variogram estimation method

NASA Astrophysics Data System (ADS)

Voss, Sebastian; Zimmermann, Beate; Zimmermann, Alexander

2016-04-01

In the last three decades, an increasing number of studies analyzed spatial patterns in throughfall to investigate the consequences of rainfall redistribution for biogeochemical and hydrological processes in forests. In the majority of cases, variograms were used to characterize the spatial properties of the throughfall data. The estimation of the variogram from sample data requires an appropriate sampling scheme: most importantly, a large sample and an appropriate layout of sampling locations that often has to serve both variogram estimation and geostatistical prediction. While some recommendations on these aspects exist, they focus on Gaussian data and high ratios of the variogram range to the extent of the study area. However, many hydrological data, and throughfall data in particular, do not follow a Gaussian distribution. In this study, we examined the effect of extent, sample size, sampling design, and calculation methods on variogram estimation of throughfall data. For our investigation, we first generated non-Gaussian random fields based on throughfall data with heavy outliers. Subsequently, we sampled the fields with three extents (plots with edge lengths of 25 m, 50 m, and 100 m), four common sampling designs (two grid-based layouts, transect and random sampling), and five sample sizes (50, 100, 150, 200, 400). We then estimated the variogram parameters by method-of-moments and residual maximum likelihood. Our key findings are threefold. First, the choice of the extent has a substantial influence on the estimation of the variogram. A comparatively small ratio of the extent to the correlation length is beneficial for variogram estimation. Second, a combination of a minimum sample size of 150, a design that ensures the sampling of small distances and variogram estimation by residual maximum likelihood offers a good compromise between accuracy and efficiency. Third, studies relying on method-of-moments based variogram estimation may have to employ at least 200 sampling points for reliable variogram estimates. These suggested sample sizes exceed the numbers recommended by studies dealing with Gaussian data by up to 100 %. Given that most previous throughfall studies relied on method-of-moments variogram estimation and sample sizes << 200, our current knowledge about throughfall spatial variability stands on shaky ground.

Detecting spatial structures in throughfall data: The effect of extent, sample size, sampling design, and variogram estimation method

NASA Astrophysics Data System (ADS)

Voss, Sebastian; Zimmermann, Beate; Zimmermann, Alexander

2016-09-01

In the last decades, an increasing number of studies analyzed spatial patterns in throughfall by means of variograms. The estimation of the variogram from sample data requires an appropriate sampling scheme: most importantly, a large sample and a layout of sampling locations that often has to serve both variogram estimation and geostatistical prediction. While some recommendations on these aspects exist, they focus on Gaussian data and high ratios of the variogram range to the extent of the study area. However, many hydrological data, and throughfall data in particular, do not follow a Gaussian distribution. In this study, we examined the effect of extent, sample size, sampling design, and calculation method on variogram estimation of throughfall data. For our investigation, we first generated non-Gaussian random fields based on throughfall data with large outliers. Subsequently, we sampled the fields with three extents (plots with edge lengths of 25 m, 50 m, and 100 m), four common sampling designs (two grid-based layouts, transect and random sampling) and five sample sizes (50, 100, 150, 200, 400). We then estimated the variogram parameters by method-of-moments (non-robust and robust estimators) and residual maximum likelihood. Our key findings are threefold. First, the choice of the extent has a substantial influence on the estimation of the variogram. A comparatively small ratio of the extent to the correlation length is beneficial for variogram estimation. Second, a combination of a minimum sample size of 150, a design that ensures the sampling of small distances and variogram estimation by residual maximum likelihood offers a good compromise between accuracy and efficiency. Third, studies relying on method-of-moments based variogram estimation may have to employ at least 200 sampling points for reliable variogram estimates. These suggested sample sizes exceed the number recommended by studies dealing with Gaussian data by up to 100 %. Given that most previous throughfall studies relied on method-of-moments variogram estimation and sample sizes ≪200, currently available data are prone to large uncertainties.

Clustering of Multispectral Airborne Laser Scanning Data Using Gaussian Decomposition

NASA Astrophysics Data System (ADS)

Morsy, S.; Shaker, A.; El-Rabbany, A.

2017-09-01

With the evolution of the LiDAR technology, multispectral airborne laser scanning systems are currently available. The first operational multispectral airborne LiDAR sensor, the Optech Titan, acquires LiDAR point clouds at three different wavelengths (1.550, 1.064, 0.532 μm), allowing the acquisition of different spectral information of land surface. Consequently, the recent studies are devoted to use the radiometric information (i.e., intensity) of the LiDAR data along with the geometric information (e.g., height) for classification purposes. In this study, a data clustering method, based on Gaussian decomposition, is presented. First, a ground filtering mechanism is applied to separate non-ground from ground points. Then, three normalized difference vegetation indices (NDVIs) are computed for both non-ground and ground points, followed by histograms construction from each NDVI. The Gaussian function model is used to decompose the histograms into a number of Gaussian components. The maximum likelihood estimate of the Gaussian components is then optimized using Expectation - Maximization algorithm. The intersection points of the adjacent Gaussian components are subsequently used as threshold values, whereas different classes can be clustered. This method is used to classify the terrain of an urban area in Oshawa, Ontario, Canada, into four main classes, namely roofs, trees, asphalt and grass. It is shown that the proposed method has achieved an overall accuracy up to 95.1 % using different NDVIs.

ExGUtils: A Python Package for Statistical Analysis With the ex-Gaussian Probability Density.

PubMed

Moret-Tatay, Carmen; Gamermann, Daniel; Navarro-Pardo, Esperanza; Fernández de Córdoba Castellá, Pedro

2018-01-01

The study of reaction times and their underlying cognitive processes is an important field in Psychology. Reaction times are often modeled through the ex-Gaussian distribution, because it provides a good fit to multiple empirical data. The complexity of this distribution makes the use of computational tools an essential element. Therefore, there is a strong need for efficient and versatile computational tools for the research in this area. In this manuscript we discuss some mathematical details of the ex-Gaussian distribution and apply the ExGUtils package, a set of functions and numerical tools, programmed for python, developed for numerical analysis of data involving the ex-Gaussian probability density. In order to validate the package, we present an extensive analysis of fits obtained with it, discuss advantages and differences between the least squares and maximum likelihood methods and quantitatively evaluate the goodness of the obtained fits (which is usually an overlooked point in most literature in the area). The analysis done allows one to identify outliers in the empirical datasets and criteriously determine if there is a need for data trimming and at which points it should be done.

ExGUtils: A Python Package for Statistical Analysis With the ex-Gaussian Probability Density

PubMed Central

Moret-Tatay, Carmen; Gamermann, Daniel; Navarro-Pardo, Esperanza; Fernández de Córdoba Castellá, Pedro

2018-01-01

The study of reaction times and their underlying cognitive processes is an important field in Psychology. Reaction times are often modeled through the ex-Gaussian distribution, because it provides a good fit to multiple empirical data. The complexity of this distribution makes the use of computational tools an essential element. Therefore, there is a strong need for efficient and versatile computational tools for the research in this area. In this manuscript we discuss some mathematical details of the ex-Gaussian distribution and apply the ExGUtils package, a set of functions and numerical tools, programmed for python, developed for numerical analysis of data involving the ex-Gaussian probability density. In order to validate the package, we present an extensive analysis of fits obtained with it, discuss advantages and differences between the least squares and maximum likelihood methods and quantitatively evaluate the goodness of the obtained fits (which is usually an overlooked point in most literature in the area). The analysis done allows one to identify outliers in the empirical datasets and criteriously determine if there is a need for data trimming and at which points it should be done. PMID:29765345

The 6dFGS Peculiar Velocity Field

NASA Astrophysics Data System (ADS)

Springob, Chris M.; Magoulas, C.; Colless, M.; Mould, J.; Erdogdu, P.; Jones, D. H.; Lucey, J.; Campbell, L.; Merson, A.; Jarrett, T.

2012-01-01

The 6dF Galaxy Survey (6dFGS) is an all southern sky galaxy survey, including 125,000 redshifts and a Fundamental Plane (FP) subsample of 10,000 peculiar velocities, making it the largest peculiar velocity sample to date. We have fit the FP using a maximum likelihood fit to a tri-variate Gaussian. We subsequently compute a Bayesian probability distribution for every possible peculiar velocity for each of the 10,000 galaxies, derived from the tri-variate Gaussian probability density distribution, accounting for our selection effects and measurement errors. We construct a predicted peculiar velocity field from the 2MASS redshift survey, and compare our observed 6dFGS velocity field to the predicted field. We discuss the resulting agreement between the observed and predicted fields, and the implications for measurements of the bias parameter and bulk flow.

Efficient, adaptive estimation of two-dimensional firing rate surfaces via Gaussian process methods.

PubMed

Rad, Kamiar Rahnama; Paninski, Liam

2010-01-01

Estimating two-dimensional firing rate maps is a common problem, arising in a number of contexts: the estimation of place fields in hippocampus, the analysis of temporally nonstationary tuning curves in sensory and motor areas, the estimation of firing rates following spike-triggered covariance analyses, etc. Here we introduce methods based on Gaussian process nonparametric Bayesian techniques for estimating these two-dimensional rate maps. These techniques offer a number of advantages: the estimates may be computed efficiently, come equipped with natural errorbars, adapt their smoothness automatically to the local density and informativeness of the observed data, and permit direct fitting of the model hyperparameters (e.g., the prior smoothness of the rate map) via maximum marginal likelihood. We illustrate the method's flexibility and performance on a variety of simulated and real data.

Lévy-like diffusion in eye movements during spoken-language comprehension.

PubMed

Stephen, Damian G; Mirman, Daniel; Magnuson, James S; Dixon, James A

2009-05-01

This study explores the diffusive properties of human eye movements during a language comprehension task. In this task, adults are given auditory instructions to locate named objects on a computer screen. Although it has been convention to model visual search as standard Brownian diffusion, we find evidence that eye movements are hyperdiffusive. Specifically, we use comparisons of maximum-likelihood fit as well as standard deviation analysis and diffusion entropy analysis to show that visual search during language comprehension exhibits Lévy-like rather than Gaussian diffusion.

Lévy-like diffusion in eye movements during spoken-language comprehension

NASA Astrophysics Data System (ADS)

Stephen, Damian G.; Mirman, Daniel; Magnuson, James S.; Dixon, James A.

2009-05-01

This study explores the diffusive properties of human eye movements during a language comprehension task. In this task, adults are given auditory instructions to locate named objects on a computer screen. Although it has been convention to model visual search as standard Brownian diffusion, we find evidence that eye movements are hyperdiffusive. Specifically, we use comparisons of maximum-likelihood fit as well as standard deviation analysis and diffusion entropy analysis to show that visual search during language comprehension exhibits Lévy-like rather than Gaussian diffusion.

Robust geostatistical analysis of spatial data

NASA Astrophysics Data System (ADS)

Papritz, Andreas; Künsch, Hans Rudolf; Schwierz, Cornelia; Stahel, Werner A.

2013-04-01

Most of the geostatistical software tools rely on non-robust algorithms. This is unfortunate, because outlying observations are rather the rule than the exception, in particular in environmental data sets. Outliers affect the modelling of the large-scale spatial trend, the estimation of the spatial dependence of the residual variation and the predictions by kriging. Identifying outliers manually is cumbersome and requires expertise because one needs parameter estimates to decide which observation is a potential outlier. Moreover, inference after the rejection of some observations is problematic. A better approach is to use robust algorithms that prevent automatically that outlying observations have undue influence. Former studies on robust geostatistics focused on robust estimation of the sample variogram and ordinary kriging without external drift. Furthermore, Richardson and Welsh (1995) proposed a robustified version of (restricted) maximum likelihood ([RE]ML) estimation for the variance components of a linear mixed model, which was later used by Marchant and Lark (2007) for robust REML estimation of the variogram. We propose here a novel method for robust REML estimation of the variogram of a Gaussian random field that is possibly contaminated by independent errors from a long-tailed distribution. It is based on robustification of estimating equations for the Gaussian REML estimation (Welsh and Richardson, 1997). Besides robust estimates of the parameters of the external drift and of the variogram, the method also provides standard errors for the estimated parameters, robustified kriging predictions at both sampled and non-sampled locations and kriging variances. Apart from presenting our modelling framework, we shall present selected simulation results by which we explored the properties of the new method. This will be complemented by an analysis a data set on heavy metal contamination of the soil in the vicinity of a metal smelter. Marchant, B.P. and Lark, R.M. 2007. Robust estimation of the variogram by residual maximum likelihood. Geoderma 140: 62-72. Richardson, A.M. and Welsh, A.H. 1995. Robust restricted maximum likelihood in mixed linear models. Biometrics 51: 1429-1439. Welsh, A.H. and Richardson, A.M. 1997. Approaches to the robust estimation of mixed models. In: Handbook of Statistics Vol. 15, Elsevier, pp. 343-384.

a Threshold-Free Filtering Algorithm for Airborne LIDAR Point Clouds Based on Expectation-Maximization

NASA Astrophysics Data System (ADS)

Hui, Z.; Cheng, P.; Ziggah, Y. Y.; Nie, Y.

2018-04-01

Filtering is a key step for most applications of airborne LiDAR point clouds. Although lots of filtering algorithms have been put forward in recent years, most of them suffer from parameters setting or thresholds adjusting, which will be time-consuming and reduce the degree of automation of the algorithm. To overcome this problem, this paper proposed a threshold-free filtering algorithm based on expectation-maximization. The proposed algorithm is developed based on an assumption that point clouds are seen as a mixture of Gaussian models. The separation of ground points and non-ground points from point clouds can be replaced as a separation of a mixed Gaussian model. Expectation-maximization (EM) is applied for realizing the separation. EM is used to calculate maximum likelihood estimates of the mixture parameters. Using the estimated parameters, the likelihoods of each point belonging to ground or object can be computed. After several iterations, point clouds can be labelled as the component with a larger likelihood. Furthermore, intensity information was also utilized to optimize the filtering results acquired using the EM method. The proposed algorithm was tested using two different datasets used in practice. Experimental results showed that the proposed method can filter non-ground points effectively. To quantitatively evaluate the proposed method, this paper adopted the dataset provided by the ISPRS for the test. The proposed algorithm can obtain a 4.48 % total error which is much lower than most of the eight classical filtering algorithms reported by the ISPRS.

The impact of covariance misspecification in multivariate Gaussian mixtures on estimation and inference: an application to longitudinal modeling.

PubMed

Heggeseth, Brianna C; Jewell, Nicholas P

2013-07-20

Multivariate Gaussian mixtures are a class of models that provide a flexible parametric approach for the representation of heterogeneous multivariate outcomes. When the outcome is a vector of repeated measurements taken on the same subject, there is often inherent dependence between observations. However, a common covariance assumption is conditional independence-that is, given the mixture component label, the outcomes for subjects are independent. In this paper, we study, through asymptotic bias calculations and simulation, the impact of covariance misspecification in multivariate Gaussian mixtures. Although maximum likelihood estimators of regression and mixing probability parameters are not consistent under misspecification, they have little asymptotic bias when mixture components are well separated or if the assumed correlation is close to the truth even when the covariance is misspecified. We also present a robust standard error estimator and show that it outperforms conventional estimators in simulations and can indicate that the model is misspecified. Body mass index data from a national longitudinal study are used to demonstrate the effects of misspecification on potential inferences made in practice. Copyright © 2013 John Wiley & Sons, Ltd.

Hunting high and low: disentangling primordial and late-time non-Gaussianity with cosmic densities in spheres

NASA Astrophysics Data System (ADS)

Uhlemann, C.; Pajer, E.; Pichon, C.; Nishimichi, T.; Codis, S.; Bernardeau, F.

2018-03-01

Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point probability distribution function and the two-point clustering of spherically averaged cosmic densities (sphere bias). Sphere bias extends the idea of halo bias to intermediate density environments and voids as underdense regions. In the presence of primordial non-Gaussianity, sphere bias displays a strong scale dependence relevant for both high- and low-density regions, which is predicted analytically. The statistics of densities in spheres are built to model primordial non-Gaussianity via an initial skewness with a scale dependence that depends on the bispectrum of the underlying model. The analytical formulas with the measured non-linear dark matter variance as input are successfully tested against numerical simulations. For local non-Gaussianity with a range from fNL = -100 to +100, they are found to agree within 2 per cent or better for densities ρ ∈ [0.5, 3] in spheres of radius 15 Mpc h-1 down to z = 0.35. The validity of the large deviation statistics formalism is thereby established for all observationally relevant local-type departures from perfectly Gaussian initial conditions. The corresponding estimators for the amplitude of the non-linear variance σ8 and primordial skewness fNL are validated using a fiducial joint maximum likelihood experiment. The influence of observational effects and the prospects for a future detection of primordial non-Gaussianity from joint one- and two-point densities-in-spheres statistics are discussed.

Automated thematic mapping and change detection of ERTS-A images. [digital interpretation of Arizona imagery

NASA Technical Reports Server (NTRS)

Gramenopoulos, N. (Principal Investigator)

1973-01-01

The author has identified the following significant results. For the recognition of terrain types, spatial signatures are developed from the diffraction patterns of small areas of ERTS-1 images. This knowledge is exploited for the measurements of a small number of meaningful spatial features from the digital Fourier transforms of ERTS-1 image cells containing 32 x 32 picture elements. Using these spatial features and a heuristic algorithm, the terrain types in the vicinity of Phoenix, Arizona were recognized by the computer with a high accuracy. Then, the spatial features were combined with spectral features and using the maximum likelihood criterion the recognition accuracy of terrain types increased substantially. It was determined that the recognition accuracy with the maximum likelihood criterion depends on the statistics of the feature vectors. Nonlinear transformations of the feature vectors are required so that the terrain class statistics become approximately Gaussian. It was also determined that for a given geographic area the statistics of the classes remain invariable for a period of a month but vary substantially between seasons.

Maximum-likelihood spectral estimation and adaptive filtering techniques with application to airborne Doppler weather radar. Thesis Technical Report No. 20

NASA Technical Reports Server (NTRS)

Lai, Jonathan Y.

1994-01-01

This dissertation focuses on the signal processing problems associated with the detection of hazardous windshears using airborne Doppler radar when weak weather returns are in the presence of strong clutter returns. In light of the frequent inadequacy of spectral-processing oriented clutter suppression methods, we model a clutter signal as multiple sinusoids plus Gaussian noise, and propose adaptive filtering approaches that better capture the temporal characteristics of the signal process. This idea leads to two research topics in signal processing: (1) signal modeling and parameter estimation, and (2) adaptive filtering in this particular signal environment. A high-resolution, low SNR threshold maximum likelihood (ML) frequency estimation and signal modeling algorithm is devised and proves capable of delineating both the spectral and temporal nature of the clutter return. Furthermore, the Least Mean Square (LMS) -based adaptive filter's performance for the proposed signal model is investigated, and promising simulation results have testified to its potential for clutter rejection leading to more accurate estimation of windspeed thus obtaining a better assessment of the windshear hazard.

Comparison of Kasai Autocorrelation and Maximum Likelihood Estimators for Doppler Optical Coherence Tomography

PubMed Central

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

Upper bounds on sequential decoding performance parameters

NASA Technical Reports Server (NTRS)

Jelinek, F.

1974-01-01

This paper presents the best obtainable random coding and expurgated upper bounds on the probabilities of undetectable error, of t-order failure (advance to depth t into an incorrect subset), and of likelihood rise in the incorrect subset, applicable to sequential decoding when the metric bias G is arbitrary. Upper bounds on the Pareto exponent are also presented. The G-values optimizing each of the parameters of interest are determined, and are shown to lie in intervals that in general have nonzero widths. The G-optimal expurgated bound on undetectable error is shown to agree with that for maximum likelihood decoding of convolutional codes, and that on failure agrees with the block code expurgated bound. Included are curves evaluating the bounds for interesting choices of G and SNR for a binary-input quantized-output Gaussian additive noise channel.

Combining MLC and SVM Classifiers for Learning Based Decision Making: Analysis and Evaluations

PubMed Central

Zhang, Yi; Ren, Jinchang; Jiang, Jianmin

2015-01-01

Maximum likelihood classifier (MLC) and support vector machines (SVM) are two commonly used approaches in machine learning. MLC is based on Bayesian theory in estimating parameters of a probabilistic model, whilst SVM is an optimization based nonparametric method in this context. Recently, it is found that SVM in some cases is equivalent to MLC in probabilistically modeling the learning process. In this paper, MLC and SVM are combined in learning and classification, which helps to yield probabilistic output for SVM and facilitate soft decision making. In total four groups of data are used for evaluations, covering sonar, vehicle, breast cancer, and DNA sequences. The data samples are characterized in terms of Gaussian/non-Gaussian distributed and balanced/unbalanced samples which are then further used for performance assessment in comparing the SVM and the combined SVM-MLC classifier. Interesting results are reported to indicate how the combined classifier may work under various conditions. PMID:26089862

Combining MLC and SVM Classifiers for Learning Based Decision Making: Analysis and Evaluations.

PubMed

Zhang, Yi; Ren, Jinchang; Jiang, Jianmin

2015-01-01

Maximum likelihood classifier (MLC) and support vector machines (SVM) are two commonly used approaches in machine learning. MLC is based on Bayesian theory in estimating parameters of a probabilistic model, whilst SVM is an optimization based nonparametric method in this context. Recently, it is found that SVM in some cases is equivalent to MLC in probabilistically modeling the learning process. In this paper, MLC and SVM are combined in learning and classification, which helps to yield probabilistic output for SVM and facilitate soft decision making. In total four groups of data are used for evaluations, covering sonar, vehicle, breast cancer, and DNA sequences. The data samples are characterized in terms of Gaussian/non-Gaussian distributed and balanced/unbalanced samples which are then further used for performance assessment in comparing the SVM and the combined SVM-MLC classifier. Interesting results are reported to indicate how the combined classifier may work under various conditions.

Cardiac conduction velocity estimation from sequential mapping assuming known Gaussian distribution for activation time estimation error.

PubMed

Shariat, Mohammad Hassan; Gazor, Saeed; Redfearn, Damian

2016-08-01

In this paper, we study the problem of the cardiac conduction velocity (CCV) estimation for the sequential intracardiac mapping. We assume that the intracardiac electrograms of several cardiac sites are sequentially recorded, their activation times (ATs) are extracted, and the corresponding wavefronts are specified. The locations of the mapping catheter's electrodes and the ATs of the wavefronts are used here for the CCV estimation. We assume that the extracted ATs include some estimation errors, which we model with zero-mean white Gaussian noise values with known variances. Assuming stable planar wavefront propagation, we derive the maximum likelihood CCV estimator, when the synchronization times between various recording sites are unknown. We analytically evaluate the performance of the CCV estimator and provide its mean square estimation error. Our simulation results confirm the accuracy of the proposed method and the error analysis of the proposed CCV estimator.

BAO from Angular Clustering: Optimization and Mitigation of Theoretical Systematics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crocce, M.; et al.

We study the theoretical systematics and optimize the methodology in Baryon Acoustic Oscillations (BAO) detections using the angular correlation function with tomographic bins. We calibrate and optimize the pipeline for the Dark Energy Survey Year 1 dataset using 1800 mocks. We compare the BAO fitting results obtained with three estimators: the Maximum Likelihood Estimator (MLE), Profile Likelihood, and Markov Chain Monte Carlo. The MLE method yields the least bias in the fit results (bias/spreadmore » $$\\sim 0.02$$) and the error bar derived is the closest to the Gaussian results (1% from 68% Gaussian expectation). When there is mismatch between the template and the data either due to incorrect fiducial cosmology or photo-$z$ error, the MLE again gives the least-biased results. The BAO angular shift that is estimated based on the sound horizon and the angular diameter distance agree with the numerical fit. Various analysis choices are further tested: the number of redshift bins, cross-correlations, and angular binning. We propose two methods to correct the mock covariance when the final sample properties are slightly different from those used to create the mock. We show that the sample changes can be accommodated with the help of the Gaussian covariance matrix or more effectively using the eigenmode expansion of the mock covariance. The eigenmode expansion is significantly less susceptible to statistical fluctuations relative to the direct measurements of the covariance matrix because the number of free parameters is substantially reduced [$p$ parameters versus $p(p+1)/2$ from direct measurement].« less

Assessing compatibility of direct detection data: halo-independent global likelihood analyses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gelmini, Graciela B.; Huh, Ji-Haeng; Witte, Samuel J.

2016-10-18

We present two different halo-independent methods to assess the compatibility of several direct dark matter detection data sets for a given dark matter model using a global likelihood consisting of at least one extended likelihood and an arbitrary number of Gaussian or Poisson likelihoods. In the first method we find the global best fit halo function (we prove that it is a unique piecewise constant function with a number of down steps smaller than or equal to a maximum number that we compute) and construct a two-sided pointwise confidence band at any desired confidence level, which can then be comparedmore » with those derived from the extended likelihood alone to assess the joint compatibility of the data. In the second method we define a “constrained parameter goodness-of-fit” test statistic, whose p-value we then use to define a “plausibility region” (e.g. where p≥10%). For any halo function not entirely contained within the plausibility region, the level of compatibility of the data is very low (e.g. p<10%). We illustrate these methods by applying them to CDMS-II-Si and SuperCDMS data, assuming dark matter particles with elastic spin-independent isospin-conserving interactions or exothermic spin-independent isospin-violating interactions.« less

Robust Gaussian Graphical Modeling via l1 Penalization

PubMed Central

Sun, Hokeun; Li, Hongzhe

2012-01-01

Summary Gaussian graphical models have been widely used as an effective method for studying the conditional independency structure among genes and for constructing genetic networks. However, gene expression data typically have heavier tails or more outlying observations than the standard Gaussian distribution. Such outliers in gene expression data can lead to wrong inference on the dependency structure among the genes. We propose a l1 penalized estimation procedure for the sparse Gaussian graphical models that is robustified against possible outliers. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its own likelihood. An efficient computational algorithm based on the coordinate gradient descent method is developed to obtain the minimizer of the negative penalized robustified-likelihood, where nonzero elements of the concentration matrix represents the graphical links among the genes. After the graphical structure is obtained, we re-estimate the positive definite concentration matrix using an iterative proportional fitting algorithm. Through simulations, we demonstrate that the proposed robust method performs much better than the graphical Lasso for the Gaussian graphical models in terms of both graph structure selection and estimation when outliers are present. We apply the robust estimation procedure to an analysis of yeast gene expression data and show that the resulting graph has better biological interpretation than that obtained from the graphical Lasso. PMID:23020775

A Variational Approach to Simultaneous Image Segmentation and Bias Correction.

PubMed

Zhang, Kaihua; Liu, Qingshan; Song, Huihui; Li, Xuelong

2015-08-01

This paper presents a novel variational approach for simultaneous estimation of bias field and segmentation of images with intensity inhomogeneity. We model intensity of inhomogeneous objects to be Gaussian distributed with different means and variances, and then introduce a sliding window to map the original image intensity onto another domain, where the intensity distribution of each object is still Gaussian but can be better separated. The means of the Gaussian distributions in the transformed domain can be adaptively estimated by multiplying the bias field with a piecewise constant signal within the sliding window. A maximum likelihood energy functional is then defined on each local region, which combines the bias field, the membership function of the object region, and the constant approximating the true signal from its corresponding object. The energy functional is then extended to the whole image domain by the Bayesian learning approach. An efficient iterative algorithm is proposed for energy minimization, via which the image segmentation and bias field correction are simultaneously achieved. Furthermore, the smoothness of the obtained optimal bias field is ensured by the normalized convolutions without extra cost. Experiments on real images demonstrated the superiority of the proposed algorithm to other state-of-the-art representative methods.

Beyond Roughness: Maximum-Likelihood Estimation of Topographic "Structure" on Venus and Elsewhere in the Solar System

NASA Astrophysics Data System (ADS)

Simons, F. J.; Eggers, G. L.; Lewis, K. W.; Olhede, S. C.

2015-12-01

What numbers "capture" topography? If stationary, white, and Gaussian: mean and variance. But "whiteness" is strong; we are led to a "baseline" over which to compute means and variances. We then have subscribed to topography as a correlated process, and to the estimation (noisy, afftected by edge effects) of the parameters of a spatial or spectral covariance function. What if the covariance function or the point process itself aren't Gaussian? What if the region under study isn't regularly shaped or sampled? How can results from differently sized patches be compared robustly? We present a spectral-domain "Whittle" maximum-likelihood procedure that circumvents these difficulties and answers the above questions. The key is the Matern form, whose parameters (variance, range, differentiability) define the shape of the covariance function (Gaussian, exponential, ..., are all special cases). We treat edge effects in simulation and in estimation. Data tapering allows for the irregular regions. We determine the estimation variance of all parameters. And the "best" estimate may not be "good enough": we test whether the "model" itself warrants rejection. We illustrate our methodology on geologically mapped patches of Venus. Surprisingly few numbers capture planetary topography. We derive them, with uncertainty bounds, we simulate "new" realizations of patches that look to the geologists exactly as if they were derived from similar processes. Our approach holds in 1, 2, and 3 spatial dimensions, and generalizes to multiple variables, e.g. when topography and gravity are being considered jointly (perhaps linked by flexural rigidity, erosion, or other surface and sub-surface modifying processes). Our results have widespread implications for the study of planetary topography in the Solar System, and are interpreted in the light of trying to derive "process" from "parameters", the end goal to assign likely formation histories for the patches under consideration. Our results should also be relevant for whomever needed to perform spatial interpolation or out-of-sample extension (e.g. kriging), machine learning and feature detection, on geological data. We present procedural details but focus on high-level results that have real-world implications for the study of Venus, Earth, other planets, and moons.

Gaussian process based intelligent sampling for measuring nano-structure surfaces

NASA Astrophysics Data System (ADS)

Sun, L. J.; Ren, M. J.; Yin, Y. H.

2016-09-01

Nanotechnology is the science and engineering that manipulate matters at nano scale, which can be used to create many new materials and devices with a vast range of applications. As the nanotech product increasingly enters the commercial marketplace, nanometrology becomes a stringent and enabling technology for the manipulation and the quality control of the nanotechnology. However, many measuring instruments, for instance scanning probe microscopy, are limited to relatively small area of hundreds of micrometers with very low efficiency. Therefore some intelligent sampling strategies should be required to improve the scanning efficiency for measuring large area. This paper presents a Gaussian process based intelligent sampling method to address this problem. The method makes use of Gaussian process based Bayesian regression as a mathematical foundation to represent the surface geometry, and the posterior estimation of Gaussian process is computed by combining the prior probability distribution with the maximum likelihood function. Then each sampling point is adaptively selected by determining the position which is the most likely outside of the required tolerance zone among the candidates and then inserted to update the model iteratively. Both simulationson the nominal surface and manufactured surface have been conducted on nano-structure surfaces to verify the validity of the proposed method. The results imply that the proposed method significantly improves the measurement efficiency in measuring large area structured surfaces.

Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic.

PubMed

Yokoyama, Jun'ichi

2014-01-01

After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping where the observed marginal distribution and the two-body correlation function are fully taken into account. We then apply these two approaches to Student's t-distribution which has a larger tails than Gaussian. It is shown that while both methods work well in the case the non-Gaussianity is small, only the latter method works well for highly non-Gaussian case.

The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey's h Transformation as a Special Case

PubMed Central

Goerg, Georg M.

2015-01-01

I present a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables. The tail behavior of this heavy tail Lambert  W × F X random variable depends on a tail parameter δ ≥ 0: for δ = 0, Y ≡ X, for δ > 0 Y has heavier tails than X. For X being Gaussian it reduces to Tukey's h distribution. The Lambert W function provides an explicit inverse transformation, which can thus remove heavy tails from observed data. It also provides closed-form expressions for the cumulative distribution (cdf) and probability density function (pdf). As a special case, these yield analytic expression for Tukey's h pdf and cdf. Parameters can be estimated by maximum likelihood and applications to S&P 500 log-returns demonstrate the usefulness of the presented methodology. The R package LambertW implements most of the introduced methodology and is publicly available on CRAN. PMID:26380372

A comparison of image restoration approaches applied to three-dimensional confocal and wide-field fluorescence microscopy.

PubMed

Verveer, P. J; Gemkow, M. J; Jovin, T. M

1999-01-01

We have compared different image restoration approaches for fluorescence microscopy. The most widely used algorithms were classified with a Bayesian theory according to the assumed noise model and the type of regularization imposed. We considered both Gaussian and Poisson models for the noise in combination with Tikhonov regularization, entropy regularization, Good's roughness and without regularization (maximum likelihood estimation). Simulations of fluorescence confocal imaging were used to examine the different noise models and regularization approaches using the mean squared error criterion. The assumption of a Gaussian noise model yielded only slightly higher errors than the Poisson model. Good's roughness was the best choice for the regularization. Furthermore, we compared simulated confocal and wide-field data. In general, restored confocal data are superior to restored wide-field data, but given sufficient higher signal level for the wide-field data the restoration result may rival confocal data in quality. Finally, a visual comparison of experimental confocal and wide-field data is presented.

Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic

PubMed Central

YOKOYAMA, Jun’ichi

2014-01-01

After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping where the observed marginal distribution and the two-body correlation function are fully taken into account. We then apply these two approaches to Student’s t-distribution which has a larger tails than Gaussian. It is shown that while both methods work well in the case the non-Gaussianity is small, only the latter method works well for highly non-Gaussian case. PMID:25504231

The meta-Gaussian Bayesian Processor of forecasts and associated preliminary experiments

NASA Astrophysics Data System (ADS)

Chen, Fajing; Jiao, Meiyan; Chen, Jing

2013-04-01

Public weather services are trending toward providing users with probabilistic weather forecasts, in place of traditional deterministic forecasts. Probabilistic forecasting techniques are continually being improved to optimize available forecasting information. The Bayesian Processor of Forecast (BPF), a new statistical method for probabilistic forecast, can transform a deterministic forecast into a probabilistic forecast according to the historical statistical relationship between observations and forecasts generated by that forecasting system. This technique accounts for the typical forecasting performance of a deterministic forecasting system in quantifying the forecast uncertainty. The meta-Gaussian likelihood model is suitable for a variety of stochastic dependence structures with monotone likelihood ratios. The meta-Gaussian BPF adopting this kind of likelihood model can therefore be applied across many fields, including meteorology and hydrology. The Bayes theorem with two continuous random variables and the normal-linear BPF are briefly introduced. The meta-Gaussian BPF for a continuous predictand using a single predictor is then presented and discussed. The performance of the meta-Gaussian BPF is tested in a preliminary experiment. Control forecasts of daily surface temperature at 0000 UTC at Changsha and Wuhan stations are used as the deterministic forecast data. These control forecasts are taken from ensemble predictions with a 96-h lead time generated by the National Meteorological Center of the China Meteorological Administration, the European Centre for Medium-Range Weather Forecasts, and the US National Centers for Environmental Prediction during January 2008. The results of the experiment show that the meta-Gaussian BPF can transform a deterministic control forecast of surface temperature from any one of the three ensemble predictions into a useful probabilistic forecast of surface temperature. These probabilistic forecasts quantify the uncertainty of the control forecast; accordingly, the performance of the probabilistic forecasts differs based on the source of the underlying deterministic control forecasts.

Empirical Bayes Gaussian likelihood estimation of exposure distributions from pooled samples in human biomonitoring.

PubMed

Li, Xiang; Kuk, Anthony Y C; Xu, Jinfeng

2014-12-10

Human biomonitoring of exposure to environmental chemicals is important. Individual monitoring is not viable because of low individual exposure level or insufficient volume of materials and the prohibitive cost of taking measurements from many subjects. Pooling of samples is an efficient and cost-effective way to collect data. Estimation is, however, complicated as individual values within each pool are not observed but are only known up to their average or weighted average. The distribution of such averages is intractable when the individual measurements are lognormally distributed, which is a common assumption. We propose to replace the intractable distribution of the pool averages by a Gaussian likelihood to obtain parameter estimates. If the pool size is large, this method produces statistically efficient estimates, but regardless of pool size, the method yields consistent estimates as the number of pools increases. An empirical Bayes (EB) Gaussian likelihood approach, as well as its Bayesian analog, is developed to pool information from various demographic groups by using a mixed-effect formulation. We also discuss methods to estimate the underlying mean-variance relationship and to select a good model for the means, which can be incorporated into the proposed EB or Bayes framework. By borrowing strength across groups, the EB estimator is more efficient than the individual group-specific estimator. Simulation results show that the EB Gaussian likelihood estimates outperform a previous method proposed for the National Health and Nutrition Examination Surveys with much smaller bias and better coverage in interval estimation, especially after correction of bias. Copyright © 2014 John Wiley & Sons, Ltd.

Corn and soybean Landsat MSS classification performance as a function of scene characteristics

NASA Technical Reports Server (NTRS)

Batista, G. T.; Hixson, M. M.; Bauer, M. E.

1982-01-01

In order to fully utilize remote sensing to inventory crop production, it is important to identify the factors that affect the accuracy of Landsat classifications. The objective of this study was to investigate the effect of scene characteristics involving crop, soil, and weather variables on the accuracy of Landsat classifications of corn and soybeans. Segments sampling the U.S. Corn Belt were classified using a Gaussian maximum likelihood classifier on multitemporally registered data from two key acquisition periods. Field size had a strong effect on classification accuracy with small fields tending to have low accuracies even when the effect of mixed pixels was eliminated. Other scene characteristics accounting for variability in classification accuracy included proportions of corn and soybeans, crop diversity index, proportion of all field crops, soil drainage, slope, soil order, long-term average soybean yield, maximum yield, relative position of the segment in the Corn Belt, weather, and crop development stage.

A Modularized Efficient Framework for Non-Markov Time Series Estimation

NASA Astrophysics Data System (ADS)

Schamberg, Gabriel; Ba, Demba; Coleman, Todd P.

2018-06-01

We present a compartmentalized approach to finding the maximum a-posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal processing problems with non-Markov signal dynamics (e.g. group sparsity) and/or non-Gaussian measurement models (e.g. point process observation models used in neuroscience). Through the use of auxiliary variables in the MAP estimation problem, we show that a consensus formulation of the alternating direction method of multipliers (ADMM) enables iteratively computing separate estimates based on the likelihood and prior and subsequently "averaging" them in an appropriate sense using a Kalman smoother. As such, this can be applied to a broad class of problem settings and only requires modular adjustments when interchanging various aspects of the statistical model. Under broad log-concavity assumptions, we show that the separate estimation problems are convex optimization problems and that the iterative algorithm converges to the MAP estimate. As such, this framework can capture non-Markov latent time series models and non-Gaussian measurement models. We provide example applications involving (i) group-sparsity priors, within the context of electrophysiologic specrotemporal estimation, and (ii) non-Gaussian measurement models, within the context of dynamic analyses of learning with neural spiking and behavioral observations.

Probabilistic Elastic Part Model: A Pose-Invariant Representation for Real-World Face Verification.

PubMed

Li, Haoxiang; Hua, Gang

2018-04-01

Pose variation remains to be a major challenge for real-world face recognition. We approach this problem through a probabilistic elastic part model. We extract local descriptors (e.g., LBP or SIFT) from densely sampled multi-scale image patches. By augmenting each descriptor with its location, a Gaussian mixture model (GMM) is trained to capture the spatial-appearance distribution of the face parts of all face images in the training corpus, namely the probabilistic elastic part (PEP) model. Each mixture component of the GMM is confined to be a spherical Gaussian to balance the influence of the appearance and the location terms, which naturally defines a part. Given one or multiple face images of the same subject, the PEP-model builds its PEP representation by sequentially concatenating descriptors identified by each Gaussian component in a maximum likelihood sense. We further propose a joint Bayesian adaptation algorithm to adapt the universally trained GMM to better model the pose variations between the target pair of faces/face tracks, which consistently improves face verification accuracy. Our experiments show that we achieve state-of-the-art face verification accuracy with the proposed representations on the Labeled Face in the Wild (LFW) dataset, the YouTube video face database, and the CMU MultiPIE dataset.

Examining the effect of initialization strategies on the performance of Gaussian mixture modeling.

PubMed

Shireman, Emilie; Steinley, Douglas; Brusco, Michael J

2017-02-01

Mixture modeling is a popular technique for identifying unobserved subpopulations (e.g., components) within a data set, with Gaussian (normal) mixture modeling being the form most widely used. Generally, the parameters of these Gaussian mixtures cannot be estimated in closed form, so estimates are typically obtained via an iterative process. The most common estimation procedure is maximum likelihood via the expectation-maximization (EM) algorithm. Like many approaches for identifying subpopulations, finite mixture modeling can suffer from locally optimal solutions, and the final parameter estimates are dependent on the initial starting values of the EM algorithm. Initial values have been shown to significantly impact the quality of the solution, and researchers have proposed several approaches for selecting the set of starting values. Five techniques for obtaining starting values that are implemented in popular software packages are compared. Their performances are assessed in terms of the following four measures: (1) the ability to find the best observed solution, (2) settling on a solution that classifies observations correctly, (3) the number of local solutions found by each technique, and (4) the speed at which the start values are obtained. On the basis of these results, a set of recommendations is provided to the user.

Extreme deconvolution: Inferring complete distribution functions from noisy, heterogeneous and incomplete observations

NASA Astrophysics Data System (ADS)

Bovy Jo; Hogg, David W.; Roweis, Sam T.

2011-06-01

We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation-Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point carries an individual d-dimensional uncertainty covariance and has unique missing data properties. This algorithm reconstructs the error-deconvolved or "underlying" distribution function common to all samples, even when the individual data points are samples from different distributions, obtained by convolving the underlying distribution with the heteroskedastic uncertainty distribution of the data point and projecting out the missing data directions. We show how this basic algorithm can be extended with conjugate priors on all of the model parameters and a "split-and-"erge- procedure designed to avoid local maxima of the likelihood. We demonstrate the full method by applying it to the problem of inferring the three-dimensional veloc! ity distribution of stars near the Sun from noisy two-dimensional, transverse velocity measurements from the Hipparcos satellite.

Gaussian copula as a likelihood function for environmental models

NASA Astrophysics Data System (ADS)

Wani, O.; Espadas, G.; Cecinati, F.; Rieckermann, J.

2017-12-01

Parameter estimation of environmental models always comes with uncertainty. To formally quantify this parametric uncertainty, a likelihood function needs to be formulated, which is defined as the probability of observations given fixed values of the parameter set. A likelihood function allows us to infer parameter values from observations using Bayes' theorem. The challenge is to formulate a likelihood function that reliably describes the error generating processes which lead to the observed monitoring data, such as rainfall and runoff. If the likelihood function is not representative of the error statistics, the parameter inference will give biased parameter values. Several uncertainty estimation methods that are currently being used employ Gaussian processes as a likelihood function, because of their favourable analytical properties. Box-Cox transformation is suggested to deal with non-symmetric and heteroscedastic errors e.g. for flow data which are typically more uncertain in high flows than in periods with low flows. Problem with transformations is that the results are conditional on hyper-parameters, for which it is difficult to formulate the analyst's belief a priori. In an attempt to address this problem, in this research work we suggest learning the nature of the error distribution from the errors made by the model in the "past" forecasts. We use a Gaussian copula to generate semiparametric error distributions . 1) We show that this copula can be then used as a likelihood function to infer parameters, breaking away from the practice of using multivariate normal distributions. Based on the results from a didactical example of predicting rainfall runoff, 2) we demonstrate that the copula captures the predictive uncertainty of the model. 3) Finally, we find that the properties of autocorrelation and heteroscedasticity of errors are captured well by the copula, eliminating the need to use transforms. In summary, our findings suggest that copulas are an interesting departure from the usage of fully parametric distributions as likelihood functions - and they could help us to better capture the statistical properties of errors and make more reliable predictions.

Signal-to-noise ratio estimation in digital computer simulation of lowpass and bandpass systems with applications to analog and digital communications, volume 3

NASA Technical Reports Server (NTRS)

Tranter, W. H.; Turner, M. D.

1977-01-01

Techniques are developed to estimate power gain, delay, signal-to-noise ratio, and mean square error in digital computer simulations of lowpass and bandpass systems. The techniques are applied to analog and digital communications. The signal-to-noise ratio estimates are shown to be maximum likelihood estimates in additive white Gaussian noise. The methods are seen to be especially useful for digital communication systems where the mapping from the signal-to-noise ratio to the error probability can be obtained. Simulation results show the techniques developed to be accurate and quite versatile in evaluating the performance of many systems through digital computer simulation.

Real-time antenna fault diagnosis experiments at DSS 13

NASA Technical Reports Server (NTRS)

Mellstrom, J.; Pierson, C.; Smyth, P.

1992-01-01

Experimental results obtained when a previously described fault diagnosis system was run online in real time at the 34-m beam waveguide antenna at Deep Space Station (DSS) 13 are described. Experimental conditions and the quality of results are described. A neural network model and a maximum-likelihood Gaussian classifier are compared with and without a Markov component to model temporal context. At the rate of a state update every 6.4 seconds, over a period of roughly 1 hour, the neural-Markov system had zero errors (incorrect state estimates) while monitoring both faulty and normal operations. The overall results indicate that the neural-Markov combination is the most accurate model and has significant practical potential.

IMFIT: A FAST, FLEXIBLE NEW PROGRAM FOR ASTRONOMICAL IMAGE FITTING

DOE Office of Scientific and Technical Information (OSTI.GOV)

Erwin, Peter; Universitäts-Sternwarte München, Scheinerstrasse 1, D-81679 München

2015-02-01

I describe a new, open-source astronomical image-fitting program called IMFIT, specialized for galaxies but potentially useful for other sources, which is fast, flexible, and highly extensible. A key characteristic of the program is an object-oriented design that allows new types of image components (two-dimensional surface-brightness functions) to be easily written and added to the program. Image functions provided with IMFIT include the usual suspects for galaxy decompositions (Sérsic, exponential, Gaussian), along with Core-Sérsic and broken-exponential profiles, elliptical rings, and three components that perform line-of-sight integration through three-dimensional luminosity-density models of disks and rings seen at arbitrary inclinations. Available minimization algorithmsmore » include Levenberg-Marquardt, Nelder-Mead simplex, and Differential Evolution, allowing trade-offs between speed and decreased sensitivity to local minima in the fit landscape. Minimization can be done using the standard χ{sup 2} statistic (using either data or model values to estimate per-pixel Gaussian errors, or else user-supplied error images) or Poisson-based maximum-likelihood statistics; the latter approach is particularly appropriate for cases of Poisson data in the low-count regime. I show that fitting low-signal-to-noise ratio galaxy images using χ{sup 2} minimization and individual-pixel Gaussian uncertainties can lead to significant biases in fitted parameter values, which are avoided if a Poisson-based statistic is used; this is true even when Gaussian read noise is present.« less

Maximum-likelihood-based extended-source spatial acquisition and tracking for planetary optical communications

NASA Astrophysics Data System (ADS)

Tsou, Haiping; Yan, Tsun-Yee

1999-04-01

This paper describes an extended-source spatial acquisition and tracking scheme for planetary optical communications. This scheme uses the Sun-lit Earth image as the beacon signal, which can be computed according to the current Sun-Earth-Probe angle from a pre-stored Earth image or a received snapshot taken by other Earth-orbiting satellite. Onboard the spacecraft, the reference image is correlated in the transform domain with the received image obtained from a detector array, which is assumed to have each of its pixels corrupted by an independent additive white Gaussian noise. The coordinate of the ground station is acquired and tracked, respectively, by an open-loop acquisition algorithm and a closed-loop tracking algorithm derived from the maximum likelihood criterion. As shown in the paper, the optimal spatial acquisition requires solving two nonlinear equations, or iteratively solving their linearized variants, to estimate the coordinate when translation in the relative positions of onboard and ground transceivers is considered. Similar assumption of linearization leads to the closed-loop spatial tracking algorithm in which the loop feedback signals can be derived from the weighted transform-domain correlation. Numerical results using a sample Sun-lit Earth image demonstrate that sub-pixel resolutions can be achieved by this scheme in a high disturbance environment.

CFHTLenS: a Gaussian likelihood is a sufficient approximation for a cosmological analysis of third-order cosmic shear statistics

NASA Astrophysics Data System (ADS)

Simon, P.; Semboloni, E.; van Waerbeke, L.; Hoekstra, H.; Erben, T.; Fu, L.; Harnois-Déraps, J.; Heymans, C.; Hildebrandt, H.; Kilbinger, M.; Kitching, T. D.; Miller, L.; Schrabback, T.

