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

Estimation Methods for Non-Homogeneous Regression - Minimum CRPS vs Maximum Likelihood

NASA Astrophysics Data System (ADS)

Gebetsberger, Manuel; Messner, Jakob W.; Mayr, Georg J.; Zeileis, Achim

2017-04-01

Non-homogeneous regression models are widely used to statistically post-process numerical weather prediction models. Such regression models correct for errors in mean and variance and are capable to forecast a full probability distribution. In order to estimate the corresponding regression coefficients, CRPS minimization is performed in many meteorological post-processing studies since the last decade. In contrast to maximum likelihood estimation, CRPS minimization is claimed to yield more calibrated forecasts. Theoretically, both scoring rules used as an optimization score should be able to locate a similar and unknown optimum. Discrepancies might result from a wrong distributional assumption of the observed quantity. To address this theoretical concept, this study compares maximum likelihood and minimum CRPS estimation for different distributional assumptions. First, a synthetic case study shows that, for an appropriate distributional assumption, both estimation methods yield to similar regression coefficients. The log-likelihood estimator is slightly more efficient. A real world case study for surface temperature forecasts at different sites in Europe confirms these results but shows that surface temperature does not always follow the classical assumption of a Gaussian distribution. KEYWORDS: ensemble post-processing, maximum likelihood estimation, CRPS minimization, probabilistic temperature forecasting, distributional regression models

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

Statistical inference based on the nonparametric maximum likelihood estimator under double-truncation.

PubMed

Emura, Takeshi; Konno, Yoshihiko; Michimae, Hirofumi

2015-07-01

Doubly truncated data consist of samples whose observed values fall between the right- and left- truncation limits. With such samples, the distribution function of interest is estimated using the nonparametric maximum likelihood estimator (NPMLE) that is obtained through a self-consistency algorithm. Owing to the complicated asymptotic distribution of the NPMLE, the bootstrap method has been suggested for statistical inference. This paper proposes a closed-form estimator for the asymptotic covariance function of the NPMLE, which is computationally attractive alternative to bootstrapping. Furthermore, we develop various statistical inference procedures, such as confidence interval, goodness-of-fit tests, and confidence bands to demonstrate the usefulness of the proposed covariance estimator. Simulations are performed to compare the proposed method with both the bootstrap and jackknife methods. The methods are illustrated using the childhood cancer dataset.

Program for Weibull Analysis of Fatigue Data

NASA Technical Reports Server (NTRS)

Krantz, Timothy L.

2005-01-01

A Fortran computer program has been written for performing statistical analyses of fatigue-test data that are assumed to be adequately represented by a two-parameter Weibull distribution. This program calculates the following: (1) Maximum-likelihood estimates of the Weibull distribution; (2) Data for contour plots of relative likelihood for two parameters; (3) Data for contour plots of joint confidence regions; (4) Data for the profile likelihood of the Weibull-distribution parameters; (5) Data for the profile likelihood of any percentile of the distribution; and (6) Likelihood-based confidence intervals for parameters and/or percentiles of the distribution. The program can account for tests that are suspended without failure (the statistical term for such suspension of tests is "censoring"). The analytical approach followed in this program for the software is valid for type-I censoring, which is the removal of unfailed units at pre-specified times. Confidence regions and intervals are calculated by use of the likelihood-ratio method.

Do-it-yourself statistics: A computer-assisted likelihood approach to analysis of data from genetic crosses.

PubMed Central

Robbins, L G

2000-01-01

Graduate school programs in genetics have become so full that courses in statistics have often been eliminated. In addition, typical introductory statistics courses for the "statistics user" rather than the nascent statistician are laden with methods for analysis of measured variables while genetic data are most often discrete numbers. These courses are often seen by students and genetics professors alike as largely irrelevant cookbook courses. The powerful methods of likelihood analysis, although commonly employed in human genetics, are much less often used in other areas of genetics, even though current computational tools make this approach readily accessible. This article introduces the MLIKELY.PAS computer program and the logic of do-it-yourself maximum-likelihood statistics. The program itself, course materials, and expanded discussions of some examples that are only summarized here are available at http://www.unisi. it/ricerca/dip/bio_evol/sitomlikely/mlikely.h tml. PMID:10628965

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

Evaluation of a New Mean Scaled and Moment Adjusted Test Statistic for SEM

ERIC Educational Resources Information Center

Tong, Xiaoxiao; Bentler, Peter M.

2013-01-01

Recently a new mean scaled and skewness adjusted test statistic was developed for evaluating structural equation models in small samples and with potentially nonnormal data, but this statistic has received only limited evaluation. The performance of this statistic is compared to normal theory maximum likelihood and 2 well-known robust test…

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.

Comparison of wheat classification accuracy using different classifiers of the image-100 system

NASA Technical Reports Server (NTRS)

Dejesusparada, N. (Principal Investigator); Chen, S. C.; Moreira, M. A.; Delima, A. M.

1981-01-01

Classification results using single-cell and multi-cell signature acquisition options, a point-by-point Gaussian maximum-likelihood classifier, and K-means clustering of the Image-100 system are presented. Conclusions reached are that: a better indication of correct classification can be provided by using a test area which contains various cover types of the study area; classification accuracy should be evaluated considering both the percentages of correct classification and error of commission; supervised classification approaches are better than K-means clustering; Gaussian distribution maximum likelihood classifier is better than Single-cell and Multi-cell Signature Acquisition Options of the Image-100 system; and in order to obtain a high classification accuracy in a large and heterogeneous crop area, using Gaussian maximum-likelihood classifier, homogeneous spectral subclasses of the study crop should be created to derive training statistics.

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.

Pearson-type goodness-of-fit test with bootstrap maximum likelihood estimation.

PubMed

Yin, Guosheng; Ma, Yanyuan

2013-01-01

The Pearson test statistic is constructed by partitioning the data into bins and computing the difference between the observed and expected counts in these bins. If the maximum likelihood estimator (MLE) of the original data is used, the statistic generally does not follow a chi-squared distribution or any explicit distribution. We propose a bootstrap-based modification of the Pearson test statistic to recover the chi-squared distribution. We compute the observed and expected counts in the partitioned bins by using the MLE obtained from a bootstrap sample. This bootstrap-sample MLE adjusts exactly the right amount of randomness to the test statistic, and recovers the chi-squared distribution. The bootstrap chi-squared test is easy to implement, as it only requires fitting exactly the same model to the bootstrap data to obtain the corresponding MLE, and then constructs the bin counts based on the original data. We examine the test size and power of the new model diagnostic procedure using simulation studies and illustrate it with a real data set.

Selection of the Maximum Spatial Cluster Size of the Spatial Scan Statistic by Using the Maximum Clustering Set-Proportion Statistic.