2015-05-01

We study the correlations of the shear signal between triplets of sources in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) to probe cosmological parameters via the matter bispectrum. In contrast to previous studies, we adopt a non-Gaussian model of the data likelihood which is supported by our simulations of the survey. We find that for state-of-the-art surveys, similar to CFHTLenS, a Gaussian likelihood analysis is a reasonable approximation, albeit small differences in the parameter constraints are already visible. For future surveys we expect that a Gaussian model becomes inaccurate. Our algorithm for a refined non-Gaussian analysis and data compression is then of great utility especially because it is not much more elaborate if simulated data are available. Applying this algorithm to the third-order correlations of shear alone in a blind analysis, we find a good agreement with the standard cosmological model: Σ _8=σ _8(Ω _m/0.27)^{0.64}=0.79^{+0.08}_{-0.11} for a flat Λ cold dark matter cosmology with h = 0.7 ± 0.04 (68 per cent credible interval). Nevertheless our models provide only moderately good fits as indicated by χ2/dof = 2.9, including a 20 per cent rms uncertainty in the predicted signal amplitude. The models cannot explain a signal drop on scales around 15 arcmin, which may be caused by systematics. It is unclear whether the discrepancy can be fully explained by residual point spread function systematics of which we find evidence at least on scales of a few arcmin. Therefore we need a better understanding of higher order correlations of cosmic shear and their systematics to confidently apply them as cosmological probes.

Gaussian Mixture Models of Between-Source Variation for Likelihood Ratio Computation from Multivariate Data

PubMed Central

Franco-Pedroso, Javier; Ramos, Daniel; Gonzalez-Rodriguez, Joaquin

2016-01-01

In forensic science, trace evidence found at a crime scene and on suspect has to be evaluated from the measurements performed on them, usually in the form of multivariate data (for example, several chemical compound or physical characteristics). In order to assess the strength of that evidence, the likelihood ratio framework is being increasingly adopted. Several methods have been derived in order to obtain likelihood ratios directly from univariate or multivariate data by modelling both the variation appearing between observations (or features) coming from the same source (within-source variation) and that appearing between observations coming from different sources (between-source variation). In the widely used multivariate kernel likelihood-ratio, the within-source distribution is assumed to be normally distributed and constant among different sources and the between-source variation is modelled through a kernel density function (KDF). In order to better fit the observed distribution of the between-source variation, this paper presents a different approach in which a Gaussian mixture model (GMM) is used instead of a KDF. As it will be shown, this approach provides better-calibrated likelihood ratios as measured by the log-likelihood ratio cost (Cllr) in experiments performed on freely available forensic datasets involving different trace evidences: inks, glass fragments and car paints. PMID:26901680

The probabilistic neural network architecture for high speed classification of remotely sensed imagery

NASA Technical Reports Server (NTRS)

Chettri, Samir R.; Cromp, Robert F.

1993-01-01

In this paper we discuss a neural network architecture (the Probabilistic Neural Net or the PNN) that, to the best of our knowledge, has not previously been applied to remotely sensed data. The PNN is a supervised non-parametric classification algorithm as opposed to the Gaussian maximum likelihood classifier (GMLC). The PNN works by fitting a Gaussian kernel to each training point. The width of the Gaussian is controlled by a tuning parameter called the window width. If very small widths are used, the method is equivalent to the nearest neighbor method. For large windows, the PNN behaves like the GMLC. The basic implementation of the PNN requires no training time at all. In this respect it is far better than the commonly used backpropagation neural network which can be shown to take O(N6) time for training where N is the dimensionality of the input vector. In addition the PNN can be implemented in a feed forward mode in hardware. The disadvantage of the PNN is that it requires all the training data to be stored. Some solutions to this problem are discussed in the paper. Finally, we discuss the accuracy of the PNN with respect to the GMLC and the backpropagation neural network (BPNN). The PNN is shown to be better than GMLC and not as good as the BPNN with regards to classification accuracy.

Adaptive channel estimation for soft decision decoding over non-Gaussian optical channel

NASA Astrophysics Data System (ADS)

Xiang, Jing-song; Miao, Tao-tao; Huang, Sheng; Liu, Huan-lin

2016-10-01

An adaptive priori likelihood ratio (LLR) estimation method is proposed over non-Gaussian channel in the intensity modulation/direct detection (IM/DD) optical communication systems. Using the nonparametric histogram and the weighted least square linear fitting in the tail regions, the LLR is estimated and used for the soft decision decoding of the low-density parity-check (LDPC) codes. This method can adapt well to the three main kinds of intensity modulation/direct detection (IM/DD) optical channel, i.e., the chi-square channel, the Webb-Gaussian channel and the additive white Gaussian noise (AWGN) channel. The performance penalty of channel estimation is neglected.

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.

System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm

NASA Astrophysics Data System (ADS)

Wang, Danshi; Zhang, Min; Li, Ze; Song, Chuang; Fu, Meixia; Li, Jin; Chen, Xue

2017-09-01

A bio-inspired detector based on the artificial neural network (ANN) and genetic algorithm is proposed in the context of a coherent optical transmission system. The ANN is designed to mitigate 16-quadrature amplitude modulation system impairments, including linear impairment: Gaussian white noise, laser phase noise, in-phase/quadrature component imbalance, and nonlinear impairment: nonlinear phase. Without prior information or heuristic assumptions, the ANN, functioning as a machine learning algorithm, can learn and capture the characteristics of impairments from observed data. Numerical simulations were performed, and dispersion-shifted, dispersion-managed, and dispersion-unmanaged fiber links were investigated. The launch power dynamic range and maximum transmission distance for the bio-inspired method were 2.7 dBm and 240 km greater, respectively, than those of the maximum likelihood estimation algorithm. Moreover, the linewidth tolerance of the bio-inspired technique was 170 kHz greater than that of the k-means method, demonstrating its usability for digital signal processing in coherent systems.

Fast estimation of diffusion tensors under Rician noise by the EM algorithm.

PubMed

Liu, Jia; Gasbarra, Dario; Railavo, Juha

2016-01-15

Diffusion tensor imaging (DTI) is widely used to characterize, in vivo, the white matter of the central nerve system (CNS). This biological tissue contains much anatomic, structural and orientational information of fibers in human brain. Spectral data from the displacement distribution of water molecules located in the brain tissue are collected by a magnetic resonance scanner and acquired in the Fourier domain. After the Fourier inversion, the noise distribution is Gaussian in both real and imaginary parts and, as a consequence, the recorded magnitude data are corrupted by Rician noise. Statistical estimation of diffusion leads a non-linear regression problem. In this paper, we present a fast computational method for maximum likelihood estimation (MLE) of diffusivities under the Rician noise model based on the expectation maximization (EM) algorithm. By using data augmentation, we are able to transform a non-linear regression problem into the generalized linear modeling framework, reducing dramatically the computational cost. The Fisher-scoring method is used for achieving fast convergence of the tensor parameter. The new method is implemented and applied using both synthetic and real data in a wide range of b-amplitudes up to 14,000s/mm(2). Higher accuracy and precision of the Rician estimates are achieved compared with other log-normal based methods. In addition, we extend the maximum likelihood (ML) framework to the maximum a posteriori (MAP) estimation in DTI under the aforementioned scheme by specifying the priors. We will describe how close numerically are the estimators of model parameters obtained through MLE and MAP estimation. Copyright © 2015 Elsevier B.V. All rights reserved.

A Variance Distribution Model of Surface EMG Signals Based on Inverse Gamma Distribution.

PubMed

Hayashi, Hideaki; Furui, Akira; Kurita, Yuichi; Tsuji, Toshio

2017-11-01

Objective: This paper describes the formulation of a surface electromyogram (EMG) model capable of representing the variance distribution of EMG signals. Methods: In the model, EMG signals are handled based on a Gaussian white noise process with a mean of zero for each variance value. EMG signal variance is taken as a random variable that follows inverse gamma distribution, allowing the representation of noise superimposed onto this variance. Variance distribution estimation based on marginal likelihood maximization is also outlined in this paper. The procedure can be approximated using rectified and smoothed EMG signals, thereby allowing the determination of distribution parameters in real time at low computational cost. Results: A simulation experiment was performed to evaluate the accuracy of distribution estimation using artificially generated EMG signals, with results demonstrating that the proposed model's accuracy is higher than that of maximum-likelihood-based estimation. Analysis of variance distribution using real EMG data also suggested a relationship between variance distribution and signal-dependent noise. Conclusion: The study reported here was conducted to examine the performance of a proposed surface EMG model capable of representing variance distribution and a related distribution parameter estimation method. Experiments using artificial and real EMG data demonstrated the validity of the model. Significance: Variance distribution estimated using the proposed model exhibits potential in the estimation of muscle force. Objective: This paper describes the formulation of a surface electromyogram (EMG) model capable of representing the variance distribution of EMG signals. Methods: In the model, EMG signals are handled based on a Gaussian white noise process with a mean of zero for each variance value. EMG signal variance is taken as a random variable that follows inverse gamma distribution, allowing the representation of noise superimposed onto this variance. Variance distribution estimation based on marginal likelihood maximization is also outlined in this paper. The procedure can be approximated using rectified and smoothed EMG signals, thereby allowing the determination of distribution parameters in real time at low computational cost. Results: A simulation experiment was performed to evaluate the accuracy of distribution estimation using artificially generated EMG signals, with results demonstrating that the proposed model's accuracy is higher than that of maximum-likelihood-based estimation. Analysis of variance distribution using real EMG data also suggested a relationship between variance distribution and signal-dependent noise. Conclusion: The study reported here was conducted to examine the performance of a proposed surface EMG model capable of representing variance distribution and a related distribution parameter estimation method. Experiments using artificial and real EMG data demonstrated the validity of the model. Significance: Variance distribution estimated using the proposed model exhibits potential in the estimation of muscle force.

Numerical modelling of instantaneous plate tectonics

NASA Technical Reports Server (NTRS)

Minster, J. B.; Haines, E.; Jordan, T. H.; Molnar, P.

1974-01-01

Assuming lithospheric plates to be rigid, 68 spreading rates, 62 fracture zones trends, and 106 earthquake slip vectors are systematically inverted to obtain a self-consistent model of instantaneous relative motions for eleven major plates. The inverse problem is linearized and solved iteratively by a maximum-likelihood procedure. Because the uncertainties in the data are small, Gaussian statistics are shown to be adequate. The use of a linear theory permits (1) the calculation of the uncertainties in the various angular velocity vectors caused by uncertainties in the data, and (2) quantitative examination of the distribution of information within the data set. The existence of a self-consistent model satisfying all the data is strong justification of the rigid plate assumption. Slow movement between North and South America is shown to be resolvable.

Gaussian Decomposition of Laser Altimeter Waveforms

NASA Technical Reports Server (NTRS)

Hofton, Michelle A.; Minster, J. Bernard; Blair, J. Bryan

1999-01-01

We develop a method to decompose a laser altimeter return waveform into its Gaussian components assuming that the position of each Gaussian within the waveform can be used to calculate the mean elevation of a specific reflecting surface within the laser footprint. We estimate the number of Gaussian components from the number of inflection points of a smoothed copy of the laser waveform, and obtain initial estimates of the Gaussian half-widths and positions from the positions of its consecutive inflection points. Initial amplitude estimates are obtained using a non-negative least-squares method. To reduce the likelihood of fitting the background noise within the waveform and to minimize the number of Gaussians needed in the approximation, we rank the "importance" of each Gaussian in the decomposition using its initial half-width and amplitude estimates. The initial parameter estimates of all Gaussians ranked "important" are optimized using the Levenburg-Marquardt method. If the sum of the Gaussians does not approximate the return waveform to a prescribed accuracy, then additional Gaussians are included in the optimization procedure. The Gaussian decomposition method is demonstrated on data collected by the airborne Laser Vegetation Imaging Sensor (LVIS) in October 1997 over the Sequoia National Forest, California.

A new estimator method for GARCH models

NASA Astrophysics Data System (ADS)

Onody, R. N.; Favaro, G. M.; Cazaroto, E. R.

2007-06-01

The GARCH (p, q) model is a very interesting stochastic process with widespread applications and a central role in empirical finance. The Markovian GARCH (1, 1) model has only 3 control parameters and a much discussed question is how to estimate them when a series of some financial asset is given. Besides the maximum likelihood estimator technique, there is another method which uses the variance, the kurtosis and the autocorrelation time to determine them. We propose here to use the standardized 6th moment. The set of parameters obtained in this way produces a very good probability density function and a much better time autocorrelation function. This is true for both studied indexes: NYSE Composite and FTSE 100. The probability of return to the origin is investigated at different time horizons for both Gaussian and Laplacian GARCH models. In spite of the fact that these models show almost identical performances with respect to the final probability density function and to the time autocorrelation function, their scaling properties are, however, very different. The Laplacian GARCH model gives a better scaling exponent for the NYSE time series, whereas the Gaussian dynamics fits better the FTSE scaling exponent.

Non-Gaussian noise-weakened stability in a foraging colony system with time delay

NASA Astrophysics Data System (ADS)

Dong, Xiaohui; Zeng, Chunhua; Yang, Fengzao; Guan, Lin; Xie, Qingshuang; Duan, Weilong

2018-02-01

In this paper, the dynamical properties in a foraging colony system with time delay and non-Gaussian noise were investigated. Using delay Fokker-Planck approach, the stationary probability distribution (SPD), the associated relaxation time (ART) and normalization correlation function (NCF) are obtained, respectively. The results show that: (i) the time delay and non-Gaussian noise can induce transition from a single peak to double peaks in the SPD, i.e., a type of bistability occurring in a foraging colony system where time delay and non-Gaussian noise not only cause transitions between stable states, but also construct the states themselves. Numerical simulations are presented and are in good agreement with the approximate theoretical results; (ii) there exists a maximum in the ART as a function of the noise intensity, this maximum for ART is identified as the characteristic of the non-Gaussian noise-weakened stability of the foraging colonies in the steady state; (iii) the ART as a function of the noise correlation time exhibits a maximum and a minimum, where the minimum for ART is identified as the signature of the non-Gaussian noise-enhanced stability of the foraging colonies; and (iv) the time delay can enhance the stability of the foraging colonies in the steady state, while the departure from Gaussian noise can weaken it, namely, the time delay and departure from Gaussian noise play opposite roles in ART or NCF.

Bayesian model selection: Evidence estimation based on DREAM simulation and bridge sampling

NASA Astrophysics Data System (ADS)

Volpi, Elena; Schoups, Gerrit; Firmani, Giovanni; Vrugt, Jasper A.

2017-04-01

Bayesian inference has found widespread application in Earth and Environmental Systems Modeling, providing an effective tool for prediction, data assimilation, parameter estimation, uncertainty analysis and hypothesis testing. Under multiple competing hypotheses, the Bayesian approach also provides an attractive alternative to traditional information criteria (e.g. AIC, BIC) for model selection. The key variable for Bayesian model selection is the evidence (or marginal likelihood) that is the normalizing constant in the denominator of Bayes theorem; while it is fundamental for model selection, the evidence is not required for Bayesian inference. It is computed for each hypothesis (model) by averaging the likelihood function over the prior parameter distribution, rather than maximizing it as by information criteria; the larger a model evidence the more support it receives among a collection of hypothesis as the simulated values assign relatively high probability density to the observed data. Hence, the evidence naturally acts as an Occam's razor, preferring simpler and more constrained models against the selection of over-fitted ones by information criteria that incorporate only the likelihood maximum. Since it is not particularly easy to estimate the evidence in practice, Bayesian model selection via the marginal likelihood has not yet found mainstream use. We illustrate here the properties of a new estimator of the Bayesian model evidence, which provides robust and unbiased estimates of the marginal likelihood; the method is coined Gaussian Mixture Importance Sampling (GMIS). GMIS uses multidimensional numerical integration of the posterior parameter distribution via bridge sampling (a generalization of importance sampling) of a mixture distribution fitted to samples of the posterior distribution derived from the DREAM algorithm (Vrugt et al., 2008; 2009). Some illustrative examples are presented to show the robustness and superiority of the GMIS estimator with respect to other commonly used approaches in the literature.

Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies

PubMed Central

Rukhin, Andrew L.

2011-01-01

A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is assumed not to be the same for all methods. We investigate maximum likelihood solutions in this model. By representing the likelihood equations as simultaneous polynomial equations, the exact form of the Groebner basis for their stationary points is derived when there are two methods. A parametrization of these solutions which allows their comparison is suggested. A numerical method for solving likelihood equations is outlined, and an alternative to the maximum likelihood method, the restricted maximum likelihood, is studied. In the situation when methods variances are considered to be known an upper bound on the between-method variance is obtained. The relationship between likelihood equations and moment-type equations is also discussed. PMID:26989583

Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies.

PubMed

Rukhin, Andrew L

2011-01-01

A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is assumed not to be the same for all methods. We investigate maximum likelihood solutions in this model. By representing the likelihood equations as simultaneous polynomial equations, the exact form of the Groebner basis for their stationary points is derived when there are two methods. A parametrization of these solutions which allows their comparison is suggested. A numerical method for solving likelihood equations is outlined, and an alternative to the maximum likelihood method, the restricted maximum likelihood, is studied. In the situation when methods variances are considered to be known an upper bound on the between-method variance is obtained. The relationship between likelihood equations and moment-type equations is also discussed.

Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise

NASA Astrophysics Data System (ADS)

Wang, Hui; Cheng, Xiujun; Duan, Jinqiao; Kurths, Jürgen; Li, Xiaofan

2018-01-01

This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable Lévy fluctuations. By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that via examining the mean first exit time (MFET) and the first escape probability (FEP), the asymmetric fluctuations, interacting with nonlinearity in the system, lead to peculiar likelihood for transcription. This includes, in the additive noise case, realizing higher likelihood of transcription for larger positive skewness (i.e., asymmetry) index β, causing a stochastic bifurcation at the non-Gaussianity index value α = 1 (i.e., it is a separating point or line for the likelihood for transcription), and achieving a turning point at the threshold value β ≈ - 0.5 (i.e., beyond which the likelihood for transcription suddenly reversed for α values). The stochastic bifurcation and turning point phenomena do not occur in the symmetric noise case (β = 0). While in the multiplicative noise case, non-Gaussianity index value α = 1 is a separating point or line for both the MFET and the FEP. We also investigate the noise enhanced stability phenomenon. Additionally, we are able to specify the regions in the whole parameter space for the asymmetric noise, in which we attain desired likelihood for transcription. We have conducted a series of numerical experiments in "regulating" the likelihood of gene transcription by tuning asymmetric stable Lévy noise indexes. This work offers insights for possible ways of achieving gene regulation in experimental research.

Fast Component Pursuit for Large-Scale Inverse Covariance Estimation.

PubMed

Han, Lei; Zhang, Yu; Zhang, Tong

2016-08-01

The maximum likelihood estimation (MLE) for the Gaussian graphical model, which is also known as the inverse covariance estimation problem, has gained increasing interest recently. Most existing works assume that inverse covariance estimators contain sparse structure and then construct models with the ℓ 1 regularization. In this paper, different from existing works, we study the inverse covariance estimation problem from another perspective by efficiently modeling the low-rank structure in the inverse covariance, which is assumed to be a combination of a low-rank part and a diagonal matrix. One motivation for this assumption is that the low-rank structure is common in many applications including the climate and financial analysis, and another one is that such assumption can reduce the computational complexity when computing its inverse. Specifically, we propose an efficient COmponent Pursuit (COP) method to obtain the low-rank part, where each component can be sparse. For optimization, the COP method greedily learns a rank-one component in each iteration by maximizing the log-likelihood. Moreover, the COP algorithm enjoys several appealing properties including the existence of an efficient solution in each iteration and the theoretical guarantee on the convergence of this greedy approach. Experiments on large-scale synthetic and real-world datasets including thousands of millions variables show that the COP method is faster than the state-of-the-art techniques for the inverse covariance estimation problem when achieving comparable log-likelihood on test data.

MXLKID: a maximum likelihood parameter identifier. [In LRLTRAN for CDC 7600

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gavel, D.T.

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.

Anomalous and non-Gaussian diffusion in Hertzian spheres

NASA Astrophysics Data System (ADS)

Ouyang, Wenze; Sun, Bin; Sun, Zhiwei; Xu, Shenghua

2018-09-01

By means of molecular dynamics simulations, we study the non-Gaussian diffusion in the fluid of Hertzian spheres. The time dependent non-Gaussian parameter, as an indicator of the dynamic heterogeneity, is increased with the increasing of temperature. When the temperature is high enough, the dynamic heterogeneity becomes very significant, and it seems counterintuitive that the maximum of non-Gaussian parameter and the position of its peak decrease monotonically with the increasing of density. By fitting the curves of self intermediate scattering function, we find that the character relaxation time τα is surprisingly not coupled with the time τmax where the non-Gaussian parameter reaches to a maximum. The intriguing features of non-Gaussian diffusion at high enough temperatures can be associated with the weakly correlated mean-field behavior of Hertzian spheres. Especially the time τmax is nearly inversely proportional to the density at extremely high temperatures.

The numerical evaluation of maximum-likelihood estimates of the parameters for a mixture of normal distributions from partially identified samples

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.

Offline handwritten word recognition using MQDF-HMMs

NASA Astrophysics Data System (ADS)

Ramachandrula, Sitaram; Hambarde, Mangesh; Patial, Ajay; Sahoo, Dushyant; Kochar, Shaivi

2015-01-01

We propose an improved HMM formulation for offline handwriting recognition (HWR). The main contribution of this work is using modified quadratic discriminant function (MQDF) [1] within HMM framework. In an MQDF-HMM the state observation likelihood is calculated by a weighted combination of MQDF likelihoods of individual Gaussians of GMM (Gaussian Mixture Model). The quadratic discriminant function (QDF) of a multivariate Gaussian can be rewritten by avoiding the inverse of covariance matrix by using the Eigen values and Eigen vectors of it. The MQDF is derived from QDF by substituting few of badly estimated lower-most Eigen values by an appropriate constant. The estimation errors of non-dominant Eigen vectors and Eigen values of covariance matrix for which the training data is insufficient can be controlled by this approach. MQDF has been successfully shown to improve the character recognition performance [1]. The usage of MQDF in HMM improves the computation, storage and modeling power of HMM when there is limited training data. We have got encouraging results on offline handwritten character (NIST database) and word recognition in English using MQDF HMMs.

Model-based decoding, information estimation, and change-point detection techniques for multineuron spike trains.

PubMed

Pillow, Jonathan W; Ahmadian, Yashar; Paninski, Liam

2011-01-01

One of the central problems in systems neuroscience is to understand how neural spike trains convey sensory information. Decoding methods, which provide an explicit means for reading out the information contained in neural spike responses, offer a powerful set of tools for studying the neural coding problem. Here we develop several decoding methods based on point-process neural encoding models, or forward models that predict spike responses to stimuli. These models have concave log-likelihood functions, which allow efficient maximum-likelihood model fitting and stimulus decoding. We present several applications of the encoding model framework to the problem of decoding stimulus information from population spike responses: (1) a tractable algorithm for computing the maximum a posteriori (MAP) estimate of the stimulus, the most probable stimulus to have generated an observed single- or multiple-neuron spike train response, given some prior distribution over the stimulus; (2) a gaussian approximation to the posterior stimulus distribution that can be used to quantify the fidelity with which various stimulus features are encoded; (3) an efficient method for estimating the mutual information between the stimulus and the spike trains emitted by a neural population; and (4) a framework for the detection of change-point times (the time at which the stimulus undergoes a change in mean or variance) by marginalizing over the posterior stimulus distribution. We provide several examples illustrating the performance of these estimators with simulated and real neural data.

Multi-Contrast Multi-Atlas Parcellation of Diffusion Tensor Imaging of the Human Brain

PubMed Central

Tang, Xiaoying; Yoshida, Shoko; Hsu, John; Huisman, Thierry A. G. M.; Faria, Andreia V.; Oishi, Kenichi; Kutten, Kwame; Poretti, Andrea; Li, Yue; Miller, Michael I.; Mori, Susumu

2014-01-01

In this paper, we propose a novel method for parcellating the human brain into 193 anatomical structures based on diffusion tensor images (DTIs). This was accomplished in the setting of multi-contrast diffeomorphic likelihood fusion using multiple DTI atlases. DTI images are modeled as high dimensional fields, with each voxel exhibiting a vector valued feature comprising of mean diffusivity (MD), fractional anisotropy (FA), and fiber angle. For each structure, the probability distribution of each element in the feature vector is modeled as a mixture of Gaussians, the parameters of which are estimated from the labeled atlases. The structure-specific feature vector is then used to parcellate the test image. For each atlas, a likelihood is iteratively computed based on the structure-specific vector feature. The likelihoods from multiple atlases are then fused. The updating and fusing of the likelihoods is achieved based on the expectation-maximization (EM) algorithm for maximum a posteriori (MAP) estimation problems. We first demonstrate the performance of the algorithm by examining the parcellation accuracy of 18 structures from 25 subjects with a varying degree of structural abnormality. Dice values ranging 0.8–0.9 were obtained. In addition, strong correlation was found between the volume size of the automated and the manual parcellation. Then, we present scan-rescan reproducibility based on another dataset of 16 DTI images – an average of 3.73%, 1.91%, and 1.79% for volume, mean FA, and mean MD respectively. Finally, the range of anatomical variability in the normal population was quantified for each structure. PMID:24809486

Finite mixture model: A maximum likelihood estimation approach on time series data

NASA Astrophysics Data System (ADS)

Yen, Phoong Seuk; Ismail, Mohd Tahir; Hamzah, Firdaus Mohamad

2014-09-01

Recently, statistician emphasized on the fitting of finite mixture model by using maximum likelihood estimation as it provides asymptotic properties. In addition, it shows consistency properties as the sample sizes increases to infinity. This illustrated that maximum likelihood estimation is an unbiased estimator. Moreover, the estimate parameters obtained from the application of maximum likelihood estimation have smallest variance as compared to others statistical method as the sample sizes increases. Thus, maximum likelihood estimation is adopted in this paper to fit the two-component mixture model in order to explore the relationship between rubber price and exchange rate for Malaysia, Thailand, Philippines and Indonesia. Results described that there is a negative effect among rubber price and exchange rate for all selected countries.

celerite: Scalable 1D Gaussian Processes in C++, Python, and Julia

NASA Astrophysics Data System (ADS)

Foreman-Mackey, Daniel; Agol, Eric; Ambikasaran, Sivaram; Angus, Ruth

2017-09-01

celerite provides fast and scalable Gaussian Process (GP) Regression in one dimension and is implemented in C++, Python, and Julia. The celerite API is designed to be familiar to users of george and, like george, celerite is designed to efficiently evaluate the marginalized likelihood of a dataset under a GP model. This is then be used alongside a non-linear optimization or posterior inference library for the best results.

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.

Markov chain Monte Carlo estimation of quantum states

NASA Astrophysics Data System (ADS)

Diguglielmo, James; Messenger, Chris; Fiurášek, Jaromír; Hage, Boris; Samblowski, Aiko; Schmidt, Tabea; Schnabel, Roman

2009-03-01

We apply a Bayesian data analysis scheme known as the Markov chain Monte Carlo to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical information concerning all reconstruction parameters including their statistical correlations with no a priori assumptions as to the form of the distribution from which it has been obtained. From this vector we can derive, e.g., the marginal distributions and uncertainties of all model parameters, and also of other quantities such as the purity of the reconstructed state. We demonstrate the utility of this scheme by reconstructing the Wigner function of phase-diffused squeezed states. These states possess non-Gaussian statistics and therefore represent a nontrivial case of tomographic reconstruction. We compare our results to those obtained through pure maximum-likelihood and Fisher information approaches.

MIDAS, prototype Multivariate Interactive Digital Analysis System, phase 1. Volume 1: System description

NASA Technical Reports Server (NTRS)

Kriegler, F. J.

1974-01-01

The MIDAS System is described as a third-generation fast multispectral recognition system able to keep pace with the large quantity and high rates of data acquisition from present and projected sensors. A principal objective of the MIDAS program is to provide a system well interfaced with the human operator and thus to obtain large overall reductions in turnaround time and significant gains in throughput. The hardware and software are described. The system contains a mini-computer to control the various high-speed processing elements in the data path, and a classifier which implements an all-digital prototype multivariate-Gaussian maximum likelihood decision algorithm operating at 200,000 pixels/sec. Sufficient hardware was developed to perform signature extraction from computer-compatible tapes, compute classifier coefficients, control the classifier operation, and diagnose operation.

PET image reconstruction using multi-parametric anato-functional priors

NASA Astrophysics Data System (ADS)

Mehranian, Abolfazl; Belzunce, Martin A.; Niccolini, Flavia; Politis, Marios; Prieto, Claudia; Turkheimer, Federico; Hammers, Alexander; Reader, Andrew J.

2017-08-01

In this study, we investigate the application of multi-parametric anato-functional (MR-PET) priors for the maximum a posteriori (MAP) reconstruction of brain PET data in order to address the limitations of the conventional anatomical priors in the presence of PET-MR mismatches. In addition to partial volume correction benefits, the suitability of these priors for reconstruction of low-count PET data is also introduced and demonstrated, comparing to standard maximum-likelihood (ML) reconstruction of high-count data. The conventional local Tikhonov and total variation (TV) priors and current state-of-the-art anatomical priors including the Kaipio, non-local Tikhonov prior with Bowsher and Gaussian similarity kernels are investigated and presented in a unified framework. The Gaussian kernels are calculated using both voxel- and patch-based feature vectors. To cope with PET and MR mismatches, the Bowsher and Gaussian priors are extended to multi-parametric priors. In addition, we propose a modified joint Burg entropy prior that by definition exploits all parametric information in the MAP reconstruction of PET data. The performance of the priors was extensively evaluated using 3D simulations and two clinical brain datasets of [18F]florbetaben and [18F]FDG radiotracers. For simulations, several anato-functional mismatches were intentionally introduced between the PET and MR images, and furthermore, for the FDG clinical dataset, two PET-unique active tumours were embedded in the PET data. Our simulation results showed that the joint Burg entropy prior far outperformed the conventional anatomical priors in terms of preserving PET unique lesions, while still reconstructing functional boundaries with corresponding MR boundaries. In addition, the multi-parametric extension of the Gaussian and Bowsher priors led to enhanced preservation of edge and PET unique features and also an improved bias-variance performance. In agreement with the simulation results, the clinical results also showed that the Gaussian prior with voxel-based feature vectors, the Bowsher and the joint Burg entropy priors were the best performing priors. However, for the FDG dataset with simulated tumours, the TV and proposed priors were capable of preserving the PET-unique tumours. Finally, an important outcome was the demonstration that the MAP reconstruction of a low-count FDG PET dataset using the proposed joint entropy prior can lead to comparable image quality to a conventional ML reconstruction with up to 5 times more counts. In conclusion, multi-parametric anato-functional priors provide a solution to address the pitfalls of the conventional priors and are therefore likely to increase the diagnostic confidence in MR-guided PET image reconstructions.

Research on adaptive optics image restoration algorithm based on improved joint maximum a posteriori method

NASA Astrophysics Data System (ADS)

Zhang, Lijuan; Li, Yang; Wang, Junnan; Liu, Ying

2018-03-01

In this paper, we propose a point spread function (PSF) reconstruction method and joint maximum a posteriori (JMAP) estimation method for the adaptive optics image restoration. Using the JMAP method as the basic principle, we establish the joint log likelihood function of multi-frame adaptive optics (AO) images based on the image Gaussian noise models. To begin with, combining the observed conditions and AO system characteristics, a predicted PSF model for the wavefront phase effect is developed; then, we build up iterative solution formulas of the AO image based on our proposed algorithm, addressing the implementation process of multi-frame AO images joint deconvolution method. We conduct a series of experiments on simulated and real degraded AO images to evaluate our proposed algorithm. Compared with the Wiener iterative blind deconvolution (Wiener-IBD) algorithm and Richardson-Lucy IBD algorithm, our algorithm has better restoration effects including higher peak signal-to-noise ratio ( PSNR) and Laplacian sum ( LS) value than the others. The research results have a certain application values for actual AO image restoration.

Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise.

PubMed

Wang, Hui; Cheng, Xiujun; Duan, Jinqiao; Kurths, Jürgen; Li, Xiaofan

2018-01-01

This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable Lévy fluctuations. By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that via examining the mean first exit time (MFET) and the first escape probability (FEP), the asymmetric fluctuations, interacting with nonlinearity in the system, lead to peculiar likelihood for transcription. This includes, in the additive noise case, realizing higher likelihood of transcription for larger positive skewness (i.e., asymmetry) index β, causing a stochastic bifurcation at the non-Gaussianity index value α = 1 (i.e., it is a separating point or line for the likelihood for transcription), and achieving a turning point at the threshold value β≈-0.5 (i.e., beyond which the likelihood for transcription suddenly reversed for α values). The stochastic bifurcation and turning point phenomena do not occur in the symmetric noise case (β = 0). While in the multiplicative noise case, non-Gaussianity index value α = 1 is a separating point or line for both the MFET and the FEP. We also investigate the noise enhanced stability phenomenon. Additionally, we are able to specify the regions in the whole parameter space for the asymmetric noise, in which we attain desired likelihood for transcription. We have conducted a series of numerical experiments in "regulating" the likelihood of gene transcription by tuning asymmetric stable Lévy noise indexes. This work offers insights for possible ways of achieving gene regulation in experimental research.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

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.

Probabilistic inference using linear Gaussian importance sampling for hybrid Bayesian networks

NASA Astrophysics Data System (ADS)

Sun, Wei; Chang, K. C.

2005-05-01

Probabilistic inference for Bayesian networks is in general NP-hard using either exact algorithms or approximate methods. However, for very complex networks, only the approximate methods such as stochastic sampling could be used to provide a solution given any time constraint. There are several simulation methods currently available. They include logic sampling (the first proposed stochastic method for Bayesian networks, the likelihood weighting algorithm) the most commonly used simulation method because of its simplicity and efficiency, the Markov blanket scoring method, and the importance sampling algorithm. In this paper, we first briefly review and compare these available simulation methods, then we propose an improved importance sampling algorithm called linear Gaussian importance sampling algorithm for general hybrid model (LGIS). LGIS is aimed for hybrid Bayesian networks consisting of both discrete and continuous random variables with arbitrary distributions. It uses linear function and Gaussian additive noise to approximate the true conditional probability distribution for continuous variable given both its parents and evidence in a Bayesian network. One of the most important features of the newly developed method is that it can adaptively learn the optimal important function from the previous samples. We test the inference performance of LGIS using a 16-node linear Gaussian model and a 6-node general hybrid model. The performance comparison with other well-known methods such as Junction tree (JT) and likelihood weighting (LW) shows that LGIS-GHM is very promising.

New prior sampling methods for nested sampling - Development and testing

NASA Astrophysics Data System (ADS)

Stokes, Barrie; Tuyl, Frank; Hudson, Irene

2017-06-01

Nested Sampling is a powerful algorithm for fitting models to data in the Bayesian setting, introduced by Skilling [1]. The nested sampling algorithm proceeds by carrying out a series of compressive steps, involving successively nested iso-likelihood boundaries, starting with the full prior distribution of the problem parameters. The "central problem" of nested sampling is to draw at each step a sample from the prior distribution whose likelihood is greater than the current likelihood threshold, i.e., a sample falling inside the current likelihood-restricted region. For both flat and informative priors this ultimately requires uniform sampling restricted to the likelihood-restricted region. We present two new methods of carrying out this sampling step, and illustrate their use with the lighthouse problem [2], a bivariate likelihood used by Gregory [3] and a trivariate Gaussian mixture likelihood. All the algorithm development and testing reported here has been done with Mathematica® [4].

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…

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.

Analysis of Point Based Image Registration Errors With Applications in Single Molecule Microscopy

PubMed Central

Cohen, E. A. K.; Ober, R. J.

2014-01-01

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data. PMID:24634573

Uncertainty estimation of Intensity-Duration-Frequency relationships: A regional analysis

NASA Astrophysics Data System (ADS)

Mélèse, Victor; Blanchet, Juliette; Molinié, Gilles

2018-03-01

We propose in this article a regional study of uncertainties in IDF curves derived from point-rainfall maxima. We develop two generalized extreme value models based on the simple scaling assumption, first in the frequentist framework and second in the Bayesian framework. Within the frequentist framework, uncertainties are obtained i) from the Gaussian density stemming from the asymptotic normality theorem of the maximum likelihood and ii) with a bootstrap procedure. Within the Bayesian framework, uncertainties are obtained from the posterior densities. We confront these two frameworks on the same database covering a large region of 100, 000 km2 in southern France with contrasted rainfall regime, in order to be able to draw conclusion that are not specific to the data. The two frameworks are applied to 405 hourly stations with data back to the 1980's, accumulated in the range 3 h-120 h. We show that i) the Bayesian framework is more robust than the frequentist one to the starting point of the estimation procedure, ii) the posterior and the bootstrap densities are able to better adjust uncertainty estimation to the data than the Gaussian density, and iii) the bootstrap density give unreasonable confidence intervals, in particular for return levels associated to large return period. Therefore our recommendation goes towards the use of the Bayesian framework to compute uncertainty.

Revealing transient strain in geodetic data with Gaussian process regression

NASA Astrophysics Data System (ADS)

Hines, T. T.; Hetland, E. A.

2018-03-01

Transient strain derived from global navigation satellite system (GNSS) data can be used to detect and understand geophysical processes such as slow slip events and post-seismic deformation. Here we propose using Gaussian process regression (GPR) as a tool for estimating transient strain from GNSS data. GPR is a non-parametric, Bayesian method for interpolating scattered data. In our approach, we assume a stochastic prior model for transient displacements. The prior describes how much we expect transient displacements to covary spatially and temporally. A posterior estimate of transient strain is obtained by differentiating the posterior transient displacements, which are formed by conditioning the prior with the GNSS data. As a demonstration, we use GPR to detect transient strain resulting from slow slip events in the Pacific Northwest. Maximum likelihood methods are used to constrain a prior model for transient displacements in this region. The temporal covariance of our prior model is described by a compact Wendland covariance function, which significantly reduces the computational burden that can be associated with GPR. Our results reveal the spatial and temporal evolution of strain from slow slip events. We verify that the transient strain estimated with GPR is in fact geophysical signal by comparing it to the seismic tremor that is associated with Pacific Northwest slow slip events.

A clustering package for nucleotide sequences using Laplacian Eigenmaps and Gaussian Mixture Model.

PubMed

Bruneau, Marine; Mottet, Thierry; Moulin, Serge; Kerbiriou, Maël; Chouly, Franz; Chretien, Stéphane; Guyeux, Christophe

2018-02-01

In this article, a new Python package for nucleotide sequences clustering is proposed. This package, freely available on-line, implements a Laplacian eigenmap embedding and a Gaussian Mixture Model for DNA clustering. It takes nucleotide sequences as input, and produces the optimal number of clusters along with a relevant visualization. Despite the fact that we did not optimise the computational speed, our method still performs reasonably well in practice. Our focus was mainly on data analytics and accuracy and as a result, our approach outperforms the state of the art, even in the case of divergent sequences. Furthermore, an a priori knowledge on the number of clusters is not required here. For the sake of illustration, this method is applied on a set of 100 DNA sequences taken from the mitochondrially encoded NADH dehydrogenase 3 (ND3) gene, extracted from a collection of Platyhelminthes and Nematoda species. The resulting clusters are tightly consistent with the phylogenetic tree computed using a maximum likelihood approach on gene alignment. They are coherent too with the NCBI taxonomy. Further test results based on synthesized data are then provided, showing that the proposed approach is better able to recover the clusters than the most widely used software, namely Cd-hit-est and BLASTClust. Copyright © 2017 Elsevier Ltd. All rights reserved.

Bayesian Recurrent Neural Network for Language Modeling.

PubMed

Chien, Jen-Tzung; Ku, Yuan-Chu

2016-02-01

A language model (LM) is calculated as the probability of a word sequence that provides the solution to word prediction for a variety of information systems. A recurrent neural network (RNN) is powerful to learn the large-span dynamics of a word sequence in the continuous space. However, the training of the RNN-LM is an ill-posed problem because of too many parameters from a large dictionary size and a high-dimensional hidden layer. This paper presents a Bayesian approach to regularize the RNN-LM and apply it for continuous speech recognition. We aim to penalize the too complicated RNN-LM by compensating for the uncertainty of the estimated model parameters, which is represented by a Gaussian prior. The objective function in a Bayesian classification network is formed as the regularized cross-entropy error function. The regularized model is constructed not only by calculating the regularized parameters according to the maximum a posteriori criterion but also by estimating the Gaussian hyperparameter by maximizing the marginal likelihood. A rapid approximation to a Hessian matrix is developed to implement the Bayesian RNN-LM (BRNN-LM) by selecting a small set of salient outer-products. The proposed BRNN-LM achieves a sparser model than the RNN-LM. Experiments on different corpora show the robustness of system performance by applying the rapid BRNN-LM under different conditions.

A Maximum Likelihood Ensemble Data Assimilation Method Tailored to the Inner Radiation Belt

NASA Astrophysics Data System (ADS)

Guild, T. B.; O'Brien, T. P., III; Mazur, J. E.

2014-12-01

The Earth's radiation belts are composed of energetic protons and electrons whose fluxes span many orders of magnitude, whose distributions are log-normal, and where data-model differences can be large and also log-normal. This physical system thus challenges standard data assimilation methods relying on underlying assumptions of Gaussian distributions of measurements and data-model differences, where innovations to the model are small. We have therefore developed a data assimilation method tailored to these properties of the inner radiation belt, analogous to the ensemble Kalman filter but for the unique cases of non-Gaussian model and measurement errors, and non-linear model and measurement distributions. We apply this method to the inner radiation belt proton populations, using the SIZM inner belt model [Selesnick et al., 2007] and SAMPEX/PET and HEO proton observations to select the most likely ensemble members contributing to the state of the inner belt. We will describe the algorithm, the method of generating ensemble members, our choice of minimizing the difference between instrument counts not phase space densities, and demonstrate the method with our reanalysis of the inner radiation belt throughout solar cycle 23. We will report on progress to continue our assimilation into solar cycle 24 using the Van Allen Probes/RPS observations.

Idealized models of the joint probability distribution of wind speeds

NASA Astrophysics Data System (ADS)

Monahan, Adam H.

2018-05-01

The joint probability distribution of wind speeds at two separate locations in space or points in time completely characterizes the statistical dependence of these two quantities, providing more information than linear measures such as correlation. In this study, we consider two models of the joint distribution of wind speeds obtained from idealized models of the dependence structure of the horizontal wind velocity components. The bivariate Rice distribution follows from assuming that the wind components have Gaussian and isotropic fluctuations. The bivariate Weibull distribution arises from power law transformations of wind speeds corresponding to vector components with Gaussian, isotropic, mean-zero variability. Maximum likelihood estimates of these distributions are compared using wind speed data from the mid-troposphere, from different altitudes at the Cabauw tower in the Netherlands, and from scatterometer observations over the sea surface. While the bivariate Rice distribution is more flexible and can represent a broader class of dependence structures, the bivariate Weibull distribution is mathematically simpler and may be more convenient in many applications. The complexity of the mathematical expressions obtained for the joint distributions suggests that the development of explicit functional forms for multivariate speed distributions from distributions of the components will not be practical for more complicated dependence structure or more than two speed variables.

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.

New applications of maximum likelihood and Bayesian statistics in macromolecular crystallography.

PubMed

McCoy, Airlie J

2002-10-01

Maximum likelihood methods are well known to macromolecular crystallographers as the methods of choice for isomorphous phasing and structure refinement. Recently, the use of maximum likelihood and Bayesian statistics has extended to the areas of molecular replacement and density modification, placing these methods on a stronger statistical foundation and making them more accurate and effective.

Statistical characteristics of the sequential detection of signals in correlated noise

NASA Astrophysics Data System (ADS)

Averochkin, V. A.; Baranov, P. E.

1985-10-01

A solution is given to the problem of determining the distribution of the duration of the sequential two-threshold Wald rule for the time-discrete detection of determinate and Gaussian correlated signals on a background of Gaussian correlated noise. Expressions are obtained for the joint probability densities of the likelihood ratio logarithms, and an analysis is made of the effect of correlation and SNR on the duration distribution and the detection efficiency. Comparison is made with Neumann-Pearson detection.

On the existence of maximum likelihood estimates for presence-only data

USGS Publications Warehouse

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.

Robust Foregrounds Removal for 21-cm Experiments

NASA Astrophysics Data System (ADS)

Mertens, F.; Ghosh, A.; Koopmans, L. V. E.

2018-05-01

Direct detection of the Epoch of Reionization via the redshifted 21-cm line will have unprecedented implications on the study of structure formation in the early Universe. To fulfill this promise current and future 21-cm experiments will need to detect the weak 21-cm signal over foregrounds several order of magnitude greater. This requires accurate modeling of the galactic and extragalactic emission and of its contaminants due to instrument chromaticity, ionosphere and imperfect calibration. To solve for this complex modeling, we propose a new method based on Gaussian Process Regression (GPR) which is able to cleanly separate the cosmological signal from most of the foregrounds contaminants. We also propose a new imaging method based on a maximum likelihood framework which solves for the interferometric equation directly on the sphere. Using this method, chromatic effects causing the so-called ``wedge'' are effectively eliminated (i.e. deconvolved) in the cylindrical (k⊥, k∥) power spectrum.

MIDAS, prototype Multivariate Interactive Digital Analysis System, phase 1. Volume 3: Wiring diagrams

NASA Technical Reports Server (NTRS)

Kriegler, F. J.; Christenson, D.; Gordon, M.; Kistler, R.; Lampert, S.; Marshall, R.; Mclaughlin, R.

1974-01-01

The Midas System is a third-generation, fast, multispectral recognition system able to keep pace with the large quantity and high rates of data acquisition from present and projected sensors. A principal objective of the MIDAS Program is to provide a system well interfaced with the human operator and thus to obtain large overall reductions in turn-around time and significant gains in throughput. The hardware and software generated in Phase I of the overall program are described. The system contains a mini-computer to control the various high-speed processing elements in the data path and a classifier which implements an all-digital prototype multivariate-Gaussian maximum likelihood decision algorithm operating at 2 x 100,000 pixels/sec. Sufficient hardware was developed to perform signature extraction from computer-compatible tapes, compute classifier coefficients, control the classifier operation, and diagnose operation. The MIDAS construction and wiring diagrams are given.

MIDAS, prototype Multivariate Interactive Digital Analysis System, Phase 1. Volume 2: Diagnostic system

NASA Technical Reports Server (NTRS)

Kriegler, F. J.; Christenson, D.; Gordon, M.; Kistler, R.; Lampert, S.; Marshall, R.; Mclaughlin, R.

1974-01-01

The MIDAS System is a third-generation, fast, multispectral recognition system able to keep pace with the large quantity and high rates of data acquisition from present and projected sensors. A principal objective of the MIDAS Program is to provide a system well interfaced with the human operator and thus to obtain large overall reductions in turn-around time and significant gains in throughout. The hardware and software generated in Phase I of the over-all program are described. The system contains a mini-computer to control the various high-speed processing elements in the data path and a classifier which implements an all-digital prototype multivariate-Gaussian maximum likelihood decision algorithm operating 2 x 105 pixels/sec. Sufficient hardware was developed to perform signature extraction from computer-compatible tapes, compute classifier coefficients, control the classifier operation, and diagnose operation. Diagnostic programs used to test MIDAS' operations are presented.

Optimal thresholds for the estimation of area rain-rate moments by the threshold method

NASA Technical Reports Server (NTRS)

Short, David A.; Shimizu, Kunio; Kedem, Benjamin

1993-01-01

Optimization of the threshold method, achieved by determination of the threshold that maximizes the correlation between an area-average rain-rate moment and the area coverage of rain rates exceeding the threshold, is demonstrated empirically and theoretically. Empirical results for a sequence of GATE radar snapshots show optimal thresholds of 5 and 27 mm/h for the first and second moments, respectively. Theoretical optimization of the threshold method by the maximum-likelihood approach of Kedem and Pavlopoulos (1991) predicts optimal thresholds near 5 and 26 mm/h for lognormally distributed rain rates with GATE-like parameters. The agreement between theory and observations suggests that the optimal threshold can be understood as arising due to sampling variations, from snapshot to snapshot, of a parent rain-rate distribution. Optimal thresholds for gamma and inverse Gaussian distributions are also derived and compared.

Evaluation of SLAR and thematic mapper MSS data for forest cover mapping using computer-aided analysis techniques

NASA Technical Reports Server (NTRS)

Hoffer, R. M. (Principal Investigator); Knowlton, D. J.; Dean, M. E.

1981-01-01

A set of training statistics for the 30 meter resolution simulated thematic mapper MSS data was generated based on land use/land cover classes. In addition to this supervised data set, a nonsupervised multicluster block of training statistics is being defined in order to compare the classification results and evaluate the effect of the different training selection methods on classification performance. Two test data sets, defined using a stratified sampling procedure incorporating a grid system with dimensions of 50 lines by 50 columns, and another set based on an analyst supervised set of test fields were used to evaluate the classifications of the TMS data. The supervised training data set generated training statistics, and a per point Gaussian maximum likelihood classification of the 1979 TMS data was obtained. The August 1980 MSS data was radiometrically adjusted. The SAR data was redigitized and the SAR imagery was qualitatively analyzed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blaut, Arkadiusz; Babak, Stanislav; Krolak, Andrzej

We present data analysis methods used in the detection and estimation of parameters of gravitational-wave signals from the white dwarf binaries in the mock LISA data challenge. Our main focus is on the analysis of challenge 3.1, where the gravitational-wave signals from more than 6x10{sup 7} Galactic binaries were added to the simulated Gaussian instrumental noise. The majority of the signals at low frequencies are not resolved individually. The confusion between the signals is strongly reduced at frequencies above 5 mHz. Our basic data analysis procedure is the maximum likelihood detection method. We filter the data through the template bankmore » at the first step of the search, then we refine parameters using the Nelder-Mead algorithm, we remove the strongest signal found and we repeat the procedure. We detect reliably and estimate parameters accurately of more than ten thousand signals from white dwarf binaries.« less

Statistics of equivalent width data and new oscillator strengths for Si II, Fe II, and Mn II. [in interstellar medium

NASA Technical Reports Server (NTRS)

Van Buren, Dave

1986-01-01

Equivalent width data from Copernicus and IUE appear to have an exponential, rather than a Gaussian distribution of errors. This is probably because there is one dominant source of error: the assignment of the background continuum shape. The maximum likelihood method of parameter estimation is presented for the case of exponential statistics, in enough generality for application to many problems. The method is applied to global fitting of Si II, Fe II, and Mn II oscillator strengths and interstellar gas parameters along many lines of sight. The new values agree in general with previous determinations but are usually much more tightly constrained. Finally, it is shown that care must be taken in deriving acceptable regions of parameter space because the probability contours are not generally ellipses whose axes are parallel to the coordinate axes.

Population genetics inference for longitudinally-sampled mutants under strong selection.

PubMed

Lacerda, Miguel; Seoighe, Cathal

2014-11-01

Longitudinal allele frequency data are becoming increasingly prevalent. Such samples permit statistical inference of the population genetics parameters that influence the fate of mutant variants. To infer these parameters by maximum likelihood, the mutant frequency is often assumed to evolve according to the Wright-Fisher model. For computational reasons, this discrete model is commonly approximated by a diffusion process that requires the assumption that the forces of natural selection and mutation are weak. This assumption is not always appropriate. For example, mutations that impart drug resistance in pathogens may evolve under strong selective pressure. Here, we present an alternative approximation to the mutant-frequency distribution that does not make any assumptions about the magnitude of selection or mutation and is much more computationally efficient than the standard diffusion approximation. Simulation studies are used to compare the performance of our method to that of the Wright-Fisher and Gaussian diffusion approximations. For large populations, our method is found to provide a much better approximation to the mutant-frequency distribution when selection is strong, while all three methods perform comparably when selection is weak. Importantly, maximum-likelihood estimates of the selection coefficient are severely attenuated when selection is strong under the two diffusion models, but not when our method is used. This is further demonstrated with an application to mutant-frequency data from an experimental study of bacteriophage evolution. We therefore recommend our method for estimating the selection coefficient when the effective population size is too large to utilize the discrete Wright-Fisher model. Copyright © 2014 by the Genetics Society of America.

The numerical evaluation of maximum-likelihood estimates of the parameters for a mixture of normal distributions from partially identified samples

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 are considered. These equations, suggest certain successive-approximations iterative procedures for obtaining maximum-likelihood estimates. These are generalized steepest ascent (deflected gradient) procedures. It is shown that, with probability 1 as N sub 0 approaches infinity (regardless of the relative sizes of N sub 0 and N sub 1, i=1,...,m), these procedures converge locally to the strongly consistent maximum-likelihood estimates whenever the step size is between 0 and 2. Furthermore, the value of the step size which yields optimal local convergence rates is bounded from below by a number which always lies between 1 and 2.

Computation of nonparametric convex hazard estimators via profile methods.

PubMed

Jankowski, Hanna K; Wellner, Jon A

2009-05-01

This paper proposes a profile likelihood algorithm to compute the nonparametric maximum likelihood estimator of a convex hazard function. The maximisation is performed in two steps: First the support reduction algorithm is used to maximise the likelihood over all hazard functions with a given point of minimum (or antimode). Then it is shown that the profile (or partially maximised) likelihood is quasi-concave as a function of the antimode, so that a bisection algorithm can be applied to find the maximum of the profile likelihood, and hence also the global maximum. The new algorithm is illustrated using both artificial and real data, including lifetime data for Canadian males and females.

Approximate Bayesian computation in large-scale structure: constraining the galaxy-halo connection

NASA Astrophysics Data System (ADS)

Hahn, ChangHoon; Vakili, Mohammadjavad; Walsh, Kilian; Hearin, Andrew P.; Hogg, David W.; Campbell, Duncan

2017-08-01

Standard approaches to Bayesian parameter inference in large-scale structure assume a Gaussian functional form (chi-squared form) for the likelihood. This assumption, in detail, cannot be correct. Likelihood free inferences such as approximate Bayesian computation (ABC) relax these restrictions and make inference possible without making any assumptions on the likelihood. Instead ABC relies on a forward generative model of the data and a metric for measuring the distance between the model and data. In this work, we demonstrate that ABC is feasible for LSS parameter inference by using it to constrain parameters of the halo occupation distribution (HOD) model for populating dark matter haloes with galaxies. Using specific implementation of ABC supplemented with population Monte Carlo importance sampling, a generative forward model using HOD and a distance metric based on galaxy number density, two-point correlation function and galaxy group multiplicity function, we constrain the HOD parameters of mock observation generated from selected 'true' HOD parameters. The parameter constraints we obtain from ABC are consistent with the 'true' HOD parameters, demonstrating that ABC can be reliably used for parameter inference in LSS. Furthermore, we compare our ABC constraints to constraints we obtain using a pseudo-likelihood function of Gaussian form with MCMC and find consistent HOD parameter constraints. Ultimately, our results suggest that ABC can and should be applied in parameter inference for LSS analyses.

A maximum likelihood map of chromosome 1.

PubMed Central

Rao, D C; Keats, B J; Lalouel, J M; Morton, N E; Yee, S

1979-01-01

Thirteen loci are mapped on chromosome 1 from genetic evidence. The maximum likelihood map presented permits confirmation that Scianna (SC) and a fourteenth locus, phenylketonuria (PKU), are on chromosome 1, although the location of the latter on the PGM1-AMY segment is uncertain. Eight other controversial genetic assignments are rejected, providing a practical demonstration of the resolution which maximum likelihood theory brings to mapping. PMID:293128

Variance Difference between Maximum Likelihood Estimation Method and Expected A Posteriori Estimation Method Viewed from Number of Test Items

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…

Comparison of Maximum Likelihood Estimation Approach and Regression Approach in Detecting Quantitative Trait Lco Using RAPD Markers

Treesearch

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...

Rayleigh-maximum-likelihood bilateral filter for ultrasound image enhancement.

PubMed

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 added with Gaussian distributed noise. Meanwhile clinical breast ultrasound images are used to visually evaluate the effectiveness of the method. To examine the performance, comparison tests between the proposed RSBF and six state-of-the-art methods for ultrasound speckle removal are performed on simulated ultrasound images with various noise and speckle levels. The results of the proposed RSBF are satisfying since the Gaussian noise and the Rayleigh speckle are greatly suppressed. The proposed method can improve the SNRs of the enhanced images to nearly 15 and 13 dB compared with images corrupted by speckle as well as images contaminated by speckle and noise under various SNR levels, respectively. The RSBF is effective in enhancing edge while smoothing the speckle and noise in clinical ultrasound images. In the comparison experiments, the proposed method demonstrates its superiority in accuracy and robustness for denoising and edge preserving under various levels of noise and speckle in terms of visual quality as well as numeric metrics, such as peak signal to noise ratio, SNR and root mean squared error. The experimental results show that the proposed method is effective for removing the speckle and the background noise in ultrasound images. The main reason is that it performs a "detect and replace" two-step mechanism. The advantages of the proposed RBSF lie in two aspects. Firstly, each central pixel is classified as noise, speckle or noise-free texture according to the absolute difference between the target pixel and the reference median. Subsequently, the Rayleigh-maximum-likelihood filter and the bilateral filter are switched to eliminate speckle and noise, respectively, while the noise-free pixels are unaltered. Therefore, it is implemented with better accuracy and robustness than the traditional methods. Generally, these traits declare that the proposed RSBF would have significant clinical application.

Improvement and comparison of likelihood functions for model calibration and parameter uncertainty analysis within a Markov chain Monte Carlo scheme

NASA Astrophysics Data System (ADS)

Cheng, Qin-Bo; Chen, Xi; Xu, Chong-Yu; Reinhardt-Imjela, Christian; Schulte, Achim

2014-11-01

In this study, the likelihood functions for uncertainty analysis of hydrological models are compared and improved through the following steps: (1) the equivalent relationship between the Nash-Sutcliffe Efficiency coefficient (NSE) and the likelihood function with Gaussian independent and identically distributed residuals is proved; (2) a new estimation method of the Box-Cox transformation (BC) parameter is developed to improve the effective elimination of the heteroscedasticity of model residuals; and (3) three likelihood functions-NSE, Generalized Error Distribution with BC (BC-GED) and Skew Generalized Error Distribution with BC (BC-SGED)-are applied for SWAT-WB-VSA (Soil and Water Assessment Tool - Water Balance - Variable Source Area) model calibration in the Baocun watershed, Eastern China. Performances of calibrated models are compared using the observed river discharges and groundwater levels. The result shows that the minimum variance constraint can effectively estimate the BC parameter. The form of the likelihood function significantly impacts on the calibrated parameters and the simulated results of high and low flow components. SWAT-WB-VSA with the NSE approach simulates flood well, but baseflow badly owing to the assumption of Gaussian error distribution, where the probability of the large error is low, but the small error around zero approximates equiprobability. By contrast, SWAT-WB-VSA with the BC-GED or BC-SGED approach mimics baseflow well, which is proved in the groundwater level simulation. The assumption of skewness of the error distribution may be unnecessary, because all the results of the BC-SGED approach are nearly the same as those of the BC-GED approach.

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.

Minimization for conditional simulation: Relationship to optimal transport

NASA Astrophysics Data System (ADS)

Oliver, Dean S.

2014-05-01

In this paper, we consider the problem of generating independent samples from a conditional distribution when independent samples from the prior distribution are available. Although there are exact methods for sampling from the posterior (e.g. Markov chain Monte Carlo or acceptance/rejection), these methods tend to be computationally demanding when evaluation of the likelihood function is expensive, as it is for most geoscience applications. As an alternative, in this paper we discuss deterministic mappings of variables distributed according to the prior to variables distributed according to the posterior. Although any deterministic mappings might be equally useful, we will focus our discussion on a class of algorithms that obtain implicit mappings by minimization of a cost function that includes measures of data mismatch and model variable mismatch. Algorithms of this type include quasi-linear estimation, randomized maximum likelihood, perturbed observation ensemble Kalman filter, and ensemble of perturbed analyses (4D-Var). When the prior pdf is Gaussian and the observation operators are linear, we show that these minimization-based simulation methods solve an optimal transport problem with a nonstandard cost function. When the observation operators are nonlinear, however, the mapping of variables from the prior to the posterior obtained from those methods is only approximate. Errors arise from neglect of the Jacobian determinant of the transformation and from the possibility of discontinuous mappings.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, Addendum

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.

Effect of radiance-to-reflectance transformation and atmosphere removal on maximum likelihood classification accuracy of high-dimensional remote sensing data

NASA Technical Reports Server (NTRS)

Hoffbeck, Joseph P.; Landgrebe, David A.

1994-01-01

Many analysis algorithms for high-dimensional remote sensing data require that the remotely sensed radiance spectra be transformed to approximate reflectance to allow comparison with a library of laboratory reflectance spectra. In maximum likelihood classification, however, the remotely sensed spectra are compared to training samples, thus a transformation to reflectance may or may not be helpful. The effect of several radiance-to-reflectance transformations on maximum likelihood classification accuracy is investigated in this paper. We show that the empirical line approach, LOWTRAN7, flat-field correction, single spectrum method, and internal average reflectance are all non-singular affine transformations, and that non-singular affine transformations have no effect on discriminant analysis feature extraction and maximum likelihood classification accuracy. (An affine transformation is a linear transformation with an optional offset.) Since the Atmosphere Removal Program (ATREM) and the log residue method are not affine transformations, experiments with Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data were conducted to determine the effect of these transformations on maximum likelihood classification accuracy. The average classification accuracy of the data transformed by ATREM and the log residue method was slightly less than the accuracy of the original radiance data. Since the radiance-to-reflectance transformations allow direct comparison of remotely sensed spectra with laboratory reflectance spectra, they can be quite useful in labeling the training samples required by maximum likelihood classification, but these transformations have only a slight effect or no effect at all on discriminant analysis and maximum likelihood classification accuracy.

Gaussian statistics for palaeomagnetic vectors

USGS Publications Warehouse

Love, J.J.; Constable, C.G.

2003-01-01

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Re??union, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

Gaussian statistics for palaeomagnetic vectors

NASA Astrophysics Data System (ADS)

Love, J. J.; Constable, C. G.

2003-03-01

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimodal) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Réunion, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

Denoising of polychromatic CT images based on their own noise properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Ji Hye; Chang, Yongjin; Ra, Jong Beom, E-mail: jbra@kaist.ac.kr

Purpose: Because of high diagnostic accuracy and fast scan time, computed tomography (CT) has been widely used in various clinical applications. Since the CT scan introduces radiation exposure to patients, however, dose reduction has recently been recognized as an important issue in CT imaging. However, low-dose CT causes an increase of noise in the image and thereby deteriorates the accuracy of diagnosis. In this paper, the authors develop an efficient denoising algorithm for low-dose CT images obtained using a polychromatic x-ray source. The algorithm is based on two steps: (i) estimation of space variant noise statistics, which are uniquely determinedmore » according to the system geometry and scanned object, and (ii) subsequent novel conversion of the estimated noise to Gaussian noise so that an existing high performance Gaussian noise filtering algorithm can be directly applied to CT images with non-Gaussian noise. Methods: For efficient polychromatic CT image denoising, the authors first reconstruct an image with the iterative maximum-likelihood polychromatic algorithm for CT to alleviate the beam-hardening problem. We then estimate the space-variant noise variance distribution on the image domain. Since there are many high performance denoising algorithms available for the Gaussian noise, image denoising can become much more efficient if they can be used. Hence, the authors propose a novel conversion scheme to transform the estimated space-variant noise to near Gaussian noise. In the suggested scheme, the authors first convert the image so that its mean and variance can have a linear relationship, and then produce a Gaussian image via variance stabilizing transform. The authors then apply a block matching 4D algorithm that is optimized for noise reduction of the Gaussian image, and reconvert the result to obtain a final denoised image. To examine the performance of the proposed method, an XCAT phantom simulation and a physical phantom experiment were conducted. Results: Both simulation and experimental results show that, unlike the existing denoising algorithms, the proposed algorithm can effectively reduce the noise over the whole region of CT images while preventing degradation of image resolution. Conclusions: To effectively denoise polychromatic low-dose CT images, a novel denoising algorithm is proposed. Because this algorithm is based on the noise statistics of a reconstructed polychromatic CT image, the spatially varying noise on the image is effectively reduced so that the denoised image will have homogeneous quality over the image domain. Through a simulation and a real experiment, it is verified that the proposed algorithm can deliver considerably better performance compared to the existing denoising algorithms.« less

Financial market dynamics: superdiffusive or not?

NASA Astrophysics Data System (ADS)

Devi, Sandhya

2017-08-01

The behavior of stock market returns over a period of 1-60 d has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are non-Gaussian. They have fat tails indicating that the stock returns do not follow a random walk model. In this work, a good fit to a Tsallis q-Gaussian distribution is obtained for the distributions of all the returns using the method of Maximum Likelihood Estimate. For all the regions of data considered, the values of the scaling parameter q, estimated from 1 d returns, lie in the range 1.4-1.65. The estimated inverse mean square deviations (beta) show a power law behavior in time with exponent values between  -0.91 and  -1.1 indicating normal to mildly subdiffusive behavior. Quite often, the dynamics of market return distributions is modelled by a Fokker-Plank (FP) equation either with a linear drift and a nonlinear diffusion term or with just a nonlinear diffusion term. Both of these cases support a q-Gaussian distribution as a solution. The distributions obtained from current estimated parameters are compared with the solutions of the FP equations. For negligible drift term, the inverse mean square deviations (betaFP) from the FP model follow a power law with exponent values between  -1.25 and  -1.48 indicating superdiffusion. When the drift term is non-negligible, the corresponding betaFP do not follow a power law and become stationary after certain characteristic times that depend on the values of the drift parameter and q. Neither of these behaviors is supported by the results of the empirical fit.

SubspaceEM: A Fast Maximum-a-posteriori Algorithm for Cryo-EM Single Particle Reconstruction

PubMed Central

Dvornek, Nicha C.; Sigworth, Fred J.; Tagare, Hemant D.

2015-01-01

Single particle reconstruction methods based on the maximum-likelihood principle and the expectation-maximization (E–M) algorithm are popular because of their ability to produce high resolution structures. However, these algorithms are computationally very expensive, requiring a network of computational servers. To overcome this computational bottleneck, we propose a new mathematical framework for accelerating maximum-likelihood reconstructions. The speedup is by orders of magnitude and the proposed algorithm produces similar quality reconstructions compared to the standard maximum-likelihood formulation. Our approach uses subspace approximations of the cryo-electron microscopy (cryo-EM) data and projection images, greatly reducing the number of image transformations and comparisons that are computed. Experiments using simulated and actual cryo-EM data show that speedup in overall execution time compared to traditional maximum-likelihood reconstruction reaches factors of over 300. PMID:25839831

Anti-collusion forensics of multimedia fingerprinting using orthogonal modulation.

PubMed

Wang, Z Jane; Wu, Min; Zhao, Hong Vicky; Trappe, Wade; Liu, K J Ray

2005-06-01

Digital fingerprinting is a method for protecting digital data in which fingerprints that are embedded in multimedia are capable of identifying unauthorized use of digital content. A powerful attack that can be employed to reduce this tracing capability is collusion, where several users combine their copies of the same content to attenuate/remove the original fingerprints. In this paper, we study the collusion resistance of a fingerprinting system employing Gaussian distributed fingerprints and orthogonal modulation. We introduce the maximum detector and the thresholding detector for colluder identification. We then analyze the collusion resistance of a system to the averaging collusion attack for the performance criteria represented by the probability of a false negative and the probability of a false positive. Lower and upper bounds for the maximum number of colluders K(max) are derived. We then show that the detectors are robust to different collusion attacks. We further study different sets of performance criteria, and our results indicate that attacks based on a few dozen independent copies can confound such a fingerprinting system. We also propose a likelihood-based approach to estimate the number of colluders. Finally, we demonstrate the performance for detecting colluders through experiments using real images.

Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images.

PubMed

Elad, M; Feuer, A

1997-01-01

The three main tools in the single image restoration theory are the maximum likelihood (ML) estimator, the maximum a posteriori probability (MAP) estimator, and the set theoretic approach using projection onto convex sets (POCS). This paper utilizes the above known tools to propose a unified methodology toward the more complicated problem of superresolution restoration. In the superresolution restoration problem, an improved resolution image is restored from several geometrically warped, blurred, noisy and downsampled measured images. The superresolution restoration problem is modeled and analyzed from the ML, the MAP, and POCS points of view, yielding a generalization of the known superresolution restoration methods. The proposed restoration approach is general but assumes explicit knowledge of the linear space- and time-variant blur, the (additive Gaussian) noise, the different measured resolutions, and the (smooth) motion characteristics. A hybrid method combining the simplicity of the ML and the incorporation of nonellipsoid constraints is presented, giving improved restoration performance, compared with the ML and the POCS approaches. The hybrid method is shown to converge to the unique optimal solution of a new definition of the optimization problem. Superresolution restoration from motionless measurements is also discussed. Simulations demonstrate the power of the proposed methodology.

Precise Determination of the Absorption Maximum in Wide Bands

ERIC Educational Resources Information Center

Eriksson, Karl-Hugo; And Others

1977-01-01

A precise method of determining absorption maxima where Gaussian functions occur is described. The method is based on a logarithmic transformation of the Gaussian equation and is suited for a mini-computer. (MR)

Feasibility study on the least square method for fitting non-Gaussian noise data

NASA Astrophysics Data System (ADS)

Xu, Wei; Chen, Wen; Liang, Yingjie

2018-02-01

This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. It is stressed that the least-squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%.

Probabilistic neural networks modeling of the 48-h LC50 acute toxicity endpoint to Daphnia magna.

PubMed

Niculescu, S P; Lewis, M A; Tigner, J

2008-01-01

Two modeling experiments based on the maximum likelihood estimation paradigm and targeting prediction of the Daphnia magna 48-h LC50 acute toxicity endpoint for both organic and inorganic compounds are reported. The resulting models computational algorithms are implemented as basic probabilistic neural networks with Gaussian kernel (statistical corrections included). The first experiment uses strictly D. magna information for 971 structures as training/learning data and the resulting model targets practical applications. The second experiment uses the same training/learning information plus additional data on another 29 compounds whose endpoint information is originating from D. pulex and Ceriodaphnia dubia. It only targets investigation of the effect of mixing strictly D. magna 48-h LC50 modeling information with small amounts of similar information estimated from related species, and this is done as part of the validation process. A complementary 81 compounds dataset (involving only strictly D. magna information) is used to perform external testing. On this external test set, the Gaussian character of the distribution of the residuals is confirmed for both models. This allows the use of traditional statistical methodology to implement computation of confidence intervals for the unknown measured values based on the models predictions. Examples are provided for the model targeting practical applications. For the same model, a comparison with other existing models targeting the same endpoint is performed.

Cramer-Rao Bound, MUSIC, and Maximum Likelihood. Effects of Temporal Phase Difference

DTIC Science & Technology

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

Extracting rate coefficients from single-molecule photon trajectories and FRET efficiency histograms for a fast-folding protein.

PubMed

Chung, Hoi Sung; Gopich, Irina V; McHale, Kevin; Cellmer, Troy; Louis, John M; Eaton, William A

2011-04-28

Recently developed statistical methods by Gopich and Szabo were used to extract folding and unfolding rate coefficients from single-molecule Förster resonance energy transfer (FRET) data for proteins with kinetics too fast to measure waiting time distributions. Two types of experiments and two different analyses were performed. In one experiment bursts of photons were collected from donor and acceptor fluorophores attached to a 73-residue protein, α(3)D, freely diffusing through the illuminated volume of a confocal microscope system. In the second, the protein was immobilized by linkage to a surface, and photons were collected until one of the fluorophores bleached. Folding and unfolding rate coefficients and mean FRET efficiencies for the folded and unfolded subpopulations were obtained from a photon by photon analysis of the trajectories using a maximum likelihood method. The ability of the method to describe the data in terms of a two-state model was checked by recoloring the photon trajectories with the extracted parameters and comparing the calculated FRET efficiency histograms with the measured histograms. The sum of the rate coefficients for the two-state model agreed to within 30% with the relaxation rate obtained from the decay of the donor-acceptor cross-correlation function, confirming the high accuracy of the method. Interestingly, apparently reliable rate coefficients could be extracted using the maximum likelihood method, even at low (<10%) population of the minor component where the cross-correlation function was too noisy to obtain any useful information. The rate coefficients and mean FRET efficiencies were also obtained in an approximate procedure by simply fitting the FRET efficiency histograms, calculated by binning the donor and acceptor photons, with a sum of three-Gaussian functions. The kinetics are exposed in these histograms by the growth of a FRET efficiency peak at values intermediate between the folded and unfolded peaks as the bin size increases, a phenomenon with similarities to NMR exchange broadening. When comparable populations of folded and unfolded molecules are present, this method yields rate coefficients in very good agreement with those obtained with the maximum likelihood method. As a first step toward characterizing transition paths, the Viterbi algorithm was used to locate the most probable transition points in the photon trajectories.

A statistical method for estimating rates of soil development and ages of geologic deposits: A design for soil-chronosequence studies

USGS Publications Warehouse

Switzer, P.; Harden, J.W.; Mark, R.K.

1988-01-01

A statistical method for estimating rates of soil development in a given region based on calibration from a series of dated soils is used to estimate ages of soils in the same region that are not dated directly. The method is designed specifically to account for sampling procedures and uncertainties that are inherent in soil studies. Soil variation and measurement error, uncertainties in calibration dates and their relation to the age of the soil, and the limited number of dated soils are all considered. Maximum likelihood (ML) is employed to estimate a parametric linear calibration curve, relating soil development to time or age on suitably transformed scales. Soil variation on a geomorphic surface of a certain age is characterized by replicate sampling of soils on each surface; such variation is assumed to have a Gaussian distribution. The age of a geomorphic surface is described by older and younger bounds. This technique allows age uncertainty to be characterized by either a Gaussian distribution or by a triangular distribution using minimum, best-estimate, and maximum ages. The calibration curve is taken to be linear after suitable (in certain cases logarithmic) transformations, if required, of the soil parameter and age variables. Soil variability, measurement error, and departures from linearity are described in a combined fashion using Gaussian distributions with variances particular to each sampled geomorphic surface and the number of sample replicates. Uncertainty in age of a geomorphic surface used for calibration is described using three parameters by one of two methods. In the first method, upper and lower ages are specified together with a coverage probability; this specification is converted to a Gaussian distribution with the appropriate mean and variance. In the second method, "absolute" older and younger ages are specified together with a most probable age; this specification is converted to an asymmetric triangular distribution with mode at the most probable age. The statistical variability of the ML-estimated calibration curve is assessed by a Monte Carlo method in which simulated data sets repeatedly are drawn from the distributional specification; calibration parameters are reestimated for each such simulation in order to assess their statistical variability. Several examples are used for illustration. The age of undated soils in a related setting may be estimated from the soil data using the fitted calibration curve. A second simulation to assess age estimate variability is described and applied to the examples. ?? 1988 International Association for Mathematical Geology.

Efficient Bayesian experimental design for contaminant source identification

NASA Astrophysics Data System (ADS)

Zhang, J.; Zeng, L.

2013-12-01

In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameter identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from indirect concentration measurements in identifying unknown source parameters such as the release time, strength and location. In this approach, the sampling location that gives the maximum relative entropy is selected as the optimal one. Once the sampling location is determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown source parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. Compared with the traditional optimal design, which is based on the Gaussian linear assumption, the method developed in this study can cope with arbitrary nonlinearity. It can be used to assist in groundwater monitor network design and identification of unknown contaminant sources. Contours of the expected information gain. The optimal observing location corresponds to the maximum value. Posterior marginal probability densities of unknown parameters, the thick solid black lines are for the designed location. For comparison, other 7 lines are for randomly chosen locations. The true values are denoted by vertical lines. It is obvious that the unknown parameters are estimated better with the desinged location.

Fast maximum likelihood estimation using continuous-time neural point process models.

PubMed

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.

Likelihood Ratio, Optimal Decision Rules, and Relationship between Proportion Correct and d' in the Dual-Pair AB vs BA identification Paradigm

PubMed Central

Micheyl, Christophe; Dai, Huanping

2010-01-01

The equal-variance Gaussian signal-detection-theory (SDT) decision model for the dual-pair change-detection (or “4IAX”) paradigm has been described in earlier publications. In this note, we consider the equal-variance Gaussian SDT model for the related dual-pair AB vs BA identification paradigm. The likelihood ratios, optimal decision rules, receiver operating characteristics (ROCs), and relationships between d' and proportion-correct (PC) are analyzed for two special cases: that of statistically independent observations, which is likely to apply in constant-stimuli experiments, and that of highly correlated observations, which is likely to apply in experiments where stimuli are roved widely across trials or pairs. A surprising outcome of this analysis is that although these two situations lead to different optimal decision rules, the predicted ROCs and proportions of correct responses (PCs) for these two cases are not substantially different, and are either identical or similar to those observed in the basic Yes-No paradigm. PMID:19633356

A new model to predict weak-lensing peak counts. II. Parameter constraint strategies

NASA Astrophysics Data System (ADS)

Lin, Chieh-An; Kilbinger, Martin

2015-11-01

Context. Peak counts have been shown to be an excellent tool for extracting the non-Gaussian part of the weak lensing signal. Recently, we developed a fast stochastic forward model to predict weak-lensing peak counts. Our model is able to reconstruct the underlying distribution of observables for analysis. Aims: In this work, we explore and compare various strategies for constraining a parameter using our model, focusing on the matter density Ωm and the density fluctuation amplitude σ8. Methods: First, we examine the impact from the cosmological dependency of covariances (CDC). Second, we perform the analysis with the copula likelihood, a technique that makes a weaker assumption than does the Gaussian likelihood. Third, direct, non-analytic parameter estimations are applied using the full information of the distribution. Fourth, we obtain constraints with approximate Bayesian computation (ABC), an efficient, robust, and likelihood-free algorithm based on accept-reject sampling. Results: We find that neglecting the CDC effect enlarges parameter contours by 22% and that the covariance-varying copula likelihood is a very good approximation to the true likelihood. The direct techniques work well in spite of noisier contours. Concerning ABC, the iterative process converges quickly to a posterior distribution that is in excellent agreement with results from our other analyses. The time cost for ABC is reduced by two orders of magnitude. Conclusions: The stochastic nature of our weak-lensing peak count model allows us to use various techniques that approach the true underlying probability distribution of observables, without making simplifying assumptions. Our work can be generalized to other observables where forward simulations provide samples of the underlying distribution.

Clarifying the Hubble constant tension with a Bayesian hierarchical model of the local distance ladder

NASA Astrophysics Data System (ADS)

Feeney, Stephen M.; Mortlock, Daniel J.; Dalmasso, Niccolò

2018-05-01

Estimates of the Hubble constant, H0, from the local distance ladder and from the cosmic microwave background (CMB) are discrepant at the ˜3σ level, indicating a potential issue with the standard Λ cold dark matter (ΛCDM) cosmology. A probabilistic (i.e. Bayesian) interpretation of this tension requires a model comparison calculation, which in turn depends strongly on the tails of the H0 likelihoods. Evaluating the tails of the local H0 likelihood requires the use of non-Gaussian distributions to faithfully represent anchor likelihoods and outliers, and simultaneous fitting of the complete distance-ladder data set to ensure correct uncertainty propagation. We have hence developed a Bayesian hierarchical model of the full distance ladder that does not rely on Gaussian distributions and allows outliers to be modelled without arbitrary data cuts. Marginalizing over the full ˜3000-parameter joint posterior distribution, we find H0 = (72.72 ± 1.67) km s-1 Mpc-1 when applied to the outlier-cleaned Riess et al. data, and (73.15 ± 1.78) km s-1 Mpc-1 with supernova outliers reintroduced (the pre-cut Cepheid data set is not available). Using our precise evaluation of the tails of the H0 likelihood, we apply Bayesian model comparison to assess the evidence for deviation from ΛCDM given the distance-ladder and CMB data. The odds against ΛCDM are at worst ˜10:1 when considering the Planck 2015 XIII data, regardless of outlier treatment, considerably less dramatic than naïvely implied by the 2.8σ discrepancy. These odds become ˜60:1 when an approximation to the more-discrepant Planck Intermediate XLVI likelihood is included.

Gaussian maximally multipartite-entangled states

NASA Astrophysics Data System (ADS)

Facchi, Paolo; Florio, Giuseppe; Lupo, Cosmo; Mancini, Stefano; Pascazio, Saverio

2009-12-01

We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n≤7 .

A general methodology for maximum likelihood inference from band-recovery data

USGS Publications Warehouse

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.

Efficient Levenberg-Marquardt minimization of the maximum likelihood estimator for Poisson deviates

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 ofmore » 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) for the Poisson distribution is also well known, but has not become generally used. This is primarily because, in contrast to non-linear least squares fitting, there has been no quick, robust, and general fitting method. In the field of fluorescence lifetime spectroscopy and imaging, there have been some efforts to use this estimator through minimization routines such as Nelder-Mead optimization, exhaustive line searches, and Gauss-Newton minimization. Minimization based on specific one- or multi-exponential models has been used to obtain quick results, but this procedure does not allow the incorporation of the instrument response, and is not generally applicable to models found in other fields. Methods for using the MLE for Poisson-distributed data have been published by the wider spectroscopic community, including iterative minimization schemes based on Gauss-Newton minimization. The slow acceptance of these procedures for fitting event counting histograms may also be explained by the use of the ubiquitous, fast Levenberg-Marquardt (L-M) fitting procedure for fitting non-linear models using least squares fitting (simple searches obtain {approx}10000 references - this doesn't include those who use it, but don't know they are using it). The benefits of L-M include a seamless transition between Gauss-Newton minimization and downward gradient minimization through the use of a regularization parameter. This transition is desirable because Gauss-Newton methods converge quickly, but only within a limited domain of convergence; on the other hand the downward gradient methods have a much wider domain of convergence, but converge extremely slowly nearer the minimum. L-M has the advantages of both procedures: relative insensitivity to initial parameters and rapid convergence. Scientists, when wanting an answer quickly, will fit data using L-M, get an answer, and move on. Only those that are aware of the bias issues will bother to fit using the more appropriate MLE for Poisson deviates. However, since there is a simple, analytical formula for the appropriate MLE measure for Poisson deviates, it is inexcusable that least squares estimators are used almost exclusively when fitting event counting histograms. There have been ways found to use successive non-linear least squares fitting to obtain similarly unbiased results, but this procedure is justified by simulation, must be re-tested when conditions change significantly, and requires two successive fits. There is a great need for a fitting routine for the MLE estimator for Poisson deviates that has convergence domains and rates comparable to the non-linear least squares L-M fitting. We show in this report that a simple way to achieve that goal is to use the L-M fitting procedure not to minimize the least squares measure, but the MLE for Poisson deviates.« less

Multi-atlas segmentation for abdominal organs with Gaussian mixture models

NASA Astrophysics Data System (ADS)

Burke, Ryan P.; Xu, Zhoubing; Lee, Christopher P.; Baucom, Rebeccah B.; Poulose, Benjamin K.; Abramson, Richard G.; Landman, Bennett A.

2015-03-01

Abdominal organ segmentation with clinically acquired computed tomography (CT) is drawing increasing interest in the medical imaging community. Gaussian mixture models (GMM) have been extensively used through medical segmentation, most notably in the brain for cerebrospinal fluid / gray matter / white matter differentiation. Because abdominal CT exhibit strong localized intensity characteristics, GMM have recently been incorporated in multi-stage abdominal segmentation algorithms. In the context of variable abdominal anatomy and rich algorithms, it is difficult to assess the marginal contribution of GMM. Herein, we characterize the efficacy of an a posteriori framework that integrates GMM of organ-wise intensity likelihood with spatial priors from multiple target-specific registered labels. In our study, we first manually labeled 100 CT images. Then, we assigned 40 images to use as training data for constructing target-specific spatial priors and intensity likelihoods. The remaining 60 images were evaluated as test targets for segmenting 12 abdominal organs. The overlap between the true and the automatic segmentations was measured by Dice similarity coefficient (DSC). A median improvement of 145% was achieved by integrating the GMM intensity likelihood against the specific spatial prior. The proposed framework opens the opportunities for abdominal organ segmentation by efficiently using both the spatial and appearance information from the atlases, and creates a benchmark for large-scale automatic abdominal segmentation.

Truncated Gaussians as tolerance sets

NASA Technical Reports Server (NTRS)

Cozman, Fabio; Krotkov, Eric

1994-01-01

This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

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.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, 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.

Multimodal Likelihoods in Educational Assessment: Will the Real Maximum Likelihood Score Please Stand up?

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…

Wald Sequential Probability Ratio Test for Analysis of Orbital Conjunction Data

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Markley, F. Landis; Gold, Dara

2013-01-01

We propose a Wald Sequential Probability Ratio Test for analysis of commonly available predictions associated with spacecraft conjunctions. Such predictions generally consist of a relative state and relative state error covariance at the time of closest approach, under the assumption that prediction errors are Gaussian. We show that under these circumstances, the likelihood ratio of the Wald test reduces to an especially simple form, involving the current best estimate of collision probability, and a similar estimate of collision probability that is based on prior assumptions about the likelihood of collision.

Asymptotic Properties of Induced Maximum Likelihood Estimates of Nonlinear Models for Item Response Variables: The Finite-Generic-Item-Pool Case.

ERIC Educational Resources Information Center

Jones, Douglas H.

The progress of modern mental test theory depends very much on the techniques of maximum likelihood estimation, and many popular applications make use of likelihoods induced by logistic item response models. While, in reality, item responses are nonreplicate within a single examinee and the logistic models are only ideal, practitioners make…

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…

The Laplace method for probability measures in Banach spaces

NASA Astrophysics Data System (ADS)

Piterbarg, V. I.; Fatalov, V. R.

1995-12-01

Contents §1. Introduction Chapter I. Asymptotic analysis of continual integrals in Banach space, depending on a large parameter §2. The large deviation principle and logarithmic asymptotics of continual integrals §3. Exact asymptotics of Gaussian integrals in Banach spaces: the Laplace method 3.1. The Laplace method for Gaussian integrals taken over the whole Hilbert space: isolated minimum points ([167], I) 3.2. The Laplace method for Gaussian integrals in Hilbert space: the manifold of minimum points ([167], II) 3.3. The Laplace method for Gaussian integrals in Banach space ([90], [174], [176]) 3.4. Exact asymptotics of large deviations of Gaussian norms §4. The Laplace method for distributions of sums of independent random elements with values in Banach space 4.1. The case of a non-degenerate minimum point ([137], I) 4.2. A degenerate isolated minimum point and the manifold of minimum points ([137], II) §5. Further examples 5.1. The Laplace method for the local time functional of a Markov symmetric process ([217]) 5.2. The Laplace method for diffusion processes, a finite number of non-degenerate minimum points ([116]) 5.3. Asymptotics of large deviations for Brownian motion in the Hölder norm 5.4. Non-asymptotic expansion of a strong stable law in Hilbert space ([41]) Chapter II. The double sum method - a version of the Laplace method in the space of continuous functions §6. Pickands' method of double sums 6.1. General situations 6.2. Asymptotics of the distribution of the maximum of a Gaussian stationary process 6.3. Asymptotics of the probability of a large excursion of a Gaussian non-stationary process §7. Probabilities of large deviations of trajectories of Gaussian fields 7.1. Homogeneous fields and fields with constant dispersion 7.2. Finitely many maximum points of dispersion 7.3. Manifold of maximum points of dispersion 7.4. Asymptotics of distributions of maxima of Wiener fields §8. Exact asymptotics of large deviations of the norm of Gaussian vectors and processes with values in the spaces L_k^p and l^2. Gaussian fields with the set of parameters in Hilbert space 8.1 Exact asymptotics of the distribution of the l_k^p-norm of a Gaussian finite-dimensional vector with dependent coordinates, p > 1 8.2. Exact asymptotics of probabilities of high excursions of trajectories of processes of type \\chi^2 8.3. Asymptotics of the probabilities of large deviations of Gaussian processes with a set of parameters in Hilbert space [74] 8.4. Asymptotics of distributions of maxima of the norms of l^2-valued Gaussian processes 8.5. Exact asymptotics of large deviations for the l^2-valued Ornstein-Uhlenbeck process Bibliography

Generalized Fisher matrices

NASA Astrophysics Data System (ADS)

Heavens, A. F.; Seikel, M.; Nord, B. D.; Aich, M.; Bouffanais, Y.; Bassett, B. A.; Hobson, M. P.

2014-12-01

The Fisher Information Matrix formalism (Fisher 1935) is extended to cases where the data are divided into two parts (X, Y), where the expectation value of Y depends on X according to some theoretical model, and X and Y both have errors with arbitrary covariance. In the simplest case, (X, Y) represent data pairs of abscissa and ordinate, in which case the analysis deals with the case of data pairs with errors in both coordinates, but X can be any measured quantities on which Y depends. The analysis applies for arbitrary covariance, provided all errors are Gaussian, and provided the errors in X are small, both in comparison with the scale over which the expected signal Y changes, and with the width of the prior distribution. This generalizes the Fisher Matrix approach, which normally only considers errors in the `ordinate' Y. In this work, we include errors in X by marginalizing over latent variables, effectively employing a Bayesian hierarchical model, and deriving the Fisher Matrix for this more general case. The methods here also extend to likelihood surfaces which are not Gaussian in the parameter space, and so techniques such as DALI (Derivative Approximation for Likelihoods) can be generalized straightforwardly to include arbitrary Gaussian data error covariances. For simple mock data and theoretical models, we compare to Markov Chain Monte Carlo experiments, illustrating the method with cosmological supernova data. We also include the new method in the FISHER4CAST software.

Estimating parameter of Rayleigh distribution by using Maximum Likelihood method and Bayes method

NASA Astrophysics Data System (ADS)

Ardianti, Fitri; Sutarman

2018-01-01

In this paper, we use Maximum Likelihood estimation and Bayes method under some risk function to estimate parameter of Rayleigh distribution to know the best method. The prior knowledge which used in Bayes method is Jeffrey’s non-informative prior. Maximum likelihood estimation and Bayes method under precautionary loss function, entropy loss function, loss function-L 1 will be compared. We compare these methods by bias and MSE value using R program. After that, the result will be displayed in tables to facilitate the comparisons.

Maximum correntropy square-root cubature Kalman filter with application to SINS/GPS integrated systems.

PubMed

Liu, Xi; Qu, Hua; Zhao, Jihong; Yue, Pengcheng

2018-05-31

For a nonlinear system, the cubature Kalman filter (CKF) and its square-root version are useful methods to solve the state estimation problems, and both can obtain good performance in Gaussian noises. However, their performances often degrade significantly in the face of non-Gaussian noises, particularly when the measurements are contaminated by some heavy-tailed impulsive noises. By utilizing the maximum correntropy criterion (MCC) to improve the robust performance instead of traditional minimum mean square error (MMSE) criterion, a new square-root nonlinear filter is proposed in this study, named as the maximum correntropy square-root cubature Kalman filter (MCSCKF). The new filter not only retains the advantage of square-root cubature Kalman filter (SCKF), but also exhibits robust performance against heavy-tailed non-Gaussian noises. A judgment condition that avoids numerical problem is also given. The results of two illustrative examples, especially the SINS/GPS integrated systems, demonstrate the desirable performance of the proposed filter. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Dark Energy Survey Year 1 Results: Weak Lensing Shape Catalogues

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zuntz, J.; et al.

We present two galaxy shape catalogues from the Dark Energy Survey Year 1 data set, covering 1500 square degrees with a median redshift ofmore » $0.59$. The catalogues cover two main fields: Stripe 82, and an area overlapping the South Pole Telescope survey region. We describe our data analysis process and in particular our shape measurement using two independent shear measurement pipelines, METACALIBRATION and IM3SHAPE. The METACALIBRATION catalogue uses a Gaussian model with an innovative internal calibration scheme, and was applied to $riz$-bands, yielding 34.8M objects. The IM3SHAPE catalogue uses a maximum-likelihood bulge/disc model calibrated using simulations, and was applied to $r$-band data, yielding 21.9M objects. Both catalogues pass a suite of null tests that demonstrate their fitness for use in weak lensing science. We estimate the 1$$\\sigma$$ uncertainties in multiplicative shear calibration to be $0.013$ and $0.025$ for the METACALIBRATION and IM3SHAPE catalogues, respectively.« less

Differential detection in quadrature-quadrature phase shift keying (Q2PSK) systems

NASA Astrophysics Data System (ADS)

El-Ghandour, Osama M.; Saha, Debabrata

1991-05-01

A generalized quadrature-quadrature phase shift keying (Q2PSK) signaling format is considered for differential encoding and differential detection. Performance in the presence of additive white Gaussian noise (AWGN) is analyzed. Symbol error rate is found to be approximately twice the symbol error rate in a quaternary DPSK system operating at the same Eb/N0. However, the bandwidth efficiency of differential Q2PSK is substantially higher than that of quaternary DPSK. When the error is due to AWGN, the ratio of double error rate to single error rate can be very high, and the ratio may approach zero at high SNR. To improve error rate, differential detection through maximum-likelihood decoding based on multiple or N symbol observations is considered. If N and SNR are large this decoding gives a 3-dB advantage in error rate over conventional N = 2 differential detection, fully recovering the energy loss (as compared to coherent detection) if the observation is extended to a large number of symbol durations.

Radar modulation classification using time-frequency representation and nonlinear regression

NASA Astrophysics Data System (ADS)

De Luigi, Christophe; Arques, Pierre-Yves; Lopez, Jean-Marc; Moreau, Eric

1999-09-01

In naval electronic environment, pulses emitted by radars are collected by ESM receivers. For most of them the intrapulse signal is modulated by a particular law. To help the classical identification process, a classification and estimation of this modulation law is applied on the intrapulse signal measurements. To estimate with a good accuracy the time-varying frequency of a signal corrupted by an additive noise, one method has been chosen. This method consists on the Wigner distribution calculation, the instantaneous frequency is then estimated by the peak location of the distribution. Bias and variance of the estimator are performed by computed simulations. In a estimated sequence of frequencies, we assume the presence of false and good estimated ones, the hypothesis of Gaussian distribution is made on the errors. A robust non linear regression method, based on the Levenberg-Marquardt algorithm, is thus applied on these estimated frequencies using a Maximum Likelihood Estimator. The performances of the method are tested by using varied modulation laws and different signal to noise ratios.

Optimally resolving Lambertian surface orientation

NASA Astrophysics Data System (ADS)

Bertsatos, Ioannis; Makris, Nicholas C.

2003-10-01

Sonar images of remote surfaces are typically corrupted by signal-dependent noise known as speckle. Relative motion between source, surface, and receiver causes the received field to fluctuate over time with circular complex Gaussian random (CCGR) statistics. In many cases of practical importance, Lambert's law is appropriate to model radiant intensity from the surface. In a previous paper, maximum likelihood estimators (MLE) for Lambertian surface orientation have been derived based on CCGR measurements [N. C. Makris, SACLANT Conference Proceedings Series CP-45, 1997, pp. 339-346]. A Lambertian surface needs to be observed from more than one illumination direction for its orientation to be properly constrained. It is found, however, that MLE performance varies significantly with illumination direction due to the inherently nonlinear nature of this problem. It is shown that a large number of samples is often required to optimally resolve surface orientation using the optimality criteria of the MLE derived in Naftali and Makris [J. Acoust. Soc. Am. 110, 1917-1930 (2001)].

Identification of internal properties of fibers and micro-swimmers

NASA Astrophysics Data System (ADS)

Plouraboue, Franck; Thiam, Ibrahima; Delmotte, Blaise; Climent, Eric; PSC Collaboration

2016-11-01

In this presentation we discuss the identifiability of constitutive parameters of passive or active micro-swimmers. We first present a general framework for describing fibers or micro-swimmers using a bead-model description. Using a kinematic constraint formulation to describe fibers, flagellum or cilia, we find explicit linear relationship between elastic constitutive parameters and generalised velocities from computing contact forces. This linear formulation then permits to address explicitly identifiability conditions and solve for parameter identification. We show that both active forcing and passive parameters are both identifiable independently but not simultaneously. We also provide unbiased estimators for elastic parameters as well as active ones in the presence of Langevin-like forcing with Gaussian noise using normal linear regression models and maximum likelihood method. These theoretical results are illustrated in various configurations of relaxed or actuated passives fibers, and active filament of known passive properties, showing the efficiency of the proposed approach for direct parameter identification. The convergence of the proposed estimators is successfully tested numerically.

Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence

NASA Astrophysics Data System (ADS)

Adesso, Gerardo; Serafini, Alessio; Illuminati, Fabrizio

2006-03-01

We present a complete analysis of the multipartite entanglement of three-mode Gaussian states of continuous-variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations can be quantified by a proper convex roof extension of the squared logarithmic negativity, the continuous-variable tangle, or contangle. We review and elucidate in detail the proof that in multimode Gaussian states the contangle satisfies a monogamy inequality constraint [G. Adesso and F. Illuminati, New J. Phys8, 15 (2006)]. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communications and defines a measure of genuine tripartite entanglements. We determine the analytical expression of the residual contangle for arbitrary pure three-mode Gaussian states and study in detail the distribution of quantum correlations in such states. This analysis yields that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states GHZ/W states of continuous-variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the W states of three qubits. We finally consider the effect of decoherence on three-mode Gaussian states, studying the decay of the residual contangle. The GHZ/W states are shown to be maximally robust against losses and thermal noise.