PubMed

Ma, Yue; Yin, Fei; Zhang, Tao; Zhou, Xiaohua Andrew; Li, Xiaosong

2016-01-01

Spatial scan statistics are widely used in various fields. The performance of these statistics is influenced by parameters, such as maximum spatial cluster size, and can be improved by parameter selection using performance measures. Current performance measures are based on the presence of clusters and are thus inapplicable to data sets without known clusters. In this work, we propose a novel overall performance measure called maximum clustering set-proportion (MCS-P), which is based on the likelihood of the union of detected clusters and the applied dataset. MCS-P was compared with existing performance measures in a simulation study to select the maximum spatial cluster size. Results of other performance measures, such as sensitivity and misclassification, suggest that the spatial scan statistic achieves accurate results in most scenarios with the maximum spatial cluster sizes selected using MCS-P. Given that previously known clusters are not required in the proposed strategy, selection of the optimal maximum cluster size with MCS-P can improve the performance of the scan statistic in applications without identified clusters.

Selection of the Maximum Spatial Cluster Size of the Spatial Scan Statistic by Using the Maximum Clustering Set-Proportion Statistic

PubMed Central

Ma, Yue; Yin, Fei; Zhang, Tao; Zhou, Xiaohua Andrew; Li, Xiaosong

2016-01-01

Spatial scan statistics are widely used in various fields. The performance of these statistics is influenced by parameters, such as maximum spatial cluster size, and can be improved by parameter selection using performance measures. Current performance measures are based on the presence of clusters and are thus inapplicable to data sets without known clusters. In this work, we propose a novel overall performance measure called maximum clustering set–proportion (MCS-P), which is based on the likelihood of the union of detected clusters and the applied dataset. MCS-P was compared with existing performance measures in a simulation study to select the maximum spatial cluster size. Results of other performance measures, such as sensitivity and misclassification, suggest that the spatial scan statistic achieves accurate results in most scenarios with the maximum spatial cluster sizes selected using MCS-P. Given that previously known clusters are not required in the proposed strategy, selection of the optimal maximum cluster size with MCS-P can improve the performance of the scan statistic in applications without identified clusters. PMID:26820646

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

ASURV: Astronomical SURVival Statistics

NASA Astrophysics Data System (ADS)

Feigelson, E. D.; Nelson, P. I.; Isobe, T.; LaValley, M.

2014-06-01

ASURV (Astronomical SURVival Statistics) provides astronomy survival analysis for right- and left-censored data including the maximum-likelihood Kaplan-Meier estimator and several univariate two-sample tests, bivariate correlation measures, and linear regressions. ASURV is written in FORTRAN 77, and is stand-alone and does not call any specialized libraries.

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

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.

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.

Additive hazards regression and partial likelihood estimation for ecological monitoring data across space.

PubMed

Lin, Feng-Chang; Zhu, Jun

2012-01-01

We develop continuous-time models for the analysis of environmental or ecological monitoring data such that subjects are observed at multiple monitoring time points across space. Of particular interest are additive hazards regression models where the baseline hazard function can take on flexible forms. We consider time-varying covariates and take into account spatial dependence via autoregression in space and time. We develop statistical inference for the regression coefficients via partial likelihood. Asymptotic properties, including consistency and asymptotic normality, are established for parameter estimates under suitable regularity conditions. Feasible algorithms utilizing existing statistical software packages are developed for computation. We also consider a simpler additive hazards model with homogeneous baseline hazard and develop hypothesis testing for homogeneity. A simulation study demonstrates that the statistical inference using partial likelihood has sound finite-sample properties and offers a viable alternative to maximum likelihood estimation. For illustration, we analyze data from an ecological study that monitors bark beetle colonization of red pines in a plantation of Wisconsin.

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.

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.

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.

An Example of an Improvable Rao-Blackwell Improvement, Inefficient Maximum Likelihood Estimator, and Unbiased Generalized Bayes Estimator.

PubMed

Galili, Tal; Meilijson, Isaac

2016-01-02

The Rao-Blackwell theorem offers a procedure for converting a crude unbiased estimator of a parameter θ into a "better" one, in fact unique and optimal if the improvement is based on a minimal sufficient statistic that is complete. In contrast, behind every minimal sufficient statistic that is not complete, there is an improvable Rao-Blackwell improvement. This is illustrated via a simple example based on the uniform distribution, in which a rather natural Rao-Blackwell improvement is uniformly improvable. Furthermore, in this example the maximum likelihood estimator is inefficient, and an unbiased generalized Bayes estimator performs exceptionally well. Counterexamples of this sort can be useful didactic tools for explaining the true nature of a methodology and possible consequences when some of the assumptions are violated. [Received December 2014. Revised September 2015.].

Maximum a posteriori decoder for digital communications

NASA Technical Reports Server (NTRS)

Altes, Richard A. (Inventor)

1997-01-01

A system and method for decoding by identification of the most likely phase coded signal corresponding to received data. The present invention has particular application to communication with signals that experience spurious random phase perturbations. The generalized estimator-correlator uses a maximum a posteriori (MAP) estimator to generate phase estimates for correlation with incoming data samples and for correlation with mean phases indicative of unique hypothesized signals. The result is a MAP likelihood statistic for each hypothesized transmission, wherein the highest value statistic identifies the transmitted signal.

Variational Bayesian Parameter Estimation Techniques for the General Linear Model

PubMed Central

Starke, Ludger; Ostwald, Dirk

2017-01-01

Variational Bayes (VB), variational maximum likelihood (VML), restricted maximum likelihood (ReML), and maximum likelihood (ML) are cornerstone parametric statistical estimation techniques in the analysis of functional neuroimaging data. However, the theoretical underpinnings of these model parameter estimation techniques are rarely covered in introductory statistical texts. Because of the widespread practical use of VB, VML, ReML, and ML in the neuroimaging community, we reasoned that a theoretical treatment of their relationships and their application in a basic modeling scenario may be helpful for both neuroimaging novices and practitioners alike. In this technical study, we thus revisit the conceptual and formal underpinnings of VB, VML, ReML, and ML and provide a detailed account of their mathematical relationships and implementational details. We further apply VB, VML, ReML, and ML to the general linear model (GLM) with non-spherical error covariance as commonly encountered in the first-level analysis of fMRI data. To this end, we explicitly derive the corresponding free energy objective functions and ensuing iterative algorithms. Finally, in the applied part of our study, we evaluate the parameter and model recovery properties of VB, VML, ReML, and ML, first in an exemplary setting and then in the analysis of experimental fMRI data acquired from a single participant under visual stimulation. PMID:28966572

Empirical best linear unbiased prediction method for small areas with restricted maximum likelihood and bootstrap procedure to estimate the average of household expenditure per capita in Banjar Regency

NASA Astrophysics Data System (ADS)

Aminah, Agustin Siti; Pawitan, Gandhi; Tantular, Bertho

2017-03-01

So far, most of the data published by Statistics Indonesia (BPS) as data providers for national statistics are still limited to the district level. Less sufficient sample size for smaller area levels to make the measurement of poverty indicators with direct estimation produced high standard error. Therefore, the analysis based on it is unreliable. To solve this problem, the estimation method which can provide a better accuracy by combining survey data and other auxiliary data is required. One method often used for the estimation is the Small Area Estimation (SAE). There are many methods used in SAE, one of them is Empirical Best Linear Unbiased Prediction (EBLUP). EBLUP method of maximum likelihood (ML) procedures does not consider the loss of degrees of freedom due to estimating β with β ^. This drawback motivates the use of the restricted maximum likelihood (REML) procedure. This paper proposed EBLUP with REML procedure for estimating poverty indicators by modeling the average of household expenditures per capita and implemented bootstrap procedure to calculate MSE (Mean Square Error) to compare the accuracy EBLUP method with the direct estimation method. Results show that EBLUP method reduced MSE in small area estimation.