XENON100 exclusion limit without considering Leff as a nuisance parameter

NASA Astrophysics Data System (ADS)

Davis, Jonathan H.; Bœhm, Céline; Oppermann, Niels; Ensslin, Torsten; Lacroix, Thomas

2012-07-01

In 2011, the XENON100 experiment has set unprecedented constraints on dark matter-nucleon interactions, excluding dark matter candidates with masses down to 6 GeV if the corresponding cross section is larger than 10-39cm2. The dependence of the exclusion limit in terms of the scintillation efficiency (Leff) has been debated at length. To overcome possible criticisms XENON100 performed an analysis in which Leff was considered as a nuisance parameter and its uncertainties were profiled out by using a Gaussian likelihood in which the mean value corresponds to the best fit Leff value (smoothly extrapolated to 0 below 3 keVnr). Although such a method seems fairly robust, it does not account for more extreme types of extrapolation nor does it enable us to anticipate how much the exclusion limit would vary if new data were to support a flat behavior for Leff below 3 keVnr, for example. Yet, such a question is crucial for light dark matter models which are close to the published XENON100 limit. To answer this issue, we use a maximum likelihood ratio analysis, as done by the XENON100 Collaboration, but do not consider Leff as a nuisance parameter. Instead, Leff is obtained directly from the fits to the data. This enables us to define frequentist confidence intervals by marginalizing over Leff.

Maximum Likelihood Implementation of an Isolation-with-Migration Model for Three Species.

PubMed

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 behalf of the Society of Systematic Biologists. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Spherical Deconvolution of Multichannel Diffusion MRI Data with Non-Gaussian Noise Models and Spatial Regularization

PubMed Central

Canales-Rodríguez, Erick J.; Caruyer, Emmanuel; Aja-Fernández, Santiago; Radua, Joaquim; Yurramendi Mendizabal, Jesús M.; Iturria-Medina, Yasser; Melie-García, Lester; Alemán-Gómez, Yasser; Thiran, Jean-Philippe; Sarró, Salvador; Pomarol-Clotet, Edith; Salvador, Raymond

2015-01-01

Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in human brain data. PMID:26470024

The skewed weak lensing likelihood: why biases arise, despite data and theory being sound

NASA Astrophysics Data System (ADS)

Sellentin, Elena; Heymans, Catherine; Harnois-Déraps, Joachim

2018-07-01

We derive the essentials of the skewed weak lensing likelihood via a simple hierarchical forward model. Our likelihood passes four objective and cosmology-independent tests which a standard Gaussian likelihood fails. We demonstrate that sound weak lensing data are naturally biased low, since they are drawn from a skewed distribution. This occurs already in the framework of Lambda cold dark matter. Mathematically, the biases arise because noisy two-point functions follow skewed distributions. This form of bias is already known from cosmic microwave background analyses, where the low multipoles have asymmetric error bars. Weak lensing is more strongly affected by this asymmetry as galaxies form a discrete set of shear tracer particles, in contrast to a smooth shear field. We demonstrate that the biases can be up to 30 per cent of the standard deviation per data point, dependent on the properties of the weak lensing survey and the employed filter function. Our likelihood provides a versatile framework with which to address this bias in future weak lensing analyses.

The skewed weak lensing likelihood: why biases arise, despite data and theory being sound.

NASA Astrophysics Data System (ADS)

Sellentin, Elena; Heymans, Catherine; Harnois-Déraps, Joachim

2018-04-01

We derive the essentials of the skewed weak lensing likelihood via a simple Hierarchical Forward Model. Our likelihood passes four objective and cosmology-independent tests which a standard Gaussian likelihood fails. We demonstrate that sound weak lensing data are naturally biased low, since they are drawn from a skewed distribution. This occurs already in the framework of ΛCDM. Mathematically, the biases arise because noisy two-point functions follow skewed distributions. This form of bias is already known from CMB analyses, where the low multipoles have asymmetric error bars. Weak lensing is more strongly affected by this asymmetry as galaxies form a discrete set of shear tracer particles, in contrast to a smooth shear field. We demonstrate that the biases can be up to 30% of the standard deviation per data point, dependent on the properties of the weak lensing survey and the employed filter function. Our likelihood provides a versatile framework with which to address this bias in future weak lensing analyses.

Closed-loop carrier phase synchronization techniques motivated by likelihood functions

NASA Technical Reports Server (NTRS)

Tsou, H.; Hinedi, S.; Simon, M.

1994-01-01

This article reexamines the notion of closed-loop carrier phase synchronization motivated by the theory of maximum a posteriori phase estimation with emphasis on the development of new structures based on both maximum-likelihood and average-likelihood functions. The criterion of performance used for comparison of all the closed-loop structures discussed is the mean-squared phase error for a fixed-loop bandwidth.

Theory of Genuine Tripartite Nonlocality of Gaussian States

NASA Astrophysics Data System (ADS)

Adesso, Gerardo; Piano, Samanta

2014-01-01

We investigate the genuine multipartite nonlocality of three-mode Gaussian states of continuous variable systems. For pure states, we present a simplified procedure to obtain the maximum violation of the Svetlichny inequality based on displaced parity measurements, and we analyze its interplay with genuine tripartite entanglement measured via Rényi-2 entropy. The maximum Svetlichny violation admits tight upper and lower bounds at fixed tripartite entanglement. For mixed states, no violation is possible when the purity falls below 0.86. We also explore a set of recently derived weaker inequalities for three-way nonlocality, finding violations for all tested pure states. Our results provide a strong signature for the nonclassical and nonlocal nature of Gaussian states despite their positive Wigner function, and lead to precise recipes for its experimental verification.

Modeling Multi-Variate Gaussian Distributions and Analysis of Higgs Boson Couplings with the ATLAS Detector

NASA Astrophysics Data System (ADS)

Krohn, Olivia; Armbruster, Aaron; Gao, Yongsheng; Atlas Collaboration

2017-01-01

Software tools developed for the purpose of modeling CERN LHC pp collision data to aid in its interpretation are presented. Some measurements are not adequately described by a Gaussian distribution; thus an interpretation assuming Gaussian uncertainties will inevitably introduce bias, necessitating analytical tools to recreate and evaluate non-Gaussian features. One example is the measurements of Higgs boson production rates in different decay channels, and the interpretation of these measurements. The ratios of data to Standard Model expectations (μ) for five arbitrary signals were modeled by building five Poisson distributions with mixed signal contributions such that the measured values of μ are correlated. Algorithms were designed to recreate probability distribution functions of μ as multi-variate Gaussians, where the standard deviation (σ) and correlation coefficients (ρ) are parametrized. There was good success with modeling 1-D likelihood contours of μ, and the multi-dimensional distributions were well modeled within 1- σ but the model began to diverge after 2- σ due to unmerited assumptions in developing ρ. Future plans to improve the algorithms and develop a user-friendly analysis package will also be discussed. NSF International Research Experiences for Students

Fast maximum likelihood estimation of mutation rates using a birth-death process.

PubMed

Wu, Xiaowei; Zhu, Hongxiao

2015-02-07

Since fluctuation analysis was first introduced by Luria and Delbrück in 1943, it has been widely used to make inference about spontaneous mutation rates in cultured cells. Under certain model assumptions, the probability distribution of the number of mutants that appear in a fluctuation experiment can be derived explicitly, which provides the basis of mutation rate estimation. It has been shown that, among various existing estimators, the maximum likelihood estimator usually demonstrates some desirable properties such as consistency and lower mean squared error. However, its application in real experimental data is often hindered by slow computation of likelihood due to the recursive form of the mutant-count distribution. We propose a fast maximum likelihood estimator of mutation rates, MLE-BD, based on a birth-death process model with non-differential growth assumption. Simulation studies demonstrate that, compared with the conventional maximum likelihood estimator derived from the Luria-Delbrück distribution, MLE-BD achieves substantial improvement on computational speed and is applicable to arbitrarily large number of mutants. In addition, it still retains good accuracy on point estimation. Published by Elsevier Ltd.

Vegetation mapping from high-resolution satellite images in the heterogeneous arid environments of Socotra Island (Yemen)

NASA Astrophysics Data System (ADS)

Malatesta, Luca; Attorre, Fabio; Altobelli, Alfredo; Adeeb, Ahmed; De Sanctis, Michele; Taleb, Nadim M.; Scholte, Paul T.; Vitale, Marcello

2013-01-01

Socotra Island (Yemen), a global biodiversity hotspot, is characterized by high geomorphological and biological diversity. In this study, we present a high-resolution vegetation map of the island based on combining vegetation analysis and classification with remote sensing. Two different image classification approaches were tested to assess the most accurate one in mapping the vegetation mosaic of Socotra. Spectral signatures of the vegetation classes were obtained through a Gaussian mixture distribution model, and a sequential maximum a posteriori (SMAP) classification was applied to account for the heterogeneity and the complex spatial pattern of the arid vegetation. This approach was compared to the traditional maximum likelihood (ML) classification. Satellite data were represented by a RapidEye image with 5 m pixel resolution and five spectral bands. Classified vegetation relevés were used to obtain the training and evaluation sets for the main plant communities. Postclassification sorting was performed to adjust the classification through various rule-based operations. Twenty-eight classes were mapped, and SMAP, with an accuracy of 87%, proved to be more effective than ML (accuracy: 66%). The resulting map will represent an important instrument for the elaboration of conservation strategies and the sustainable use of natural resources in the island.

Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition

NASA Astrophysics Data System (ADS)

Huo, Xiaoming; Elad, Michael; Flesia, Ana G.; Muise, Robert R.; Stanfill, S. Robert; Friedman, Jerome; Popescu, Bogdan; Chen, Jihong; Mahalanobis, Abhijit; Donoho, David L.

2003-09-01

In target recognition applications of discriminant of classification analysis, each 'feature' is a result of a convolution of an imagery with a filter, which may be derived from a feature vector. It is important to use relatively few features. We analyze an optimal reduced-rank classifier under the two-class situation. Assuming each population is Gaussian and has zero mean, and the classes differ through the covariance matrices: ∑1 and ∑2. The following matrix is considered: Λ=(∑1+∑2)-1/2∑1(∑1+∑2)-1/2. We show that the k eigenvectors of this matrix whose eigenvalues are most different from 1/2 offer the best rank k approximation to the maximum likelihood classifier. The matrix Λ and its eigenvectors have been introduced by Fukunaga and Koontz; hence this analysis gives a new interpretation of the well known Fukunaga-Koontz transform. The optimality that is promised in this method hold if the two populations are exactly Guassian with the same means. To check the applicability of this approach to real data, an experiment is performed, in which several 'modern' classifiers were used on an Infrared ATR data. In these experiments, a reduced-rank classifier-Tuned Basis Functions-outperforms others. The competitive performance of the optimal reduced-rank quadratic classifier suggests that, at least for classification purposes, the imagery data behaves in a nearly-Gaussian fashion.

Maximum likelihood decoding analysis of accumulate-repeat-accumulate codes

NASA Technical Reports Server (NTRS)

Abbasfar, A.; Divsalar, D.; Yao, K.

2004-01-01

In this paper, the performance of the repeat-accumulate codes with (ML) decoding are analyzed and compared to random codes by very tight bounds. Some simple codes are shown that perform very close to Shannon limit with maximum likelihood decoding.

The Maximum Likelihood Estimation of Signature Transformation /MLEST/ algorithm. [for affine transformation of crop inventory data

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.

Design of simplified maximum-likelihood receivers for multiuser CPM systems.

PubMed

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.

On the validity of cosmological Fisher matrix forecasts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolz, Laura; Kilbinger, Martin; Weller, Jochen

2012-09-01

We present a comparison of Fisher matrix forecasts for cosmological probes with Monte Carlo Markov Chain (MCMC) posterior likelihood estimation methods. We analyse the performance of future Dark Energy Task Force (DETF) stage-III and stage-IV dark-energy surveys using supernovae, baryon acoustic oscillations and weak lensing as probes. We concentrate in particular on the dark-energy equation of state parameters w{sub 0} and w{sub a}. For purely geometrical probes, and especially when marginalising over w{sub a}, we find considerable disagreement between the two methods, since in this case the Fisher matrix can not reproduce the highly non-elliptical shape of the likelihood function.more » More quantitatively, the Fisher method underestimates the marginalized errors for purely geometrical probes between 30%-70%. For cases including structure formation such as weak lensing, we find that the posterior probability contours from the Fisher matrix estimation are in good agreement with the MCMC contours and the forecasted errors only changing on the 5% level. We then explore non-linear transformations resulting in physically-motivated parameters and investigate whether these parameterisations exhibit a Gaussian behaviour. We conclude that for the purely geometrical probes and, more generally, in cases where it is not known whether the likelihood is close to Gaussian, the Fisher matrix is not the appropriate tool to produce reliable forecasts.« less

A partial differential equation-based general framework adapted to Rayleigh's, Rician's and Gaussian's distributed noise for restoration and enhancement of magnetic resonance image.

PubMed

Yadav, Ram Bharos; Srivastava, Subodh; Srivastava, Rajeev

2016-01-01

The proposed framework is obtained by casting the noise removal problem into a variational framework. This framework automatically identifies the various types of noise present in the magnetic resonance image and filters them by choosing an appropriate filter. This filter includes two terms: the first term is a data likelihood term and the second term is a prior function. The first term is obtained by minimizing the negative log likelihood of the corresponding probability density functions: Gaussian or Rayleigh or Rician. Further, due to the ill-posedness of the likelihood term, a prior function is needed. This paper examines three partial differential equation based priors which include total variation based prior, anisotropic diffusion based prior, and a complex diffusion (CD) based prior. A regularization parameter is used to balance the trade-off between data fidelity term and prior. The finite difference scheme is used for discretization of the proposed method. The performance analysis and comparative study of the proposed method with other standard methods is presented for brain web dataset at varying noise levels in terms of peak signal-to-noise ratio, mean square error, structure similarity index map, and correlation parameter. From the simulation results, it is observed that the proposed framework with CD based prior is performing better in comparison to other priors in consideration.

An Iterative Maximum a Posteriori Estimation of Proficiency Level to Detect Multiple Local Likelihood Maxima

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…

Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adesso, Gerardo; Centre for Quantum Computation, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA; Serafini, Alessio

2006-03-15

We present a complete analysis of the multipartite entanglement of three-mode Gaussian states of continuous-variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations can be quantified by a proper convex roof extension of the squared logarithmic negativity, the continuous-variable tangle, or contangle. We review and elucidate in detail the proof that in multimode Gaussian states the contangle satisfies a monogamy inequalitymore » constraint [G. Adesso and F. Illuminati, New J. Phys8, 15 (2006)]. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communications and defines a measure of genuine tripartite entanglements. We determine the analytical expression of the residual contangle for arbitrary pure three-mode Gaussian states and study in detail the distribution of quantum correlations in such states. This analysis yields that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states GHZ/W states of continuous-variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the W states of three qubits. We finally consider the effect of decoherence on three-mode Gaussian states, studying the decay of the residual contangle. The GHZ/W states are shown to be maximally robust against losses and thermal noise.« less

Bayesian Computation for Log-Gaussian Cox Processes: A Comparative Analysis of Methods

PubMed Central

Teng, Ming; Nathoo, Farouk S.; Johnson, Timothy D.

2017-01-01

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data. PMID:29200537

Generalized massive optimal data compression

NASA Astrophysics Data System (ADS)

Alsing, Justin; Wandelt, Benjamin

2018-05-01

In this paper, we provide a general procedure for optimally compressing N data down to n summary statistics, where n is equal to the number of parameters of interest. We show that compression to the score function - the gradient of the log-likelihood with respect to the parameters - yields n compressed statistics that are optimal in the sense that they preserve the Fisher information content of the data. Our method generalizes earlier work on linear Karhunen-Loéve compression for Gaussian data whilst recovering both lossless linear compression and quadratic estimation as special cases when they are optimal. We give a unified treatment that also includes the general non-Gaussian case as long as mild regularity conditions are satisfied, producing optimal non-linear summary statistics when appropriate. As a worked example, we derive explicitly the n optimal compressed statistics for Gaussian data in the general case where both the mean and covariance depend on the parameters.

Flat-top beam for laser-stimulated pain

NASA Astrophysics Data System (ADS)

McCaughey, Ryan; Nadeau, Valerie; Dickinson, Mark

2005-04-01

One of the main problems during laser stimulation in human pain research is the risk of tissue damage caused by excessive heating of the skin. This risk has been reduced by using a laser beam with a flattop (or superGaussian) intensity profile, instead of the conventional Gaussian beam. A finite difference approximation to the heat conduction equation has been applied to model the temperature distribution in skin as a result of irradiation by flattop and Gaussian profile CO2 laser beams. The model predicts that a 15 mm diameter, 15 W, 100 ms CO2 laser pulse with an order 6 superGaussian profile produces a maximum temperature 6 oC less than a Gaussian beam with the same energy density. A superGaussian profile was created by passing a Gaussian beam through a pair of zinc selenide aspheric lenses which refract the more intense central region of the beam towards the less intense periphery. The profiles of the lenses were determined by geometrical optics. In human pain trials the superGaussian beam required more power than the Gaussian beam to reach sensory and pain thresholds.

A double-gaussian, percentile-based method for estimating maximum blood flow velocity.

PubMed

Marzban, Caren; Illian, Paul R; Morison, David; Mourad, Pierre D

2013-11-01

Transcranial Doppler sonography allows for the estimation of blood flow velocity, whose maximum value, especially at systole, is often of clinical interest. Given that observed values of flow velocity are subject to noise, a useful notion of "maximum" requires a criterion for separating the signal from the noise. All commonly used criteria produce a point estimate (ie, a single value) of maximum flow velocity at any time and therefore convey no information on the distribution or uncertainty of flow velocity. This limitation has clinical consequences especially for patients in vasospasm, whose largest flow velocities can be difficult to measure. Therefore, a method for estimating flow velocity and its uncertainty is desirable. A gaussian mixture model is used to separate the noise from the signal distribution. The time series of a given percentile of the latter, then, provides a flow velocity envelope. This means of estimating the flow velocity envelope naturally allows for displaying several percentiles (e.g., 95th and 99th), thereby conveying uncertainty in the highest flow velocity. Such envelopes were computed for 59 patients and were shown to provide reasonable and useful estimates of the largest flow velocities compared to a standard algorithm. Moreover, we found that the commonly used envelope was generally consistent with the 90th percentile of the signal distribution derived via the gaussian mixture model. Separating the observed distribution of flow velocity into a noise component and a signal component, using a double-gaussian mixture model, allows for the percentiles of the latter to provide meaningful measures of the largest flow velocities and their uncertainty.

Some Small Sample Results for Maximum Likelihood Estimation in Multidimensional Scaling.

ERIC Educational Resources Information Center

Ramsay, J. O.

1980-01-01

Some aspects of the small sample behavior of maximum likelihood estimates in multidimensional scaling are investigated with Monte Carlo techniques. In particular, the chi square test for dimensionality is examined and a correction for bias is proposed and evaluated. (Author/JKS)

ATAC Autocuer Modeling Analysis.

DTIC Science & Technology

1981-01-01

the analysis of the simple rectangular scrnentation (1) is based on detection and estimation theory (2). This approach uses the concept of maximum ...continuous wave forms. In order to develop the principles of maximum likelihood, it is con- venient to develop the principles for the "classical...the concept of maximum likelihood is significant in that it provides the optimum performance of the detection/estimation problem. With a knowledge of

Epidemiologic programs for computers and calculators. A microcomputer program for multiple logistic regression by unconditional and conditional maximum likelihood methods.

PubMed

Campos-Filho, N; Franco, E L

1989-02-01

A frequent procedure in matched case-control studies is to report results from the multivariate unmatched analyses if they do not differ substantially from the ones obtained after conditioning on the matching variables. Although conceptually simple, this rule requires that an extensive series of logistic regression models be evaluated by both the conditional and unconditional maximum likelihood methods. Most computer programs for logistic regression employ only one maximum likelihood method, which requires that the analyses be performed in separate steps. This paper describes a Pascal microcomputer (IBM PC) program that performs multiple logistic regression by both maximum likelihood estimation methods, which obviates the need for switching between programs to obtain relative risk estimates from both matched and unmatched analyses. The program calculates most standard statistics and allows factoring of categorical or continuous variables by two distinct methods of contrast. A built-in, descriptive statistics option allows the user to inspect the distribution of cases and controls across categories of any given variable.

The Maximum Likelihood Solution for Inclination-only Data

NASA Astrophysics Data System (ADS)

Arason, P.; Levi, S.

2006-12-01

The arithmetic means of inclination-only data are known to introduce a shallowing bias. Several methods have been proposed to estimate unbiased means of the inclination along with measures of the precision. Most of the 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 these methods require various assumptions and approximations that are inappropriate for many data sets. For some steep and dispersed data sets, the estimates provided by these methods are significantly displaced from the peak of the likelihood function to systematically shallower inclinations. The problem in locating the maximum of the likelihood function is partly due to difficulties in accurately evaluating the function for all values of interest. This is because some elements of the log-likelihood function increase exponentially as precision parameters increase, leading to numerical instabilities. In this study we succeeded in analytically cancelling exponential elements from the likelihood function, and we are now able to calculate its value for any location in the parameter space and for any inclination-only data set, with full accuracy. Furtermore, we can now calculate the partial derivatives of the likelihood function with desired accuracy. Locating the maximum likelihood without the assumptions required by previous methods is now straight forward. The information to separate the mean inclination from the precision parameter will be lost for very steep and dispersed data sets. It is worth noting that the likelihood function always has a maximum value. However, for some dispersed and steep data sets with few samples, the likelihood function takes its highest value on the boundary of the parameter space, i.e. at inclinations of +/- 90 degrees, but with relatively well defined dispersion. Our simulations indicate that this occurs quite frequently for certain data sets, and relatively small perturbations in the data will drive the maxima to the boundary. We interpret this to indicate that, for such data sets, the information needed to separate the mean inclination and the precision parameter is permanently lost. To assess the reliability and accuracy of our method we generated large number of random Fisher-distributed data sets and used seven methods to estimate the mean inclination and precision paramenter. These comparisons are described by Levi and Arason at the 2006 AGU Fall meeting. The results of the various methods is very favourable to our new robust maximum likelihood method, which, on average, is the most reliable, and the mean inclination estimates are the least biased toward shallow values. Further information on our inclination-only analysis can be obtained from: http://www.vedur.is/~arason/paleomag

Algorithms of maximum likelihood data clustering with applications

NASA Astrophysics Data System (ADS)

Giada, Lorenzo; Marsili, Matteo

2002-12-01

We address the problem of data clustering by introducing an unsupervised, parameter-free approach based on maximum likelihood principle. Starting from the observation that data sets belonging to the same cluster share a common information, we construct an expression for the likelihood of any possible cluster structure. The likelihood in turn depends only on the Pearson's coefficient of the data. We discuss clustering algorithms that provide a fast and reliable approximation to maximum likelihood configurations. Compared to standard clustering methods, our approach has the advantages that (i) it is parameter free, (ii) the number of clusters need not be fixed in advance and (iii) the interpretation of the results is transparent. In order to test our approach and compare it with standard clustering algorithms, we analyze two very different data sets: time series of financial market returns and gene expression data. We find that different maximization algorithms produce similar cluster structures whereas the outcome of standard algorithms has a much wider variability.

A low-power, high-throughput maximum-likelihood convolutional decoder chip for NASA's 30/20 GHz program

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.

PAMLX: a graphical user interface for PAML.

PubMed

Xu, Bo; Yang, Ziheng

2013-12-01

This note announces pamlX, a graphical user interface/front end for the paml (for Phylogenetic Analysis by Maximum Likelihood) program package (Yang Z. 1997. PAML: a program package for phylogenetic analysis by maximum likelihood. Comput Appl Biosci. 13:555-556; Yang Z. 2007. PAML 4: Phylogenetic analysis by maximum likelihood. Mol Biol Evol. 24:1586-1591). pamlX is written in C++ using the Qt library and communicates with paml programs through files. It can be used to create, edit, and print control files for paml programs and to launch paml runs. The interface is available for free download at http://abacus.gene.ucl.ac.uk/software/paml.html.

A robust multi-kernel change detection framework for detecting leaf beetle defoliation using Landsat 7 ETM+ data

NASA Astrophysics Data System (ADS)

Anees, Asim; Aryal, Jagannath; O'Reilly, Małgorzata M.; Gale, Timothy J.; Wardlaw, Tim

2016-12-01

A robust non-parametric framework, based on multiple Radial Basic Function (RBF) kernels, is proposed in this study, for detecting land/forest cover changes using Landsat 7 ETM+ images. One of the widely used frameworks is to find change vectors (difference image) and use a supervised classifier to differentiate between change and no-change. The Bayesian Classifiers e.g. Maximum Likelihood Classifier (MLC), Naive Bayes (NB), are widely used probabilistic classifiers which assume parametric models, e.g. Gaussian function, for the class conditional distributions. However, their performance can be limited if the data set deviates from the assumed model. The proposed framework exploits the useful properties of Least Squares Probabilistic Classifier (LSPC) formulation i.e. non-parametric and probabilistic nature, to model class posterior probabilities of the difference image using a linear combination of a large number of Gaussian kernels. To this end, a simple technique, based on 10-fold cross-validation is also proposed for tuning model parameters automatically instead of selecting a (possibly) suboptimal combination from pre-specified lists of values. The proposed framework has been tested and compared with Support Vector Machine (SVM) and NB for detection of defoliation, caused by leaf beetles (Paropsisterna spp.) in Eucalyptus nitens and Eucalyptus globulus plantations of two test areas, in Tasmania, Australia, using raw bands and band combination indices of Landsat 7 ETM+. It was observed that due to multi-kernel non-parametric formulation and probabilistic nature, the LSPC outperforms parametric NB with Gaussian assumption in change detection framework, with Overall Accuracy (OA) ranging from 93.6% (κ = 0.87) to 97.4% (κ = 0.94) against 85.3% (κ = 0.69) to 93.4% (κ = 0.85), and is more robust to changing data distributions. Its performance was comparable to SVM, with added advantages of being probabilistic and capable of handling multi-class problems naturally with its original formulation.

Maximum Likelihood Estimation of Nonlinear Structural Equation Models.

ERIC Educational Resources Information Center

Lee, Sik-Yum; Zhu, Hong-Tu

2002-01-01

Developed an EM type algorithm for maximum likelihood estimation of a general nonlinear structural equation model in which the E-step is completed by a Metropolis-Hastings algorithm. Illustrated the methodology with results from a simulation study and two real examples using data from previous studies. (SLD)

ARMA-Based SEM When the Number of Time Points T Exceeds the Number of Cases N: Raw Data Maximum Likelihood.

ERIC Educational Resources Information Center

Hamaker, Ellen L.; Dolan, Conor V.; Molenaar, Peter C. M.

2003-01-01

Demonstrated, through simulation, that stationary autoregressive moving average (ARMA) models may be fitted readily when T>N, using normal theory raw maximum likelihood structural equation modeling. Also provides some illustrations based on real data. (SLD)

Maximum likelihood phase-retrieval algorithm: applications.

PubMed

Nahrstedt, D A; Southwell, W H

1984-12-01

The maximum likelihood estimator approach is shown to be effective in determining the wave front aberration in systems involving laser and flow field diagnostics and optical testing. The robustness of the algorithm enables convergence even in cases of severe wave front error and real, nonsymmetrical, obscured amplitude distributions.

Population Synthesis of Radio and Gamma-ray Pulsars using the Maximum Likelihood Approach

NASA Astrophysics Data System (ADS)

Billman, Caleb; Gonthier, P. L.; Harding, A. K.

2012-01-01

We present the results of a pulsar population synthesis of normal pulsars from the Galactic disk using a maximum likelihood method. We seek to maximize the likelihood of a set of parameters in a Monte Carlo population statistics code to better understand their uncertainties and the confidence region of the model's parameter space. The maximum likelihood method allows for the use of more applicable Poisson statistics in the comparison of distributions of small numbers of detected gamma-ray and radio pulsars. Our code simulates pulsars at birth using Monte Carlo techniques and evolves them to the present assuming initial spatial, kick velocity, magnetic field, and period distributions. Pulsars are spun down to the present and given radio and gamma-ray emission characteristics. We select measured distributions of radio pulsars from the Parkes Multibeam survey and Fermi gamma-ray pulsars to perform a likelihood analysis of the assumed model parameters such as initial period and magnetic field, and radio luminosity. We present the results of a grid search of the parameter space as well as a search for the maximum likelihood using a Markov Chain Monte Carlo method. We express our gratitude for the generous support of the Michigan Space Grant Consortium, of the National Science Foundation (REU and RUI), the NASA Astrophysics Theory and Fundamental Program and the NASA Fermi Guest Investigator Program.

Coalescent-based species tree inference from gene tree topologies under incomplete lineage sorting by maximum likelihood.

PubMed

Wu, Yufeng

2012-03-01

Incomplete lineage sorting can cause incongruence between the phylogenetic history of genes (the gene tree) and that of the species (the species tree), which can complicate the inference of phylogenies. In this article, I present a new coalescent-based algorithm for species tree inference with maximum likelihood. I first describe an improved method for computing the probability of a gene tree topology given a species tree, which is much faster than an existing algorithm by Degnan and Salter (2005). Based on this method, I develop a practical algorithm that takes a set of gene tree topologies and infers species trees with maximum likelihood. This algorithm searches for the best species tree by starting from initial species trees and performing heuristic search to obtain better trees with higher likelihood. This algorithm, called STELLS (which stands for Species Tree InfErence with Likelihood for Lineage Sorting), has been implemented in a program that is downloadable from the author's web page. The simulation results show that the STELLS algorithm is more accurate than an existing maximum likelihood method for many datasets, especially when there is noise in gene trees. I also show that the STELLS algorithm is efficient and can be applied to real biological datasets. © 2011 The Author. Evolution© 2011 The Society for the Study of Evolution.

Terrain Classification on Venus from Maximum-Likelihood Inversion of Parameterized Models of Topography, Gravity, and their Relation

NASA Astrophysics Data System (ADS)

Eggers, G. L.; Lewis, K. W.; Simons, F. J.; Olhede, S.

2013-12-01

Venus does not possess a plate-tectonic system like that observed on Earth, and many surface features--such as tesserae and coronae--lack terrestrial equivalents. To understand Venus' tectonics is to understand its lithosphere, requiring a study of topography and gravity, and how they relate. Past studies of topography dealt with mapping and classification of visually observed features, and studies of gravity dealt with inverting the relation between topography and gravity anomalies to recover surface density and elastic thickness in either the space (correlation) or the spectral (admittance, coherence) domain. In the former case, geological features could be delineated but not classified quantitatively. In the latter case, rectangular or circular data windows were used, lacking geological definition. While the estimates of lithospheric strength on this basis were quantitative, they lacked robust error estimates. Here, we remapped the surface into 77 regions visually and qualitatively defined from a combination of Magellan topography, gravity, and radar images. We parameterize the spectral covariance of the observed topography, treating it as a Gaussian process assumed to be stationary over the mapped regions, using a three-parameter isotropic Matern model, and perform maximum-likelihood based inversions for the parameters. We discuss the parameter distribution across the Venusian surface and across terrain types such as coronoae, dorsae, tesserae, and their relation with mean elevation and latitudinal position. We find that the three-parameter model, while mathematically established and applicable to Venus topography, is overparameterized, and thus reduce the results to a two-parameter description of the peak spectral variance and the range-to-half-peak variance (in function of the wavenumber). With the reduction the clustering of geological region types in two-parameter space becomes promising. Finally, we perform inversions for the JOINT spectral variance of topography and gravity, in which the INITIAL loading by topography retains the Matern form but the FINAL topography and gravity are the result of flexural compensation. In our modeling, we pay explicit attention to finite-field spectral estimation effects (and their remedy via tapering), and to the implementation of statistical tests (for anisotropy, for initial-loading process correlation, to ascertain the proper density contrasts and interface depth in a two-layer model), robustness assessment and uncertainty quantification, as well as to algorithmic intricacies related to low-dimensional but poorly scaled maximum-likelihood inversions. We conclude that Venusian geomorphic terrains are well described by their 2-D topographic and gravity (cross-)power spectra, and the spectral properties of distinct geologic provinces on Venus are worth quantifying via maximum-likelihood-based methods under idealized three-parameter Matern distributions. Analysis of fitted parameters and the fitted-data residuals reveals natural variability in the (sub)surface properties on Venus, as well as some directional anisotropy. Geologic regions tend to cluster according to terrain type in our parameter space, which we analyze to confirm their shared geologic histories and utilize for guidance in ongoing mapping efforts of Venus and other terrestrial bodies.

Maximum Correntropy Unscented Kalman Filter for Ballistic Missile Navigation System based on SINS/CNS Deeply Integrated Mode.

PubMed

Hou, Bowen; He, Zhangming; Li, Dong; Zhou, Haiyin; Wang, Jiongqi

2018-05-27

Strap-down inertial navigation system/celestial navigation system ( SINS/CNS) integrated navigation is a high precision navigation technique for ballistic missiles. The traditional navigation method has a divergence in the position error. A deeply integrated mode for SINS/CNS navigation system is proposed to improve the navigation accuracy of ballistic missile. The deeply integrated navigation principle is described and the observability of the navigation system is analyzed. The nonlinearity, as well as the large outliers and the Gaussian mixture noises, often exists during the actual navigation process, leading to the divergence phenomenon of the navigation filter. The new nonlinear Kalman filter on the basis of the maximum correntropy theory and unscented transformation, named the maximum correntropy unscented Kalman filter, is deduced, and the computational complexity is analyzed. The unscented transformation is used for restricting the nonlinearity of the system equation, and the maximum correntropy theory is used to deal with the non-Gaussian noises. Finally, numerical simulation illustrates the superiority of the proposed filter compared with the traditional unscented Kalman filter. The comparison results show that the large outliers and the influence of non-Gaussian noises for SINS/CNS deeply integrated navigation is significantly reduced through the proposed filter.

Estimating the variance for heterogeneity in arm-based network meta-analysis.

PubMed

Piepho, Hans-Peter; Madden, Laurence V; Roger, James; Payne, Roger; Williams, Emlyn R

2018-04-19

Network meta-analysis can be implemented by using arm-based or contrast-based models. Here we focus on arm-based models and fit them using generalized linear mixed model procedures. Full maximum likelihood (ML) estimation leads to biased trial-by-treatment interaction variance estimates for heterogeneity. Thus, our objective is to investigate alternative approaches to variance estimation that reduce bias compared with full ML. Specifically, we use penalized quasi-likelihood/pseudo-likelihood and hierarchical (h) likelihood approaches. In addition, we consider a novel model modification that yields estimators akin to the residual maximum likelihood estimator for linear mixed models. The proposed methods are compared by simulation, and 2 real datasets are used for illustration. Simulations show that penalized quasi-likelihood/pseudo-likelihood and h-likelihood reduce bias and yield satisfactory coverage rates. Sum-to-zero restriction and baseline contrasts for random trial-by-treatment interaction effects, as well as a residual ML-like adjustment, also reduce bias compared with an unconstrained model when ML is used, but coverage rates are not quite as good. Penalized quasi-likelihood/pseudo-likelihood and h-likelihood are therefore recommended. Copyright © 2018 John Wiley & Sons, Ltd.

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…

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…

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…

Consistency of Rasch Model Parameter Estimation: A Simulation Study.

ERIC Educational Resources Information Center

van den Wollenberg, Arnold L.; And Others

1988-01-01

The unconditional--simultaneous--maximum likelihood (UML) estimation procedure for the one-parameter logistic model produces biased estimators. The UML method is inconsistent and is not a good alternative to conditional maximum likelihood method, at least with small numbers of items. The minimum Chi-square estimation procedure produces unbiased…

Bayesian Monte Carlo and Maximum Likelihood Approach for Uncertainty Estimation and Risk Management: Application to Lake Oxygen Recovery Model

EPA Science Inventory

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...

IRT Item Parameter Recovery with Marginal Maximum Likelihood Estimation Using Loglinear Smoothing 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…

A Study of Item Bias for Attitudinal Measurement Using Maximum Likelihood Factor Analysis.

ERIC Educational Resources Information Center

Mayberry, Paul W.

A technique for detecting item bias that is responsive to attitudinal measurement considerations is a maximum likelihood factor analysis procedure comparing multivariate factor structures across various subpopulations, often referred to as SIFASP. The SIFASP technique allows for factorial model comparisons in the testing of various hypotheses…

The Effects of Model Misspecification and Sample Size on LISREL Maximum Likelihood Estimates.

ERIC Educational Resources Information Center

Baldwin, Beatrice

The robustness of LISREL computer program maximum likelihood estimates under specific conditions of model misspecification and sample size was examined. The population model used in this study contains one exogenous variable; three endogenous variables; and eight indicator variables, two for each latent variable. Conditions of model…

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…

Approximate likelihood approaches for detecting the influence of primordial gravitational waves in cosmic microwave background polarization

NASA Astrophysics Data System (ADS)

Pan, Zhen; Anderes, Ethan; Knox, Lloyd

2018-05-01

One of the major targets for next-generation cosmic microwave background (CMB) experiments is the detection of the primordial B-mode signal. Planning is under way for Stage-IV experiments that are projected to have instrumental noise small enough to make lensing and foregrounds the dominant source of uncertainty for estimating the tensor-to-scalar ratio r from polarization maps. This makes delensing a crucial part of future CMB polarization science. In this paper we present a likelihood method for estimating the tensor-to-scalar ratio r from CMB polarization observations, which combines the benefits of a full-scale likelihood approach with the tractability of the quadratic delensing technique. This method is a pixel space, all order likelihood analysis of the quadratic delensed B modes, and it essentially builds upon the quadratic delenser by taking into account all order lensing and pixel space anomalies. Its tractability relies on a crucial factorization of the pixel space covariance matrix of the polarization observations which allows one to compute the full Gaussian approximate likelihood profile, as a function of r , at the same computational cost of a single likelihood evaluation.

Terahertz radiation generation through the nonlinear interaction of Hermite and Laguerre Gaussian laser beams with collisional plasma: Field profile optimization

NASA Astrophysics Data System (ADS)

Safari, Samaneh; Niknam, Ali Reza; Jahangiri, Fazel; Jazi, Bahram

2018-04-01

The nonlinear interaction of Hermite-Gaussian and Laguerre-Gaussian (LG) laser beams with a collisional inhomogeneous plasma is studied, and the amplitude of the emitted terahertz (THz) electric field is evaluated. The effects of laser beams and plasma parameters, including the beams width, LG modes, the plasma collision frequency, and the amplitude of density ripple on the evolution of THz electric field amplitude, are examined. It is found that the shape of the generated THz radiation pattern can be tuned by the laser parameters. In addition, the optimum values of the effective parameters for achieving the maximum THz electric field amplitude are proposed. It is shown that a significant enhancement up to 4.5% can be obtained in our scheme, which is much greater than the maximum efficiency obtained for laser beams with the same profiles.

SCI Identification (SCIDNT) program user's guide. [maximum likelihood method for linear rotorcraft models

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.

Planck intermediate results. XVI. Profile likelihoods for cosmological parameters

NASA Astrophysics Data System (ADS)

Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartlett, J. G.; Battaner, E.; Benabed, K.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bonaldi, A.; Bond, J. R.; Bouchet, F. R.; Burigana, C.; Cardoso, J.-F.; Catalano, A.; Chamballu, A.; Chiang, H. C.; Christensen, P. R.; Clements, D. L.; Colombi, S.; Colombo, L. P. L.; Couchot, F.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Dickinson, C.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Dupac, X.; Enßlin, T. A.; Eriksen, H. K.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Héraud, Y.; González-Nuevo, J.; Górski, K. M.; Gregorio, A.; Gruppuso, A.; Hansen, F. K.; Harrison, D. L.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huffenberger, K. M.; Jaffe, A. H.; Jaffe, T. R.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T. S.; Kneissl, R.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Lawrence, C. R.; Leonardi, R.; Liddle, A.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; Maffei, B.; Maino, D.; Mandolesi, N.; Maris, M.; Martin, P. G.; Martínez-González, E.; Masi, S.; Massardi, M.; Matarrese, S.; Mazzotta, P.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nati, F.; Natoli, P.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C. A.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski∗, S.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G. W.; Puget, J.-L.; Rachen, J. P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rouillé d'Orfeuil, B.; Rubiño-Martín, J. A.; Rusholme, B.; Sandri, M.; Savelainen, M.; Savini, G.; Spencer, L. D.; Spinelli, M.; Starck, J.-L.; Sureau, F.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Umana, G.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vielva, P.; Villa, F.; Wade, L. A.; Wandelt, B. D.; White, M.; Yvon, D.; Zacchei, A.; Zonca, A.

2014-06-01

We explore the 2013 Planck likelihood function with a high-precision multi-dimensional minimizer (Minuit). This allows a refinement of the ΛCDM best-fit solution with respect to previously-released results, and the construction of frequentist confidence intervals using profile likelihoods. The agreement with the cosmological results from the Bayesian framework is excellent, demonstrating the robustness of the Planck results to the statistical methodology. We investigate the inclusion of neutrino masses, where more significant differences may appear due to the non-Gaussian nature of the posterior mass distribution. By applying the Feldman-Cousins prescription, we again obtain results very similar to those of the Bayesian methodology. However, the profile-likelihood analysis of the cosmic microwave background (CMB) combination (Planck+WP+highL) reveals a minimum well within the unphysical negative-mass region. We show that inclusion of the Planck CMB-lensing information regularizes this issue, and provide a robust frequentist upper limit ∑ mν ≤ 0.26 eV (95% confidence) from the CMB+lensing+BAO data combination.

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.

An evaluation of percentile and maximum likelihood estimators of weibull paremeters

Treesearch

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...

Quasi-Maximum Likelihood Estimation of Structural Equation Models with Multiple Interaction and Quadratic Effects

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…

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…

Unclassified Publications of Lincoln Laboratory, 1 January - 31 December 1990. Volume 16

DTIC Science & Technology

1990-12-31

Apr. 1990 ADA223419 Hopped Communication Systems with Nonuniform Hopping Distributions 880 Bistatic Radar Cross Section of a Fenn, A.J. 2 May1990...EXPERIMENT JA-6241 MS-8424 LUNAR PERTURBATION MAXIMUM LIKELIHOOD ALGORITHM JA-6241 JA-6467 LWIR SPECTRAL BAND MAXIMUM LIKELIHOOD ESTIMATOR JA-6476 MS-8466

Expected versus Observed Information in SEM with Incomplete Normal and Nonnormal Data

ERIC Educational Resources Information Center

Savalei, Victoria

2010-01-01

Maximum likelihood is the most common estimation method in structural equation modeling. Standard errors for maximum likelihood estimates are obtained from the associated information matrix, which can be estimated from the sample using either expected or observed information. It is known that, with complete data, estimates based on observed or…

Effects of Estimation Bias on Multiple-Category Classification with an IRT-Based Adaptive Classification Procedure

ERIC Educational Resources Information Center

Yang, Xiangdong; Poggio, John C.; Glasnapp, Douglas R.

2006-01-01

The effects of five ability estimators, that is, maximum likelihood estimator, weighted likelihood estimator, maximum a posteriori, expected a posteriori, and Owen's sequential estimator, on the performances of the item response theory-based adaptive classification procedure on multiple categories were studied via simulations. The following…

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,…

Five Methods for Estimating Angoff Cut Scores with IRT

ERIC Educational Resources Information Center

Wyse, Adam E.

2017-01-01

This article illustrates five different methods for estimating Angoff cut scores using item response theory (IRT) models. These include maximum likelihood (ML), expected a priori (EAP), modal a priori (MAP), and weighted maximum likelihood (WML) estimators, as well as the most commonly used approach based on translating ratings through the test…

High-Dimensional Exploratory Item Factor Analysis by a Metropolis-Hastings Robbins-Monro Algorithm

ERIC Educational Resources Information Center

Cai, Li

2010-01-01

A Metropolis-Hastings Robbins-Monro (MH-RM) algorithm for high-dimensional maximum marginal likelihood exploratory item factor analysis is proposed. The sequence of estimates from the MH-RM algorithm converges with probability one to the maximum likelihood solution. Details on the computer implementation of this algorithm are provided. The…

Comparison of standard maximum likelihood classification and polytomous logistic regression used in remote sensing

Treesearch

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...

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

NASA Technical Reports Server (NTRS)

Grove, R. D.; Bowles, R. L.; Mayhew, S. C.

1972-01-01

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Computation of nonlinear least squares estimator and maximum likelihood using principles in matrix calculus

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi; Balasiddamuni, P.

2017-11-01

This paper uses matrix calculus techniques to obtain Nonlinear Least Squares Estimator (NLSE), Maximum Likelihood Estimator (MLE) and Linear Pseudo model for nonlinear regression model. David Pollard and Peter Radchenko [1] explained analytic techniques to compute the NLSE. However the present research paper introduces an innovative method to compute the NLSE using principles in multivariate calculus. This study is concerned with very new optimization techniques used to compute MLE and NLSE. Anh [2] derived NLSE and MLE of a heteroscedatistic regression model. Lemcoff [3] discussed a procedure to get linear pseudo model for nonlinear regression model. In this research article a new technique is developed to get the linear pseudo model for nonlinear regression model using multivariate calculus. The linear pseudo model of Edmond Malinvaud [4] has been explained in a very different way in this paper. David Pollard et.al used empirical process techniques to study the asymptotic of the LSE (Least-squares estimation) for the fitting of nonlinear regression function in 2006. In Jae Myung [13] provided a go conceptual for Maximum likelihood estimation in his work “Tutorial on maximum likelihood estimation

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis: A Comparison of Maximum Likelihood and Bayesian Estimations.

PubMed

Can, Seda; van de Schoot, Rens; Hox, Joop

2015-06-01

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation coefficient (ICC) and estimation method; maximum likelihood estimation with robust chi-squares and standard errors and Bayesian estimation, on the convergence rate are investigated. The other variables of interest were rate of inadmissible solutions and the relative parameter and standard error bias on the between level. The results showed that inadmissible solutions were obtained when there was between level collinearity and the estimation method was maximum likelihood. In the within level multicollinearity condition, all of the solutions were admissible but the bias values were higher compared with the between level collinearity condition. Bayesian estimation appeared to be robust in obtaining admissible parameters but the relative bias was higher than for maximum likelihood estimation. Finally, as expected, high ICC produced less biased results compared to medium ICC conditions.

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.

A Model of Self-Monitoring Blood Glucose Measurement Error.

PubMed

Vettoretti, Martina; Facchinetti, Andrea; Sparacino, Giovanni; Cobelli, Claudio

2017-07-01

A reliable model of the probability density function (PDF) of self-monitoring of blood glucose (SMBG) measurement error would be important for several applications in diabetes, like testing in silico insulin therapies. In the literature, the PDF of SMBG error is usually described by a Gaussian function, whose symmetry and simplicity are unable to properly describe the variability of experimental data. Here, we propose a new methodology to derive more realistic models of SMBG error PDF. The blood glucose range is divided into zones where error (absolute or relative) presents a constant standard deviation (SD). In each zone, a suitable PDF model is fitted by maximum-likelihood to experimental data. Model validation is performed by goodness-of-fit tests. The method is tested on two databases collected by the One Touch Ultra 2 (OTU2; Lifescan Inc, Milpitas, CA) and the Bayer Contour Next USB (BCN; Bayer HealthCare LLC, Diabetes Care, Whippany, NJ). In both cases, skew-normal and exponential models are used to describe the distribution of errors and outliers, respectively. Two zones were identified: zone 1 with constant SD absolute error; zone 2 with constant SD relative error. Goodness-of-fit tests confirmed that identified PDF models are valid and superior to Gaussian models used so far in the literature. The proposed methodology allows to derive realistic models of SMBG error PDF. These models can be used in several investigations of present interest in the scientific community, for example, to perform in silico clinical trials to compare SMBG-based with nonadjunctive CGM-based insulin treatments.

Age-dependent biochemical quantities: an approach for calculating reference intervals.