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.

Estimation of descriptive statistics for multiply censored water quality data

USGS Publications Warehouse

Helsel, Dennis R.; Cohn, Timothy A.

1988-01-01

This paper extends the work of Gilliom and Helsel (1986) on procedures for estimating descriptive statistics of water quality data that contain “less than” observations. Previously, procedures were evaluated when only one detection limit was present. Here we investigate the performance of estimators for data that have multiple detection limits. Probability plotting and maximum likelihood methods perform substantially better than simple substitution procedures now commonly in use. Therefore simple substitution procedures (e.g., substitution of the detection limit) should be avoided. Probability plotting methods are more robust than maximum likelihood methods to misspecification of the parent distribution and their use should be encouraged in the typical situation where the parent distribution is unknown. When utilized correctly, less than values frequently contain nearly as much information for estimating population moments and quantiles as would the same observations had the detection limit been below them.

Equivalence between Step Selection Functions and Biased Correlated Random Walks for Statistical Inference on Animal Movement.

PubMed

Duchesne, Thierry; Fortin, Daniel; Rivest, Louis-Paul

2015-01-01

Animal movement has a fundamental impact on population and community structure and dynamics. Biased correlated random walks (BCRW) and step selection functions (SSF) are commonly used to study movements. Because no studies have contrasted the parameters and the statistical properties of their estimators for models constructed under these two Lagrangian approaches, it remains unclear whether or not they allow for similar inference. First, we used the Weak Law of Large Numbers to demonstrate that the log-likelihood function for estimating the parameters of BCRW models can be approximated by the log-likelihood of SSFs. Second, we illustrated the link between the two approaches by fitting BCRW with maximum likelihood and with SSF to simulated movement data in virtual environments and to the trajectory of bison (Bison bison L.) trails in natural landscapes. Using simulated and empirical data, we found that the parameters of a BCRW estimated directly from maximum likelihood and by fitting an SSF were remarkably similar. Movement analysis is increasingly used as a tool for understanding the influence of landscape properties on animal distribution. In the rapidly developing field of movement ecology, management and conservation biologists must decide which method they should implement to accurately assess the determinants of animal movement. We showed that BCRW and SSF can provide similar insights into the environmental features influencing animal movements. Both techniques have advantages. BCRW has already been extended to allow for multi-state modeling. Unlike BCRW, however, SSF can be estimated using most statistical packages, it can simultaneously evaluate habitat selection and movement biases, and can easily integrate a large number of movement taxes at multiple scales. SSF thus offers a simple, yet effective, statistical technique to identify movement taxis.

Nonlinear Statistical Estimation with Numerical Maximum Likelihood

DTIC Science & Technology

1974-10-01

probably most directly attributable to the speed, precision and compactness of the linear programming algorithm exercised ; the mutual primal-dual...discriminant analysis is to classify the individual as a member of T# or IT, 1 2 according to the relative...Introduction to the Dissertation 1 Introduction to Statistical Estimation Theory 3 Choice of Estimator.. .Density Functions 12 Choice of Estimator

Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics

NASA Astrophysics Data System (ADS)

Abe, Sumiyoshi

2014-11-01

The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach to systems governed by dynamics with largely separated time scales and is based on three key concepts: conjugate pairs of variables, dimensionless integration measures with coarse-graining factors and partial maximization of the joint entropy. The method enables one to calculate a prior purely from a likelihood in a simple way. It is shown, in particular, how it not only yields Jeffreys's rules but also reveals new structures hidden behind them.

Statistical field estimators for multiscale simulations.

PubMed

Eapen, Jacob; Li, Ju; Yip, Sidney

2005-11-01

We present a systematic approach for generating smooth and accurate fields from particle simulation data using the notions of statistical inference. As an extension to a parametric representation based on the maximum likelihood technique previously developed for velocity and temperature fields, a nonparametric estimator based on the principle of maximum entropy is proposed for particle density and stress fields. Both estimators are applied to represent molecular dynamics data on shear-driven flow in an enclosure which exhibits a high degree of nonlinear characteristics. We show that the present density estimator is a significant improvement over ad hoc bin averaging and is also free of systematic boundary artifacts that appear in the method of smoothing kernel estimates. Similarly, the velocity fields generated by the maximum likelihood estimator do not show any edge effects that can be erroneously interpreted as slip at the wall. For low Reynolds numbers, the velocity fields and streamlines generated by the present estimator are benchmarked against Newtonian continuum calculations. For shear velocities that are a significant fraction of the thermal speed, we observe a form of shear localization that is induced by the confining boundary.

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

Statistical Techniques to Analyze Pesticide Data Program Food Residue Observations.

PubMed

Szarka, Arpad Z; Hayworth, Carol G; Ramanarayanan, Tharacad S; Joseph, Robert S I

2018-06-26

The U.S. EPA conducts dietary-risk assessments to ensure that levels of pesticides on food in the U.S. food supply are safe. Often these assessments utilize conservative residue estimates, maximum residue levels (MRLs), and a high-end estimate derived from registrant-generated field-trial data sets. A more realistic estimate of consumers' pesticide exposure from food may be obtained by utilizing residues from food-monitoring programs, such as the Pesticide Data Program (PDP) of the U.S. Department of Agriculture. A substantial portion of food-residue concentrations in PDP monitoring programs are below the limits of detection (left-censored), which makes the comparison of regulatory-field-trial and PDP residue levels difficult. In this paper, we present a novel adaption of established statistical techniques, the Kaplan-Meier estimator (K-M), the robust regression on ordered statistic (ROS), and the maximum-likelihood estimator (MLE), to quantify the pesticide-residue concentrations in the presence of heavily censored data sets. The examined statistical approaches include the most commonly used parametric and nonparametric methods for handling left-censored data that have been used in the fields of medical and environmental sciences. This work presents a case study in which data of thiamethoxam residue on bell pepper generated from registrant field trials were compared with PDP-monitoring residue values. The results from the statistical techniques were evaluated and compared with commonly used simple substitution methods for the determination of summary statistics. It was found that the maximum-likelihood estimator (MLE) is the most appropriate statistical method to analyze this residue data set. Using the MLE technique, the data analyses showed that the median and mean PDP bell pepper residue levels were approximately 19 and 7 times lower, respectively, than the corresponding statistics of the field-trial residues.

Confidence Intervals for the Between-Study Variance in Random Effects Meta-Analysis Using Generalised Cochran Heterogeneity Statistics

ERIC Educational Resources Information Center

Jackson, Dan

2013-01-01

Statistical inference is problematic in the common situation in meta-analysis where the random effects model is fitted to just a handful of studies. In particular, the asymptotic theory of maximum likelihood provides a poor approximation, and Bayesian methods are sensitive to the prior specification. Hence, less efficient, but easily computed and…

Maximum Likelihood Estimation of Spectra Information from Multiple Independent Astrophysics Data Sets

NASA Technical Reports Server (NTRS)

Howell, Leonard W., Jr.; Six, N. Frank (Technical Monitor)

2002-01-01

The Maximum Likelihood (ML) statistical theory required to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments is developed in this paper. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral information based on the combination of data sets. The procedure is of significant value to both existing data sets and those to be produced by future astrophysics missions consisting of two or more detectors by allowing instrument developers to optimize each detector's design parameters through simulation studies in order to design and build complementary detectors that will maximize the precision with which the science objectives may be obtained. The benefits of this ML theory and its application is measured in terms of the reduction of the statistical errors (standard deviations) of the spectra information using the multiple data sets in concert as compared to the statistical errors of the spectra information when the data sets are considered separately, as well as any biases resulting from poor statistics in one or more of the individual data sets that might be reduced when the data sets are combined.

A likelihood ratio test for evolutionary rate shifts and functional divergence among proteins

PubMed Central

Knudsen, Bjarne; Miyamoto, Michael M.

2001-01-01

Changes in protein function can lead to changes in the selection acting on specific residues. This can often be detected as evolutionary rate changes at the sites in question. A maximum-likelihood method for detecting evolutionary rate shifts at specific protein positions is presented. The method determines significance values of the rate differences to give a sound statistical foundation for the conclusions drawn from the analyses. A statistical test for detecting slowly evolving sites is also described. The methods are applied to a set of Myc proteins for the identification of both conserved sites and those with changing evolutionary rates. Those positions with conserved and changing rates are related to the structures and functions of their proteins. The results are compared with an earlier Bayesian method, thereby highlighting the advantages of the new likelihood ratio tests. PMID:11734650

Neandertal admixture in Eurasia confirmed by maximum-likelihood analysis of three genomes.

PubMed

Lohse, Konrad; Frantz, Laurent A F

2014-04-01

Although there has been much interest in estimating histories of divergence and admixture from genomic data, it has proved difficult to distinguish recent admixture from long-term structure in the ancestral population. Thus, recent genome-wide analyses based on summary statistics have sparked controversy about the possibility of interbreeding between Neandertals and modern humans in Eurasia. Here we derive the probability of full mutational configurations in nonrecombining sequence blocks under both admixture and ancestral structure scenarios. Dividing the genome into short blocks gives an efficient way to compute maximum-likelihood estimates of parameters. We apply this likelihood scheme to triplets of human and Neandertal genomes and compare the relative support for a model of admixture from Neandertals into Eurasian populations after their expansion out of Africa against a history of persistent structure in their common ancestral population in Africa. Our analysis allows us to conclusively reject a model of ancestral structure in Africa and instead reveals strong support for Neandertal admixture in Eurasia at a higher rate (3.4-7.3%) than suggested previously. Using analysis and simulations we show that our inference is more powerful than previous summary statistics and robust to realistic levels of recombination.

Neandertal Admixture in Eurasia Confirmed by Maximum-Likelihood Analysis of Three Genomes

PubMed Central

Lohse, Konrad; Frantz, Laurent A. F.

2014-01-01

Although there has been much interest in estimating histories of divergence and admixture from genomic data, it has proved difficult to distinguish recent admixture from long-term structure in the ancestral population. Thus, recent genome-wide analyses based on summary statistics have sparked controversy about the possibility of interbreeding between Neandertals and modern humans in Eurasia. Here we derive the probability of full mutational configurations in nonrecombining sequence blocks under both admixture and ancestral structure scenarios. Dividing the genome into short blocks gives an efficient way to compute maximum-likelihood estimates of parameters. We apply this likelihood scheme to triplets of human and Neandertal genomes and compare the relative support for a model of admixture from Neandertals into Eurasian populations after their expansion out of Africa against a history of persistent structure in their common ancestral population in Africa. Our analysis allows us to conclusively reject a model of ancestral structure in Africa and instead reveals strong support for Neandertal admixture in Eurasia at a higher rate (3.4−7.3%) than suggested previously. Using analysis and simulations we show that our inference is more powerful than previous summary statistics and robust to realistic levels of recombination. PMID:24532731

New robust statistical procedures for the polytomous logistic regression models.

PubMed

Castilla, Elena; Ghosh, Abhik; Martin, Nirian; Pardo, Leandro

2018-05-17

This article derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a family of Wald-type test statistics for linear hypotheses is introduced. Robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis. Appropriate real life examples are presented to justify the requirement of suitable robust statistical procedures in place of the likelihood based inference for the polytomous logistic regression model. The validity of the theoretical results established in the article are further confirmed empirically through suitable simulation studies. Finally, an approach for the data-driven selection of the robustness tuning parameter is proposed with empirical justifications. © 2018, The International Biometric Society.

Estimation of Multinomial Probabilities.

DTIC Science & Technology

1978-11-01

1971) and Alam (1978) have shown that the maximum likelihood estimator is admissible with respect to the quadratic loss. Steinhaus (1957) and Trybula...appear). Johnson, B. Mck. (1971). On admissible estimators for certain fixed sample binomial populations. Ann. Math. Statist. 92, 1579-1587. Steinhaus , H

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.

Lateral stability and control derivatives of a jet fighter airplane extracted from flight test data by utilizing maximum likelihood estimation

NASA Technical Reports Server (NTRS)

Parrish, R. V.; Steinmetz, G. G.

1972-01-01

A method of parameter extraction for stability and control derivatives of aircraft from flight test data, implementing maximum likelihood estimation, has been developed and successfully applied to actual lateral flight test data from a modern sophisticated jet fighter. This application demonstrates the important role played by the analyst in combining engineering judgment and estimator statistics to yield meaningful results. During the analysis, the problems of uniqueness of the extracted set of parameters and of longitudinal coupling effects were encountered and resolved. The results for all flight runs are presented in tabular form and as time history comparisons between the estimated states and the actual flight test data.

Characterization, parameter estimation, and aircraft response statistics of atmospheric turbulence

NASA Technical Reports Server (NTRS)

Mark, W. D.

1981-01-01

A nonGaussian three component model of atmospheric turbulence is postulated that accounts for readily observable features of turbulence velocity records, their autocorrelation functions, and their spectra. Methods for computing probability density functions and mean exceedance rates of a generic aircraft response variable are developed using nonGaussian turbulence characterizations readily extracted from velocity recordings. A maximum likelihood method is developed for optimal estimation of the integral scale and intensity of records possessing von Karman transverse of longitudinal spectra. Formulas for the variances of such parameter estimates are developed. The maximum likelihood and least-square approaches are combined to yield a method for estimating the autocorrelation function parameters of a two component model for turbulence.

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.

Evaluation of statistical treatments of left-censored environmental data using coincident uncensored data sets: I. Summary statistics

USGS Publications Warehouse

Antweiler, Ronald C.; Taylor, Howard E.