PubMed

Bjerner, J

2007-01-01

A parametric method is often preferred when calculating reference intervals for biochemical quantities, as non-parametric methods are less efficient and require more observations/study subjects. Parametric methods are complicated, however, because of three commonly encountered features. First, biochemical quantities seldom display a Gaussian distribution, and there must either be a transformation procedure to obtain such a distribution or a more complex distribution has to be used. Second, biochemical quantities are often dependent on a continuous covariate, exemplified by rising serum concentrations of MUC1 (episialin, CA15.3) with increasing age. Third, outliers often exert substantial influence on parametric estimations and therefore need to be excluded before calculations are made. The International Federation of Clinical Chemistry (IFCC) currently recommends that confidence intervals be calculated for the reference centiles obtained. However, common statistical packages allowing for the adjustment of a continuous covariate do not make this calculation. In the method described in the current study, Tukey's fence is used to eliminate outliers and two-stage transformations (modulus-exponential-normal) in order to render Gaussian distributions. Fractional polynomials are employed to model functions for mean and standard deviations dependent on a covariate, and the model is selected by maximum likelihood. Confidence intervals are calculated for the fitted centiles by combining parameter estimation and sampling uncertainties. Finally, the elimination of outliers was made dependent on covariates by reiteration. Though a good knowledge of statistical theory is needed when performing the analysis, the current method is rewarding because the results are of practical use in patient care.

Galaxy Properties Across and Through the 6dFGS Fundamental Plane

NASA Astrophysics Data System (ADS)

Springob, Chris M.; Magoulas, C.; Proctor, R.; Colless, M.; Jones, D. H.; Kobayashi, C.; Campbell, L.; Lucey, J.; Mould, J.; Merson, A.

2011-05-01

The 6dF Galaxy Survey (6dFGS) is an all southern sky galaxy survey, including 125,000 redshifts and a Fundamental Plane (FP) subsample of 10,000 peculiar velocities, making it the largest peculiar velocity sample to date. We have developed a robust procedure for fitting the FP, performing a maximum likelihood fit to a tri-variate Gaussian. We have subsequently examined the variation of a variety of properties across and through the FP, including environment, morphology, metallicity, alpha-enhancement, and stellar age. We find little variation in the FP with global environment. Some variation of morphology is found along the plane, though this is likely a consequence of selection effects. Elemental abundances are found to vary both across and through the FP. The parameter that varies most directly through the FP is stellar age. We find that galaxies with stellar populations with average ages older than 3 Gyr occupy a thinner FP than those younger than 3 Gyr. Thus, a modest improvement in distance errors is realized if one divides the sample into subsamples segregated by age, and fits the FP of each subsample independently.

Quaternion Averaging

NASA Technical Reports Server (NTRS)

Markley, F. Landis; Cheng, Yang; Crassidis, John L.; Oshman, Yaakov

2007-01-01

Many applications require an algorithm that averages quaternions in an optimal manner. For example, when combining the quaternion outputs of multiple star trackers having this output capability, it is desirable to properly average the quaternions without recomputing the attitude from the the raw star tracker data. Other applications requiring some sort of optimal quaternion averaging include particle filtering and multiple-model adaptive estimation, where weighted quaternions are used to determine the quaternion estimate. For spacecraft attitude estimation applications, derives an optimal averaging scheme to compute the average of a set of weighted attitude matrices using the singular value decomposition method. Focusing on a 4-dimensional quaternion Gaussian distribution on the unit hypersphere, provides an approach to computing the average quaternion by minimizing a quaternion cost function that is equivalent to the attitude matrix cost function Motivated by and extending its results, this Note derives an algorithm that deterniines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Rirthermore, a sufficient condition for the uniqueness of the average quaternion, and the equivalence of the mininiization problem, stated herein, to maximum likelihood estimation, are shown.

MIDAS, prototype Multivariate Interactive Digital Analysis System for large area earth resources surveys. Volume 1: System description

NASA Technical Reports Server (NTRS)

Christenson, D.; Gordon, M.; Kistler, R.; Kriegler, F.; Lampert, S.; Marshall, R.; Mclaughlin, R.

1977-01-01

A third-generation, fast, low cost, multispectral recognition system (MIDAS) able to keep pace with the large quantity and high rates of data acquisition from large regions with present and projected sensots is described. The program can process a complete ERTS frame in forty seconds and provide a color map of sixteen constituent categories in a few minutes. A principle objective of the MIDAS program is to provide a system well interfaced with the human operator and thus to obtain large overall reductions in turn-around time and significant gains in throughput. The hardware and software generated in the overall program is described. The system contains a midi-computer to control the various high speed processing elements in the data path, a preprocessor to condition data, and a classifier which implements an all digital prototype multivariate Gaussian maximum likelihood or a Bayesian decision algorithm. Sufficient software was developed to perform signature extraction, control the preprocessor, compute classifier coefficients, control the classifier operation, operate the color display and printer, and diagnose operation.

MIXREG: a computer program for mixed-effects regression analysis with autocorrelated errors.

PubMed

Hedeker, D; Gibbons, R D

1996-05-01

MIXREG is a program that provides estimates for a mixed-effects regression model (MRM) for normally-distributed response data including autocorrelated errors. This model can be used for analysis of unbalanced longitudinal data, where individuals may be measured at a different number of timepoints, or even at different timepoints. Autocorrelated errors of a general form or following an AR(1), MA(1), or ARMA(1,1) form are allowable. This model can also be used for analysis of clustered data, where the mixed-effects model assumes data within clusters are dependent. The degree of dependency is estimated jointly with estimates of the usual model parameters, thus adjusting for clustering. MIXREG uses maximum marginal likelihood estimation, utilizing both the EM algorithm and a Fisher-scoring solution. For the scoring solution, the covariance matrix of the random effects is expressed in its Gaussian decomposition, and the diagonal matrix reparameterized using the exponential transformation. Estimation of the individual random effects is accomplished using an empirical Bayes approach. Examples illustrating usage and features of MIXREG are provided.

Model-Based Clustering of Regression Time Series Data via APECM -- An AECM Algorithm Sung to an Even Faster Beat

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Wei-Chen; Maitra, Ranjan

2011-01-01

We propose a model-based approach for clustering time series regression data in an unsupervised machine learning framework to identify groups under the assumption that each mixture component follows a Gaussian autoregressive regression model of order p. Given the number of groups, the traditional maximum likelihood approach of estimating the parameters using the expectation-maximization (EM) algorithm can be employed, although it is computationally demanding. The somewhat fast tune to the EM folk song provided by the Alternating Expectation Conditional Maximization (AECM) algorithm can alleviate the problem to some extent. In this article, we develop an alternative partial expectation conditional maximization algorithmmore » (APECM) that uses an additional data augmentation storage step to efficiently implement AECM for finite mixture models. Results on our simulation experiments show improved performance in both fewer numbers of iterations and computation time. The methodology is applied to the problem of clustering mutual funds data on the basis of their average annual per cent returns and in the presence of economic indicators.« less

The weighted function method: A handy tool for flood frequency analysis or just a curiosity?

NASA Astrophysics Data System (ADS)

Bogdanowicz, Ewa; Kochanek, Krzysztof; Strupczewski, Witold G.

2018-04-01

The idea of the Weighted Function (WF) method for estimation of Pearson type 3 (Pe3) distribution introduced by Ma in 1984 has been revised and successfully applied for shifted inverse Gaussian (IGa3) distribution. Also the conditions of WF applicability to a shifted distribution have been formulated. The accuracy of WF flood quantiles for both Pe3 and IGa3 distributions was assessed by Monte Caro simulations under the true and false distribution assumption versus the maximum likelihood (MLM), moment (MOM) and L-moments (LMM) methods. Three datasets of annual peak flows of Polish catchments serve the case studies to compare the results of the WF, MOM, MLM and LMM performance for the real flood data. For the hundred-year flood the WF method revealed the explicit superiority only over the MLM surpassing the MOM and especially LMM both for the true and false distributional assumption with respect to relative bias and relative mean root square error values. Generally, the WF method performs well and for hydrological sample size and constitutes good alternative for the estimation of the flood upper quantiles.

An information-based approach to change-point analysis with applications to biophysics and cell biology.

PubMed

Wiggins, Paul A

2015-07-21

This article describes the application of a change-point algorithm to the analysis of stochastic signals in biological systems whose underlying state dynamics consist of transitions between discrete states. Applications of this analysis include molecular-motor stepping, fluorophore bleaching, electrophysiology, particle and cell tracking, detection of copy number variation by sequencing, tethered-particle motion, etc. We present a unified approach to the analysis of processes whose noise can be modeled by Gaussian, Wiener, or Ornstein-Uhlenbeck processes. To fit the model, we exploit explicit, closed-form algebraic expressions for maximum-likelihood estimators of model parameters and estimated information loss of the generalized noise model, which can be computed extremely efficiently. We implement change-point detection using the frequentist information criterion (which, to our knowledge, is a new information criterion). The frequentist information criterion specifies a single, information-based statistical test that is free from ad hoc parameters and requires no prior probability distribution. We demonstrate this information-based approach in the analysis of simulated and experimental tethered-particle-motion data. Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.

A Copula-Based Conditional Probabilistic Forecast Model for Wind Power Ramps

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hodge, Brian S; Krishnan, Venkat K; Zhang, Jie

Efficient management of wind ramping characteristics can significantly reduce wind integration costs for balancing authorities. By considering the stochastic dependence of wind power ramp (WPR) features, this paper develops a conditional probabilistic wind power ramp forecast (cp-WPRF) model based on Copula theory. The WPRs dataset is constructed by extracting ramps from a large dataset of historical wind power. Each WPR feature (e.g., rate, magnitude, duration, and start-time) is separately forecasted by considering the coupling effects among different ramp features. To accurately model the marginal distributions with a copula, a Gaussian mixture model (GMM) is adopted to characterize the WPR uncertaintymore » and features. The Canonical Maximum Likelihood (CML) method is used to estimate parameters of the multivariable copula. The optimal copula model is chosen based on the Bayesian information criterion (BIC) from each copula family. Finally, the best conditions based cp-WPRF model is determined by predictive interval (PI) based evaluation metrics. Numerical simulations on publicly available wind power data show that the developed copula-based cp-WPRF model can predict WPRs with a high level of reliability and sharpness.« less

Bayesian statistics applied to the location of the source of explosions at Stromboli Volcano, Italy

USGS Publications Warehouse

Saccorotti, G.; Chouet, B.; Martini, M.; Scarpa, R.

1998-01-01

We present a method for determining the location and spatial extent of the source of explosions at Stromboli Volcano, Italy, based on a Bayesian inversion of the slowness vector derived from frequency-slowness analyses of array data. The method searches for source locations that minimize the error between the expected and observed slowness vectors. For a given set of model parameters, the conditional probability density function of slowness vectors is approximated by a Gaussian distribution of expected errors. The method is tested with synthetics using a five-layer velocity model derived for the north flank of Stromboli and a smoothed velocity model derived from a power-law approximation of the layered structure. Application to data from Stromboli allows for a detailed examination of uncertainties in source location due to experimental errors and incomplete knowledge of the Earth model. Although the solutions are not constrained in the radial direction, excellent resolution is achieved in both transverse and depth directions. Under the assumption that the horizontal extent of the source does not exceed the crater dimension, the 90% confidence region in the estimate of the explosive source location corresponds to a small volume extending from a depth of about 100 m to a maximum depth of about 300 m beneath the active vents, with a maximum likelihood source region located in the 120- to 180-m-depth interval.

Optimized Kernel Entropy Components.

PubMed

Izquierdo-Verdiguier, Emma; Laparra, Valero; Jenssen, Robert; Gomez-Chova, Luis; Camps-Valls, Gustau

2017-06-01

This brief addresses two main issues of the standard kernel entropy component analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of variance, as in the kernel principal components analysis. In this brief, we propose an extension of the KECA method, named optimized KECA (OKECA), that directly extracts the optimal features retaining most of the data entropy by means of compacting the information in very few features (often in just one or two). The proposed method produces features which have higher expressive power. In particular, it is based on the independent component analysis framework, and introduces an extra rotation to the eigen decomposition, which is optimized via gradient-ascent search. This maximum entropy preservation suggests that OKECA features are more efficient than KECA features for density estimation. In addition, a critical issue in both the methods is the selection of the kernel parameter, since it critically affects the resulting performance. Here, we analyze the most common kernel length-scale selection criteria. The results of both the methods are illustrated in different synthetic and real problems. Results show that OKECA returns projections with more expressive power than KECA, the most successful rule for estimating the kernel parameter is based on maximum likelihood, and OKECA is more robust to the selection of the length-scale parameter in kernel density estimation.

Approximated maximum likelihood estimation in multifractal random walks

NASA Astrophysics Data System (ADS)

Løvsletten, O.; Rypdal, M.

2012-04-01

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry , Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.64.026103 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package in the r computer language. Its performance is tested on synthetic data and compared to an inference approach based on the generalized method of moments. The method is applied to estimate parameters for various financial stock indices.

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…

12-mode OFDM transmission using reduced-complexity maximum likelihood detection.

PubMed

Lobato, Adriana; Chen, Yingkan; Jung, Yongmin; Chen, Haoshuo; Inan, Beril; Kuschnerov, Maxim; Fontaine, Nicolas K; Ryf, Roland; Spinnler, Bernhard; Lankl, Berthold

2015-02-01

We report the transmission of 163-Gb/s MDM-QPSK-OFDM and 245-Gb/s MDM-8QAM-OFDM transmission over 74 km of few-mode fiber supporting 12 spatial and polarization modes. A low-complexity maximum likelihood detector is employed to enhance the performance of a system impaired by mode-dependent loss.

Impact of Violation of the Missing-at-Random Assumption on Full-Information Maximum Likelihood Method in Multidimensional Adaptive Testing

ERIC Educational Resources Information Center

Han, Kyung T.; Guo, Fanmin

2014-01-01

The full-information maximum likelihood (FIML) method makes it possible to estimate and analyze structural equation models (SEM) even when data are partially missing, enabling incomplete data to contribute to model estimation. The cornerstone of FIML is the missing-at-random (MAR) assumption. In (unidimensional) computerized adaptive testing…

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…

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…

Computing Maximum Likelihood Estimates of Loglinear Models from Marginal Sums with Special Attention to Loglinear Item Response Theory.

ERIC Educational Resources Information Center

Kelderman, Henk

1992-01-01

Describes algorithms used in the computer program LOGIMO for obtaining maximum likelihood estimates of the parameters in loglinear models. These algorithms are also useful for the analysis of loglinear item-response theory models. Presents modified versions of the iterative proportional fitting and Newton-Raphson algorithms. Simulated data…

Applying a Weighted Maximum Likelihood Latent Trait Estimator to the Generalized Partial Credit Model

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…

Recovery of Graded Response Model Parameters: A Comparison of Marginal Maximum Likelihood and Markov Chain Monte Carlo Estimation

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…

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…

Attitude determination and calibration using a recursive maximum likelihood-based adaptive Kalman filter

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.

Maximum Likelihood Compton Polarimetry with the Compton Spectrometer and Imager

NASA Astrophysics Data System (ADS)

Lowell, A. W.; Boggs, S. E.; Chiu, C. L.; Kierans, C. A.; Sleator, C.; Tomsick, J. A.; Zoglauer, A. C.; Chang, H.-K.; Tseng, C.-H.; Yang, C.-Y.; Jean, P.; von Ballmoos, P.; Lin, C.-H.; Amman, M.

2017-10-01

Astrophysical polarization measurements in the soft gamma-ray band are becoming more feasible as detectors with high position and energy resolution are deployed. Previous work has shown that the minimum detectable polarization (MDP) of an ideal Compton polarimeter can be improved by ˜21% when an unbinned, maximum likelihood method (MLM) is used instead of the standard approach of fitting a sinusoid to a histogram of azimuthal scattering angles. Here we outline a procedure for implementing this maximum likelihood approach for real, nonideal polarimeters. As an example, we use the recent observation of GRB 160530A with the Compton Spectrometer and Imager. We find that the MDP for this observation is reduced by 20% when the MLM is used instead of the standard method.

Maximum likelihood estimation for Cox's regression model under nested case-control sampling.

PubMed

Scheike, Thomas H; Juul, Anders

2004-04-01

Nested case-control sampling is designed to reduce the costs of large cohort studies. It is important to estimate the parameters of interest as efficiently as possible. We present a new maximum likelihood estimator (MLE) for nested case-control sampling in the context of Cox's proportional hazards model. The MLE is computed by the EM-algorithm, which is easy to implement in the proportional hazards setting. Standard errors are estimated by a numerical profile likelihood approach based on EM aided differentiation. The work was motivated by a nested case-control study that hypothesized that insulin-like growth factor I was associated with ischemic heart disease. The study was based on a population of 3784 Danes and 231 cases of ischemic heart disease where controls were matched on age and gender. We illustrate the use of the MLE for these data and show how the maximum likelihood framework can be used to obtain information additional to the relative risk estimates of covariates.

The maximum entropy method of moments and Bayesian probability theory

NASA Astrophysics Data System (ADS)

Bretthorst, G. Larry

2013-08-01

The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) may be generated. In a given tissue type there is no single intensity that characterizes the tissue, rather there is a distribution of intensities. Often this distributions can be characterized by a Gaussian, but just as often it is much more complicated. Either way, estimating the distribution of intensities is an inference problem. In the case of a Gaussian distribution, one must estimate the mean and standard deviation. However, in the Non-Gaussian case the shape of the density function itself must be inferred. Three common techniques for estimating density functions are binned histograms [1, 2], kernel density estimation [3, 4], and the maximum entropy method of moments [5, 6]. In the introduction, the maximum entropy method of moments will be reviewed. Some of its problems and conditions under which it fails will be discussed. Then in later sections, the functional form of the maximum entropy method of moments probability distribution will be incorporated into Bayesian probability theory. It will be shown that Bayesian probability theory solves all of the problems with the maximum entropy method of moments. One gets posterior probabilities for the Lagrange multipliers, and, finally, one can put error bars on the resulting estimated density function.

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…

DSN telemetry system performance with convolutionally coded data using operational maximum-likelihood convolutional decoders

NASA Technical Reports Server (NTRS)

Benjauthrit, B.; Mulhall, B.; Madsen, B. D.; Alberda, M. E.

1976-01-01

The DSN telemetry system performance with convolutionally coded data using the operational maximum-likelihood convolutional decoder (MCD) being implemented in the Network is described. Data rates from 80 bps to 115.2 kbps and both S- and X-band receivers are reported. The results of both one- and two-way radio losses are included.

Recovery of Item Parameters in the Nominal Response Model: A Comparison of Marginal Maximum Likelihood Estimation and Markov Chain Monte Carlo Estimation.

ERIC Educational Resources Information Center

Wollack, James A.; Bolt, Daniel M.; Cohen, Allan S.; Lee, Young-Sun

2002-01-01

Compared the quality of item parameter estimates for marginal maximum likelihood (MML) and Markov Chain Monte Carlo (MCMC) with the nominal response model using simulation. The quality of item parameter recovery was nearly identical for MML and MCMC, and both methods tended to produce good estimates. (SLD)

The Construct Validity of Higher Order Structure-of-Intellect Abilities in a Battery of Tests Emphasizing the Product of Transformations: A Confirmatory Maximum Likelihood Factor Analysis.

ERIC Educational Resources Information Center

Khattab, Ali-Maher; And Others

1982-01-01

A causal modeling system, using confirmatory maximum likelihood factor analysis with the LISREL IV computer program, evaluated the construct validity underlying the higher order factor structure of a given correlation matrix of 46 structure-of-intellect tests emphasizing the product of transformations. (Author/PN)

Mortality table construction

NASA Astrophysics Data System (ADS)

Sutawanir

2015-12-01

Mortality tables play important role in actuarial studies such as life annuities, premium determination, premium reserve, valuation pension plan, pension funding. Some known mortality tables are CSO mortality table, Indonesian Mortality Table, Bowers mortality table, Japan Mortality table. For actuary applications some tables are constructed with different environment such as single decrement, double decrement, and multiple decrement. There exist two approaches in mortality table construction : mathematics approach and statistical approach. Distribution model and estimation theory are the statistical concepts that are used in mortality table construction. This article aims to discuss the statistical approach in mortality table construction. The distributional assumptions are uniform death distribution (UDD) and constant force (exponential). Moment estimation and maximum likelihood are used to estimate the mortality parameter. Moment estimation methods are easier to manipulate compared to maximum likelihood estimation (mle). However, the complete mortality data are not used in moment estimation method. Maximum likelihood exploited all available information in mortality estimation. Some mle equations are complicated and solved using numerical methods. The article focus on single decrement estimation using moment and maximum likelihood estimation. Some extension to double decrement will introduced. Simple dataset will be used to illustrated the mortality estimation, and mortality table.

Robust signal recovery using the prolate spherical wave functions and maximum correntropy criterion

NASA Astrophysics Data System (ADS)

Zou, Cuiming; Kou, Kit Ian

2018-05-01

Signal recovery is one of the most important problem in signal processing. This paper proposes a novel signal recovery method based on prolate spherical wave functions (PSWFs). PSWFs are a kind of special functions, which have been proved having good performance in signal recovery. However, the existing PSWFs based recovery methods used the mean square error (MSE) criterion, which depends on the Gaussianity assumption of the noise distributions. For the non-Gaussian noises, such as impulsive noise or outliers, the MSE criterion is sensitive, which may lead to large reconstruction error. Unlike the existing PSWFs based recovery methods, our proposed PSWFs based recovery method employs the maximum correntropy criterion (MCC), which is independent of the noise distribution. The proposed method can reduce the impact of the large and non-Gaussian noises. The experimental results on synthetic signals with various types of noises show that the proposed MCC based signal recovery method has better robust property against various noises compared to other existing methods.

Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions

PubMed Central

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

On non-parametric maximum likelihood estimation of the bivariate survivor function.

PubMed

Prentice, R L

The likelihood function for the bivariate survivor function F, under independent censorship, is maximized to obtain a non-parametric maximum likelihood estimator &Fcirc;. &Fcirc; may or may not be unique depending on the configuration of singly- and doubly-censored pairs. The likelihood function can be maximized by placing all mass on the grid formed by the uncensored failure times, or half lines beyond the failure time grid, or in the upper right quadrant beyond the grid. By accumulating the mass along lines (or regions) where the likelihood is flat, one obtains a partially maximized likelihood as a function of parameters that can be uniquely estimated. The score equations corresponding to these point mass parameters are derived, using a Lagrange multiplier technique to ensure unit total mass, and a modified Newton procedure is used to calculate the parameter estimates in some limited simulation studies. Some considerations for the further development of non-parametric bivariate survivor function estimators are briefly described.

Bayesian logistic regression approaches to predict incorrect DRG assignment.

PubMed

Suleiman, Mani; Demirhan, Haydar; Boyd, Leanne; Girosi, Federico; Aksakalli, Vural

2018-05-07

Episodes of care involving similar diagnoses and treatments and requiring similar levels of resource utilisation are grouped to the same Diagnosis-Related Group (DRG). In jurisdictions which implement DRG based payment systems, DRGs are a major determinant of funding for inpatient care. Hence, service providers often dedicate auditing staff to the task of checking that episodes have been coded to the correct DRG. The use of statistical models to estimate an episode's probability of DRG error can significantly improve the efficiency of clinical coding audits. This study implements Bayesian logistic regression models with weakly informative prior distributions to estimate the likelihood that episodes require a DRG revision, comparing these models with each other and to classical maximum likelihood estimates. All Bayesian approaches had more stable model parameters than maximum likelihood. The best performing Bayesian model improved overall classification per- formance by 6% compared to maximum likelihood, with a 34% gain compared to random classification, respectively. We found that the original DRG, coder and the day of coding all have a significant effect on the likelihood of DRG error. Use of Bayesian approaches has improved model parameter stability and classification accuracy. This method has already lead to improved audit efficiency in an operational capacity.

Maximum Likelihood Compton Polarimetry with the Compton Spectrometer and Imager

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lowell, A. W.; Boggs, S. E; Chiu, C. L.

2017-10-20

Astrophysical polarization measurements in the soft gamma-ray band are becoming more feasible as detectors with high position and energy resolution are deployed. Previous work has shown that the minimum detectable polarization (MDP) of an ideal Compton polarimeter can be improved by ∼21% when an unbinned, maximum likelihood method (MLM) is used instead of the standard approach of fitting a sinusoid to a histogram of azimuthal scattering angles. Here we outline a procedure for implementing this maximum likelihood approach for real, nonideal polarimeters. As an example, we use the recent observation of GRB 160530A with the Compton Spectrometer and Imager. Wemore » find that the MDP for this observation is reduced by 20% when the MLM is used instead of the standard method.« less

Valid analytical performance specifications for combined analytical bias and imprecision for the use of common reference intervals.

PubMed

Hyltoft Petersen, Per; Lund, Flemming; Fraser, Callum G; Sandberg, Sverre; Sölétormos, György

2018-01-01

Background Many clinical decisions are based on comparison of patient results with reference intervals. Therefore, an estimation of the analytical performance specifications for the quality that would be required to allow sharing common reference intervals is needed. The International Federation of Clinical Chemistry (IFCC) recommended a minimum of 120 reference individuals to establish reference intervals. This number implies a certain level of quality, which could then be used for defining analytical performance specifications as the maximum combination of analytical bias and imprecision required for sharing common reference intervals, the aim of this investigation. Methods Two methods were investigated for defining the maximum combination of analytical bias and imprecision that would give the same quality of common reference intervals as the IFCC recommendation. Method 1 is based on a formula for the combination of analytical bias and imprecision and Method 2 is based on the Microsoft Excel formula NORMINV including the fractional probability of reference individuals outside each limit and the Gaussian variables of mean and standard deviation. The combinations of normalized bias and imprecision are illustrated for both methods. The formulae are identical for Gaussian and log-Gaussian distributions. Results Method 2 gives the correct results with a constant percentage of 4.4% for all combinations of bias and imprecision. Conclusion The Microsoft Excel formula NORMINV is useful for the estimation of analytical performance specifications for both Gaussian and log-Gaussian distributions of reference intervals.

Non-Gaussian effects, space-time decoupling, and mobility bifurcation in glassy hard-sphere fluids and suspensions.

PubMed

Saltzman, Erica J; Schweizer, Kenneth S

2006-12-01

Brownian trajectory simulation methods are employed to fully establish the non-Gaussian fluctuation effects predicted by our nonlinear Langevin equation theory of single particle activated dynamics in glassy hard-sphere fluids. The consequences of stochastic mobility fluctuations associated with the space-time complexities of the transient localization and barrier hopping processes have been determined. The incoherent dynamic structure factor was computed for a range of wave vectors and becomes of an increasingly non-Gaussian form for volume fractions beyond the (naive) ideal mode coupling theory (MCT) transition. The non-Gaussian parameter (NGP) amplitude increases markedly with volume fraction and is well described by a power law in the maximum restoring force of the nonequilibrium free energy profile. The time scale associated with the NGP peak becomes much smaller than the alpha relaxation time for systems characterized by significant entropic barriers. An alternate non-Gaussian parameter that probes the long time alpha relaxation process displays a different shape, peak intensity, and time scale of its maximum. However, a strong correspondence between the classic and alternate NGP amplitudes is predicted which suggests a deep connection between the early and final stages of cage escape. Strong space-time decoupling emerges at high volume fractions as indicated by a nondiffusive wave vector dependence of the relaxation time and growth of the translation-relaxation decoupling parameter. Displacement distributions exhibit non-Gaussian behavior at intermediate times, evolving into a strongly bimodal form with slow and fast subpopulations at high volume fractions. Qualitative and semiquantitative comparisons of the theoretical results with colloid experiments, ideal MCT, and multiple simulation studies are presented.

Development and modification of a Gaussian and non-Gaussian noise exposure system

NASA Astrophysics Data System (ADS)

Schlag, Adam W.

Millions of people across the world currently have noise induced hearing loss, and many are working in conditions with both continuous Gaussian and non-Gaussian noises that could affect their hearing. It was hypothesized that the energy of the noise was the cause of the hearing loss and did not depend on temporal pattern of a noise. This was referred to as the equal energy hypothesis. This hypothesis has been shown to have limitations though. This means that there is a difference in the types of noise a person receives to induce hearing loss and it is necessary to build a system that can easily mimic various conditions to conduct research. This study builds a system that can produce both non-Gaussian impulse/impact noises and continuous Gaussian noise. It was found that the peak sound pressure level of the system could reach well above the needed 120 dB level to represent acoustic trauma and could replicate well above the 85 dB A-weighted sound pressure level to produce conditions of gradual developing hearing loss. The system reached a maximum of 150 dB sound peak pressure level and a maximum of 133 dB A-weighted sound pressure level. Various parameters could easily be adjusted to control the sound, such as the high and low cutoff frequency to center the sound at 4 kHz. The system build can easily be adjusted to create numerous sound conditions and will hopefully be modified and improved in hopes of eventually being used for animal studies to lead to the creation of a method to treat or prevent noise induced hearing loss.

Lod scores for gene mapping in the presence of marker map uncertainty.

PubMed

Stringham, H M; Boehnke, M

2001-07-01

Multipoint lod scores are typically calculated for a grid of locus positions, moving the putative disease locus across a fixed map of genetic markers. Changing the order of a set of markers and/or the distances between the markers can make a substantial difference in the resulting lod score curve and the location and height of its maximum. The typical approach of using the best maximum likelihood marker map is not easily justified if other marker orders are nearly as likely and give substantially different lod score curves. To deal with this problem, we propose three weighted multipoint lod score statistics that make use of information from all plausible marker orders. In each of these statistics, the information conditional on a particular marker order is included in a weighted sum, with weight equal to the posterior probability of that order. We evaluate the type 1 error rate and power of these three statistics on the basis of results from simulated data, and compare these results to those obtained using the best maximum likelihood map and the map with the true marker order. We find that the lod score based on a weighted sum of maximum likelihoods improves on using only the best maximum likelihood map, having a type 1 error rate and power closest to that of using the true marker order in the simulation scenarios we considered. Copyright 2001 Wiley-Liss, Inc.

On the Existence and Uniqueness of JML Estimates for the Partial Credit Model

ERIC Educational Resources Information Center

Bertoli-Barsotti, Lucio

2005-01-01

A necessary and sufficient condition is given in this paper for the existence and uniqueness of the maximum likelihood (the so-called joint maximum likelihood) estimate of the parameters of the Partial Credit Model. This condition is stated in terms of a structural property of the pattern of the data matrix that can be easily verified on the basis…

Formulating the Rasch Differential Item Functioning Model under the Marginal Maximum Likelihood Estimation Context and Its Comparison with Mantel-Haenszel Procedure in Short Test and Small Sample Conditions

ERIC Educational Resources Information Center

Paek, Insu; Wilson, Mark

2011-01-01

This study elaborates the Rasch differential item functioning (DIF) model formulation under the marginal maximum likelihood estimation context. Also, the Rasch DIF model performance was examined and compared with the Mantel-Haenszel (MH) procedure in small sample and short test length conditions through simulations. The theoretically known…

Distributions of extreme bursts above thresholds in a fractional Lévy toy model of natural complexity.

NASA Astrophysics Data System (ADS)

Watkins, Nicholas; Chapman, Sandra; Rosenberg, Sam; Credgington, Dan; Sanchez, Raul

2010-05-01

In 2 far-sighted contributions in the 1960s Mandelbrot showed the ubiquity of both non-Gaussian fluctuations and long-ranged temporal memory (the "Noah" and "Joseph" effects, respectively) in the natural and man-made worlds. Much subsequent work in complexity science has contributed to the physical underpinning of these effects, particularly in cases where complex interactions in a system cause a driven or random perturbation to be nonlinearly amplified in amplitude and/or spread out over a wide range of frequencies. In addition the modelling of catastrophes has begun to incorporate the insights which these approaches have offered into the likelihood of extreme and long-lived fluctuations. I will briefly survey how the application of the above ideas in the earth system has been a key focus and motivation of research into natural complexity at BAS [e.g. Watkins & Freeman, Science, 2008; Edwards et al, Nature, 2007]. I will then discuss in detail a standard toy model (linear fractional stable motion, LFSM) which combines the Noah and Joseph effects in a controllable way and explain how it differs from the widely used continuous time random walk. I will describe how LFSM is being used to explore the interplay of the above two effects in the distribution of bursts above thresholds. I will describe ongoing work to improve the accuracy of maximum likelihood-based estimation of burst size and waiting time distributions for LFSM first reported in [Watkins et al, PRE, 2009]; and will also touch on similar work for multifractal models [Watkins et al, PRL comment, 2009].

Automated model selection in covariance estimation and spatial whitening of MEG and EEG signals.

PubMed

Engemann, Denis A; Gramfort, Alexandre

2015-03-01

Magnetoencephalography and electroencephalography (M/EEG) measure non-invasively the weak electromagnetic fields induced by post-synaptic neural currents. The estimation of the spatial covariance of the signals recorded on M/EEG sensors is a building block of modern data analysis pipelines. Such covariance estimates are used in brain-computer interfaces (BCI) systems, in nearly all source localization methods for spatial whitening as well as for data covariance estimation in beamformers. The rationale for such models is that the signals can be modeled by a zero mean Gaussian distribution. While maximizing the Gaussian likelihood seems natural, it leads to a covariance estimate known as empirical covariance (EC). It turns out that the EC is a poor estimate of the true covariance when the number of samples is small. To address this issue the estimation needs to be regularized. The most common approach downweights off-diagonal coefficients, while more advanced regularization methods are based on shrinkage techniques or generative models with low rank assumptions: probabilistic PCA (PPCA) and factor analysis (FA). Using cross-validation all of these models can be tuned and compared based on Gaussian likelihood computed on unseen data. We investigated these models on simulations, one electroencephalography (EEG) dataset as well as magnetoencephalography (MEG) datasets from the most common MEG systems. First, our results demonstrate that different models can be the best, depending on the number of samples, heterogeneity of sensor types and noise properties. Second, we show that the models tuned by cross-validation are superior to models with hand-selected regularization. Hence, we propose an automated solution to the often overlooked problem of covariance estimation of M/EEG signals. The relevance of the procedure is demonstrated here for spatial whitening and source localization of MEG signals. Copyright © 2015 Elsevier Inc. All rights reserved.

NON-GAUSSIANITIES IN THE LOCAL CURVATURE OF THE FIVE-YEAR WMAP DATA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rudjord, Oeystein; Groeneboom, Nicolaas E.; Hansen, Frode K.

Using the five-year WMAP data, we re-investigate claims of non-Gaussianities and asymmetries detected in local curvature statistics of the one-year WMAP data. In Hansen et al., it was found that the northern ecliptic hemisphere was non-Gaussian at the {approx}1% level testing the densities of hill, lake, and saddle points based on the second derivatives of the cosmic microwave background temperature map. The five-year WMAP data have a much lower noise level and better control of systematics. Using these, we find that the anomalies are still present at a consistent level. Also the direction of maximum non-Gaussianity remains. Due to limitedmore » availability of computer resources, Hansen et al. were unable to calculate the full covariance matrix for the {chi}{sup 2}-test used. Here, we apply the full covariance matrix instead of the diagonal approximation and find that the non-Gaussianities disappear and there is no preferred non-Gaussian direction. We compare with simulations of weak lensing to see if this may cause the observed non-Gaussianity when using a diagonal covariance matrix. We conclude that weak lensing does not produce non-Gaussianity in the local curvature statistics at the scales investigated in this paper. The cause of the non-Gaussian detection in the case of a diagonal matrix remains unclear.« less

Simple Form of MMSE Estimator for Super-Gaussian Prior Densities

NASA Astrophysics Data System (ADS)

Kittisuwan, Pichid

2015-04-01

The denoising method that become popular in recent years for additive white Gaussian noise (AWGN) are Bayesian estimation techniques e.g., maximum a posteriori (MAP) and minimum mean square error (MMSE). In super-Gaussian prior densities, it is well known that the MMSE estimator in such a case has a complicated form. In this work, we derive the MMSE estimation with Taylor series. We show that the proposed estimator also leads to a simple formula. An extension of this estimator to Pearson type VII prior density is also offered. The experimental result shows that the proposed estimator to the original MMSE nonlinearity is reasonably good.

Forecasts of non-Gaussian parameter spaces using Box-Cox transformations

NASA Astrophysics Data System (ADS)

Joachimi, B.; Taylor, A. N.

2011-09-01

Forecasts of statistical constraints on model parameters using the Fisher matrix abound in many fields of astrophysics. The Fisher matrix formalism involves the assumption of Gaussianity in parameter space and hence fails to predict complex features of posterior probability distributions. Combining the standard Fisher matrix with Box-Cox transformations, we propose a novel method that accurately predicts arbitrary posterior shapes. The Box-Cox transformations are applied to parameter space to render it approximately multivariate Gaussian, performing the Fisher matrix calculation on the transformed parameters. We demonstrate that, after the Box-Cox parameters have been determined from an initial likelihood evaluation, the method correctly predicts changes in the posterior when varying various parameters of the experimental setup and the data analysis, with marginally higher computational cost than a standard Fisher matrix calculation. We apply the Box-Cox-Fisher formalism to forecast cosmological parameter constraints by future weak gravitational lensing surveys. The characteristic non-linear degeneracy between matter density parameter and normalization of matter density fluctuations is reproduced for several cases, and the capabilities of breaking this degeneracy by weak-lensing three-point statistics is investigated. Possible applications of Box-Cox transformations of posterior distributions are discussed, including the prospects for performing statistical data analysis steps in the transformed Gaussianized parameter space.

Computing maximum-likelihood estimates for parameters of the National Descriptive Model of Mercury in Fish

USGS Publications Warehouse

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.

Estimating a Logistic Discrimination Functions When One of the Training Samples Is Subject to Misclassification: A Maximum Likelihood Approach.

PubMed

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.

Dimension-independent likelihood-informed MCMC

DOE PAGES

Cui, Tiangang; Law, Kody J. H.; Marzouk, Youssef M.

2015-10-08

Many Bayesian inference problems require exploring the posterior distribution of highdimensional parameters that represent the discretization of an underlying function. Our work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. There are two distinct lines of research that intersect in the methods we develop here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian informationmore » and any associated lowdimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Finally, we use two nonlinear inverse problems in order to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.« less

Interactive lesion segmentation on dynamic contrast enhanced breast MRI using a Markov model

NASA Astrophysics Data System (ADS)

Wu, Qiu; Salganicoff, Marcos; Krishnan, Arun; Fussell, Donald S.; Markey, Mia K.

2006-03-01

The purpose of this study is to develop a method for segmenting lesions on Dynamic Contrast-Enhanced (DCE) breast MRI. DCE breast MRI, in which the breast is imaged before, during, and after the administration of a contrast agent, enables a truly 3D examination of breast tissues. This functional angiogenic imaging technique provides noninvasive assessment of microcirculatory characteristics of tissues in addition to traditional anatomical structure information. Since morphological features and kinetic curves from segmented lesions are to be used for diagnosis and treatment decisions, lesion segmentation is a key pre-processing step for classification. In our study, the ROI is defined by a bounding box containing the enhancement region in the subtraction image, which is generated by subtracting the pre-contrast image from 1st post-contrast image. A maximum a posteriori (MAP) estimate of the class membership (lesion vs. non-lesion) for each voxel is obtained using the Iterative Conditional Mode (ICM) method. The prior distribution of the class membership is modeled as a multi-level logistic model, a Markov Random Field model in which the class membership of each voxel is assumed to depend upon its nearest neighbors only. The likelihood distribution is assumed to be Gaussian. The parameters of each Gaussian distribution are estimated from a dozen voxels manually selected as representative of the class. The experimental segmentation results demonstrate anatomically plausible breast tissue segmentation and the predicted class membership of voxels from the interactive segmentation algorithm agrees with the manual classifications made by inspection of the kinetic enhancement curves. The proposed method is advantageous in that it is efficient, flexible, and robust.

Wide-field investigation of the Kuiper Belt

NASA Astrophysics Data System (ADS)

Trujillo, Chadwick Aaron

Two wide-field surveys have been conducted for Kuiper Belt Objects (KBOs) and Centaurs using the largest close- packed CCD Mosaic cameras in the world. The first is a wide-field ecliptic survey of 157 square degrees to limiting red magnitude 21.1, responsible for the discovery of 3 KBOs and 1 Centaur. The second is a much deeper survey of 76 square degrees to limiting red magnitude 23.7, which found 86 KBOs. Data were analysed using the same software methods, and a maximum-likelihood simulation was used to debias the observations in a consistent manner. Fundamental quantities describing the Kuiper Belt are derived from these data: size distribution, inclination distribution, radial extent, and total mass. We find that the KBOs follow a differential power law size distribution with index q = 3.8 (+0.3, -0.4 1σ = 68.27% confidence), consistent with the crushed rock size distributions measured in hypervelocity impact experiments. In addition, the debiased inclinations of the Classical KBOs are consistent with a thick Gaussian distribution with half-width 20 (+8, -2 1σ) degrees. The Scattered KBOs are consistent with a Gaussian model with half-width 11 (+6, -3 1σ) degrees, with modal inclination 20 (+9, -4 1σ) degrees. The inclination measurements indicate that the KBOs are in a highly erosive state, with velocity dispersions of 1 to 2 kilometers per second. Strong evidence is presented for a truncation of the Classical KBOs at heliocentric distances beyond 50 AU. The total number and mass of the Scattered KBOs is about 3 times larger than that of the Classical KBOs, with a combined mass from the two populations of about 0.3 Earth masses.

A Comparison of Pseudo-Maximum Likelihood and Asymptotically Distribution-Free Dynamic Factor Analysis Parameter Estimation in Fitting Covariance Structure Models to Block-Toeplitz Matrices Representing Single-Subject Multivariate Time-Series.

ERIC Educational Resources Information Center

Molenaar, Peter C. M.; Nesselroade, John R.

1998-01-01

Pseudo-Maximum Likelihood (p-ML) and Asymptotically Distribution Free (ADF) estimation methods for estimating dynamic factor model parameters within a covariance structure framework were compared through a Monte Carlo simulation. Both methods appear to give consistent model parameter estimates, but only ADF gives standard errors and chi-square…

Statistical Bias in Maximum Likelihood Estimators of Item Parameters.

DTIC Science & Technology

1982-04-01

34 a> E r’r~e r ,C Ie I# ne,..,.rVi rnd Id.,flfv b1 - bindk numb.r) I; ,t-i i-cd I ’ tiie bias in the maximum likelihood ,st i- i;, ’ t iIeiIrs in...NTC, IL 60088 Psychometric Laboratory University of North Carolina I ERIC Facility-Acquisitions Davie Hall 013A 4833 Rugby Avenue Chapel Hill, NC

On the Performance of Maximum Likelihood versus Means and Variance Adjusted Weighted Least Squares Estimation in CFA

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…

Bias correction of risk estimates in vaccine safety studies with rare adverse events using a self-controlled case series design.

PubMed

Zeng, Chan; Newcomer, Sophia R; Glanz, Jason M; Shoup, Jo Ann; Daley, Matthew F; Hambidge, Simon J; Xu, Stanley

2013-12-15

The self-controlled case series (SCCS) method is often used to examine the temporal association between vaccination and adverse events using only data from patients who experienced such events. Conditional Poisson regression models are used to estimate incidence rate ratios, and these models perform well with large or medium-sized case samples. However, in some vaccine safety studies, the adverse events studied are rare and the maximum likelihood estimates may be biased. Several bias correction methods have been examined in case-control studies using conditional logistic regression, but none of these methods have been evaluated in studies using the SCCS design. In this study, we used simulations to evaluate 2 bias correction approaches-the Firth penalized maximum likelihood method and Cordeiro and McCullagh's bias reduction after maximum likelihood estimation-with small sample sizes in studies using the SCCS design. The simulations showed that the bias under the SCCS design with a small number of cases can be large and is also sensitive to a short risk period. The Firth correction method provides finite and less biased estimates than the maximum likelihood method and Cordeiro and McCullagh's method. However, limitations still exist when the risk period in the SCCS design is short relative to the entire observation period.

Real-time forecasting and predictability of catastrophic failure events: from rock failure to volcanoes and earthquakes

NASA Astrophysics Data System (ADS)

Main, I. G.; Bell, A. F.; Naylor, M.; Atkinson, M.; Filguera, R.; Meredith, P. G.; Brantut, N.

2012-12-01

Accurate prediction of catastrophic brittle failure in rocks and in the Earth presents a significant challenge on theoretical and practical grounds. The governing equations are not known precisely, but are known to produce highly non-linear behavior similar to those of near-critical dynamical systems, with a large and irreducible stochastic component due to material heterogeneity. In a laboratory setting mechanical, hydraulic and rock physical properties are known to change in systematic ways prior to catastrophic failure, often with significant non-Gaussian fluctuations about the mean signal at a given time, for example in the rate of remotely-sensed acoustic emissions. The effectiveness of such signals in real-time forecasting has never been tested before in a controlled laboratory setting, and previous work has often been qualitative in nature, and subject to retrospective selection bias, though it has often been invoked as a basis in forecasting natural hazard events such as volcanoes and earthquakes. Here we describe a collaborative experiment in real-time data assimilation to explore the limits of predictability of rock failure in a best-case scenario. Data are streamed from a remote rock deformation laboratory to a user-friendly portal, where several proposed physical/stochastic models can be analysed in parallel in real time, using a variety of statistical fitting techniques, including least squares regression, maximum likelihood fitting, Markov-chain Monte-Carlo and Bayesian analysis. The results are posted and regularly updated on the web site prior to catastrophic failure, to ensure a true and and verifiable prospective test of forecasting power. Preliminary tests on synthetic data with known non-Gaussian statistics shows how forecasting power is likely to evolve in the live experiments. In general the predicted failure time does converge on the real failure time, illustrating the bias associated with the 'benefit of hindsight' in retrospective analyses. Inference techniques that account explicitly for non-Gaussian statistics significantly reduce the bias, and increase the reliability and accuracy, of the forecast failure time in prospective mode.

Approximate bandpass and frequency response models of the difference of Gaussian filter

NASA Astrophysics Data System (ADS)

Birch, Philip; Mitra, Bhargav; Bangalore, Nagachetan M.; Rehman, Saad; Young, Rupert; Chatwin, Chris

2010-12-01

The Difference of Gaussian (DOG) filter is widely used in optics and image processing as, among other things, an edge detection and correlation filter. It has important biological applications and appears to be part of the mammalian vision system. In this paper we analyse the filter and provide details of the full width half maximum, bandwidth and frequency response in order to aid the full characterisation of its performance.

Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adesso, Gerardo; Illuminati, Fabrizio; INFN Sezione di Napoli-Gruppo Collegato di Salerno, Via S. Allende, 84081 Baronissi, SA

2005-09-15

We study the entanglement of general (pure or mixed) two-mode Gaussian states of continuous-variable systems by comparing the two available classes of computable measures of entanglement: entropy-inspired Gaussian convex-roof measures and positive partial transposition-inspired measures (negativity and logarithmic negativity). We first review the formalism of Gaussian measures of entanglement, adopting the framework introduced in M. M. Wolf et al., Phys. Rev. A 69, 052320 (2004), where the Gaussian entanglement of formation was defined. We compute explicitly Gaussian measures of entanglement for two important families of nonsymmetric two-mode Gaussian state: namely, the states of extremal (maximal and minimal) negativities at fixedmore » global and local purities, introduced in G. Adesso et al., Phys. Rev. Lett. 92, 087901 (2004). This analysis allows us to compare the different orderings induced on the set of entangled two-mode Gaussian states by the negativities and by the Gaussian measures of entanglement. We find that in a certain range of values of the global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement of formation than states of maximum negativity. Consequently, Gaussian measures and negativities are definitely inequivalent measures of entanglement on nonsymmetric two-mode Gaussian states, even when restricted to a class of extremal states. On the other hand, the two families of entanglement measures are completely equivalent on symmetric states, for which the Gaussian entanglement of formation coincides with the true entanglement of formation. Finally, we show that the inequivalence between the two families of continuous-variable entanglement measures is somehow limited. Namely, we rigorously prove that, at fixed negativities, the Gaussian measures of entanglement are bounded from below. Moreover, we provide some strong evidence suggesting that they are as well bounded from above.« less

Geotechnical parameter spatial distribution stochastic analysis based on multi-precision information assimilation

NASA Astrophysics Data System (ADS)

Wang, C.; Rubin, Y.

2014-12-01

Spatial distribution of important geotechnical parameter named compression modulus Es contributes considerably to the understanding of the underlying geological processes and the adequate assessment of the Es mechanics effects for differential settlement of large continuous structure foundation. These analyses should be derived using an assimilating approach that combines in-situ static cone penetration test (CPT) with borehole experiments. To achieve such a task, the Es distribution of stratum of silty clay in region A of China Expo Center (Shanghai) is studied using the Bayesian-maximum entropy method. This method integrates rigorously and efficiently multi-precision of different geotechnical investigations and sources of uncertainty. Single CPT samplings were modeled as a rational probability density curve by maximum entropy theory. Spatial prior multivariate probability density function (PDF) and likelihood PDF of the CPT positions were built by borehole experiments and the potential value of the prediction point, then, preceding numerical integration on the CPT probability density curves, the posterior probability density curve of the prediction point would be calculated by the Bayesian reverse interpolation framework. The results were compared between Gaussian Sequential Stochastic Simulation and Bayesian methods. The differences were also discussed between single CPT samplings of normal distribution and simulated probability density curve based on maximum entropy theory. It is shown that the study of Es spatial distributions can be improved by properly incorporating CPT sampling variation into interpolation process, whereas more informative estimations are generated by considering CPT Uncertainty for the estimation points. Calculation illustrates the significance of stochastic Es characterization in a stratum, and identifies limitations associated with inadequate geostatistical interpolation techniques. This characterization results will provide a multi-precision information assimilation method of other geotechnical parameters.