2008-01-01

The main classes of statistical treatment of below-detection limit (left-censored) environmental data for the determination of basic statistics that have been used in the literature are substitution methods, maximum likelihood, regression on order statistics (ROS), and nonparametric techniques. These treatments, along with using all instrument-generated data (even those below detection), were evaluated by examining data sets in which the true values of the censored data were known. It was found that for data sets with less than 70% censored data, the best technique overall for determination of summary statistics was the nonparametric Kaplan-Meier technique. ROS and the two substitution methods of assigning one-half the detection limit value to censored data or assigning a random number between zero and the detection limit to censored data were adequate alternatives. The use of these two substitution methods, however, requires a thorough understanding of how the laboratory censored the data. The technique of employing all instrument-generated data - including numbers below the detection limit - was found to be less adequate than the above techniques. At high degrees of censoring (greater than 70% censored data), no technique provided good estimates of summary statistics. Maximum likelihood techniques were found to be far inferior to all other treatments except substituting zero or the detection limit value to censored data.

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.

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

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

Statistical Properties of SEE Rate Calculation in the Limits of Large and Small Event Counts

NASA Technical Reports Server (NTRS)

Ladbury, Ray

2007-01-01

This viewgraph presentation reviews the Statistical properties of Single Event Effects (SEE) rate calculations. The goal of SEE rate calculation is to bound the SEE rate, though the question is by how much. The presentation covers: (1) Understanding errors on SEE cross sections, (2) Methodology: Maximum Likelihood and confidence Contours, (3) Tests with Simulated data and (4) Applications.

Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics

NASA Technical Reports Server (NTRS)

Shantaram, S. Pai; Gyekenyesi, John P.

1989-01-01

The calculation of shape and scale parametes of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by using the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program.

Sparse representation and dictionary learning penalized image reconstruction for positron emission tomography.

PubMed

Chen, Shuhang; Liu, Huafeng; Shi, Pengcheng; Chen, Yunmei

2015-01-21

Accurate and robust reconstruction of the radioactivity concentration is of great importance in positron emission tomography (PET) imaging. Given the Poisson nature of photo-counting measurements, we present a reconstruction framework that integrates sparsity penalty on a dictionary into a maximum likelihood estimator. Patch-sparsity on a dictionary provides the regularization for our effort, and iterative procedures are used to solve the maximum likelihood function formulated on Poisson statistics. Specifically, in our formulation, a dictionary could be trained on CT images, to provide intrinsic anatomical structures for the reconstructed images, or adaptively learned from the noisy measurements of PET. Accuracy of the strategy with very promising application results from Monte-Carlo simulations, and real data are demonstrated.

Group Influences on Young Adult Warfighters’ Risk Taking

DTIC Science & Technology

2016-12-01

Statistical Analysis Latent linear growth models were fitted using the maximum likelihood estimation method in Mplus (version 7.0; Muthen & Muthen...condition had a higher net score than those in the alone condition (b = 20.53, SE = 6.29, p < .001). Results of the relevant statistical analyses are...8.56 110.86*** 22.01 158.25*** 29.91 Model fit statistics BIC 4004.50 5302.539 5540.58 Chi-square (df) 41.51*** (16) 38.10** (20) 42.19** (20

Simpson's paradox - aggregating and partitioning populations in health disparities of lung cancer patients.

PubMed

Fu, P; Panneerselvam, A; Clifford, B; Dowlati, A; Ma, P C; Zeng, G; Halmos, B; Leidner, R S

2015-12-01

It is well known that non-small cell lung cancer (NSCLC) is a heterogeneous group of diseases. Previous studies have demonstrated genetic variation among different ethnic groups in the epidermal growth factor receptor (EGFR) in NSCLC. Research by our group and others has recently shown a lower frequency of EGFR mutations in African Americans with NSCLC, as compared to their White counterparts. In this study, we use our original study data of EGFR pathway genetics in African American NSCLC as an example to illustrate that univariate analyses based on aggregation versus partition of data leads to contradictory results, in order to emphasize the importance of controlling statistical confounding. We further investigate analytic approaches in logistic regression for data with separation, as is the case in our example data set, and apply appropriate methods to identify predictors of EGFR mutation. Our simulation shows that with separated or nearly separated data, penalized maximum likelihood (PML) produces estimates with smallest bias and approximately maintains the nominal value with statistical power equal to or better than that from maximum likelihood and exact conditional likelihood methods. Application of the PML method in our example data set shows that race and EGFR-FISH are independently significant predictors of EGFR mutation. © The Author(s) 2011.

Probabilities and statistics for backscatter estimates obtained by a scatterometer with applications to new scatterometer design data

NASA Technical Reports Server (NTRS)

Pierson, Willard J., Jr.

1989-01-01

The values of the Normalized Radar Backscattering Cross Section (NRCS), sigma (o), obtained by a scatterometer are random variables whose variance is a known function of the expected value. The probability density function can be obtained from the normal distribution. Models for the expected value obtain it as a function of the properties of the waves on the ocean and the winds that generated the waves. Point estimates of the expected value were found from various statistics given the parameters that define the probability density function for each value. Random intervals were derived with a preassigned probability of containing that value. A statistical test to determine whether or not successive values of sigma (o) are truly independent was derived. The maximum likelihood estimates for wind speed and direction were found, given a model for backscatter as a function of the properties of the waves on the ocean. These estimates are biased as a result of the terms in the equation that involve natural logarithms, and calculations of the point estimates of the maximum likelihood values are used to show that the contributions of the logarithmic terms are negligible and that the terms can be omitted.

Analysis of First-Term Attrition of Non-Prior Service High-Quality U.S. Army Male Recruits

DTIC Science & Technology

1989-12-13

the estimators. Under broad conditions ( Hanushek , 1977 ), the maximum likelihood estimators are: ( a ) consistent (b) asymptotically efficient, and...Diseases, Vol. 24, 1971, pp. 125 - 158. Hanushek , Eric ., and John E. Jackson, Statistical Methods for Social Scientists, Academic Press, New York, 1977

An overview of the essential differences and similarities of system identification techniques

NASA Technical Reports Server (NTRS)

Mehra, Raman K.

1991-01-01

Information is given in the form of outlines, graphs, tables and charts. Topics include system identification, Bayesian statistical decision theory, Maximum Likelihood Estimation, identification methods, structural mode identification using a stochastic realization algorithm, and identification results regarding membrane simulations and X-29 flutter flight test data.

The amplitude and spectral index of the large angular scale anisotropy in the cosmic microwave background radiation

NASA Technical Reports Server (NTRS)

Ganga, Ken; Page, Lyman; Cheng, Edward; Meyer, Stephan

1994-01-01

In many cosmological models, the large angular scale anisotropy in the cosmic microwave background is parameterized by a spectral index, n, and a quadrupolar amplitude, Q. For a Harrison-Peebles-Zel'dovich spectrum, n = 1. Using data from the Far Infrared Survey (FIRS) and a new statistical measure, a contour plot of the likelihood for cosmological models for which -1 less than n less than 3 and 0 equal to or less than Q equal to or less than 50 micro K is obtained. Depending upon the details of the analysis, the maximum likelihood occurs at n between 0.8 and 1.4 and Q between 18 and 21 micro K. Regardless of Q, the likelihood is always less than half its maximum for n less than -0.4 and for n greater than 2.2, as it is for Q less than 8 micro K and Q greater than 44 micro K.

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.

Fitting distributions to microbial contamination data collected with an unequal probability sampling design.

PubMed

Williams, M S; Ebel, E D; Cao, Y

2013-01-01

The fitting of statistical distributions to microbial sampling data is a common application in quantitative microbiology and risk assessment applications. An underlying assumption of most fitting techniques is that data are collected with simple random sampling, which is often times not the case. This study develops a weighted maximum likelihood estimation framework that is appropriate for microbiological samples that are collected with unequal probabilities of selection. A weighted maximum likelihood estimation framework is proposed for microbiological samples that are collected with unequal probabilities of selection. Two examples, based on the collection of food samples during processing, are provided to demonstrate the method and highlight the magnitude of biases in the maximum likelihood estimator when data are inappropriately treated as a simple random sample. Failure to properly weight samples to account for how data are collected can introduce substantial biases into inferences drawn from the data. The proposed methodology will reduce or eliminate an important source of bias in inferences drawn from the analysis of microbial data. This will also make comparisons between studies and the combination of results from different studies more reliable, which is important for risk assessment applications. © 2012 No claim to US Government works.

Fast and accurate estimation of the covariance between pairwise maximum likelihood distances.

PubMed

Gil, Manuel

2014-01-01

Pairwise evolutionary distances are a model-based summary statistic for a set of molecular sequences. They represent the leaf-to-leaf path lengths of the underlying phylogenetic tree. Estimates of pairwise distances with overlapping paths covary because of shared mutation events. It is desirable to take these covariance structure into account to increase precision in any process that compares or combines distances. This paper introduces a fast estimator for the covariance of two pairwise maximum likelihood distances, estimated under general Markov models. The estimator is based on a conjecture (going back to Nei & Jin, 1989) which links the covariance to path lengths. It is proven here under a simple symmetric substitution model. A simulation shows that the estimator outperforms previously published ones in terms of the mean squared error.

Fast and accurate estimation of the covariance between pairwise maximum likelihood distances

PubMed Central

2014-01-01

Pairwise evolutionary distances are a model-based summary statistic for a set of molecular sequences. They represent the leaf-to-leaf path lengths of the underlying phylogenetic tree. Estimates of pairwise distances with overlapping paths covary because of shared mutation events. It is desirable to take these covariance structure into account to increase precision in any process that compares or combines distances. This paper introduces a fast estimator for the covariance of two pairwise maximum likelihood distances, estimated under general Markov models. The estimator is based on a conjecture (going back to Nei & Jin, 1989) which links the covariance to path lengths. It is proven here under a simple symmetric substitution model. A simulation shows that the estimator outperforms previously published ones in terms of the mean squared error. PMID:25279263

Development of advanced techniques for rotorcraft state estimation and parameter identification

NASA Technical Reports Server (NTRS)

Hall, W. E., Jr.; Bohn, J. G.; Vincent, J. H.

1980-01-01

An integrated methodology for rotorcraft system identification consists of rotorcraft mathematical modeling, three distinct data processing steps, and a technique for designing inputs to improve the identifiability of the data. These elements are as follows: (1) a Kalman filter smoother algorithm which estimates states and sensor errors from error corrupted data. Gust time histories and statistics may also be estimated; (2) a model structure estimation algorithm for isolating a model which adequately explains the data; (3) a maximum likelihood algorithm for estimating the parameters and estimates for the variance of these estimates; and (4) an input design algorithm, based on a maximum likelihood approach, which provides inputs to improve the accuracy of parameter estimates. Each step is discussed with examples to both flight and simulated data cases.

Gaussian statistics of the cosmic microwave background: Correlation of temperature extrema in the COBE DMR two-year sky maps

NASA Technical Reports Server (NTRS)

Kogut, A.; Banday, A. J.; Bennett, C. L.; Hinshaw, G.; Lubin, P. M.; Smoot, G. F.

1995-01-01

We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.

Local multiplicity adjustment for the spatial scan statistic using the Gumbel distribution.

PubMed

Gangnon, Ronald E

2012-03-01

The spatial scan statistic is an important and widely used tool for cluster detection. It is based on the simultaneous evaluation of the statistical significance of the maximum likelihood ratio test statistic over a large collection of potential clusters. In most cluster detection problems, there is variation in the extent of local multiplicity across the study region. For example, using a fixed maximum geographic radius for clusters, urban areas typically have many overlapping potential clusters, whereas rural areas have relatively few. The spatial scan statistic does not account for local multiplicity variation. We describe a previously proposed local multiplicity adjustment based on a nested Bonferroni correction and propose a novel adjustment based on a Gumbel distribution approximation to the distribution of a local scan statistic. We compare the performance of all three statistics in terms of power and a novel unbiased cluster detection criterion. These methods are then applied to the well-known New York leukemia dataset and a Wisconsin breast cancer incidence dataset. © 2011, The International Biometric Society.

Local multiplicity adjustment for the spatial scan statistic using the Gumbel distribution

PubMed Central

Gangnon, Ronald E.

2011-01-01

Summary The spatial scan statistic is an important and widely used tool for cluster detection. It is based on the simultaneous evaluation of the statistical significance of the maximum likelihood ratio test statistic over a large collection of potential clusters. In most cluster detection problems, there is variation in the extent of local multiplicity across the study region. For example, using a fixed maximum geographic radius for clusters, urban areas typically have many overlapping potential clusters, while rural areas have relatively few. The spatial scan statistic does not account for local multiplicity variation. We describe a previously proposed local multiplicity adjustment based on a nested Bonferroni correction and propose a novel adjustment based on a Gumbel distribution approximation to the distribution of a local scan statistic. We compare the performance of all three statistics in terms of power and a novel unbiased cluster detection criterion. These methods are then applied to the well-known New York leukemia dataset and a Wisconsin breast cancer incidence dataset. PMID:21762118

A Bootstrap Generalization of Modified Parallel Analysis for IRT Dimensionality Assessment

ERIC Educational Resources Information Center

Finch, Holmes; Monahan, Patrick

2008-01-01

This article introduces a bootstrap generalization to the Modified Parallel Analysis (MPA) method of test dimensionality assessment using factor analysis. This methodology, based on the use of Marginal Maximum Likelihood nonlinear factor analysis, provides for the calculation of a test statistic based on a parametric bootstrap using the MPA…

3D image reconstruction algorithms for cryo-electron-microscopy images of virus particles

NASA Astrophysics Data System (ADS)

Doerschuk, Peter C.; Johnson, John E.

2000-11-01

A statistical model for the object and the complete image formation process in cryo electron microscopy of viruses is presented. Using this model, maximum likelihood reconstructions of the 3D structure of viruses are computed using the expectation maximization algorithm and an example based on Cowpea mosaic virus is provided.

Lod score curves for phase-unknown matings.

PubMed

Hulbert-Shearon, T; Boehnke, M; Lange, K

1996-01-01

For a phase-unknown nuclear family, we show that the likelihood and lod score are unimodal, and we describe conditions under which the maximum occurs at recombination fraction theta = 0, theta = 1/2, and 0 < theta < 1/2. These simply stated necessary and sufficient conditions seem to have escaped the notice of previous statistical geneticists.