The impact of turbulent renewable energy production on power grid stability and quality

NASA Astrophysics Data System (ADS)

Schmietendorf, Katrin; Peinke, Joachim; Kamps, Oliver

2017-11-01

Feed-in fluctuations induced by renewables are one of the key challenges to the stability and quality of electrical power grids. In particular short-term fluctuations disturb the system on a time scale, on which load balancing does not operate yet and the system is intrinsically governed by self-organized synchronization. Wind and solar power are known to be strongly non-Gaussian with intermittent increment statistics in these time scales. We investigate the impact of short-term wind fluctuations on the basis of a Kuramoto-like power grid model considering stability in terms of desynchronization and frequency and voltage quality aspects. We present a procedure to generate realistic feed-in fluctuations with temporal correlations, Kolmogorov power spectrum and intermittent increments. By comparison to correlated Gaussian noise of the same spectrum and Gaussian white noise, we found out that while the correlations are essential to capture the likelihood of severe outages, the intermittent nature of wind power has significant consequences on power quality: intermittency is directly transferred into frequency and voltage fluctuations yielding a novel type of fluctuations, which is beyond engineering status of knowledge.

Bayesian modelling of the emission spectrum of the Joint European Torus Lithium Beam Emission Spectroscopy system.

PubMed

Kwak, Sehyun; Svensson, J; Brix, M; Ghim, Y-C

2016-02-01

A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam.

Composite Partial Likelihood Estimation Under Length-Biased Sampling, With Application to a Prevalent Cohort Study of Dementia

PubMed Central

Huang, Chiung-Yu; Qin, Jing

2013-01-01

The Canadian Study of Health and Aging (CSHA) employed a prevalent cohort design to study survival after onset of dementia, where patients with dementia were sampled and the onset time of dementia was determined retrospectively. The prevalent cohort sampling scheme favors individuals who survive longer. Thus, the observed survival times are subject to length bias. In recent years, there has been a rising interest in developing estimation procedures for prevalent cohort survival data that not only account for length bias but also actually exploit the incidence distribution of the disease to improve efficiency. This article considers semiparametric estimation of the Cox model for the time from dementia onset to death under a stationarity assumption with respect to the disease incidence. Under the stationarity condition, the semiparametric maximum likelihood estimation is expected to be fully efficient yet difficult to perform for statistical practitioners, as the likelihood depends on the baseline hazard function in a complicated way. Moreover, the asymptotic properties of the semiparametric maximum likelihood estimator are not well-studied. Motivated by the composite likelihood method (Besag 1974), we develop a composite partial likelihood method that retains the simplicity of the popular partial likelihood estimator and can be easily performed using standard statistical software. When applied to the CSHA data, the proposed method estimates a significant difference in survival between the vascular dementia group and the possible Alzheimer’s disease group, while the partial likelihood method for left-truncated and right-censored data yields a greater standard error and a 95% confidence interval covering 0, thus highlighting the practical value of employing a more efficient methodology. To check the assumption of stable disease for the CSHA data, we also present new graphical and numerical tests in the article. The R code used to obtain the maximum composite partial likelihood estimator for the CSHA data is available in the online Supplementary Material, posted on the journal web site. PMID:24000265

Quasi- and pseudo-maximum likelihood estimators for discretely observed continuous-time Markov branching processes

PubMed Central

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

A Solution to Separation and Multicollinearity in Multiple Logistic Regression

PubMed Central

Shen, Jianzhao; Gao, Sujuan

2010-01-01

In dementia screening tests, item selection for shortening an existing screening test can be achieved using multiple logistic regression. However, maximum likelihood estimates for such logistic regression models often experience serious bias or even non-existence because of separation and multicollinearity problems resulting from a large number of highly correlated items. Firth (1993, Biometrika, 80(1), 27–38) proposed a penalized likelihood estimator for generalized linear models and it was shown to reduce bias and the non-existence problems. The ridge regression has been used in logistic regression to stabilize the estimates in cases of multicollinearity. However, neither solves the problems for each other. In this paper, we propose a double penalized maximum likelihood estimator combining Firth’s penalized likelihood equation with a ridge parameter. We present a simulation study evaluating the empirical performance of the double penalized likelihood estimator in small to moderate sample sizes. We demonstrate the proposed approach using a current screening data from a community-based dementia study. PMID:20376286

A Solution to Separation and Multicollinearity in Multiple Logistic Regression.

PubMed

Shen, Jianzhao; Gao, Sujuan

2008-10-01

In dementia screening tests, item selection for shortening an existing screening test can be achieved using multiple logistic regression. However, maximum likelihood estimates for such logistic regression models often experience serious bias or even non-existence because of separation and multicollinearity problems resulting from a large number of highly correlated items. Firth (1993, Biometrika, 80(1), 27-38) proposed a penalized likelihood estimator for generalized linear models and it was shown to reduce bias and the non-existence problems. The ridge regression has been used in logistic regression to stabilize the estimates in cases of multicollinearity. However, neither solves the problems for each other. In this paper, we propose a double penalized maximum likelihood estimator combining Firth's penalized likelihood equation with a ridge parameter. We present a simulation study evaluating the empirical performance of the double penalized likelihood estimator in small to moderate sample sizes. We demonstrate the proposed approach using a current screening data from a community-based dementia study.

Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection

NASA Astrophysics Data System (ADS)

Liao, Qin; Guo, Ying; Huang, Duan; Huang, Peng; Zeng, Guihua

2018-02-01

We propose a long-distance continuous-variable quantum key distribution (CVQKD) with a four-state protocol using non-Gaussian state-discrimination detection. A photon subtraction operation, which is deployed at the transmitter, is used for splitting the signal required for generating the non-Gaussian operation to lengthen the maximum transmission distance of the CVQKD. Whereby an improved state-discrimination detector, which can be deemed as an optimized quantum measurement that allows the discrimination of nonorthogonal coherent states beating the standard quantum limit, is applied at the receiver to codetermine the measurement result with the conventional coherent detector. By tactfully exploiting the multiplexing technique, the resulting signals can be simultaneously transmitted through an untrusted quantum channel, and subsequently sent to the state-discrimination detector and coherent detector, respectively. Security analysis shows that the proposed scheme can lengthen the maximum transmission distance up to hundreds of kilometers. Furthermore, by taking the finite-size effect and composable security into account we obtain the tightest bound of the secure distance, which is more practical than that obtained in the asymptotic limit.

Maximum likelihood estimation of signal detection model parameters for the assessment of two-stage diagnostic strategies.

PubMed

Lirio, R B; Dondériz, I C; Pérez Abalo, M C

1992-08-01

The methodology of Receiver Operating Characteristic curves based on the signal detection model is extended to evaluate the accuracy of two-stage diagnostic strategies. A computer program is developed for the maximum likelihood estimation of parameters that characterize the sensitivity and specificity of two-stage classifiers according to this extended methodology. Its use is briefly illustrated with data collected in a two-stage screening for auditory defects.

Computing Maximum Likelihood Estimates of Loglinear Models from Marginal Sums with Special Attention to Loglinear Item Response Theory. [Project Psychometric Aspects of Item Banking No. 53.] Research Report 91-1.

ERIC Educational Resources Information Center

Kelderman, Henk

In this paper, algorithms are described for obtaining the maximum likelihood estimates of the parameters in log-linear models. Modified versions of the iterative proportional fitting and Newton-Raphson algorithms are described that work on the minimal sufficient statistics rather than on the usual counts in the full contingency table. This is…

Maximum Likelihood Item Easiness Models for Test Theory Without an Answer Key

PubMed Central

Batchelder, William H.

2014-01-01

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 two extensions to the basic model in order to account for item rating easiness/difficulty. The first extension is a multiplicative model and the second is an additive model. We show how the multiplicative model is related to the Rasch model. We describe several maximum-likelihood estimation procedures for the models and discuss issues of model fit and identifiability. We describe how the CCT models could be used to give alternative consensus-based measures of reliability. We demonstrate the utility of both the basic and extended models on a set of essay rating data and give ideas for future research. PMID:29795812

Maximum likelihood estimation of label imperfections and its use in the identification of mislabeled patterns

NASA Technical Reports Server (NTRS)

Chittineni, C. B.

1979-01-01

The problem of estimating label imperfections and the use of the estimation in identifying mislabeled patterns is presented. Expressions for the maximum likelihood estimates of classification errors and a priori probabilities are derived from the classification of a set of labeled patterns. Expressions also are given for the asymptotic variances of probability of correct classification and proportions. Simple models are developed for imperfections in the labels and for classification errors and are used in the formulation of a maximum likelihood estimation scheme. Schemes are presented for the identification of mislabeled patterns in terms of threshold on the discriminant functions for both two-class and multiclass cases. Expressions are derived for the probability that the imperfect label identification scheme will result in a wrong decision and are used in computing thresholds. The results of practical applications of these techniques in the processing of remotely sensed multispectral data are presented.

Bayesian structural equation modeling in sport and exercise psychology.

PubMed

Stenling, Andreas; Ivarsson, Andreas; Johnson, Urban; Lindwall, Magnus

2015-08-01

Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.

A comparison of maximum likelihood and other estimators of eigenvalues from several correlated Monte Carlo samples

DOE Office of Scientific and Technical Information (OSTI.GOV)

Beer, M.

1980-12-01

The maximum likelihood method for the multivariate normal distribution is applied to the case of several individual eigenvalues. Correlated Monte Carlo estimates of the eigenvalue are assumed to follow this prescription and aspects of the assumption are examined. Monte Carlo cell calculations using the SAM-CE and VIM codes for the TRX-1 and TRX-2 benchmark reactors, and SAM-CE full core results are analyzed with this method. Variance reductions of a few percent to a factor of 2 are obtained from maximum likelihood estimation as compared with the simple average and the minimum variance individual eigenvalue. The numerical results verify that themore » use of sample variances and correlation coefficients in place of the corresponding population statistics still leads to nearly minimum variance estimation for a sufficient number of histories and aggregates.« less

A Maximum Likelihood Approach to Functional Mapping of Longitudinal Binary Traits

PubMed Central

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

A Gateway for Phylogenetic Analysis Powered by Grid Computing Featuring GARLI 2.0

PubMed Central

Bazinet, Adam L.; Zwickl, Derrick J.; Cummings, Michael P.

2014-01-01

We introduce molecularevolution.org, a publicly available gateway for high-throughput, maximum-likelihood phylogenetic analysis powered by grid computing. The gateway features a garli 2.0 web service that enables a user to quickly and easily submit thousands of maximum likelihood tree searches or bootstrap searches that are executed in parallel on distributed computing resources. The garli web service allows one to easily specify partitioned substitution models using a graphical interface, and it performs sophisticated post-processing of phylogenetic results. Although the garli web service has been used by the research community for over three years, here we formally announce the availability of the service, describe its capabilities, highlight new features and recent improvements, and provide details about how the grid system efficiently delivers high-quality phylogenetic results. [garli, gateway, grid computing, maximum likelihood, molecular evolution portal, phylogenetics, web service.] PMID:24789072

A Study of Dim Object Detection for the Space Surveillance Telescope

DTIC Science & Technology

2013-03-21

ENG-13-M-32 Abstract Current methods of dim object detection for space surveillance make use of a Gaussian log-likelihood-ratio-test-based...quantitatively comparing the efficacy of two methods for dim object detection , termed in this paper the point detector and the correlator, both of which rely... applications . It is used in national defense for detecting satellites. It is used to detecting space debris, which threatens both civilian and

Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models with Factor Structures

ERIC Educational Resources Information Center

Jeon, Minjeong; Rabe-Hesketh, Sophia

2012-01-01

In this article, the authors suggest a profile-likelihood approach for estimating complex models by maximum likelihood (ML) using standard software and minimal programming. The method works whenever setting some of the parameters of the model to known constants turns the model into a standard model. An important class of models that can be…

Bulk flow in the combined 2MTF and 6dFGSv surveys

NASA Astrophysics Data System (ADS)

Qin, Fei; Howlett, Cullan; Staveley-Smith, Lister; Hong, Tao

2018-07-01

We create a combined sample of 10 904 late- and early-type galaxies from the 2MTF and 6dFGSv surveys in order to accurately measure bulk flow in the local Universe. Galaxies and groups of galaxies common between the two surveys are used to verify that the difference in zero-points is <0.02 dex. We introduce a maximum likelihood estimator (ηMLE) for bulk flow measurements that allows for more accurate measurement in the presence of non-Gaussian measurement errors. To calibrate out residual biases due to the subtle interaction of selection effects, Malmquist bias and anisotropic sky distribution, the estimator is tested on mock catalogues generated from 16 independent large-scale GiggleZ and SURFS simulations. The bulk flow of the local Universe using the combined data set, corresponding to a scale size of 40 h-1 Mpc, is 288 ± 24 km s-1 in the direction (l, b) = (296 ± 6°, 21 ± 5°). This is the most accurate bulk flow measurement to date, and the amplitude of the flow is consistent with the Λ cold dark matter expectation for similar size scales.

Bulk flow in the combined 2MTF and 6dFGSv surveys

NASA Astrophysics Data System (ADS)

Qin, Fei; Howlett, Cullan; Staveley-Smith, Lister; Hong, Tao

2018-04-01

We create a combined sample of 10,904 late and early-type galaxies from the 2MTF and 6dFGSv surveys in order to accurately measure bulk flow in the local Universe. Galaxies and groups of galaxies common between the two surveys are used to verify that the difference in zero-points is <0.02 dex. We introduce a new maximum likelihood estimator (ηMLE) for bulk flow measurements which allows for more accurate measurement in the presence non-Gaussian measurement errors. To calibrate out residual biases due to the subtle interaction of selection effects, Malmquist bias and anisotropic sky distribution, the estimator is tested on mock catalogues generated from 16 independent large-scale GiggleZ and SURFS simulations. The bulk flow of the local Universe using the combined data set, corresponding to a scale size of 40 h-1 Mpc, is 288 ± 24 km s-1 in the direction (l, b) = (296 ± 6°, 21 ± 5°). This is the most accurate bulk flow measurement to date, and the amplitude of the flow is consistent with the ΛCDM expectation for similar size scales.

Blind estimation of reverberation time

NASA Astrophysics Data System (ADS)

Ratnam, Rama; Jones, Douglas L.; Wheeler, Bruce C.; O'Brien, William D.; Lansing, Charissa R.; Feng, Albert S.

2003-11-01

The reverberation time (RT) is an important parameter for characterizing the quality of an auditory space. Sounds in reverberant environments are subject to coloration. This affects speech intelligibility and sound localization. Many state-of-the-art audio signal processing algorithms, for example in hearing-aids and telephony, are expected to have the ability to characterize the listening environment, and turn on an appropriate processing strategy accordingly. Thus, a method for characterization of room RT based on passively received microphone signals represents an important enabling technology. Current RT estimators, such as Schroeder's method, depend on a controlled sound source, and thus cannot produce an online, blind RT estimate. Here, a method for estimating RT without prior knowledge of sound sources or room geometry is presented. The diffusive tail of reverberation was modeled as an exponentially damped Gaussian white noise process. The time-constant of the decay, which provided a measure of the RT, was estimated using a maximum-likelihood procedure. The estimates were obtained continuously, and an order-statistics filter was used to extract the most likely RT from the accumulated estimates. The procedure was illustrated for connected speech. Results obtained for simulated and real room data are in good agreement with the real RT values.

Online estimation of room reverberation time

NASA Astrophysics Data System (ADS)

Ratnam, Rama; Jones, Douglas L.; Wheeler, Bruce C.; Feng, Albert S.

2003-04-01

The reverberation time (RT) is an important parameter for characterizing the quality of an auditory space. Sounds in reverberant environments are subject to coloration. This affects speech intelligibility and sound localization. State-of-the-art signal processing algorithms for hearing aids are expected to have the ability to evaluate the characteristics of the listening environment and turn on an appropriate processing strategy accordingly. Thus, a method for the characterization of room RT based on passively received microphone signals represents an important enabling technology. Current RT estimators, such as Schroeder's method or regression, depend on a controlled sound source, and thus cannot produce an online, blind RT estimate. Here, we describe a method for estimating RT without prior knowledge of sound sources or room geometry. The diffusive tail of reverberation was modeled as an exponentially damped Gaussian white noise process. The time constant of the decay, which provided a measure of the RT, was estimated using a maximum-likelihood procedure. The estimates were obtained continuously, and an order-statistics filter was used to extract the most likely RT from the accumulated estimates. The procedure was illustrated for connected speech. Results obtained for simulated and real room data are in good agreement with the real RT values.

Multivariate-$t$ nonlinear mixed models with application to censored multi-outcome AIDS studies.

PubMed

Lin, Tsung-I; Wang, Wan-Lun

2017-10-01

In multivariate longitudinal HIV/AIDS studies, multi-outcome repeated measures on each patient over time may contain outliers, and the viral loads are often subject to a upper or lower limit of detection depending on the quantification assays. In this article, we consider an extension of the multivariate nonlinear mixed-effects model by adopting a joint multivariate-$t$ distribution for random effects and within-subject errors and taking the censoring information of multiple responses into account. The proposed model is called the multivariate-$t$ nonlinear mixed-effects model with censored responses (MtNLMMC), allowing for analyzing multi-outcome longitudinal data exhibiting nonlinear growth patterns with censorship and fat-tailed behavior. Utilizing the Taylor-series linearization method, a pseudo-data version of expectation conditional maximization either (ECME) algorithm is developed for iteratively carrying out maximum likelihood estimation. We illustrate our techniques with two data examples from HIV/AIDS studies. Experimental results signify that the MtNLMMC performs favorably compared to its Gaussian analogue and some existing approaches. © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Accuracy of latent-variable estimation in Bayesian semi-supervised learning.

PubMed

Yamazaki, Keisuke

2015-09-01

Hierarchical probabilistic models, such as Gaussian mixture models, are widely used for unsupervised learning tasks. These models consist of observable and latent variables, which represent the observable data and the underlying data-generation process, respectively. Unsupervised learning tasks, such as cluster analysis, are regarded as estimations of latent variables based on the observable ones. The estimation of latent variables in semi-supervised learning, where some labels are observed, will be more precise than that in unsupervised, and one of the concerns is to clarify the effect of the labeled data. However, there has not been sufficient theoretical analysis of the accuracy of the estimation of latent variables. In a previous study, a distribution-based error function was formulated, and its asymptotic form was calculated for unsupervised learning with generative models. It has been shown that, for the estimation of latent variables, the Bayes method is more accurate than the maximum-likelihood method. The present paper reveals the asymptotic forms of the error function in Bayesian semi-supervised learning for both discriminative and generative models. The results show that the generative model, which uses all of the given data, performs better when the model is well specified. Copyright © 2015 Elsevier Ltd. All rights reserved.

Probabilistic Reasoning for Robustness in Automated Planning

NASA Technical Reports Server (NTRS)

Schaffer, Steven; Clement, Bradley; Chien, Steve

2007-01-01

A general-purpose computer program for planning the actions of a spacecraft or other complex system has been augmented by incorporating a subprogram that reasons about uncertainties in such continuous variables as times taken to perform tasks and amounts of resources to be consumed. This subprogram computes parametric probability distributions for time and resource variables on the basis of user-supplied models of actions and resources that they consume. The current system accepts bounded Gaussian distributions over action duration and resource use. The distributions are then combined during planning to determine the net probability distribution of each resource at any time point. In addition to a full combinatoric approach, several approximations for arriving at these combined distributions are available, including maximum-likelihood and pessimistic algorithms. Each such probability distribution can then be integrated to obtain a probability that execution of the plan under consideration would violate any constraints on the resource. The key idea is to use these probabilities of conflict to score potential plans and drive a search toward planning low-risk actions. An output plan provides a balance between the user s specified averseness to risk and other measures of optimality.

A semi-supervised classification algorithm using the TAD-derived background as training data

NASA Astrophysics Data System (ADS)

Fan, Lei; Ambeau, Brittany; Messinger, David W.

2013-05-01

In general, spectral image classification algorithms fall into one of two categories: supervised and unsupervised. In unsupervised approaches, the algorithm automatically identifies clusters in the data without a priori information about those clusters (except perhaps the expected number of them). Supervised approaches require an analyst to identify training data to learn the characteristics of the clusters such that they can then classify all other pixels into one of the pre-defined groups. The classification algorithm presented here is a semi-supervised approach based on the Topological Anomaly Detection (TAD) algorithm. The TAD algorithm defines background components based on a mutual k-Nearest Neighbor graph model of the data, along with a spectral connected components analysis. Here, the largest components produced by TAD are used as regions of interest (ROI's),or training data for a supervised classification scheme. By combining those ROI's with a Gaussian Maximum Likelihood (GML) or a Minimum Distance to the Mean (MDM) algorithm, we are able to achieve a semi supervised classification method. We test this classification algorithm against data collected by the HyMAP sensor over the Cooke City, MT area and University of Pavia scene.

The robustness of truncated Airy beam in PT Gaussian potentials media

NASA Astrophysics Data System (ADS)

Wang, Xianni; Fu, Xiquan; Huang, Xianwei; Yang, Yijun; Bai, Yanfeng

2018-03-01

The robustness of truncated Airy beam in parity-time (PT) symmetric Gaussian potentials media is numerically investigated. A high-peak power beam sheds from the Airy beam due to the media modulation while the Airy wavefront still retain its self-bending and non-diffraction characteristics under the influence of modulation parameters. Increasing the modulation factor results in the smaller value of maximum power of the center beam, and the opposite trend occurs with the increment of the modulation depth. However, the parabolic trajectory of the Airy wavefront does not be influenced. By utilizing the unique features, the Airy beam can be used as a long distance transmission source under the PT symmetric Gaussian potentials medium.

Kinect Posture Reconstruction Based on a Local Mixture of Gaussian Process Models.

PubMed

Liu, Zhiguang; Zhou, Liuyang; Leung, Howard; Shum, Hubert P H

2016-11-01

Depth sensor based 3D human motion estimation hardware such as Kinect has made interactive applications more popular recently. However, it is still challenging to accurately recognize postures from a single depth camera due to the inherently noisy data derived from depth images and self-occluding action performed by the user. In this paper, we propose a new real-time probabilistic framework to enhance the accuracy of live captured postures that belong to one of the action classes in the database. We adopt the Gaussian Process model as a prior to leverage the position data obtained from Kinect and marker-based motion capture system. We also incorporate a temporal consistency term into the optimization framework to constrain the velocity variations between successive frames. To ensure that the reconstructed posture resembles the accurate parts of the observed posture, we embed a set of joint reliability measurements into the optimization framework. A major drawback of Gaussian Process is its cubic learning complexity when dealing with a large database due to the inverse of a covariance matrix. To solve the problem, we propose a new method based on a local mixture of Gaussian Processes, in which Gaussian Processes are defined in local regions of the state space. Due to the significantly decreased sample size in each local Gaussian Process, the learning time is greatly reduced. At the same time, the prediction speed is enhanced as the weighted mean prediction for a given sample is determined by the nearby local models only. Our system also allows incrementally updating a specific local Gaussian Process in real time, which enhances the likelihood of adapting to run-time postures that are different from those in the database. Experimental results demonstrate that our system can generate high quality postures even under severe self-occlusion situations, which is beneficial for real-time applications such as motion-based gaming and sport training.

Thermal Characteristics and the Differential Emission Measure Distribution During a B8.3 Flare on 2009 July 4

NASA Astrophysics Data System (ADS)

Awasthi, Arun Kumar; Sylwester, Barbara; Sylwester, Janusz; Jain, Rajmal

2016-06-01

We investigate the evolution of the differential emission measure distribution (DEM[T]) in various phases of a B8.3 flare which occurred on 2009 July 04. We analyze the soft X-ray (SXR) emission in the 1.6-8.0 keV range, recorded collectively by the Solar Photometer in X-rays (SphinX; Polish) and the Solar X-ray Spectrometer (Indian) instruments. We conduct a comparative investigation of the best-fit DEM[T] distributions derived by employing various inversion schemes, namely, single Gaussian, power-law functions and a Withbroe-Sylwester (W-S) maximum likelihood algorithm. In addition, the SXR spectrum in three different energy bands, that is, 1.6-5.0 keV (low), 5.0-8.0 keV (high), and 1.6-8.0 keV (combined), is analyzed to determine the dependence of the best-fit DEM[T] distribution on the selection of the energy interval. The evolution of the DEM[T] distribution, derived using a W-S algorithm, reveals multi-thermal plasma during the rise to the maximum phase of the flare, and isothermal plasma in the post-maximum phase of the flare. The thermal energy content is estimated by considering the flare plasma to be (1) isothermal and (2) multi-thermal in nature. We find that the energy content during the flare, estimated using the multi-thermal approach, is in good agreement with that derived using the isothermal assumption, except during the flare maximum. Furthermore, the (multi-) thermal energy estimated while employing the low-energy band of the SXR spectrum results in higher values than that derived from the combined energy band. On the contrary, the analysis of the high-energy band of the SXR spectrum leads to lower thermal energy than that estimated from the combined energy band.

THERMAL CHARACTERISTICS AND THE DIFFERENTIAL EMISSION MEASURE DISTRIBUTION DURING A B8.3 FLARE ON 2009 JULY 4

DOE Office of Scientific and Technical Information (OSTI.GOV)

Awasthi, Arun Kumar; Sylwester, Barbara; Sylwester, Janusz

We investigate the evolution of the differential emission measure distribution (DEM[ T ]) in various phases of a B8.3 flare which occurred on 2009 July 04. We analyze the soft X-ray (SXR) emission in the 1.6–8.0 keV range, recorded collectively by the Solar Photometer in X-rays (SphinX; Polish) and the Solar X-ray Spectrometer (Indian) instruments. We conduct a comparative investigation of the best-fit DEM[ T ] distributions derived by employing various inversion schemes, namely, single Gaussian, power-law functions and a Withbroe–Sylwester (W–S) maximum likelihood algorithm. In addition, the SXR spectrum in three different energy bands, that is, 1.6–5.0 keV (low),more » 5.0–8.0 keV (high), and 1.6–8.0 keV (combined), is analyzed to determine the dependence of the best-fit DEM[ T ] distribution on the selection of the energy interval. The evolution of the DEM[ T ] distribution, derived using a W–S algorithm, reveals multi-thermal plasma during the rise to the maximum phase of the flare, and isothermal plasma in the post-maximum phase of the flare. The thermal energy content is estimated by considering the flare plasma to be (1) isothermal and (2) multi-thermal in nature. We find that the energy content during the flare, estimated using the multi-thermal approach, is in good agreement with that derived using the isothermal assumption, except during the flare maximum. Furthermore, the (multi-) thermal energy estimated while employing the low-energy band of the SXR spectrum results in higher values than that derived from the combined energy band. On the contrary, the analysis of the high-energy band of the SXR spectrum leads to lower thermal energy than that estimated from the combined energy band.« less

On the log-normality of historical magnetic-storm intensity statistics: implications for extreme-event probabilities

USGS Publications Warehouse

Love, Jeffrey J.; Rigler, E. Joshua; Pulkkinen, Antti; Riley, Pete

2015-01-01

An examination is made of the hypothesis that the statistics of magnetic-storm-maximum intensities are the realization of a log-normal stochastic process. Weighted least-squares and maximum-likelihood methods are used to fit log-normal functions to −Dst storm-time maxima for years 1957-2012; bootstrap analysis is used to established confidence limits on forecasts. Both methods provide fits that are reasonably consistent with the data; both methods also provide fits that are superior to those that can be made with a power-law function. In general, the maximum-likelihood method provides forecasts having tighter confidence intervals than those provided by weighted least-squares. From extrapolation of maximum-likelihood fits: a magnetic storm with intensity exceeding that of the 1859 Carrington event, −Dst≥850 nT, occurs about 1.13 times per century and a wide 95% confidence interval of [0.42,2.41] times per century; a 100-yr magnetic storm is identified as having a −Dst≥880 nT (greater than Carrington) but a wide 95% confidence interval of [490,1187] nT.

Novel transform for image description and compression with implementation by neural architectures

NASA Astrophysics Data System (ADS)

Ben-Arie, Jezekiel; Rao, Raghunath K.

1991-10-01

A general method for signal representation using nonorthogonal basis functions that are composed of Gaussians are described. The Gaussians can be combined into groups with predetermined configuration that can approximate any desired basis function. The same configuration at different scales forms a set of self-similar wavelets. The general scheme is demonstrated by representing a natural signal employing an arbitrary basis function. The basic methodology is demonstrated by two novel schemes for efficient representation of 1-D and 2- D signals using Gaussian basis functions (BFs). Special methods are required here since the Gaussian functions are nonorthogonal. The first method employs a paradigm of maximum energy reduction interlaced with the A* heuristic search. The second method uses an adaptive lattice system to find the minimum-squared error of the BFs onto the signal, and a lateral-vertical suppression network to select the most efficient representation in terms of data compression.

Maximum likelihood convolutional decoding (MCD) performance due to system losses

NASA Technical Reports Server (NTRS)

Webster, L.

1976-01-01

A model for predicting the computational performance of a maximum likelihood convolutional decoder (MCD) operating in a noisy carrier reference environment is described. This model is used to develop a subroutine that will be utilized by the Telemetry Analysis Program to compute the MCD bit error rate. When this computational model is averaged over noisy reference phase errors using a high-rate interpolation scheme, the results are found to agree quite favorably with experimental measurements.

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.

Maximum Correntropy Unscented Kalman Filter for Spacecraft Relative State Estimation.

PubMed

Liu, Xi; Qu, Hua; Zhao, Jihong; Yue, Pengcheng; Wang, Meng

2016-09-20

A new algorithm called maximum correntropy unscented Kalman filter (MCUKF) is proposed and applied to relative state estimation in space communication networks. As is well known, the unscented Kalman filter (UKF) provides an efficient tool to solve the non-linear state estimate problem. However, the UKF usually plays well in Gaussian noises. Its performance may deteriorate substantially in the presence of non-Gaussian noises, especially when the measurements are disturbed by some heavy-tailed impulsive noises. By making use of the maximum correntropy criterion (MCC), the proposed algorithm can enhance the robustness of UKF against impulsive noises. In the MCUKF, the unscented transformation (UT) is applied to obtain a predicted state estimation and covariance matrix, and a nonlinear regression method with the MCC cost is then used to reformulate the measurement information. Finally, the UT is adopted to the measurement equation to obtain the filter state and covariance matrix. Illustrative examples demonstrate the superior performance of the new algorithm.

Maximum Correntropy Unscented Kalman Filter for Spacecraft Relative State Estimation

PubMed Central

Liu, Xi; Qu, Hua; Zhao, Jihong; Yue, Pengcheng; Wang, Meng

2016-01-01

A new algorithm called maximum correntropy unscented Kalman filter (MCUKF) is proposed and applied to relative state estimation in space communication networks. As is well known, the unscented Kalman filter (UKF) provides an efficient tool to solve the non-linear state estimate problem. However, the UKF usually plays well in Gaussian noises. Its performance may deteriorate substantially in the presence of non-Gaussian noises, especially when the measurements are disturbed by some heavy-tailed impulsive noises. By making use of the maximum correntropy criterion (MCC), the proposed algorithm can enhance the robustness of UKF against impulsive noises. In the MCUKF, the unscented transformation (UT) is applied to obtain a predicted state estimation and covariance matrix, and a nonlinear regression method with the MCC cost is then used to reformulate the measurement information. Finally, the UT is adopted to the measurement equation to obtain the filter state and covariance matrix. Illustrative examples demonstrate the superior performance of the new algorithm. PMID:27657069

A Maximum Entropy Method for Particle Filtering

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.; Kim, Sangil

2006-06-01

Standard ensemble or particle filtering schemes do not properly represent states of low priori probability when the number of available samples is too small, as is often the case in practical applications. We introduce here a set of parametric resampling methods to solve this problem. Motivated by a general H-theorem for relative entropy, we construct parametric models for the filter distributions as maximum-entropy/minimum-information models consistent with moments of the particle ensemble. When the prior distributions are modeled as mixtures of Gaussians, our method naturally generalizes the ensemble Kalman filter to systems with highly non-Gaussian statistics. We apply the new particle filters presented here to two simple test cases: a one-dimensional diffusion process in a double-well potential and the three-dimensional chaotic dynamical system of Lorenz.

Flat-fielding of Solar Hα Observations Based on the Maximum Correntropy Criterion

NASA Astrophysics Data System (ADS)

Xu, Gao-Gui; Zheng, Sheng; Lin, Gang-Hua; Wang, Xiao-Fan

2016-08-01

The flat-field CCD calibration method of Kuhn et al. (KLL) is an efficient method for flat-fielding. However, since it depends on the minimum of the sum of squares error (SSE), its solution is sensitive to noise, especially non-Gaussian noise. In this paper, a new algorithm is proposed to determine the flat field. The idea is to change the criterion of gain estimate from SSE to the maximum correntropy. The result of a test on simulated data demonstrates that our method has a higher accuracy and a faster convergence than KLL’s and Chae’s. It has been found that the method effectively suppresses noise, especially in the case of typical non-Gaussian noise. And the computing time of our algorithm is the shortest.

Maximum likelihood estimates, from censored data, for mixed-Weibull distributions

NASA Astrophysics Data System (ADS)

Jiang, Siyuan; Kececioglu, Dimitri

1992-06-01

A new algorithm for estimating the parameters of mixed-Weibull distributions from censored data is presented. The algorithm follows the principle of maximum likelihood estimate (MLE) through the expectation and maximization (EM) algorithm, and it is derived for both postmortem and nonpostmortem time-to-failure data. It is concluded that the concept of the EM algorithm is easy to understand and apply (only elementary statistics and calculus are required). The log-likelihood function cannot decrease after an EM sequence; this important feature was observed in all of the numerical calculations. The MLEs of the nonpostmortem data were obtained successfully for mixed-Weibull distributions with up to 14 parameters in a 5-subpopulation, mixed-Weibull distribution. Numerical examples indicate that some of the log-likelihood functions of the mixed-Weibull distributions have multiple local maxima; therefore, the algorithm should start at several initial guesses of the parameter set.

Non-Gaussian structure of B-mode polarization after delensing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Namikawa, Toshiya; Nagata, Ryo, E-mail: namikawa@slac.stanford.edu, E-mail: rnagata@post.kek.jp

2015-10-01

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. Inmore » this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. As a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.« less

Non-Gaussian structure of B-mode polarization after delensing

NASA Astrophysics Data System (ADS)

Namikawa, Toshiya; Nagata, Ryo

2015-10-01

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. In this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. As a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.

Non-Gaussian structure of B-mode polarization after delensing

DOE PAGES

Namikawa, Toshiya; Nagata, Ryo

2015-10-01

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. Inmore » this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. Furthermore, as a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.« less

Evaluation of dynamic row-action maximum likelihood algorithm reconstruction for quantitative 15O brain PET.

PubMed

Ibaraki, Masanobu; Sato, Kaoru; Mizuta, Tetsuro; Kitamura, Keishi; Miura, Shuichi; Sugawara, Shigeki; Shinohara, Yuki; Kinoshita, Toshibumi

2009-09-01

A modified version of row-action maximum likelihood algorithm (RAMLA) using a 'subset-dependent' relaxation parameter for noise suppression, or dynamic RAMLA (DRAMA), has been proposed. The aim of this study was to assess the capability of DRAMA reconstruction for quantitative (15)O brain positron emission tomography (PET). Seventeen healthy volunteers were studied using a 3D PET scanner. The PET study included 3 sequential PET scans for C(15)O, (15)O(2) and H (2) (15) O. First, the number of main iterations (N (it)) in DRAMA was optimized in relation to image convergence and statistical image noise. To estimate the statistical variance of reconstructed images on a pixel-by-pixel basis, a sinogram bootstrap method was applied using list-mode PET data. Once the optimal N (it) was determined, statistical image noise and quantitative parameters, i.e., cerebral blood flow (CBF), cerebral blood volume (CBV), cerebral metabolic rate of oxygen (CMRO(2)) and oxygen extraction fraction (OEF) were compared between DRAMA and conventional FBP. DRAMA images were post-filtered so that their spatial resolutions were matched with FBP images with a 6-mm FWHM Gaussian filter. Based on the count recovery data, N (it) = 3 was determined as an optimal parameter for (15)O PET data. The sinogram bootstrap analysis revealed that DRAMA reconstruction resulted in less statistical noise, especially in a low-activity region compared to FBP. Agreement of quantitative values between FBP and DRAMA was excellent. For DRAMA images, average gray matter values of CBF, CBV, CMRO(2) and OEF were 46.1 +/- 4.5 (mL/100 mL/min), 3.35 +/- 0.40 (mL/100 mL), 3.42 +/- 0.35 (mL/100 mL/min) and 42.1 +/- 3.8 (%), respectively. These values were comparable to corresponding values with FBP images: 46.6 +/- 4.6 (mL/100 mL/min), 3.34 +/- 0.39 (mL/100 mL), 3.48 +/- 0.34 (mL/100 mL/min) and 42.4 +/- 3.8 (%), respectively. DRAMA reconstruction is applicable to quantitative (15)O PET study and is superior to conventional FBP in terms of image quality.

IMNN: Information Maximizing Neural Networks

NASA Astrophysics Data System (ADS)

Charnock, Tom; Lavaux, Guilhem; Wandelt, Benjamin D.

2018-04-01

This software trains artificial neural networks to find non-linear functionals of data that maximize Fisher information: information maximizing neural networks (IMNNs). As compressing large data sets vastly simplifies both frequentist and Bayesian inference, important information may be inadvertently missed. Likelihood-free inference based on automatically derived IMNN summaries produces summaries that are good approximations to sufficient statistics. IMNNs are robustly capable of automatically finding optimal, non-linear summaries of the data even in cases where linear compression fails: inferring the variance of Gaussian signal in the presence of noise, inferring cosmological parameters from mock simulations of the Lyman-α forest in quasar spectra, and inferring frequency-domain parameters from LISA-like detections of gravitational waveforms. In this final case, the IMNN summary outperforms linear data compression by avoiding the introduction of spurious likelihood maxima.

Simple Penalties on Maximum-Likelihood Estimates of Genetic Parameters to Reduce Sampling Variation

PubMed Central

Meyer, Karin

2016-01-01

Multivariate estimates of genetic parameters are subject to substantial sampling variation, especially for smaller data sets and more than a few traits. A simple modification of standard, maximum-likelihood procedures for multivariate analyses to estimate genetic covariances is described, which can improve estimates by substantially reducing their sampling variances. This is achieved by maximizing the likelihood subject to a penalty. Borrowing from Bayesian principles, we propose a mild, default penalty—derived assuming a Beta distribution of scale-free functions of the covariance components to be estimated—rather than laboriously attempting to determine the stringency of penalization from the data. An extensive simulation study is presented, demonstrating that such penalties can yield very worthwhile reductions in loss, i.e., the difference from population values, for a wide range of scenarios and without distorting estimates of phenotypic covariances. Moreover, mild default penalties tend not to increase loss in difficult cases and, on average, achieve reductions in loss of similar magnitude to computationally demanding schemes to optimize the degree of penalization. Pertinent details required for the adaptation of standard algorithms to locate the maximum of the likelihood function are outlined. PMID:27317681

Maximum Likelihood Estimations and EM Algorithms with Length-biased Data

PubMed Central

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

Perturbative Gaussianizing transforms for cosmological fields

NASA Astrophysics Data System (ADS)

Hall, Alex; Mead, Alexander

2018-01-01

Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.

Models and analysis for multivariate failure time data

NASA Astrophysics Data System (ADS)

Shih, Joanna Huang

The goal of this research is to develop and investigate models and analytic methods for multivariate failure time data. We compare models in terms of direct modeling of the margins, flexibility of dependency structure, local vs. global measures of association, and ease of implementation. In particular, we study copula models, and models produced by right neutral cumulative hazard functions and right neutral hazard functions. We examine the changes of association over time for families of bivariate distributions induced from these models by displaying their density contour plots, conditional density plots, correlation curves of Doksum et al, and local cross ratios of Oakes. We know that bivariate distributions with same margins might exhibit quite different dependency structures. In addition to modeling, we study estimation procedures. For copula models, we investigate three estimation procedures. the first procedure is full maximum likelihood. The second procedure is two-stage maximum likelihood. At stage 1, we estimate the parameters in the margins by maximizing the marginal likelihood. At stage 2, we estimate the dependency structure by fixing the margins at the estimated ones. The third procedure is two-stage partially parametric maximum likelihood. It is similar to the second procedure, but we estimate the margins by the Kaplan-Meier estimate. We derive asymptotic properties for these three estimation procedures and compare their efficiency by Monte-Carlo simulations and direct computations. For models produced by right neutral cumulative hazards and right neutral hazards, we derive the likelihood and investigate the properties of the maximum likelihood estimates. Finally, we develop goodness of fit tests for the dependency structure in the copula models. We derive a test statistic and its asymptotic properties based on the test of homogeneity of Zelterman and Chen (1988), and a graphical diagnostic procedure based on the empirical Bayes approach. We study the performance of these two methods using actual and computer generated data.

Laser plasma x-ray line spectra fitted using the Pearson VII function

NASA Astrophysics Data System (ADS)

Michette, A. G.; Pfauntsch, S. J.

2000-05-01

The Pearson VII function, which is more general than the Gaussian, Lorentzian and other profiles, is used to fit the x-ray spectral lines produced in a laser-generated plasma, instead of the more usual, but computationally expensive, Voigt function. The mean full-width half-maximum of the fitted lines is 0.102+/-0.014 nm, entirely consistent with the value expected from geometrical considerations, and the fitted line profiles are generally inconsistent with being either Lorentzian or Gaussian.

CGBayesNets: Conditional Gaussian Bayesian Network Learning and Inference with Mixed Discrete and Continuous Data

PubMed Central

Weiss, Scott T.

2014-01-01

Bayesian Networks (BN) have been a popular predictive modeling formalism in bioinformatics, but their application in modern genomics has been slowed by an inability to cleanly handle domains with mixed discrete and continuous variables. Existing free BN software packages either discretize continuous variables, which can lead to information loss, or do not include inference routines, which makes prediction with the BN impossible. We present CGBayesNets, a BN package focused around prediction of a clinical phenotype from mixed discrete and continuous variables, which fills these gaps. CGBayesNets implements Bayesian likelihood and inference algorithms for the conditional Gaussian Bayesian network (CGBNs) formalism, one appropriate for predicting an outcome of interest from, e.g., multimodal genomic data. We provide four different network learning algorithms, each making a different tradeoff between computational cost and network likelihood. CGBayesNets provides a full suite of functions for model exploration and verification, including cross validation, bootstrapping, and AUC manipulation. We highlight several results obtained previously with CGBayesNets, including predictive models of wood properties from tree genomics, leukemia subtype classification from mixed genomic data, and robust prediction of intensive care unit mortality outcomes from metabolomic profiles. We also provide detailed example analysis on public metabolomic and gene expression datasets. CGBayesNets is implemented in MATLAB and available as MATLAB source code, under an Open Source license and anonymous download at http://www.cgbayesnets.com. PMID:24922310

CGBayesNets: conditional Gaussian Bayesian network learning and inference with mixed discrete and continuous data.

PubMed

McGeachie, Michael J; Chang, Hsun-Hsien; Weiss, Scott T

2014-06-01

Bayesian Networks (BN) have been a popular predictive modeling formalism in bioinformatics, but their application in modern genomics has been slowed by an inability to cleanly handle domains with mixed discrete and continuous variables. Existing free BN software packages either discretize continuous variables, which can lead to information loss, or do not include inference routines, which makes prediction with the BN impossible. We present CGBayesNets, a BN package focused around prediction of a clinical phenotype from mixed discrete and continuous variables, which fills these gaps. CGBayesNets implements Bayesian likelihood and inference algorithms for the conditional Gaussian Bayesian network (CGBNs) formalism, one appropriate for predicting an outcome of interest from, e.g., multimodal genomic data. We provide four different network learning algorithms, each making a different tradeoff between computational cost and network likelihood. CGBayesNets provides a full suite of functions for model exploration and verification, including cross validation, bootstrapping, and AUC manipulation. We highlight several results obtained previously with CGBayesNets, including predictive models of wood properties from tree genomics, leukemia subtype classification from mixed genomic data, and robust prediction of intensive care unit mortality outcomes from metabolomic profiles. We also provide detailed example analysis on public metabolomic and gene expression datasets. CGBayesNets is implemented in MATLAB and available as MATLAB source code, under an Open Source license and anonymous download at http://www.cgbayesnets.com.

Vector Antenna and Maximum Likelihood Imaging for Radio Astronomy

DTIC Science & Technology

2016-03-05

Maximum Likelihood Imaging for Radio Astronomy Mary Knapp1, Frank Robey2, Ryan Volz3, Frank Lind3, Alan Fenn2, Alex Morris2, Mark Silver2, Sarah Klein2...haystack.mit.edu Abstract1— Radio astronomy using frequencies less than ~100 MHz provides a window into non-thermal processes in objects ranging from planets...observational astronomy . Ground-based observatories including LOFAR [1], LWA [2], [3], MWA [4], and the proposed SKA-Low [5], [6] are improving access to

A maximum pseudo-profile likelihood estimator for the Cox model under length-biased sampling

PubMed Central

Huang, Chiung-Yu; Qin, Jing; Follmann, Dean A.

2012-01-01

This paper considers semiparametric estimation of the Cox proportional hazards model for right-censored and length-biased data arising from prevalent sampling. To exploit the special structure of length-biased sampling, we propose a maximum pseudo-profile likelihood estimator, which can handle time-dependent covariates and is consistent under covariate-dependent censoring. Simulation studies show that the proposed estimator is more efficient than its competitors. A data analysis illustrates the methods and theory. PMID:23843659

The effect of lossy image compression on image classification

NASA Technical Reports Server (NTRS)

Paola, Justin D.; Schowengerdt, Robert A.

1995-01-01

We have classified four different images, under various levels of JPEG compression, using the following classification algorithms: minimum-distance, maximum-likelihood, and neural network. The training site accuracy and percent difference from the original classification were tabulated for each image compression level, with maximum-likelihood showing the poorest results. In general, as compression ratio increased, the classification retained its overall appearance, but much of the pixel-to-pixel detail was eliminated. We also examined the effect of compression on spatial pattern detection using a neural network.

Generation of vector beams using a double-wedge depolarizer: Non-quantum entanglement

NASA Astrophysics Data System (ADS)

Samlan, C. T.; Viswanathan, Nirmal K.

2016-07-01

Propagation of horizontally polarized Gaussian beam through a double-wedge depolarizer generates vector beams with spatially varying state of polarization. Jones calculus is used to show that such beams are maximally nonseparable on the basis of even (Gaussian)-odd (Hermite-Gaussian) mode parity and horizontal-vertical polarization state. The maximum nonseparability in the two degrees of freedom of the vector beam at the double wedge depolarizer output is verified experimentally using a modified Sagnac interferometer and linear analyser projected interferograms to measure the concurrence 0.94±0.002 and violation of Clauser-Horne-Shimony-Holt form of Bell-like inequality 2.704±0.024. The investigation is carried out in the context of the use of vector beams for metrological applications.

THESEUS: maximum likelihood superpositioning and analysis of macromolecular structures

PubMed Central

Theobald, Douglas L.; Wuttke, Deborah S.

2008-01-01

Summary THESEUS is a command line program for performing maximum likelihood (ML) superpositions and analysis of macromolecular structures. While conventional superpositioning methods use ordinary least-squares (LS) as the optimization criterion, ML superpositions provide substantially improved accuracy by down-weighting variable structural regions and by correcting for correlations among atoms. ML superpositioning is robust and insensitive to the specific atoms included in the analysis, and thus it does not require subjective pruning of selected variable atomic coordinates. Output includes both likelihood-based and frequentist statistics for accurate evaluation of the adequacy of a superposition and for reliable analysis of structural similarities and differences. THESEUS performs principal components analysis for analyzing the complex correlations found among atoms within a structural ensemble. PMID:16777907

Crossing statistics of laser light scattered through a nanofluid.

PubMed

Arshadi Pirlar, M; Movahed, S M S; Razzaghi, D; Karimzadeh, R

2017-09-01

In this paper, we investigate the crossing statistics of speckle patterns formed in the Fresnel diffraction region by a laser beam scattering through a nanofluid. We extend zero-crossing statistics to assess the dynamical properties of the nanofluid. According to the joint probability density function of laser beam fluctuation and its time derivative, the theoretical frameworks for Gaussian and non-Gaussian regimes are revisited. We count the number of crossings not only at zero level but also for all available thresholds to determine the average speed of moving particles. Using a probabilistic framework in determining crossing statistics, a priori Gaussianity is not essentially considered; therefore, even in the presence of deviation from Gaussian fluctuation, this modified approach is capable of computing relevant quantities, such as mean value of speed, more precisely. Generalized total crossing, which represents the weighted summation of crossings for all thresholds to quantify small deviation from Gaussian statistics, is introduced. This criterion can also manipulate the contribution of noises and trends to infer reliable physical quantities. The characteristic time scale for having successive crossings at a given threshold is defined. In our experimental setup, we find that increasing sample temperature leads to more consistency between Gaussian and perturbative non-Gaussian predictions. The maximum number of crossings does not necessarily occur at mean level, indicating that we should take into account other levels in addition to zero level to achieve more accurate assessments.

Sunspot Time Series - Relations Inferred from the Location of the Longest Spotless Segments

NASA Astrophysics Data System (ADS)

Zięba, Stanisław; Nieckarz, Zenon

2012-06-01

Spotless days ( i.e., days when no sunspots are observed on the Sun) occur during the interval between the declining phase of the old sunspot cycle and the rising phase of the new sunspot cycle, being greatest in number and of longest continuous length near a new cycle minimum. In this paper, we introduce the concept of the longest spotless segment (LSS) and examine its statistical relation to selected characteristic points in the sunspot time series (STS), such as the occurrences of first spotless day and sunspot maximum. The analysis has revealed statistically significant relations that appear to be of predictive value. For example, for Cycle 24 the last spotless day during its rising phase should be about August 2012 (± 9.1 months), the daily maximum sunspot number should be about 227 (± 50; occurring about January 2014±9.5 months), and the maximum Gaussian smoothed sunspot number should be about 87 (± 25; occurring about July 2014). Using the Gaussian-filtered values, slightly earlier dates of August 2011 and March 2013 are indicated for the last spotless day and sunspot maximum for Cycle 24, respectively.

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.

A maximum likelihood algorithm for genome mapping of cytogenetic loci from meiotic configuration data.

PubMed Central

Reyes-Valdés, M H; Stelly, D M

1995-01-01

Frequencies of meiotic configurations in cytogenetic stocks are dependent on chiasma frequencies in segments defined by centromeres, breakpoints, and telomeres. The expectation maximization algorithm is proposed as a general method to perform maximum likelihood estimations of the chiasma frequencies in the intervals between such locations. The estimates can be translated via mapping functions into genetic maps of cytogenetic landmarks. One set of observational data was analyzed to exemplify application of these methods, results of which were largely concordant with other comparable data. The method was also tested by Monte Carlo simulation of frequencies of meiotic configurations from a monotelodisomic translocation heterozygote, assuming six different sample sizes. The estimate averages were always close to the values given initially to the parameters. The maximum likelihood estimation procedures can be extended readily to other kinds of cytogenetic stocks and allow the pooling of diverse cytogenetic data to collectively estimate lengths of segments, arms, and chromosomes. Images Fig. 1 PMID:7568226

Comparisons of neural networks to standard techniques for image classification and correlation

NASA Technical Reports Server (NTRS)

Paola, Justin D.; Schowengerdt, Robert A.

1994-01-01

Neural network techniques for multispectral image classification and spatial pattern detection are compared to the standard techniques of maximum-likelihood classification and spatial correlation. The neural network produced a more accurate classification than maximum-likelihood of a Landsat scene of Tucson, Arizona. Some of the errors in the maximum-likelihood classification are illustrated using decision region and class probability density plots. As expected, the main drawback to the neural network method is the long time required for the training stage. The network was trained using several different hidden layer sizes to optimize both the classification accuracy and training speed, and it was found that one node per class was optimal. The performance improved when 3x3 local windows of image data were entered into the net. This modification introduces texture into the classification without explicit calculation of a texture measure. Larger windows were successfully used for the detection of spatial features in Landsat and Magellan synthetic aperture radar imagery.

Handling Missing Data With Multilevel Structural Equation Modeling and Full Information Maximum Likelihood Techniques.

PubMed

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.

Methods for estimating drought streamflow probabilities for Virginia streams

USGS Publications Warehouse

Austin, Samuel H.

2014-01-01

Maximum likelihood logistic regression model equations used to estimate drought flow probabilities for Virginia streams are presented for 259 hydrologic basins in Virginia. Winter streamflows were used to estimate the likelihood of streamflows during the subsequent drought-prone summer months. The maximum likelihood logistic regression models identify probable streamflows from 5 to 8 months in advance. More than 5 million streamflow daily values collected over the period of record (January 1, 1900 through May 16, 2012) were compiled and analyzed over a minimum 10-year (maximum 112-year) period of record. The analysis yielded the 46,704 equations with statistically significant fit statistics and parameter ranges published in two tables in this report. These model equations produce summer month (July, August, and September) drought flow threshold probabilities as a function of streamflows during the previous winter months (November, December, January, and February). Example calculations are provided, demonstrating how to use the equations to estimate probable streamflows as much as 8 months in advance.

DECONV-TOOL: An IDL based deconvolution software package

NASA Technical Reports Server (NTRS)

Varosi, F.; Landsman, W. B.

1992-01-01

There are a variety of algorithms for deconvolution of blurred images, each having its own criteria or statistic to be optimized in order to estimate the original image data. Using the Interactive Data Language (IDL), we have implemented the Maximum Likelihood, Maximum Entropy, Maximum Residual Likelihood, and sigma-CLEAN algorithms in a unified environment called DeConv_Tool. Most of the algorithms have as their goal the optimization of statistics such as standard deviation and mean of residuals. Shannon entropy, log-likelihood, and chi-square of the residual auto-correlation are computed by DeConv_Tool for the purpose of determining the performance and convergence of any particular method and comparisons between methods. DeConv_Tool allows interactive monitoring of the statistics and the deconvolved image during computation. The final results, and optionally, the intermediate results, are stored in a structure convenient for comparison between methods and review of the deconvolution computation. The routines comprising DeConv_Tool are available via anonymous FTP through the IDL Astronomy User's Library.

F-8C adaptive flight control laws

NASA Technical Reports Server (NTRS)

Hartmann, G. L.; Harvey, C. A.; Stein, G.; Carlson, D. N.; Hendrick, R. C.

1977-01-01

Three candidate digital adaptive control laws were designed for NASA's F-8C digital flyby wire aircraft. Each design used the same control laws but adjusted the gains with a different adaptative algorithm. The three adaptive concepts were: high-gain limit cycle, Liapunov-stable model tracking, and maximum likelihood estimation. Sensors were restricted to conventional inertial instruments (rate gyros and accelerometers) without use of air-data measurements. Performance, growth potential, and computer requirements were used as criteria for selecting the most promising of these candidates for further refinement. The maximum likelihood concept was selected primarily because it offers the greatest potential for identifying several aircraft parameters and hence for improved control performance in future aircraft application. In terms of identification and gain adjustment accuracy, the MLE design is slightly superior to the other two, but this has no significant effects on the control performance achievable with the F-8C aircraft. The maximum likelihood design is recommended for flight test, and several refinements to that design are proposed.

Application of maximum likelihood methods to laser Thomson scattering measurements of low density plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Washeleski, Robert L.; Meyer, Edmond J. IV; King, Lyon B.

2013-10-15

Laser Thomson scattering (LTS) is an established plasma diagnostic technique that has seen recent application to low density plasmas. It is difficult to perform LTS measurements when the scattered signal is weak as a result of low electron number density, poor optical access to the plasma, or both. Photon counting methods are often implemented in order to perform measurements in these low signal conditions. However, photon counting measurements performed with photo-multiplier tubes are time consuming and multi-photon arrivals are incorrectly recorded. In order to overcome these shortcomings a new data analysis method based on maximum likelihood estimation was developed. Themore » key feature of this new data processing method is the inclusion of non-arrival events in determining the scattered Thomson signal. Maximum likelihood estimation and its application to Thomson scattering at low signal levels is presented and application of the new processing method to LTS measurements performed in the plume of a 2-kW Hall-effect thruster is discussed.« less

Application of maximum likelihood methods to laser Thomson scattering measurements of low density plasmas.

PubMed

Washeleski, Robert L; Meyer, Edmond J; King, Lyon B

2013-10-01

Laser Thomson scattering (LTS) is an established plasma diagnostic technique that has seen recent application to low density plasmas. It is difficult to perform LTS measurements when the scattered signal is weak as a result of low electron number density, poor optical access to the plasma, or both. Photon counting methods are often implemented in order to perform measurements in these low signal conditions. However, photon counting measurements performed with photo-multiplier tubes are time consuming and multi-photon arrivals are incorrectly recorded. In order to overcome these shortcomings a new data analysis method based on maximum likelihood estimation was developed. The key feature of this new data processing method is the inclusion of non-arrival events in determining the scattered Thomson signal. Maximum likelihood estimation and its application to Thomson scattering at low signal levels is presented and application of the new processing method to LTS measurements performed in the plume of a 2-kW Hall-effect thruster is discussed.

Terawatt x-ray free-electron-laser optimization by transverse electron distribution shaping

DOE PAGES

Emma, C.; Wu, J.; Fang, K.; ...

2014-11-03

We study the dependence of the peak power of a 1.5 Å Terawatt (TW), tapered x-ray free-electron laser (FEL) on the transverse electron density distribution. Multidimensional optimization schemes for TW hard x-ray free-electron lasers are applied to the cases of transversely uniform and parabolic electron beam distributions and compared to a Gaussian distribution. The optimizations are performed for a 200 m undulator and a resonant wavelength of λ r = 1.5 Å using the fully three-dimensional FEL particle code GENESIS. The study shows that the flatter transverse electron distributions enhance optical guiding in the tapered section of the undulator andmore » increase the maximum radiation power from a maximum of 1.56 TW for a transversely Gaussian beam to 2.26 TW for the parabolic case and 2.63 TW for the uniform case. Spectral data also shows a 30%–70% reduction in energy deposited in the sidebands for the uniform and parabolic beams compared with a Gaussian. An analysis of the transverse coherence of the radiation shows the coherence area to be much larger than the beam spotsize for all three distributions, making coherent diffraction imaging experiments possible.« less

Real-Time Noise Reduction for Mossbauer Spectroscopy through Online Implementation of a Modified Kalman Filter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abrecht, David G.; Schwantes, Jon M.; Kukkadapu, Ravi K.

2015-02-01

Spectrum-processing software that incorporates a gaussian smoothing kernel within the statistics of first-order Kalman filtration has been developed to provide cross-channel spectral noise reduction for increased real-time signal-to-noise ratios for Mossbauer spectroscopy. The filter was optimized for the breadth of the gaussian using the Mossbauer spectrum of natural iron foil, and comparisons between the peak broadening, signal-to-noise ratios, and shifts in the calculated hyperfine parameters are presented. The results of optimization give a maximum improvement in the signal-to-noise ratio of 51.1% over the unfiltered spectrum at a gaussian breadth of 27 channels, or 2.5% of the total spectrum width. Themore » full-width half-maximum of the spectrum peaks showed an increase of 19.6% at this optimum point, indicating a relatively weak increase in the peak broadening relative to the signal enhancement, leading to an overall increase in the observable signal. Calculations of the hyperfine parameters showed no statistically significant deviations were introduced from the application of the filter, confirming the utility of this filter for spectroscopy applications.« less

Inverse sequential procedures for the monitoring of time series

NASA Technical Reports Server (NTRS)

Radok, Uwe; Brown, Timothy J.

1995-01-01

When one or more new values are added to a developing time series, they change its descriptive parameters (mean, variance, trend, coherence). A 'change index (CI)' is developed as a quantitative indicator that the changed parameters remain compatible with the existing 'base' data. CI formulate are derived, in terms of normalized likelihood ratios, for small samples from Poisson, Gaussian, and Chi-Square distributions, and for regression coefficients measuring linear or exponential trends. A substantial parameter change creates a rapid or abrupt CI decrease which persists when the length of the bases is changed. Except for a special Gaussian case, the CI has no simple explicit regions for tests of hypotheses. However, its design ensures that the series sampled need not conform strictly to the distribution form assumed for the parameter estimates. The use of the CI is illustrated with both constructed and observed data samples, processed with a Fortran code 'Sequitor'.

A Maximum Likelihood Approach to Determine Sensor Radiometric Response Coefficients for NPP VIIRS Reflective Solar Bands

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.

Inferring Phylogenetic Networks Using PhyloNet.

PubMed

Wen, Dingqiao; Yu, Yun; Zhu, Jiafan; Nakhleh, Luay

2018-07-01

PhyloNet was released in 2008 as a software package for representing and analyzing phylogenetic networks. At the time of its release, the main functionalities in PhyloNet consisted of measures for comparing network topologies and a single heuristic for reconciling gene trees with a species tree. Since then, PhyloNet has grown significantly. The software package now includes a wide array of methods for inferring phylogenetic networks from data sets of unlinked loci while accounting for both reticulation (e.g., hybridization) and incomplete lineage sorting. In particular, PhyloNet now allows for maximum parsimony, maximum likelihood, and Bayesian inference of phylogenetic networks from gene tree estimates. Furthermore, Bayesian inference directly from sequence data (sequence alignments or biallelic markers) is implemented. Maximum parsimony is based on an extension of the "minimizing deep coalescences" criterion to phylogenetic networks, whereas maximum likelihood and Bayesian inference are based on the multispecies network coalescent. All methods allow for multiple individuals per species. As computing the likelihood of a phylogenetic network is computationally hard, PhyloNet allows for evaluation and inference of networks using a pseudolikelihood measure. PhyloNet summarizes the results of the various analyzes and generates phylogenetic networks in the extended Newick format that is readily viewable by existing visualization software.

Regression estimators for generic health-related quality of life and quality-adjusted life years.

PubMed

Basu, Anirban; Manca, Andrea

2012-01-01

To develop regression models for outcomes with truncated supports, such as health-related quality of life (HRQoL) data, and account for features typical of such data such as a skewed distribution, spikes at 1 or 0, and heteroskedasticity. Regression estimators based on features of the Beta distribution. First, both a single equation and a 2-part model are presented, along with estimation algorithms based on maximum-likelihood, quasi-likelihood, and Bayesian Markov-chain Monte Carlo methods. A novel Bayesian quasi-likelihood estimator is proposed. Second, a simulation exercise is presented to assess the performance of the proposed estimators against ordinary least squares (OLS) regression for a variety of HRQoL distributions that are encountered in practice. Finally, the performance of the proposed estimators is assessed by using them to quantify the treatment effect on QALYs in the EVALUATE hysterectomy trial. Overall model fit is studied using several goodness-of-fit tests such as Pearson's correlation test, link and reset tests, and a modified Hosmer-Lemeshow test. The simulation results indicate that the proposed methods are more robust in estimating covariate effects than OLS, especially when the effects are large or the HRQoL distribution has a large spike at 1. Quasi-likelihood techniques are more robust than maximum likelihood estimators. When applied to the EVALUATE trial, all but the maximum likelihood estimators produce unbiased estimates of the treatment effect. One and 2-part Beta regression models provide flexible approaches to regress the outcomes with truncated supports, such as HRQoL, on covariates, after accounting for many idiosyncratic features of the outcomes distribution. This work will provide applied researchers with a practical set of tools to model outcomes in cost-effectiveness analysis.

Parameter estimation of history-dependent leaky integrate-and-fire neurons using maximum-likelihood methods

PubMed Central

Dong, Yi; Mihalas, Stefan; Russell, Alexander; Etienne-Cummings, Ralph; Niebur, Ernst

2012-01-01

When a neuronal spike train is observed, what can we say about the properties of the neuron that generated it? A natural way to answer this question is to make an assumption about the type of neuron, select an appropriate model for this type, and then to choose the model parameters as those that are most likely to generate the observed spike train. This is the maximum likelihood method. If the neuron obeys simple integrate and fire dynamics, Paninski, Pillow, and Simoncelli (2004) showed that its negative log-likelihood function is convex and that its unique global minimum can thus be found by gradient descent techniques. The global minimum property requires independence of spike time intervals. Lack of history dependence is, however, an important constraint that is not fulfilled in many biological neurons which are known to generate a rich repertoire of spiking behaviors that are incompatible with history independence. Therefore, we expanded the integrate and fire model by including one additional variable, a variable threshold (Mihalas & Niebur, 2009) allowing for history-dependent firing patterns. This neuronal model produces a large number of spiking behaviors while still being linear. Linearity is important as it maintains the distribution of the random variables and still allows for maximum likelihood methods to be used. In this study we show that, although convexity of the negative log-likelihood is not guaranteed for this model, the minimum of the negative log-likelihood function yields a good estimate for the model parameters, in particular if the noise level is treated as a free parameter. Furthermore, we show that a nonlinear function minimization method (r-algorithm with space dilation) frequently reaches the global minimum. PMID:21851282

A unified framework for penalized statistical muon tomography reconstruction with edge preservation priors of lp norm type

NASA Astrophysics Data System (ADS)

Yu, Baihui; Zhao, Ziran; Wang, Xuewu; Wu, Dufan; Zeng, Zhi; Zeng, Ming; Wang, Yi; Cheng, Jianping

2016-01-01

The Tsinghua University MUon Tomography facilitY (TUMUTY) has been built up and it is utilized to reconstruct the special objects with complex structure. Since fine image is required, the conventional Maximum likelihood Scattering and Displacement (MLSD) algorithm is employed. However, due to the statistical characteristics of muon tomography and the data incompleteness, the reconstruction is always instable and accompanied with severe noise. In this paper, we proposed a Maximum a Posterior (MAP) algorithm for muon tomography regularization, where an edge-preserving prior on the scattering density image is introduced to the object function. The prior takes the lp norm (p>0) of the image gradient magnitude, where p=1 and p=2 are the well-known total-variation (TV) and Gaussian prior respectively. The optimization transfer principle is utilized to minimize the object function in a unified framework. At each iteration the problem is transferred to solving a cubic equation through paraboloidal surrogating. To validate the method, the French Test Object (FTO) is imaged by both numerical simulation and TUMUTY. The proposed algorithm is used for the reconstruction where different norms are detailedly studied, including l2, l1, l0.5, and an l2-0.5 mixture norm. Compared with MLSD method, MAP achieves better image quality in both structure preservation and noise reduction. Furthermore, compared with the previous work where one dimensional image was acquired, we achieve the relatively clear three dimensional images of FTO, where the inner air hole and the tungsten shell is visible.

Transfer Entropy as a Log-Likelihood Ratio

NASA Astrophysics Data System (ADS)

Barnett, Lionel; Bossomaier, Terry

2012-09-01

Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology, and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic χ2 distribution is established for the transfer entropy estimator. The result generalizes the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense.

Transfer entropy as a log-likelihood ratio.

PubMed

Barnett, Lionel; Bossomaier, Terry

2012-09-28

Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology, and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic χ2 distribution is established for the transfer entropy estimator. The result generalizes the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense.

On modeling animal movements using Brownian motion with measurement error.

PubMed

Pozdnyakov, Vladimir; Meyer, Thomas; Wang, Yu-Bo; Yan, Jun

2014-02-01

Modeling animal movements with Brownian motion (or more generally by a Gaussian process) has a long tradition in ecological studies. The recent Brownian bridge movement model (BBMM), which incorporates measurement errors, has been quickly adopted by ecologists because of its simplicity and tractability. We discuss some nontrivial properties of the discrete-time stochastic process that results from observing a Brownian motion with added normal noise at discrete times. In particular, we demonstrate that the observed sequence of random variables is not Markov. Consequently the expected occupation time between two successively observed locations does not depend on just those two observations; the whole path must be taken into account. Nonetheless, the exact likelihood function of the observed time series remains tractable; it requires only sparse matrix computations. The likelihood-based estimation procedure is described in detail and compared to the BBMM estimation.

A survey of kernel-type estimators for copula and their applications

NASA Astrophysics Data System (ADS)

Sumarjaya, I. W.

2017-10-01

Copulas have been widely used to model nonlinear dependence structure. Main applications of copulas include areas such as finance, insurance, hydrology, rainfall to name but a few. The flexibility of copula allows researchers to model dependence structure beyond Gaussian distribution. Basically, a copula is a function that couples multivariate distribution functions to their one-dimensional marginal distribution functions. In general, there are three methods to estimate copula. These are parametric, nonparametric, and semiparametric method. In this article we survey kernel-type estimators for copula such as mirror reflection kernel, beta kernel, transformation method and local likelihood transformation method. Then, we apply these kernel methods to three stock indexes in Asia. The results of our analysis suggest that, albeit variation in information criterion values, the local likelihood transformation method performs better than the other kernel methods.

Accurate Structural Correlations from Maximum Likelihood Superpositions

PubMed Central

Theobald, Douglas L; Wuttke, Deborah S

2008-01-01

The cores of globular proteins are densely packed, resulting in complicated networks of structural interactions. These interactions in turn give rise to dynamic structural correlations over a wide range of time scales. Accurate analysis of these complex correlations is crucial for understanding biomolecular mechanisms and for relating structure to function. Here we report a highly accurate technique for inferring the major modes of structural correlation in macromolecules using likelihood-based statistical analysis of sets of structures. This method is generally applicable to any ensemble of related molecules, including families of nuclear magnetic resonance (NMR) models, different crystal forms of a protein, and structural alignments of homologous proteins, as well as molecular dynamics trajectories. Dominant modes of structural correlation are determined using principal components analysis (PCA) of the maximum likelihood estimate of the correlation matrix. The correlations we identify are inherently independent of the statistical uncertainty and dynamic heterogeneity associated with the structural coordinates. We additionally present an easily interpretable method (“PCA plots”) for displaying these positional correlations by color-coding them onto a macromolecular structure. Maximum likelihood PCA of structural superpositions, and the structural PCA plots that illustrate the results, will facilitate the accurate determination of dynamic structural correlations analyzed in diverse fields of structural biology. PMID:18282091

Robust Multi-Frame Adaptive Optics Image Restoration Algorithm Using Maximum Likelihood Estimation with Poisson Statistics.

PubMed

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.

Robust Multi-Frame Adaptive Optics Image Restoration Algorithm Using Maximum Likelihood Estimation with Poisson Statistics

PubMed Central

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

Evaluation of Shiryaev-Roberts procedure for on-line environmental radiation monitoring.

PubMed

Watson, Mara M; Seliman, Ayman F; Bliznyuk, Valery N; DeVol, Timothy A

2018-04-30

Water can become contaminated as a result of a leak from a nuclear facility, such as a waste facility, or from clandestine nuclear activity. Low-level on-line radiation monitoring is needed to detect these events in real time. A Bayesian control chart method, Shiryaev-Roberts (SR) procedure, was compared with classical methods, 3-σ and cumulative sum (CUSUM), for quantifying an accumulating signal from an extractive scintillating resin flow-cell detection system. Solutions containing 0.10-5.0 Bq/L of 99 Tc, as T99cO 4 - were pumped through a flow cell packed with extractive scintillating resin used in conjunction with a Beta-RAM Model 5 HPLC detector. While T99cO 4 - accumulated on the resin, time series data were collected. Control chart methods were applied to the data using statistical algorithms developed in MATLAB. SR charts were constructed using Poisson (Poisson SR) and Gaussian (Gaussian SR) probability distributions of count data to estimate the likelihood ratio. Poisson and Gaussian SR charts required less volume of radioactive solution at a fixed concentration to exceed the control limit in most cases than 3-σ and CUSUM control charts, particularly solutions with lower activity. SR is thus the ideal control chart for low-level on-line radiation monitoring. Once the control limit was exceeded, activity concentrations were estimated from the SR control chart using the control chart slope on a semi-logarithmic plot. A linear regression fit was applied to averaged slope data for five activity concentration groupings for Poisson and Gaussian SR control charts. A correlation coefficient (R 2 ) of 0.77 for Poisson SR and 0.90 for Gaussian SR suggest this method will adequately estimate activity concentration for an unknown solution. Copyright © 2018 Elsevier Ltd. All rights reserved.

Maximum-Likelihood Methods for Processing Signals From Gamma-Ray Detectors

PubMed Central

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

A novel retinal vessel extraction algorithm based on matched filtering and gradient vector flow

NASA Astrophysics Data System (ADS)

Yu, Lei; Xia, Mingliang; Xuan, Li

2013-10-01

The microvasculature network of retina plays an important role in the study and diagnosis of retinal diseases (age-related macular degeneration and diabetic retinopathy for example). Although it is possible to noninvasively acquire high-resolution retinal images with modern retinal imaging technologies, non-uniform illumination, the low contrast of thin vessels and the background noises all make it difficult for diagnosis. In this paper, we introduce a novel retinal vessel extraction algorithm based on gradient vector flow and matched filtering to segment retinal vessels with different likelihood. Firstly, we use isotropic Gaussian kernel and adaptive histogram equalization to smooth and enhance the retinal images respectively. Secondly, a multi-scale matched filtering method is adopted to extract the retinal vessels. Then, the gradient vector flow algorithm is introduced to locate the edge of the retinal vessels. Finally, we combine the results of matched filtering method and gradient vector flow algorithm to extract the vessels at different likelihood levels. The experiments demonstrate that our algorithm is efficient and the intensities of vessel images exactly represent the likelihood of the vessels.

A MATLAB toolbox for the efficient estimation of the psychometric function using the updated maximum-likelihood adaptive procedure.

PubMed

Shen, Yi; Dai, Wei; Richards, Virginia M

2015-03-01

A MATLAB toolbox for the efficient estimation of the threshold, slope, and lapse rate of the psychometric function is described. The toolbox enables the efficient implementation of the updated maximum-likelihood (UML) procedure. The toolbox uses an object-oriented architecture for organizing the experimental variables and computational algorithms, which provides experimenters with flexibility in experimental design and data management. Descriptions of the UML procedure and the UML Toolbox are provided, followed by toolbox use examples. Finally, guidelines and recommendations of parameter configurations are given.

A maximum likelihood convolutional decoder model vs experimental data comparison

NASA Technical Reports Server (NTRS)

Chen, R. Y.

1979-01-01

This article describes the comparison of a maximum likelihood convolutional decoder (MCD) prediction model and the actual performance of the MCD at the Madrid Deep Space Station. The MCD prediction model is used to develop a subroutine that has been utilized by the Telemetry Analysis Program (TAP) to compute the MCD bit error rate for a given signal-to-noise ratio. The results indicate that that the TAP can predict quite well compared to the experimental measurements. An optimal modulation index also can be found through TAP.

Analysis of crackling noise using the maximum-likelihood method: Power-law mixing and exponential damping.

PubMed

Salje, Ekhard K H; Planes, Antoni; Vives, Eduard

2017-10-01

Crackling noise can be initiated by competing or coexisting mechanisms. These mechanisms can combine to generate an approximate scale invariant distribution that contains two or more contributions. The overall distribution function can be analyzed, to a good approximation, using maximum-likelihood methods and assuming that it follows a power law although with nonuniversal exponents depending on a varying lower cutoff. We propose that such distributions are rather common and originate from a simple superposition of crackling noise distributions or exponential damping.

Comparison of two weighted integration models for the cueing task: linear and likelihood

NASA Technical Reports Server (NTRS)

Shimozaki, Steven S.; Eckstein, Miguel P.; Abbey, Craig K.

2003-01-01

In a task in which the observer must detect a signal at two locations, presenting a precue that predicts the location of a signal leads to improved performance with a valid cue (signal location matches the cue), compared to an invalid cue (signal location does not match the cue). The cue validity effect has often been explained with a limited capacity attentional mechanism improving the perceptual quality at the cued location. Alternatively, the cueing effect can also be explained by unlimited capacity models that assume a weighted combination of noisy responses across the two locations. We compare two weighted integration models, a linear model and a sum of weighted likelihoods model based on a Bayesian observer. While qualitatively these models are similar, quantitatively they predict different cue validity effects as the signal-to-noise ratios (SNR) increase. To test these models, 3 observers performed in a cued discrimination task of Gaussian targets with an 80% valid precue across a broad range of SNR's. Analysis of a limited capacity attentional switching model was also included and rejected. The sum of weighted likelihoods model best described the psychophysical results, suggesting that human observers approximate a weighted combination of likelihoods, and not a weighted linear combination.

The Topology of Large-Scale Structure in the 1.2 Jy IRAS Redshift Survey

NASA Astrophysics Data System (ADS)

Protogeros, Zacharias A. M.; Weinberg, David H.

1997-11-01

We measure the topology (genus) of isodensity contour surfaces in volume-limited subsets of the 1.2 Jy IRAS redshift survey, for smoothing scales λ = 4, 7, and 12 h-1 Mpc. At 12 h-1 Mpc, the observed genus curve has a symmetric form similar to that predicted for a Gaussian random field. At the shorter smoothing lengths, the observed genus curve shows a modest shift in the direction of an isolated cluster or ``meatball'' topology. We use mock catalogs drawn from cosmological N-body simulations to investigate the systematic biases that affect topology measurements in samples of this size and to determine the full covariance matrix of the expected random errors. We incorporate the error correlations into our evaluations of theoretical models, obtaining both frequentist assessments of absolute goodness of fit and Bayesian assessments of models' relative likelihoods. We compare the observed topology of the 1.2 Jy survey to the predictions of dynamically evolved, unbiased, gravitational instability models that have Gaussian initial conditions. The model with an n = -1 power-law initial power spectrum achieves the best overall agreement with the data, though models with a low-density cold dark matter power spectrum and an n = 0 power-law spectrum are also consistent. The observed topology is inconsistent with an initially Gaussian model that has n = -2, and it is strongly inconsistent with a Voronoi foam model, which has a non-Gaussian, bubble topology.

Likelihood-based modification of experimental crystal structure electron density maps

DOEpatents

Terwilliger, Thomas C [Sante Fe, NM

2005-04-16

A maximum-likelihood method for improves an electron density map of an experimental crystal structure. A likelihood of a set of structure factors {F.sub.h } is formed for the experimental crystal structure as (1) the likelihood of having obtained an observed set of structure factors {F.sub.h.sup.OBS } if structure factor set {F.sub.h } was correct, and (2) the likelihood that an electron density map resulting from {F.sub.h } is consistent with selected prior knowledge about the experimental crystal structure. The set of structure factors {F.sub.h } is then adjusted to maximize the likelihood of {F.sub.h } for the experimental crystal structure. An improved electron density map is constructed with the maximized structure factors.

TH-AB-209-03: Overcoming Resolution Limitations of Diffuse Optical Signals in X-Ray Induced Luminescence (XIL) Imaging Via Selective Plane Illumination and 2D Deconvolution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quigley, B; Smith, C; La Riviere, P

2016-06-15

Purpose: To evaluate the resolution and sensitivity of XIL imaging using a surface radiance simulation based on optical diffusion and maximum likelihood expectation maximization (MLEM) image reconstruction. XIL imaging seeks to determine the distribution of luminescent nanophosphors, which could be used as nanodosimeters or radiosensitizers. Methods: The XIL simulation generated a homogeneous slab with optical properties similar to tissue. X-ray activated nanophosphors were placed at 1.0 cm depth in the tissue in concentrations of 10{sup −4} g/mL in two volumes of 10 mm{sup 3} with varying separations between each other. An analytical optical diffusion model determined the surface radiance frommore » the photon distributions generated at depth in the tissue by the nanophosphors. The simulation then determined the detected luminescent signal collected with a f/1.0 aperture lens and back-illuminated EMCCD camera. The surface radiance was deconvolved using a MLEM algorithm to estimate the nanophosphors distribution and the resolution. To account for both Poisson and Gaussian noise, a shifted Poisson imaging model was used in the deconvolution. The deconvolved distributions were fitted to a Gaussian after radial averaging to measure the full width at half maximum (FWHM) and the peak to peak distance between distributions was measured to determine the resolving power. Results: Simulated surface radiances for doses from 1mGy to 100 cGy were computed. Each image was deconvolved using 1000 iterations. At 1mGy, deconvolution reduced the FWHM of the nanophosphors distribution by 65% and had a resolving power is 3.84 mm. Decreasing the dose from 100 cGy to 1 mGy increased the FWHM by 22% but allowed for a dose reduction of a factor of 1000. Conclusion: Deconvolving the detected surface radiance allows for dose reduction while maintaining the resolution of the nanophosphors. It proves to be a useful technique in overcoming the resolution limitations of diffuse optical imaging in tissue. C. S. acknowledges support from the NIH National Institute of General Medical Sciences (Award number R25GM109439, Project Title: University of Chicago Initiative for Maximizing Student Development, IMSD). B. Q. and P. L. acknowledge support from NIH grant R01EB017293.« less

Gaussian quantum steering and its asymmetry in curved spacetime

NASA Astrophysics Data System (ADS)

Wang, Jieci; Cao, Haixin; Jing, Jiliang; Fan, Heng

2016-06-01

We study Gaussian quantum steering and its asymmetry in the background of a Schwarzschild black hole. We present a Gaussian channel description of quantum state evolution under the influence of Hawking radiation. We find that thermal noise introduced by the Hawking effect will destroy the steerability between an inertial observer Alice and an accelerated observer Bob who hovers outside the event horizon, while it generates steerability between Bob and a hypothetical observer anti-Bob inside the event horizon. Unlike entanglement behaviors in curved spacetime, here the steering from Alice to Bob suffers from a "sudden death" and the steering from anti-Bob to Bob experiences a "sudden birth" with increasing Hawking temperature. We also find that the Gaussian steering is always asymmetric and the maximum steering asymmetry cannot exceed ln 2 , which means the state never evolves to an extremal asymmetry state. Furthermore, we obtain the parameter settings that maximize steering asymmetry and find that (i) s =arccosh cosh/2r 1 -sinh2r is the critical point of steering asymmetry and (ii) the attainment of maximal steering asymmetry indicates the transition between one-way steerability and both-way steerability for the two-mode Gaussian state under the influence of Hawking radiation.

THE DISTRIBUTION OF COOK’S D STATISTIC

PubMed Central

Muller, Keith E.; Mok, Mario Chen

2013-01-01

Cook (1977) proposed a diagnostic to quantify the impact of deleting an observation on the estimated regression coefficients of a General Linear Univariate Model (GLUM). Simulations of models with Gaussian response and predictors demonstrate that his suggestion of comparing the diagnostic to the median of the F for overall regression captures an erratically varying proportion of the values. We describe the exact distribution of Cook’s statistic for a GLUM with Gaussian predictors and response. We also present computational forms, simple approximations, and asymptotic results. A simulation supports the accuracy of the results. The methods allow accurate evaluation of a single value or the maximum value from a regression analysis. The approximations work well for a single value, but less well for the maximum. In contrast, the cut-point suggested by Cook provides widely varying tail probabilities. As with all diagnostics, the data analyst must use scientific judgment in deciding how to treat highlighted observations. PMID:24363487

Phylogenetic place of guinea pigs: no support of the rodent-polyphyly hypothesis from maximum-likelihood analyses of multiple protein sequences.

PubMed

Cao, Y; Adachi, J; Yano, T; Hasegawa, M

1994-07-01

Graur et al.'s (1991) hypothesis that the guinea pig-like rodents have an evolutionary origin within mammals that is separate from that of other rodents (the rodent-polyphyly hypothesis) was reexamined by the maximum-likelihood method for protein phylogeny, as well as by the maximum-parsimony and neighbor-joining methods. The overall evidence does not support Graur et al.'s hypothesis, which radically contradicts the traditional view of rodent monophyly. This work demonstrates that we must be careful in choosing a proper method for phylogenetic inference and that an argument based on a small data set (with respect to the length of the sequence and especially the number of species) may be unstable.

Task Performance with List-Mode Data

NASA Astrophysics Data System (ADS)

Caucci, Luca

This dissertation investigates the application of list-mode data to detection, estimation, and image reconstruction problems, with an emphasis on emission tomography in medical imaging. We begin by introducing a theoretical framework for list-mode data and we use it to define two observers that operate on list-mode data. These observers are applied to the problem of detecting a signal (known in shape and location) buried in a random lumpy background. We then consider maximum-likelihood methods for the estimation of numerical parameters from list-mode data, and we characterize the performance of these estimators via the so-called Fisher information matrix. Reconstruction from PET list-mode data is then considered. In a process we called "double maximum-likelihood" reconstruction, we consider a simple PET imaging system and we use maximum-likelihood methods to first estimate a parameter vector for each pair of gamma-ray photons that is detected by the hardware. The collection of these parameter vectors forms a list, which is then fed to another maximum-likelihood algorithm for volumetric reconstruction over a grid of voxels. Efficient parallel implementation of the algorithms discussed above is then presented. In this work, we take advantage of two low-cost, mass-produced computing platforms that have recently appeared on the market, and we provide some details on implementing our algorithms on these devices. We conclude this dissertation work by elaborating on a possible application of list-mode data to X-ray digital mammography. We argue that today's CMOS detectors and computing platforms have become fast enough to make X-ray digital mammography list-mode data acquisition and processing feasible.

Improved relocatable over-the-horizon radar detection and tracking using the maximum likelihood adaptive neural system algorithm

NASA Astrophysics Data System (ADS)

Perlovsky, Leonid I.; Webb, Virgil H.; Bradley, Scott R.; Hansen, Christopher A.

1998-07-01

An advanced detection and tracking system is being developed for the U.S. Navy's Relocatable Over-the-Horizon Radar (ROTHR) to provide improved tracking performance against small aircraft typically used in drug-smuggling activities. The development is based on the Maximum Likelihood Adaptive Neural System (MLANS), a model-based neural network that combines advantages of neural network and model-based algorithmic approaches. The objective of the MLANS tracker development effort is to address user requirements for increased detection and tracking capability in clutter and improved track position, heading, and speed accuracy. The MLANS tracker is expected to outperform other approaches to detection and tracking for the following reasons. It incorporates adaptive internal models of target return signals, target tracks and maneuvers, and clutter signals, which leads to concurrent clutter suppression, detection, and tracking (track-before-detect). It is not combinatorial and thus does not require any thresholding or peak picking and can track in low signal-to-noise conditions. It incorporates superresolution spectrum estimation techniques exceeding the performance of conventional maximum likelihood and maximum entropy methods. The unique spectrum estimation method is based on the Einsteinian interpretation of the ROTHR received energy spectrum as a probability density of signal frequency. The MLANS neural architecture and learning mechanism are founded on spectrum models and maximization of the "Einsteinian" likelihood, allowing knowledge of the physical behavior of both targets and clutter to be injected into the tracker algorithms. The paper describes the addressed requirements and expected improvements, theoretical foundations, engineering methodology, and results of the development effort to date.

SPECT reconstruction using DCT-induced tight framelet regularization

NASA Astrophysics Data System (ADS)

Zhang, Jiahan; Li, Si; Xu, Yuesheng; Schmidtlein, C. R.; Lipson, Edward D.; Feiglin, David H.; Krol, Andrzej

2015-03-01

Wavelet transforms have been successfully applied in many fields of image processing. Yet, to our knowledge, they have never been directly incorporated to the objective function in Emission Computed Tomography (ECT) image reconstruction. Our aim has been to investigate if the ℓ1-norm of non-decimated discrete cosine transform (DCT) coefficients of the estimated radiotracer distribution could be effectively used as the regularization term for the penalized-likelihood (PL) reconstruction, where a regularizer is used to enforce the image smoothness in the reconstruction. In this study, the ℓ1-norm of 2D DCT wavelet decomposition was used as a regularization term. The Preconditioned Alternating Projection Algorithm (PAPA), which we proposed in earlier work to solve penalized likelihood (PL) reconstruction with non-differentiable regularizers, was used to solve this optimization problem. The DCT wavelet decompositions were performed on the transaxial reconstructed images. We reconstructed Monte Carlo simulated SPECT data obtained for a numerical phantom with Gaussian blobs as hot lesions and with a warm random lumpy background. Reconstructed images using the proposed method exhibited better noise suppression and improved lesion conspicuity, compared with images reconstructed using expectation maximization (EM) algorithm with Gaussian post filter (GPF). Also, the mean square error (MSE) was smaller, compared with EM-GPF. A critical and challenging aspect of this method was selection of optimal parameters. In summary, our numerical experiments demonstrated that the ℓ1-norm of discrete cosine transform (DCT) wavelet frame transform DCT regularizer shows promise for SPECT image reconstruction using PAPA method.

Approximate Bayesian computation for forward modeling in cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akeret, Joël; Refregier, Alexandre; Amara, Adam

Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In many practical situations, the likelihood function may however be unavailable or intractable due to non-gaussian errors, non-linear measurements processes, or complex data formats such as catalogs and maps. In these cases, the simulation of mock data sets can often be made through forward modeling. We discuss how Approximate Bayesian Computation (ABC) can be used in these cases to derive an approximation to themore » posterior constraints using simulated data sets. This technique relies on the sampling of the parameter set, a distance metric to quantify the difference between the observation and the simulations and summary statistics to compress the information in the data. We first review the principles of ABC and discuss its implementation using a Population Monte-Carlo (PMC) algorithm and the Mahalanobis distance metric. We test the performance of the implementation using a Gaussian toy model. We then apply the ABC technique to the practical case of the calibration of image simulations for wide field cosmological surveys. We find that the ABC analysis is able to provide reliable parameter constraints for this problem and is therefore a promising technique for other applications in cosmology and astrophysics. Our implementation of the ABC PMC method is made available via a public code release.« less

Histogram equalization with Bayesian estimation for noise robust speech recognition.

PubMed

Suh, Youngjoo; Kim, Hoirin

2018-02-01

The histogram equalization approach is an efficient feature normalization technique for noise robust automatic speech recognition. However, it suffers from performance degradation when some fundamental conditions are not satisfied in the test environment. To remedy these limitations of the original histogram equalization methods, class-based histogram equalization approach has been proposed. Although this approach showed substantial performance improvement under noise environments, it still suffers from performance degradation due to the overfitting problem when test data are insufficient. To address this issue, the proposed histogram equalization technique employs the Bayesian estimation method in the test cumulative distribution function estimation. It was reported in a previous study conducted on the Aurora-4 task that the proposed approach provided substantial performance gains in speech recognition systems based on the acoustic modeling of the Gaussian mixture model-hidden Markov model. In this work, the proposed approach was examined in speech recognition systems with deep neural network-hidden Markov model (DNN-HMM), the current mainstream speech recognition approach where it also showed meaningful performance improvement over the conventional maximum likelihood estimation-based method. The fusion of the proposed features with the mel-frequency cepstral coefficients provided additional performance gains in DNN-HMM systems, which otherwise suffer from performance degradation in the clean test condition.

A Recommended Procedure for Estimating the Cosmic-Ray Spectral Parameter of a Simple Power Law With Applications to Detector Design

NASA Technical Reports Server (NTRS)

Howell, L. W.

2001-01-01

A simple power law model consisting of a single spectral index alpha-1 is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV. Two procedures for estimating alpha-1 the method of moments and maximum likelihood (ML), are developed and their statistical performance compared. It is concluded that the ML procedure attains the most desirable statistical properties and is hence the recommended statistical estimation procedure for estimating alpha-1. The ML procedure is then generalized for application to a set of real cosmic-ray data and thereby makes this approach applicable to existing cosmic-ray data sets. Several other important results, such as the relationship between collecting power and detector energy resolution, as well as inclusion of a non-Gaussian detector response function, are presented. These results have many practical benefits in the design phase of a cosmic-ray detector as they permit instrument developers to make important trade studies in design parameters as a function of one of the science objectives. This is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose rigorous practical limits to the design envelope.

Spectroscopic identification of individual fluorophores using photoluminescence excitation spectra.

PubMed

Czerski, J; Colomb, W; Cannataro, F; Sarkar, S K

2018-01-25

The identity of a fluorophore can be ambiguous if other fluorophores or nonspecific fluorescent impurities have overlapping emission spectra. The presence of overlapping spectra makes it difficult to differentiate fluorescent species using discrete detection channels and unmixing of spectra. The unique absorption and emission signatures of fluorophores provide an opportunity for spectroscopic identification. However, absorption spectroscopy may be affected by scattering, whereas fluorescence emission spectroscopy suffers from signal loss by gratings or other dispersive optics. Photoluminescence excitation spectra, where excitation is varied and emission is detected at a fixed wavelength, allows hyperspectral imaging with a single emission filter for high signal-to-background ratio without any moving optics on the emission side. We report a high throughput method for measuring the photoluminescence excitation spectra of individual fluorophores using a tunable supercontinuum laser and prism-type total internal reflection fluorescence microscope. We used the system to measure and sort the photoluminescence excitation spectra of individual Alexa dyes, fluorescent nanodiamonds (FNDs), and fluorescent polystyrene beads. We used a Gaussian mixture model with maximum likelihood estimation to objectively separate the spectra. Finally, we spectroscopically identified different species of fluorescent nanodiamonds with overlapping spectra and characterized the heterogeneity of fluorescent nanodiamonds of varying size. © 2018 The Authors Journal of Microscopy © 2018 Royal Microscopical Society.

A fresh approach to forecasting in astroparticle physics and dark matter searches

NASA Astrophysics Data System (ADS)

Edwards, Thomas D. P.; Weniger, Christoph

2018-02-01

We present a toolbox of new techniques and concepts for the efficient forecasting of experimental sensitivities. These are applicable to a large range of scenarios in (astro-)particle physics, and based on the Fisher information formalism. Fisher information provides an answer to the question 'what is the maximum extractable information from a given observation?'. It is a common tool for the forecasting of experimental sensitivities in many branches of science, but rarely used in astroparticle physics or searches for particle dark matter. After briefly reviewing the Fisher information matrix of general Poisson likelihoods, we propose very compact expressions for estimating expected exclusion and discovery limits ('equivalent counts method'). We demonstrate by comparison with Monte Carlo results that they remain surprisingly accurate even deep in the Poisson regime. We show how correlated background systematics can be efficiently accounted for by a treatment based on Gaussian random fields. Finally, we introduce the novel concept of Fisher information flux. It can be thought of as a generalization of the commonly used signal-to-noise ratio, while accounting for the non-local properties and saturation effects of background and instrumental uncertainties. It is a powerful and flexible tool ready to be used as core concept for informed strategy development in astroparticle physics and searches for particle dark matter.

Bayes classification of interferometric TOPSAR data

NASA Technical Reports Server (NTRS)

Michel, T. R.; Rodriguez, E.; Houshmand, B.; Carande, R.

1995-01-01

We report the Bayes classification of terrain types at different sites using airborne interferometric synthetic aperture radar (INSAR) data. A Gaussian maximum likelihood classifier was applied on multidimensional observations derived from the SAR intensity, the terrain elevation model, and the magnitude of the interferometric correlation. Training sets for forested, urban, agricultural, or bare areas were obtained either by selecting samples with known ground truth, or by k-means clustering of random sets of samples uniformly distributed across all sites, and subsequent assignments of these clusters using ground truth. The accuracy of the classifier was used to optimize the discriminating efficiency of the set of features that was chosen. The most important features include the SAR intensity, a canopy penetration depth model, and the terrain slope. We demonstrate the classifier's performance across sites using a unique set of training classes for the four main terrain categories. The scenes examined include San Francisco (CA) (predominantly urban and water), Mount Adams (WA) (forested with clear cuts), Pasadena (CA) (urban with mountains), and Antioch Hills (CA) (water, swamps, fields). Issues related to the effects of image calibration and the robustness of the classification to calibration errors are explored. The relative performance of single polarization Interferometric data classification is contrasted against classification schemes based on polarimetric SAR data.

Sensor data fusion for spectroscopy-based detection of explosives

NASA Astrophysics Data System (ADS)

Shah, Pratik V.; Singh, Abhijeet; Agarwal, Sanjeev; Sedigh, Sahra; Ford, Alan; Waterbury, Robert

2009-05-01

In-situ trace detection of explosive compounds such as RDX, TNT, and ammonium nitrate, is an important problem for the detection of IEDs and IED precursors. Spectroscopic techniques such as LIBS and Raman have shown promise for the detection of residues of explosive compounds on surfaces from standoff distances. Individually, both LIBS and Raman techniques suffer from various limitations, e.g., their robustness and reliability suffers due to variations in peak strengths and locations. However, the orthogonal nature of the spectral and compositional information provided by these techniques makes them suitable candidates for the use of sensor fusion to improve the overall detection performance. In this paper, we utilize peak energies in a region by fitting Lorentzian or Gaussian peaks around the location of interest. The ratios of peak energies are used for discrimination, in order to normalize the effect of changes in overall signal strength. Two data fusion techniques are discussed in this paper. Multi-spot fusion is performed on a set of independent samples from the same region based on the maximum likelihood formulation. Furthermore, the results from LIBS and Raman sensors are fused using linear discriminators. Improved detection performance with significantly reduced false alarm rates is reported using fusion techniques on data collected for sponsor demonstration at Fort Leonard Wood.