A Statistical Model for Misreported Binary Outcomes in Clustered RCTs of Education Interventions

ERIC Educational Resources Information Center

Schochet, Peter Z.

2013-01-01

In randomized control trials (RCTs) of educational interventions, there is a growing literature on impact estimation methods to adjust for missing student outcome data using such methods as multiple imputation, the construction of nonresponse weights, casewise deletion, and maximum likelihood methods (see, for example, Allison, 2002; Graham, 2009;…

Maximum likelihood sequence estimation for optical complex direct modulation.

PubMed

Che, Di; Yuan, Feng; Shieh, William

2017-04-17

Semiconductor lasers are versatile optical transmitters in nature. Through the direct modulation (DM), the intensity modulation is realized by the linear mapping between the injection current and the light power, while various angle modulations are enabled by the frequency chirp. Limited by the direct detection, DM lasers used to be exploited only as 1-D (intensity or angle) transmitters by suppressing or simply ignoring the other modulation. Nevertheless, through the digital coherent detection, simultaneous intensity and angle modulations (namely, 2-D complex DM, CDM) can be realized by a single laser diode. The crucial technique of CDM is the joint demodulation of intensity and differential phase with the maximum likelihood sequence estimation (MLSE), supported by a closed-form discrete signal approximation of frequency chirp to characterize the MLSE transition probability. This paper proposes a statistical method for the transition probability to significantly enhance the accuracy of the chirp model. Using the statistical estimation, we demonstrate the first single-channel 100-Gb/s PAM-4 transmission over 1600-km fiber with only 10G-class DM lasers.

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

Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics

NASA Technical Reports Server (NTRS)

Pai, Shantaram S.; Gyekenyesi, John P.

1988-01-01

The calculation of shape and scale parameters of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by uing the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded. The techniques described were verified with several example problems from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program.

The Extended Erlang-Truncated Exponential distribution: Properties and application to rainfall data.

PubMed

Okorie, I E; Akpanta, A C; Ohakwe, J; Chikezie, D C

2017-06-01

The Erlang-Truncated Exponential ETE distribution is modified and the new lifetime distribution is called the Extended Erlang-Truncated Exponential EETE distribution. Some statistical and reliability properties of the new distribution are given and the method of maximum likelihood estimate was proposed for estimating the model parameters. The usefulness and flexibility of the EETE distribution was illustrated with an uncensored data set and its fit was compared with that of the ETE and three other three-parameter distributions. Results based on the minimized log-likelihood ([Formula: see text]), Akaike information criterion (AIC), Bayesian information criterion (BIC) and the generalized Cramér-von Mises [Formula: see text] statistics shows that the EETE distribution provides a more reasonable fit than the one based on the other competing distributions.

Maximum likelihood: Extracting unbiased information from complex networks

NASA Astrophysics Data System (ADS)

Garlaschelli, Diego; Loffredo, Maria I.

2008-07-01

The choice of free parameters in network models is subjective, since it depends on what topological properties are being monitored. However, we show that the maximum likelihood (ML) principle indicates a unique, statistically rigorous parameter choice, associated with a well-defined topological feature. We then find that, if the ML condition is incompatible with the built-in parameter choice, network models turn out to be intrinsically ill defined or biased. To overcome this problem, we construct a class of safely unbiased models. We also propose an extension of these results that leads to the fascinating possibility to extract, only from topological data, the “hidden variables” underlying network organization, making them “no longer hidden.” We test our method on World Trade Web data, where we recover the empirical gross domestic product using only topological information.

Image classification at low light levels

NASA Astrophysics Data System (ADS)

Wernick, Miles N.; Morris, G. Michael

1986-12-01

An imaging photon-counting detector is used to achieve automatic sorting of two image classes. The classification decision is formed on the basis of the cross correlation between a photon-limited input image and a reference function stored in computer memory. Expressions for the statistical parameters of the low-light-level correlation signal are given and are verified experimentally. To obtain a correlation-based system for two-class sorting, it is necessary to construct a reference function that produces useful information for class discrimination. An expression for such a reference function is derived using maximum-likelihood decision theory. Theoretically predicted results are used to compare on the basis of performance the maximum-likelihood reference function with Fukunaga-Koontz basis vectors and average filters. For each method, good class discrimination is found to result in milliseconds from a sparse sampling of the input image.

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.

Empirical likelihood method for non-ignorable missing data problems.

PubMed

Guan, Zhong; Qin, Jing

2017-01-01

Missing response problem is ubiquitous in survey sampling, medical, social science and epidemiology studies. It is well known that non-ignorable missing is the most difficult missing data problem where the missing of a response depends on its own value. In statistical literature, unlike the ignorable missing data problem, not many papers on non-ignorable missing data are available except for the full parametric model based approach. In this paper we study a semiparametric model for non-ignorable missing data in which the missing probability is known up to some parameters, but the underlying distributions are not specified. By employing Owen (1988)'s empirical likelihood method we can obtain the constrained maximum empirical likelihood estimators of the parameters in the missing probability and the mean response which are shown to be asymptotically normal. Moreover the likelihood ratio statistic can be used to test whether the missing of the responses is non-ignorable or completely at random. The theoretical results are confirmed by a simulation study. As an illustration, the analysis of a real AIDS trial data shows that the missing of CD4 counts around two years are non-ignorable and the sample mean based on observed data only is biased.

High-Performance Clock Synchronization Algorithms for Distributed Wireless Airborne Computer Networks with Applications to Localization and Tracking of Targets

DTIC Science & Technology

2010-06-01

GMKPF represents a better and more flexible alternative to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ...accurate results relative to GML and EML when the network delays are modeled in terms of a single non-Gaussian/non-exponential distribution or as a...to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ) estimators for clock offset estimation in non-Gaussian or non

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.

ReplacementMatrix: a web server for maximum-likelihood estimation of amino acid replacement rate matrices.

PubMed

Dang, Cuong Cao; Lefort, Vincent; Le, Vinh Sy; Le, Quang Si; Gascuel, Olivier

2011-10-01

Amino acid replacement rate matrices are an essential basis of protein studies (e.g. in phylogenetics and alignment). A number of general purpose matrices have been proposed (e.g. JTT, WAG, LG) since the seminal work of Margaret Dayhoff and co-workers. However, it has been shown that matrices specific to certain protein groups (e.g. mitochondrial) or life domains (e.g. viruses) differ significantly from general average matrices, and thus perform better when applied to the data to which they are dedicated. This Web server implements the maximum-likelihood estimation procedure that was used to estimate LG, and provides a number of tools and facilities. Users upload a set of multiple protein alignments from their domain of interest and receive the resulting matrix by email, along with statistics and comparisons with other matrices. A non-parametric bootstrap is performed optionally to assess the variability of replacement rate estimates. Maximum-likelihood trees, inferred using the estimated rate matrix, are also computed optionally for each input alignment. Finely tuned procedures and up-to-date ML software (PhyML 3.0, XRATE) are combined to perform all these heavy calculations on our clusters. http://www.atgc-montpellier.fr/ReplacementMatrix/ olivier.gascuel@lirmm.fr Supplementary data are available at http://www.atgc-montpellier.fr/ReplacementMatrix/

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.