Spatiotemporal modelling of groundwater extraction in semi-arid central Queensland, Australia

NASA Astrophysics Data System (ADS)

Keir, Greg; Bulovic, Nevenka; McIntyre, Neil

2016-04-01

The semi-arid Surat Basin in central Queensland, Australia, forms part of the Great Artesian Basin, a groundwater resource of national significance. While this area relies heavily on groundwater supply bores to sustain agricultural industries and rural life in general, measurement of groundwater extraction rates is very limited. Consequently, regional groundwater extraction rates are not well known, which may have implications for regional numerical groundwater modelling. However, flows from a small number of bores are metered, and less precise anecdotal estimates of extraction are increasingly available. There is also an increasing number of other spatiotemporal datasets which may help predict extraction rates (e.g. rainfall, temperature, soils, stocking rates etc.). These can be used to construct spatial multivariate regression models to estimate extraction. The data exhibit complicated statistical features, such as zero-valued observations, non-Gaussianity, and non-stationarity, which limit the use of many classical estimation techniques, such as kriging. As well, water extraction histories may exhibit temporal autocorrelation. To account for these features, we employ a separable space-time model to predict bore extraction rates using the R-INLA package for computationally efficient Bayesian inference. A joint approach is used to model both the probability (using a binomial likelihood) and magnitude (using a gamma likelihood) of extraction. The correlation between extraction rates in space and time is modelled using a Gaussian Markov Random Field (GMRF) with a Matérn spatial covariance function which can evolve over time according to an autoregressive model. To reduce computational burden, we allow the GMRF to be evaluated at a relatively coarse temporal resolution, while still allowing predictions to be made at arbitrarily small time scales. We describe the process of model selection and inference using an information criterion approach, and present some preliminary results from the study area. We conclude by discussing issues related with upscaling of the modelling approach to the entire basin, including merging of extraction rate observations with different precision, temporal resolution, and even potentially different likelihoods.

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3; A Recursive Maximum Likelihood Decoding

NASA Technical Reports Server (NTRS)

Lin, Shu; Fossorier, Marc

1998-01-01

The Viterbi algorithm is indeed a very simple and efficient method of implementing the maximum likelihood decoding. However, if we take advantage of the structural properties in a trellis section, other efficient trellis-based decoding algorithms can be devised. Recently, an efficient trellis-based recursive maximum likelihood decoding (RMLD) algorithm for linear block codes has been proposed. This algorithm is more efficient than the conventional Viterbi algorithm in both computation and hardware requirements. Most importantly, the implementation of this algorithm does not require the construction of the entire code trellis, only some special one-section trellises of relatively small state and branch complexities are needed for constructing path (or branch) metric tables recursively. At the end, there is only one table which contains only the most likely code-word and its metric for a given received sequence r = (r(sub 1), r(sub 2),...,r(sub n)). This algorithm basically uses the divide and conquer strategy. Furthermore, it allows parallel/pipeline processing of received sequences to speed up decoding.

Testing students' e-learning via Facebook through Bayesian structural equation modeling.

PubMed

Salarzadeh Jenatabadi, Hashem; Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students' intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods' results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated.

Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stoneking, M.R.; Den Hartog, D.J.

1996-06-01

The fitting of data by {chi}{sup 2}-minimization is valid only when the uncertainties in the data are normally distributed. When analyzing spectroscopic or particle counting data at very low signal level (e.g., a Thomson scattering diagnostic), the uncertainties are distributed with a Poisson distribution. The authors have developed a maximum-likelihood method for fitting data that correctly treats the Poisson statistical character of the uncertainties. This method maximizes the total probability that the observed data are drawn from the assumed fit function using the Poisson probability function to determine the probability for each data point. The algorithm also returns uncertainty estimatesmore » for the fit parameters. They compare this method with a {chi}{sup 2}-minimization routine applied to both simulated and real data. Differences in the returned fits are greater at low signal level (less than {approximately}20 counts per measurement). the maximum-likelihood method is found to be more accurate and robust, returning a narrower distribution of values for the fit parameters with fewer outliers.« less

Land cover mapping after the tsunami event over Nanggroe Aceh Darussalam (NAD) province, Indonesia

NASA Astrophysics Data System (ADS)

Lim, H. S.; MatJafri, M. Z.; Abdullah, K.; Alias, A. N.; Mohd. Saleh, N.; Wong, C. J.; Surbakti, M. S.

2008-03-01

Remote sensing offers an important means of detecting and analyzing temporal changes occurring in our landscape. This research used remote sensing to quantify land use/land cover changes at the Nanggroe Aceh Darussalam (Nad) province, Indonesia on a regional scale. The objective of this paper is to assess the changed produced from the analysis of Landsat TM data. A Landsat TM image was used to develop land cover classification map for the 27 March 2005. Four supervised classifications techniques (Maximum Likelihood, Minimum Distance-to- Mean, Parallelepiped and Parallelepiped with Maximum Likelihood Classifier Tiebreaker classifier) were performed to the satellite image. Training sites and accuracy assessment were needed for supervised classification techniques. The training sites were established using polygons based on the colour image. High detection accuracy (>80%) and overall Kappa (>0.80) were achieved by the Parallelepiped with Maximum Likelihood Classifier Tiebreaker classifier in this study. This preliminary study has produced a promising result. This indicates that land cover mapping can be carried out using remote sensing classification method of the satellite digital imagery.

Evidence of seasonal variation in longitudinal growth of height in a sample of boys from Stuttgart Carlsschule, 1771-1793, using combined principal component analysis and maximum likelihood principle.

PubMed

Lehmann, A; Scheffler, Ch; Hermanussen, M

2010-02-01

Recent progress in modelling individual growth has been achieved by combining the principal component analysis and the maximum likelihood principle. This combination models growth even in incomplete sets of data and in data obtained at irregular intervals. We re-analysed late 18th century longitudinal growth of German boys from the boarding school Carlsschule in Stuttgart. The boys, aged 6-23 years, were measured at irregular 3-12 monthly intervals during the period 1771-1793. At the age of 18 years, mean height was 1652 mm, but height variation was large. The shortest boy reached 1474 mm, the tallest 1826 mm. Measured height closely paralleled modelled height, with mean difference of 4 mm, SD 7 mm. Seasonal height variation was found. Low growth rates occurred in spring and high growth rates in summer and autumn. The present study demonstrates that combining the principal component analysis and the maximum likelihood principle enables growth modelling in historic height data also. Copyright (c) 2009 Elsevier GmbH. All rights reserved.

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis

PubMed Central

van de Schoot, Rens; Hox, Joop

2014-01-01

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation coefficient (ICC) and estimation method; maximum likelihood estimation with robust chi-squares and standard errors and Bayesian estimation, on the convergence rate are investigated. The other variables of interest were rate of inadmissible solutions and the relative parameter and standard error bias on the between level. The results showed that inadmissible solutions were obtained when there was between level collinearity and the estimation method was maximum likelihood. In the within level multicollinearity condition, all of the solutions were admissible but the bias values were higher compared with the between level collinearity condition. Bayesian estimation appeared to be robust in obtaining admissible parameters but the relative bias was higher than for maximum likelihood estimation. Finally, as expected, high ICC produced less biased results compared to medium ICC conditions. PMID:29795827

Testing students’ e-learning via Facebook through Bayesian structural equation modeling

PubMed Central

Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students’ intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods’ results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated. PMID:28886019

Fuzzy multinomial logistic regression analysis: A multi-objective programming approach

NASA Astrophysics Data System (ADS)

Abdalla, Hesham A.; El-Sayed, Amany A.; Hamed, Ramadan

2017-05-01

Parameter estimation for multinomial logistic regression is usually based on maximizing the likelihood function. For large well-balanced datasets, Maximum Likelihood (ML) estimation is a satisfactory approach. Unfortunately, ML can fail completely or at least produce poor results in terms of estimated probabilities and confidence intervals of parameters, specially for small datasets. In this study, a new approach based on fuzzy concepts is proposed to estimate parameters of the multinomial logistic regression. The study assumes that the parameters of multinomial logistic regression are fuzzy. Based on the extension principle stated by Zadeh and Bárdossy's proposition, a multi-objective programming approach is suggested to estimate these fuzzy parameters. A simulation study is used to evaluate the performance of the new approach versus Maximum likelihood (ML) approach. Results show that the new proposed model outperforms ML in cases of small datasets.

On the Log-Normality of Historical Magnetic-Storm Intensity Statistics: Implications for Extreme-Event Probabilities

NASA Astrophysics Data System (ADS)

Love, J. J.; Rigler, E. J.; Pulkkinen, A. A.; Riley, P.

2015-12-01

An examination is made of the hypothesis that the statistics of magnetic-storm-maximum intensities are the realization of a log-normal stochastic process. Weighted least-squares and maximum-likelihood methods are used to fit log-normal functions to -Dst storm-time maxima for years 1957-2012; bootstrap analysis is used to established confidence limits on forecasts. Both methods provide fits that are reasonably consistent with the data; both methods also provide fits that are superior to those that can be made with a power-law function. In general, the maximum-likelihood method provides forecasts having tighter confidence intervals than those provided by weighted least-squares. From extrapolation of maximum-likelihood fits: a magnetic storm with intensity exceeding that of the 1859 Carrington event, -Dst > 850 nT, occurs about 1.13 times per century and a wide 95% confidence interval of [0.42, 2.41] times per century; a 100-yr magnetic storm is identified as having a -Dst > 880 nT (greater than Carrington) but a wide 95% confidence interval of [490, 1187] nT. This work is partially motivated by United States National Science and Technology Council and Committee on Space Research and International Living with a Star priorities and strategic plans for the assessment and mitigation of space-weather hazards.

Assessment of the non-Gaussianity and non-linearity levels of simulated sEMG signals on stationary segments.

PubMed

Messaoudi, Noureddine; Bekka, Raïs El'hadi; Ravier, Philippe; Harba, Rachid

2017-02-01

The purpose of this paper was to evaluate the effects of the longitudinal single differential (LSD), the longitudinal double differential (LDD) and the normal double differential (NDD) spatial filters, the electrode shape, the inter-electrode distance (IED) on non-Gaussianity and non-linearity levels of simulated surface EMG (sEMG) signals when the maximum voluntary contraction (MVC) varied from 10% to 100% by a step of 10%. The effects of recruitment range thresholds (RR), the firing rate (FR) strategy and the peak firing rate (PFR) of motor units were also considered. A cylindrical multilayer model of the volume conductor and a model of motor unit (MU) recruitment and firing rate were used to simulate sEMG signals in a pool of 120 MUs for 5s. Firstly, the stationarity of sEMG signals was tested by the runs, the reverse arrangements (RA) and the modified reverse arrangements (MRA) tests. Then the non-Gaussianity was characterised with bicoherence and kurtosis, and non-linearity levels was evaluated with linearity test. The kurtosis analysis showed that the sEMG signals detected by the LSD filter were the most Gaussian and those detected by the NDD filter were the least Gaussian. In addition, the sEMG signals detected by the LSD filter were the most linear. For a given filter, the sEMG signals detected by using rectangular electrodes were more Gaussian and more linear than that detected with circular electrodes. Moreover, the sEMG signals are less non-Gaussian and more linear with reverse onion-skin firing rate strategy than those with onion-skin strategy. The levels of sEMG signal Gaussianity and linearity increased with the increase of the IED, RR and PFR. Copyright © 2016 Elsevier Ltd. All rights reserved.

Progress in integrated-circuit horn antennas for receiver applications. Part 1: Antenna design

NASA Technical Reports Server (NTRS)

Eleftheriades, George V.; Ali-Ahmad, Walid Y.; Rebeiz, Gabriel M.

1992-01-01

The purpose of this work is to present a systematic method for the design of multimode quasi-integrated horn antennas. The design methodology is based on the Gaussian beam approach and the structures are optimized for achieving maximum fundamental Gaussian coupling efficiency. For this purpose, a hybrid technique is employed in which the integrated part of the antennas is treated using full-wave analysis, whereas the machined part is treated using an approximate method. This results in a simple and efficient design process. The developed design procedure has been applied for the design of a 20, a 23, and a 25 dB quasi-integrated horn antennas, all with a Gaussian coupling efficiency exceeding 97 percent. The designed antennas have been tested and characterized using both full-wave analysis and 90 GHz/370 GHz measurements.

Evaluation of higher order statistics parameters for multi channel sEMG using different force levels.

PubMed

Naik, Ganesh R; Kumar, Dinesh K

2011-01-01

The electromyograpy (EMG) signal provides information about the performance of muscles and nerves. The shape of the muscle signal and motor unit action potential (MUAP) varies due to the movement of the position of the electrode or due to changes in contraction level. This research deals with evaluating the non-Gaussianity in Surface Electromyogram signal (sEMG) using higher order statistics (HOS) parameters. To achieve this, experiments were conducted for four different finger and wrist actions at different levels of Maximum Voluntary Contractions (MVCs). Our experimental analysis shows that at constant force and for non-fatiguing contractions, probability density functions (PDF) of sEMG signals were non-Gaussian. For lesser MVCs (below 30% of MVC) PDF measures tends to be Gaussian process. The above measures were verified by computing the Kurtosis values for different MVCs.

Production of neutrinos and neutrino-like particles in proton-nucleus interactions. [400 GeV, cross sections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dishaw, J.P.

1979-03-01

An experimental search was performed to look for the direct production of neutrinos or neutrino-like particles, i.e., neutral particles which interact weakly with hadrons, in proton-nucleus interactions at 400 GeV incident proton energy. Possible sources of such particles include the semi-leptonic decay of new heavy particles such as charm, and the direct production of a light neutral Higgs particle such as the axion. The production of these particles has been inferred in this experiment by energy nonconservation in the collision of a proton with an iron nucleus. The total visible energy of the interaction was measured using a sampling ionizationmore » calorimeter. After correcting for beam intensity effects and cutting the data to eliminate systematic effects in the measurement, the final resolution of the calorimeter was 3.51% and increased with decreasing incident beam energy with a square root dependence on the beam energy. Energy nonconservation in the data is manifest as a non-Gaussian distribution on the low side of the calorimeter measured energy. Model calculations yield the fraction of events expected in this non-Gaussian behavior for the various sources of neutrinos or neutrino-like particles. A maximum likelihood fit to the data with the theoretical fraction of events expected yields the 95% confidence level production cross section upper limit values. The upper limits for general production of neutrino-like particles for various parameterizations of the production cross section are presented. The following specific upper limits have been established: charm particle production < 670 ..mu..barns, supersymmetric particle production carrying an additional quantum number R < 33 ..mu..barns (mass of 1 GeV), 8 ..mu..barns (mass of 3 GeV); axion production < 10/sup -3/ times the ..pi../sup 0/ production cross section. 144 references.« less

Inference of reaction rate parameters based on summary statistics from experiments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khalil, Mohammad; Chowdhary, Kamaljit Singh; Safta, Cosmin

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2/O 2-mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the givenmore » summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.« less

Inference of reaction rate parameters based on summary statistics from experiments

DOE PAGES

Khalil, Mohammad; Chowdhary, Kamaljit Singh; Safta, Cosmin; ...

2016-10-15

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2/O 2-mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the givenmore » summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.« less

Systematic effects of foreground removal in 21-cm surveys of reionization

NASA Astrophysics Data System (ADS)

Petrovic, Nada; Oh, S. Peng

2011-05-01

21-cm observations have the potential to revolutionize our understanding of the high-redshift Universe. Whilst extremely bright radio continuum foregrounds exist at these frequencies, their spectral smoothness can be exploited to allow efficient foreground subtraction. It is well known that - regardless of other instrumental effects - this removes power on scales comparable to the survey bandwidth. We investigate associated systematic biases. We show that removing line-of-sight fluctuations on large scales aliases into suppression of the 3D power spectrum across a broad range of scales. This bias can be dealt with by correctly marginalizing over small wavenumbers in the 1D power spectrum; however, the unbiased estimator will have unavoidably larger variance. We also show that Gaussian realizations of the power spectrum permit accurate and extremely rapid Monte Carlo simulations for error analysis; repeated realizations of the fully non-Gaussian field are unnecessary. We perform Monte Carlo maximum likelihood simulations of foreground removal which yield unbiased, minimum variance estimates of the power spectrum in agreement with Fisher matrix estimates. Foreground removal also distorts the 21-cm probability distribution function (PDF), reducing the contrast between neutral and ionized regions, with potentially serious consequences for efforts to extract information from the PDF. We show that it is the subtraction of large-scale modes which is responsible for this distortion, and that it is less severe in the earlier stages of reionization. It can be reduced by using larger bandwidths. In the late stages of reionization, identification of the largest ionized regions (which consist of foreground emission only) provides calibration points which potentially allow recovery of large-scale modes. Finally, we also show that (i) the broad frequency response of synchrotron and free-free emission will smear out any features in the electron momentum distribution and ensure spectrally smooth foregrounds and (ii) extragalactic radio recombination lines should be negligible foregrounds.

Development of an LSI maximum-likelihood convolutional decoder for advanced forward error correction capability on the NASA 30/20 GHz program

NASA Technical Reports Server (NTRS)

Clark, R. T.; Mccallister, R. D.

1982-01-01

The particular coding option identified as providing the best level of coding gain performance in an LSI-efficient implementation was the optimal constraint length five, rate one-half convolutional code. To determine the specific set of design parameters which optimally matches this decoder to the LSI constraints, a breadboard MCD (maximum-likelihood convolutional decoder) was fabricated and used to generate detailed performance trade-off data. The extensive performance testing data gathered during this design tradeoff study are summarized, and the functional and physical MCD chip characteristics are presented.

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,

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.

Gyre and gimble: a maximum-likelihood replacement for Patterson correlation refinement.

PubMed

McCoy, Airlie J; Oeffner, Robert D; Millán, Claudia; Sammito, Massimo; Usón, Isabel; Read, Randy J

2018-04-01

Descriptions are given of the maximum-likelihood gyre method implemented in Phaser for optimizing the orientation and relative position of rigid-body fragments of a model after the orientation of the model has been identified, but before the model has been positioned in the unit cell, and also the related gimble method for the refinement of rigid-body fragments of the model after positioning. Gyre refinement helps to lower the root-mean-square atomic displacements between model and target molecular-replacement solutions for the test case of antibody Fab(26-10) and improves structure solution with ARCIMBOLDO_SHREDDER.

A MATLAB toolbox for the efficient estimation of the psychometric function using the updated maximum-likelihood adaptive procedure

PubMed Central

Richards, V. M.; Dai, W.

2014-01-01

A MATLAB toolbox for the efficient estimation of the threshold, slope, and lapse rate of the psychometric function is described. The toolbox enables the efficient implementation of the updated maximum-likelihood (UML) procedure. The toolbox uses an object-oriented architecture for organizing the experimental variables and computational algorithms, which provides experimenters with flexibility in experimental design and data management. Descriptions of the UML procedure and the UML Toolbox are provided, followed by toolbox use examples. Finally, guidelines and recommendations of parameter configurations are given. PMID:24671826

Equalization of nonlinear transmission impairments by maximum-likelihood-sequence estimation in digital coherent receivers.

PubMed

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.

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.

The epoch state navigation filter. [for maximum likelihood estimates of position and velocity vectors

NASA Technical Reports Server (NTRS)

Battin, R. H.; Croopnick, S. R.; Edwards, J. A.

1977-01-01

The formulation of a recursive maximum likelihood navigation system employing reference position and velocity vectors as state variables is presented. Convenient forms of the required variational equations of motion are developed together with an explicit form of the associated state transition matrix needed to refer measurement data from the measurement time to the epoch time. Computational advantages accrue from this design in that the usual forward extrapolation of the covariance matrix of estimation errors can be avoided without incurring unacceptable system errors. Simulation data for earth orbiting satellites are provided to substantiate this assertion.

A 3D approximate maximum likelihood localization solver

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.

Estimation of Dynamic Discrete Choice Models by Maximum Likelihood and the Simulated Method of Moments

PubMed Central

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

Search for Point Sources of Ultra-High-Energy Cosmic Rays above 4.0 × 1019 eV Using a Maximum Likelihood Ratio Test

NASA Astrophysics Data System (ADS)

Abbasi, R. U.; Abu-Zayyad, T.; Amann, J. F.; Archbold, G.; Atkins, R.; Bellido, J. A.; Belov, K.; Belz, J. W.; Ben-Zvi, S. Y.; Bergman, D. R.; Boyer, J. H.; Burt, G. W.; Cao, Z.; Clay, R. W.; Connolly, B. M.; Dawson, B. R.; Deng, W.; Farrar, G. R.; Fedorova, Y.; Findlay, J.; Finley, C. B.; Hanlon, W. F.; Hoffman, C. M.; Holzscheiter, M. H.; Hughes, G. A.; Hüntemeyer, P.; Jui, C. C. H.; Kim, K.; Kirn, M. A.; Knapp, B. C.; Loh, E. C.; Maestas, M. M.; Manago, N.; Mannel, E. J.; Marek, L. J.; Martens, K.; Matthews, J. A. J.; Matthews, J. N.; O'Neill, A.; Painter, C. A.; Perera, L.; Reil, K.; Riehle, R.; Roberts, M. D.; Sasaki, M.; Schnetzer, S. R.; Seman, M.; Simpson, K. M.; Sinnis, G.; Smith, J. D.; Snow, R.; Sokolsky, P.; Song, C.; Springer, R. W.; Stokes, B. T.; Thomas, J. R.; Thomas, S. B.; Thomson, G. B.; Tupa, D.; Westerhoff, S.; Wiencke, L. R.; Zech, A.

2005-04-01

We present the results of a search for cosmic-ray point sources at energies in excess of 4.0×1019 eV in the combined data sets recorded by the Akeno Giant Air Shower Array and High Resolution Fly's Eye stereo experiments. The analysis is based on a maximum likelihood ratio test using the probability density function for each event rather than requiring an a priori choice of a fixed angular bin size. No statistically significant clustering of events consistent with a point source is found.

Self-repeating properties of four-petal Gaussian vortex beams in quadratic index medium

NASA Astrophysics Data System (ADS)

Zou, Defeng; Li, Xiaohui; Chai, Tong; Zheng, Hairong

2018-05-01

In this paper, we investigate the propagation properties of four-petal Gaussian vortex (FPGV) beams propagating through the quadratic index medium, obtaining the analytical expression of FPGV beams. The effects of beam order n, topological charge m and beam waist ω0 are investigated. Results show that quadratic index medium support periodic distributions of FPGV beams. A hollow optical wall or an optical central principal maximum surrounded by symmetrical sidelobes will occur at the center of a period. At length, they will evolve into four petals structure, exactly same as the intensity distributions at source plane.

The Equivalence of Two Methods of Parameter Estimation for the Rasch Model.

ERIC Educational Resources Information Center

Blackwood, Larry G.; Bradley, Edwin L.

1989-01-01

Two methods of estimating parameters in the Rasch model are compared. The equivalence of likelihood estimations from the model of G. J. Mellenbergh and P. Vijn (1981) and from usual unconditional maximum likelihood (UML) estimation is demonstrated. Mellenbergh and Vijn's model is a convenient method of calculating UML estimates. (SLD)

Using the β-binomial distribution to characterize forest health

Treesearch

S.J. Zarnoch; R.L. Anderson; R.M. Sheffield

1995-01-01

The β-binomial distribution is suggested as a model for describing and analyzing the dichotomous data obtained from programs monitoring the health of forests in the United States. Maximum likelihood estimation of the parameters is given as well as asymptotic likelihood ratio tests. The procedure is illustrated with data on dogwood anthracnose infection (caused...

Power and Sample Size Calculations for Logistic Regression Tests for Differential Item Functioning

ERIC Educational Resources Information Center

Li, Zhushan

2014-01-01

Logistic regression is a popular method for detecting uniform and nonuniform differential item functioning (DIF) effects. Theoretical formulas for the power and sample size calculations are derived for likelihood ratio tests and Wald tests based on the asymptotic distribution of the maximum likelihood estimators for the logistic regression model.…

A Note on Three Statistical Tests in the Logistic Regression DIF Procedure

ERIC Educational Resources Information Center

Paek, Insu

2012-01-01

Although logistic regression became one of the well-known methods in detecting differential item functioning (DIF), its three statistical tests, the Wald, likelihood ratio (LR), and score tests, which are readily available under the maximum likelihood, do not seem to be consistently distinguished in DIF literature. This paper provides a clarifying…

Contributions to the Underlying Bivariate Normal Method for Factor Analyzing Ordinal Data

ERIC Educational Resources Information Center

Xi, Nuo; Browne, Michael W.

2014-01-01

A promising "underlying bivariate normal" approach was proposed by Jöreskog and Moustaki for use in the factor analysis of ordinal data. This was a limited information approach that involved the maximization of a composite likelihood function. Its advantage over full-information maximum likelihood was that very much less computation was…

Investigating the Impact of Uncertainty about Item Parameters on Ability Estimation

ERIC Educational Resources Information Center

Zhang, Jinming; Xie, Minge; Song, Xiaolan; Lu, Ting

2011-01-01

Asymptotic expansions of the maximum likelihood estimator (MLE) and weighted likelihood estimator (WLE) of an examinee's ability are derived while item parameter estimators are treated as covariates measured with error. The asymptotic formulae present the amount of bias of the ability estimators due to the uncertainty of item parameter estimators.…

Estimation of Complex Generalized Linear Mixed Models for Measurement and Growth

ERIC Educational Resources Information Center

Jeon, Minjeong

2012-01-01

Maximum likelihood (ML) estimation of generalized linear mixed models (GLMMs) is technically challenging because of the intractable likelihoods that involve high dimensional integrations over random effects. The problem is magnified when the random effects have a crossed design and thus the data cannot be reduced to small independent clusters. A…

A likelihood-based time series modeling approach for application in dendrochronology to examine the growth-climate relations and forest disturbance history

EPA Science Inventory

A time series intervention analysis (TSIA) of dendrochronological data to infer the tree growth-climate-disturbance relations and forest disturbance history is described. Maximum likelihood is used to estimate the parameters of a structural time series model with components for ...

Shape, Illumination, and Reflectance from Shading

DTIC Science & Technology

2013-05-29

the global entropy of log-reflectance. 3) An “absolute” prior on reflectance which prefers to paint the scene with some colors ( white , gray, green...in log- RGB from pixel i to pixel j, and c (· ;α, σ) is the negative log-likelihood of a discrete univariate Gaussian scale mixture (GSM), parametrized...gs(R) = ∑ i ∑ j∈N(i) C (Ri −Rj ;αR, σR,ΣR) (6) Where Ri−Rj is now a 3-vector of the log- RGB differ- ences, α are mixing coefficients, σ are the

Exploring a potential energy surface by machine learning for characterizing atomic transport

NASA Astrophysics Data System (ADS)

Kanamori, Kenta; Toyoura, Kazuaki; Honda, Junya; Hattori, Kazuki; Seko, Atsuto; Karasuyama, Masayuki; Shitara, Kazuki; Shiga, Motoki; Kuwabara, Akihide; Takeuchi, Ichiro

2018-03-01

We propose a machine-learning method for evaluating the potential barrier governing atomic transport based on the preferential selection of dominant points for atomic transport. The proposed method generates numerous random samples of the entire potential energy surface (PES) from a probabilistic Gaussian process model of the PES, which enables defining the likelihood of the dominant points. The robustness and efficiency of the method are demonstrated on a dozen model cases for proton diffusion in oxides, in comparison with a conventional nudge elastic band method.

Analysis of the Hessian for Inverse Scattering Problems. Part 3. Inverse Medium Scattering of Electromagnetic Waves in Three Dimensions

DTIC Science & Technology

2012-08-01

small data noise and model error, the discrete Hessian can be approximated by a low-rank matrix. This in turn enables fast solution of an appropriately...implication of the compactness of the Hessian is that for small data noise and model error, the discrete Hessian can be approximated by a low-rank matrix. This...probability distribution is given by the inverse of the Hessian of the negative log likelihood function. For Gaussian data noise and model error, this

Gaussian fluctuation of the diffusion exponent of virus capsid in a living cell nucleus

NASA Astrophysics Data System (ADS)

Itto, Yuichi

2018-05-01

In their work [4], Bosse et al. experimentally showed that virus capsid exhibits not only normal diffusion but also anomalous diffusion in nucleus of a living cell. There, it was found that the distribution of fluctuations of the diffusion exponent characterizing them takes the Gaussian form, which is, quite remarkably, the same form for two different types of the virus. This suggests high robustness of such fluctuations. Here, the statistical property of local fluctuations of the diffusion exponent of the virus capsid in the nucleus is studied. A maximum-entropy-principle approach (originally proposed for a different virus in a different cell) is applied for obtaining the fluctuation distribution of the exponent. Largeness of the number of blocks identified with local areas of interchromatin corrals is also examined based on the experimental data. It is shown that the Gaussian distribution of the local fluctuations can be derived, in accordance with the above form. In addition, it is quantified how the fluctuation distribution on a long time scale is different from the Gaussian distribution.

Free kick instead of cross-validation in maximum-likelihood refinement of macromolecular crystal structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pražnikar, Jure; University of Primorska,; Turk, Dušan, E-mail: dusan.turk@ijs.si

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. Theymore » 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.« less

Marginal Maximum A Posteriori Item Parameter Estimation for the Generalized Graded Unfolding Model

ERIC Educational Resources Information Center

Roberts, James S.; Thompson, Vanessa M.

2011-01-01

A marginal maximum a posteriori (MMAP) procedure was implemented to estimate item parameters in the generalized graded unfolding model (GGUM). Estimates from the MMAP method were compared with those derived from marginal maximum likelihood (MML) and Markov chain Monte Carlo (MCMC) procedures in a recovery simulation that varied sample size,…

THESEUS: maximum likelihood superpositioning and analysis of macromolecular structures.

PubMed

Theobald, Douglas L; Wuttke, Deborah S

2006-09-01

THESEUS is a command line program for performing maximum likelihood (ML) superpositions and analysis of macromolecular structures. While conventional superpositioning methods use ordinary least-squares (LS) as the optimization criterion, ML superpositions provide substantially improved accuracy by down-weighting variable structural regions and by correcting for correlations among atoms. ML superpositioning is robust and insensitive to the specific atoms included in the analysis, and thus it does not require subjective pruning of selected variable atomic coordinates. Output includes both likelihood-based and frequentist statistics for accurate evaluation of the adequacy of a superposition and for reliable analysis of structural similarities and differences. THESEUS performs principal components analysis for analyzing the complex correlations found among atoms within a structural ensemble. ANSI C source code and selected binaries for various computing platforms are available under the GNU open source license from http://monkshood.colorado.edu/theseus/ or http://www.theseus3d.org.

Simulation-Based Evaluation of Hybridization Network Reconstruction Methods in the Presence of Incomplete Lineage Sorting

PubMed Central

Kamneva, Olga K; Rosenberg, Noah A

2017-01-01

Hybridization events generate reticulate species relationships, giving rise to species networks rather than species trees. We report a comparative study of consensus, maximum parsimony, and maximum likelihood methods of species network reconstruction using gene trees simulated assuming a known species history. We evaluate the role of the divergence time between species involved in a hybridization event, the relative contributions of the hybridizing species, and the error in gene tree estimation. When gene tree discordance is mostly due to hybridization and not due to incomplete lineage sorting (ILS), most of the methods can detect even highly skewed hybridization events between highly divergent species. For recent divergences between hybridizing species, when the influence of ILS is sufficiently high, likelihood methods outperform parsimony and consensus methods, which erroneously identify extra hybridizations. The more sophisticated likelihood methods, however, are affected by gene tree errors to a greater extent than are consensus and parsimony. PMID:28469378

Free energy reconstruction from steered dynamics without post-processing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Athenes, Manuel, E-mail: Manuel.Athenes@cea.f; Condensed Matter and Materials Division, Physics and Life Sciences Directorate, LLNL, Livermore, CA 94551; Marinica, Mihai-Cosmin

2010-09-20

Various methods achieving importance sampling in ensembles of nonequilibrium trajectories enable one to estimate free energy differences and, by maximum-likelihood post-processing, to reconstruct free energy landscapes. Here, based on Bayes theorem, we propose a more direct method in which a posterior likelihood function is used both to construct the steered dynamics and to infer the contribution to equilibrium of all the sampled states. The method is implemented with two steering schedules. First, using non-autonomous steering, we calculate the migration barrier of the vacancy in Fe-{alpha}. Second, using an autonomous scheduling related to metadynamics and equivalent to temperature-accelerated molecular dynamics, wemore » accurately reconstruct the two-dimensional free energy landscape of the 38-atom Lennard-Jones cluster as a function of an orientational bond-order parameter and energy, down to the solid-solid structural transition temperature of the cluster and without maximum-likelihood post-processing.« less

Master teachers' responses to twenty literacy and science/mathematics practices in deaf education.

PubMed

Easterbrooks, Susan R; Stephenson, Brenda; Mertens, Donna

2006-01-01

Under a grant to improve outcomes for students who are deaf or hard of hearing awarded to the Association of College Educators--Deaf/Hard of Hearing, a team identified content that all teachers of students who are deaf and hard of hearing must understand and be able to teach. Also identified were 20 practices associated with content standards (10 each, literacy and science/mathematics). Thirty-seven master teachers identified by grant agents rated the practices on a Likert-type scale indicating the maximum benefit of each practice and maximum likelihood that they would use the practice, yielding a likelihood-impact analysis. The teachers showed strong agreement on the benefits and likelihood of use of the rated practices. Concerns about implementation of many of the practices related to time constraints and mixed-ability classrooms were themes of the reviews. Actions for teacher preparation programs were recommended.

Generic evolution of mixing in heterogeneous media

NASA Astrophysics Data System (ADS)

De Dreuzy, J.; Carrera, J.; Dentz, M.; Le Borgne, T.

2011-12-01

Mixing in heterogeneous media results from the competition bewteen flow fluctuations and local scale diffusion. Flow fluctuations quickly create concentration contrasts and thus heterogeneity of the concentration field, which is slowly homogenized by local scale diffusion. Mixing first deviates from Gaussian mixing, which represents the potential mixing induced by spreading before approaching it. This deviation fundamentally expresses the evolution of the interaction between spreading and local scale diffusion. We characterize it by the ratio γ of the non-Gaussian to the Gaussian mixing states. We define the Gaussian mixing state as the integrated squared concentration of the Gaussian plume that has the same longitudinal dispersion as the real plume. The non-Gaussian mixing state is the difference between the overall mixing state defined as the integrated squared concentration and the Gaussian mixing state. The main advantage of this definition is to use the full knowledge previously acquired on dispersion for characterizing mixing even when the solute concentration field is highly non Gaussian. Using high precision numerical simulations, we show that γ quickly increases, peaks and slowly decreases. γ can be derived from two scales characterizing spreading and local mixing, at least for large flux-weighted solute injection conditions into classically log-normal Gaussian correlated permeability fields. The spreading scale is directly related to the longitudinal dispersion. The local mixing scale is the largest scale over which solute concentrations can be considered locally uniform. More generally, beyond the characteristics of its maximum, γ turns out to have a highly generic scaling form. Its fast increase and slow decrease depend neither on the heterogeneity level, nor on the ratio of diffusion to advection, nor on the injection conditions. They might even not depend on the particularities of the flow fields as the same generic features also prevail for Taylor dispersion. This generic characterization of mixing can offer new ways to set up transport equations that honor not only advection and spreading (dispersion), but also mixing.

New algorithms and methods to estimate maximum-likelihood phylogenies: assessing the performance of PhyML 3.0.

PubMed

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/.

Novel active contour model based on multi-variate local Gaussian distribution for local segmentation of MR brain images

NASA Astrophysics Data System (ADS)

Zheng, Qiang; Li, Honglun; Fan, Baode; Wu, Shuanhu; Xu, Jindong

2017-12-01

Active contour model (ACM) has been one of the most widely utilized methods in magnetic resonance (MR) brain image segmentation because of its ability of capturing topology changes. However, most of the existing ACMs only consider single-slice information in MR brain image data, i.e., the information used in ACMs based segmentation method is extracted only from one slice of MR brain image, which cannot take full advantage of the adjacent slice images' information, and cannot satisfy the local segmentation of MR brain images. In this paper, a novel ACM is proposed to solve the problem discussed above, which is based on multi-variate local Gaussian distribution and combines the adjacent slice images' information in MR brain image data to satisfy segmentation. The segmentation is finally achieved through maximizing the likelihood estimation. Experiments demonstrate the advantages of the proposed ACM over the single-slice ACM in local segmentation of MR brain image series.

Maximum-likelihood estimation of parameterized wavefronts from multifocal data

PubMed Central

Sakamoto, Julia A.; Barrett, Harrison H.

2012-01-01

A method for determining the pupil phase distribution of an optical system is demonstrated. Coefficients in a wavefront expansion were estimated using likelihood methods, where the data consisted of multiple irradiance patterns near focus. Proof-of-principle results were obtained in both simulation and experiment. Large-aberration wavefronts were handled in the numerical study. Experimentally, we discuss the handling of nuisance parameters. Fisher information matrices, Cramér-Rao bounds, and likelihood surfaces are examined. ML estimates were obtained by simulated annealing to deal with numerous local extrema in the likelihood function. Rapid processing techniques were employed to reduce the computational time. PMID:22772282

Analytical template protection performance and maximum key size given a Gaussian-modeled biometric source

NASA Astrophysics Data System (ADS)

Kelkboom, Emile J. C.; Breebaart, Jeroen; Buhan, Ileana; Veldhuis, Raymond N. J.

2010-04-01

Template protection techniques are used within biometric systems in order to protect the stored biometric template against privacy and security threats. A great portion of template protection techniques are based on extracting a key from or binding a key to a biometric sample. The achieved protection depends on the size of the key and its closeness to being random. In the literature it can be observed that there is a large variation on the reported key lengths at similar classification performance of the same template protection system, even when based on the same biometric modality and database. In this work we determine the analytical relationship between the system performance and the theoretical maximum key size given a biometric source modeled by parallel Gaussian channels. We consider the case where the source capacity is evenly distributed across all channels and the channels are independent. We also determine the effect of the parameters such as the source capacity, the number of enrolment and verification samples, and the operating point selection on the maximum key size. We show that a trade-off exists between the privacy protection of the biometric system and its convenience for its users.

Gaussianity versus intermittency in solar system plasma turbulence

NASA Astrophysics Data System (ADS)

Echim, M.

2014-12-01

Statistical properties of plasma and magnetic field fluctuations exhibit features linked with the dynamics of the targeted system and sometimes with the physical processes that are at the origin of these fluctuations. Intermittency is sometimes discussed in terms of non-Gaussianity of the Probability Distribution Functions (PDFs) of fluctuations for ranges of spatio/temporal scales. Some examples of self-similarity have been however shown for PDFs whose wings are not Gaussian. In this study we discuss intermittency in terms of non-Gaussianity as well as scale dependence of the higher order moments of PDFs, in particular the flatness. We use magnetic field and plasma data from several space missions, in the solar wind (Ulysses, Cluster, and Venus Express), and in the planetary magnetosheaths (Cluster and Venus Express). We analyze Ulysses data that satisfy a consolidated set of selection criteria able to identify "pure" fast and slow wind. We investigate Venus Express data close to the orbital apogee, in the solar wind, at 0.72 AU, and in the Venus magnetosheath. We study Cluster data in the solar wind (for time intervals not affected by planetary ions effects), and the magnetosheath. We organize our results in three solar wind data bases (one for the solar maximum, 1999-2001, two for the solar minimum, 1997-1998 and respectively, 2007-2008), and two planetary databases (one for the solar maximum, 2000-2001, that includes PDFs obtained in the terrestrial magnetosphere, and one for the solar minimum, 2007-2008, that includes PDFs obtained in the terrestrial and Venus magnetospheres and magnetosheaths). In addition to investigating the statistical properties of fluctuations for the minimum and maximum of the solar cycle we also analyze the similarities and differences between fast and slow wind. We emphasize the importance of our data survey and analysis in the context of understanding the solar wind turbulence and complexity, and the exploitation of data bases and as a first step towards developing a (virtual) laboratory for studying solar system plasma turbulence and intermittency. Research supported by the European FP7 Programme (grant agreement 313038/STORM), and a grant of the Romanian CNCS -UEFISCDI, project number PN-II-ID-PCE-2012-4-0418.

Propagation of Airy Gaussian vortex beams in uniaxial crystals

NASA Astrophysics Data System (ADS)

Weihao, Yu; Ruihuang, Zhao; Fu, Deng; Jiayao, Huang; Chidao, Chen; Xiangbo, Yang; Yanping, Zhao; Dongmei, Deng

2016-04-01

The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108, 11374107, 10904041, and 11547212), the Foundation of Cultivating Outstanding Young Scholars of Guangdong Province, China, the CAS Key Laboratory of Geospace Environment, University of Science and Technology of China, the National Training Program of Innovation and Entrepreneurship for Undergraduates (Grant No. 2015093), and the Science and Technology Projects of Guangdong Province, China (Grant No. 2013B031800011).

Spot size characterization of focused non-Gaussian X-ray laser beams.

PubMed

Chalupský, J; Krzywinski, J; Juha, L; Hájková, V; Cihelka, J; Burian, T; Vysín, L; Gaudin, J; Gleeson, A; Jurek, M; Khorsand, A R; Klinger, D; Wabnitz, H; Sobierajski, R; Störmer, M; Tiedtke, K; Toleikis, S

2010-12-20

We present a new technique for the characterization of non-Gaussian laser beams which cannot be described by an analytical formula. As a generalization of the beam spot area we apply and refine the definition of so called effective area (A(eff)) [1] in order to avoid using the full-width at half maximum (FWHM) parameter which is inappropriate for non-Gaussian beams. Furthermore, we demonstrate a practical utilization of our technique for a femtosecond soft X-ray free-electron laser. The ablative imprints in poly(methyl methacrylate) - PMMA and amorphous carbon (a-C) are used to characterize the spatial beam profile and to determine the effective area. Two procedures of the effective area determination are presented in this work. An F-scan method, newly developed in this paper, appears to be a good candidate for the spatial beam diagnostics applicable to lasers of various kinds.

On focusing of a ring ripple on a Gaussian electromagnetic beam in a plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Misra, Shikha; Mishra, S. K.

In this communication the authors have investigated the focusing of a ring ripple on a Gaussian electromagnetic beam propagating in a plasma, considering each of the three kinds of basic nonlinearities, namely, ponderomotive, collisional, and relativistic. In this analysis, the electric field profile of the propagating beam is assumed to be composed of the radial electric field distribution of the Gaussian beam as well as that of the ring ripple; a paraxial like approach has been adopted to analyze the characteristics of the propagation. Thus, one considers a unique dielectric function for the beam propagation and a radial field sensitivemore » diffraction term, appropriate to the vicinity of the maximum of the irradiance distribution of the ring ripple. Further, the variation of the phase associated with the beam on account of the r independent terms in the eikonal has also been accounted for.« less

A tree island approach to inferring phylogeny in the ant subfamily Formicinae, with especial reference to the evolution of weaving.

PubMed

Johnson, Rebecca N; Agapow, Paul-Michael; Crozier, Ross H

2003-11-01

The ant subfamily Formicinae is a large assemblage (2458 species (J. Nat. Hist. 29 (1995) 1037), including species that weave leaf nests together with larval silk and in which the metapleural gland-the ancestrally defining ant character-has been secondarily lost. We used sequences from two mitochondrial genes (cytochrome b and cytochrome oxidase 2) from 18 formicine and 4 outgroup taxa to derive a robust phylogeny, employing a search for tree islands using 10000 randomly constructed trees as starting points and deriving a maximum likelihood consensus tree from the ML tree and those not significantly different from it. Non-parametric bootstrapping showed that the ML consensus tree fit the data significantly better than three scenarios based on morphology, with that of Bolton (Identification Guide to the Ant Genera of the World, Harvard University Press, Cambridge, MA) being the best among these alternative trees. Trait mapping showed that weaving had arisen at least four times and possibly been lost once. A maximum likelihood analysis showed that loss of the metapleural gland is significantly associated with the weaver life-pattern. The graph of the frequencies with which trees were discovered versus their likelihood indicates that trees with high likelihoods have much larger basins of attraction than those with lower likelihoods. While this result indicates that single searches are more likely to find high- than low-likelihood tree islands, it also indicates that searching only for the single best tree may lose important information.

Occupancy Modeling Species-Environment Relationships with Non-ignorable Survey Designs.

PubMed

Irvine, Kathryn M; Rodhouse, Thomas J; Wright, Wilson J; Olsen, Anthony R

2018-05-26

Statistical models supporting inferences about species occurrence patterns in relation to environmental gradients are fundamental to ecology and conservation biology. A common implicit assumption is that the sampling design is ignorable and does not need to be formally accounted for in analyses. The analyst assumes data are representative of the desired population and statistical modeling proceeds. However, if datasets from probability and non-probability surveys are combined or unequal selection probabilities are used, the design may be non ignorable. We outline the use of pseudo-maximum likelihood estimation for site-occupancy models to account for such non-ignorable survey designs. This estimation method accounts for the survey design by properly weighting the pseudo-likelihood equation. In our empirical example, legacy and newer randomly selected locations were surveyed for bats to bridge a historic statewide effort with an ongoing nationwide program. We provide a worked example using bat acoustic detection/non-detection data and show how analysts can diagnose whether their design is ignorable. Using simulations we assessed whether our approach is viable for modeling datasets composed of sites contributed outside of a probability design Pseudo-maximum likelihood estimates differed from the usual maximum likelihood occu31 pancy estimates for some bat species. Using simulations we show the maximum likelihood estimator of species-environment relationships with non-ignorable sampling designs was biased, whereas the pseudo-likelihood estimator was design-unbiased. However, in our simulation study the designs composed of a large proportion of legacy or non-probability sites resulted in estimation issues for standard errors. These issues were likely a result of highly variable weights confounded by small sample sizes (5% or 10% sampling intensity and 4 revisits). Aggregating datasets from multiple sources logically supports larger sample sizes and potentially increases spatial extents for statistical inferences. Our results suggest that ignoring the mechanism for how locations were selected for data collection (e.g., the sampling design) could result in erroneous model-based conclusions. Therefore, in order to ensure robust and defensible recommendations for evidence-based conservation decision-making, the survey design information in addition to the data themselves must be available for analysts. Details for constructing the weights used in estimation and code for implementation are provided. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

DSN telemetry system performance using a maximum likelihood convolutional decoder

NASA Technical Reports Server (NTRS)

Benjauthrit, B.; Kemp, R. P.

1977-01-01

Results are described of telemetry system performance testing using DSN equipment and a Maximum Likelihood Convolutional Decoder (MCD) for code rates 1/2 and 1/3, constraint length 7 and special test software. The test results confirm the superiority of the rate 1/3 over that of the rate 1/2. The overall system performance losses determined at the output of the Symbol Synchronizer Assembly are less than 0.5 db for both code rates. Comparison of the performance is also made with existing mathematical models. Error statistics of the decoded data are examined. The MCD operational threshold is found to be about 1.96 db.

Multifrequency InSAR height reconstruction through maximum likelihood estimation of local planes parameters.

PubMed

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.

Soft decoding a self-dual (48, 24; 12) code

NASA Technical Reports Server (NTRS)

Solomon, G.

1993-01-01

A self-dual (48,24;12) code comes from restricting a binary cyclic (63,18;36) code to a 6 x 7 matrix, adding an eighth all-zero column, and then adjoining six dimensions to this extended 6 x 8 matrix. These six dimensions are generated by linear combinations of row permutations of a 6 x 8 matrix of weight 12, whose sums of rows and columns add to one. A soft decoding using these properties and approximating maximum likelihood is presented here. This is preliminary to a possible soft decoding of the box (72,36;15) code that promises a 7.7-dB theoretical coding under maximum likelihood.

Effects of time-shifted data on flight determined stability and control derivatives

NASA Technical Reports Server (NTRS)

Steers, S. T.; Iliff, K. W.

1975-01-01

Flight data were shifted in time by various increments to assess the effects of time shifts on estimates of stability and control derivatives produced by a maximum likelihood estimation method. Derivatives could be extracted from flight data with the maximum likelihood estimation method even if there was a considerable time shift in the data. Time shifts degraded the estimates of the derivatives, but the degradation was in a consistent rather than a random pattern. Time shifts in the control variables caused the most degradation, and the lateral-directional rotary derivatives were affected the most by time shifts in any variable.