Composite Linear Models | Division of Cancer Prevention

Cancer.gov

By Stuart G. Baker The composite linear models software is a matrix approach to compute maximum likelihood estimates and asymptotic standard errors for models for incomplete multinomial data. It implements the method described in Baker SG. Composite linear models for incomplete multinomial data. Statistics in Medicine 1994;13:609-622. The software includes a library of thirty

Implementing Restricted Maximum Likelihood Estimation in Structural Equation Models

ERIC Educational Resources Information Center

Cheung, Mike W.-L.

2013-01-01

Structural equation modeling (SEM) is now a generic modeling framework for many multivariate techniques applied in the social and behavioral sciences. Many statistical models can be considered either as special cases of SEM or as part of the latent variable modeling framework. One popular extension is the use of SEM to conduct linear mixed-effects…

Fisher, Sir Ronald Aylmer (1890-1962)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Statistician, born in London, England. After studying astronomy using AIRY's manual on the Theory of Errors he became interested in statistics, and laid the foundation of randomization in experimental design, the analysis of variance and the use of data in estimating the properties of the parent population from which it was drawn. Invented the maximum likelihood method for estimating from random ...

The Effect of Missing Data Handling Methods on Goodness of Fit Indices in Confirmatory Factor Analysis

ERIC Educational Resources Information Center

Köse, Alper

2014-01-01

The primary objective of this study was to examine the effect of missing data on goodness of fit statistics in confirmatory factor analysis (CFA). For this aim, four missing data handling methods; listwise deletion, full information maximum likelihood, regression imputation and expectation maximization (EM) imputation were examined in terms of…

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.

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.

The Inverse Problem for Confined Aquifer Flow: Identification and Estimation With Extensions

NASA Astrophysics Data System (ADS)

Loaiciga, Hugo A.; MariñO, Miguel A.

1987-01-01

The contributions of this work are twofold. First, a methodology for estimating the elements of parameter matrices in the governing equation of flow in a confined aquifer is developed. The estimation techniques for the distributed-parameter inverse problem pertain to linear least squares and generalized least squares methods. The linear relationship among the known heads and unknown parameters of the flow equation provides the background for developing criteria for determining the identifiability status of unknown parameters. Under conditions of exact or overidentification it is possible to develop statistically consistent parameter estimators and their asymptotic distributions. The estimation techniques, namely, two-stage least squares and three stage least squares, are applied to a specific groundwater inverse problem and compared between themselves and with an ordinary least squares estimator. The three-stage estimator provides the closer approximation to the actual parameter values, but it also shows relatively large standard errors as compared to the ordinary and two-stage estimators. The estimation techniques provide the parameter matrices required to simulate the unsteady groundwater flow equation. Second, a nonlinear maximum likelihood estimation approach to the inverse problem is presented. The statistical properties of maximum likelihood estimators are derived, and a procedure to construct confidence intervals and do hypothesis testing is given. The relative merits of the linear and maximum likelihood estimators are analyzed. Other topics relevant to the identification and estimation methodologies, i.e., a continuous-time solution to the flow equation, coping with noise-corrupted head measurements, and extension of the developed theory to nonlinear cases are also discussed. A simulation study is used to evaluate the methods developed in this study.

Probabilistic properties of the date of maximum river flow, an approach based on circular statistics in lowland, highland and mountainous catchment

NASA Astrophysics Data System (ADS)

Rutkowska, Agnieszka; Kohnová, Silvia; Banasik, Kazimierz

2018-04-01

Probabilistic properties of dates of winter, summer and annual maximum flows were studied using circular statistics in three catchments differing in topographic conditions; a lowland, highland and mountainous catchment. The circular measures of location and dispersion were used in the long-term samples of dates of maxima. The mixture of von Mises distributions was assumed as the theoretical distribution function of the date of winter, summer and annual maximum flow. The number of components was selected on the basis of the corrected Akaike Information Criterion and the parameters were estimated by means of the Maximum Likelihood method. The goodness of fit was assessed using both the correlation between quantiles and a version of the Kuiper's and Watson's test. Results show that the number of components varied between catchments and it was different for seasonal and annual maxima. Differences between catchments in circular characteristics were explained using climatic factors such as precipitation and temperature. Further studies may include circular grouping catchments based on similarity between distribution functions and the linkage between dates of maximum precipitation and maximum flow.

Signal Statistics and Maximum Likelihood Sequence Estimation in Intensity Modulated Fiber Optic Links Containing a Single Optical Pre-amplifier.

PubMed

Alić, Nikola; Papen, George; Saperstein, Robert; Milstein, Laurence; Fainman, Yeshaiahu

2005-06-13

Exact signal statistics for fiber-optic links containing a single optical pre-amplifier are calculated and applied to sequence estimation for electronic dispersion compensation. The performance is evaluated and compared with results based on the approximate chi-square statistics. We show that detection in existing systems based on exact statistics can be improved relative to using a chi-square distribution for realistic filter shapes. In contrast, for high-spectral efficiency systems the difference between the two approaches diminishes, and performance tends to be less dependent on the exact shape of the filter used.

Evidence and Clinical Trials.

NASA Astrophysics Data System (ADS)

Goodman, Steven N.

1989-11-01

This dissertation explores the use of a mathematical measure of statistical evidence, the log likelihood ratio, in clinical trials. The methods and thinking behind the use of an evidential measure are contrasted with traditional methods of analyzing data, which depend primarily on a p-value as an estimate of the statistical strength of an observed data pattern. It is contended that neither the behavioral dictates of Neyman-Pearson hypothesis testing methods, nor the coherency dictates of Bayesian methods are realistic models on which to base inference. The use of the likelihood alone is applied to four aspects of trial design or conduct: the calculation of sample size, the monitoring of data, testing for the equivalence of two treatments, and meta-analysis--the combining of results from different trials. Finally, a more general model of statistical inference, using belief functions, is used to see if it is possible to separate the assessment of evidence from our background knowledge. It is shown that traditional and Bayesian methods can be modeled as two ends of a continuum of structured background knowledge, methods which summarize evidence at the point of maximum likelihood assuming no structure, and Bayesian methods assuming complete knowledge. Both schools are seen to be missing a concept of ignorance- -uncommitted belief. This concept provides the key to understanding the problem of sampling to a foregone conclusion and the role of frequency properties in statistical inference. The conclusion is that statistical evidence cannot be defined independently of background knowledge, and that frequency properties of an estimator are an indirect measure of uncommitted belief. Several likelihood summaries need to be used in clinical trials, with the quantitative disparity between summaries being an indirect measure of our ignorance. This conclusion is linked with parallel ideas in the philosophy of science and cognitive psychology.

A flexible spatial scan statistic with a restricted likelihood ratio for detecting disease clusters.

PubMed

Tango, Toshiro; Takahashi, Kunihiko

2012-12-30

Spatial scan statistics are widely used tools for detection of disease clusters. Especially, the circular spatial scan statistic proposed by Kulldorff (1997) has been utilized in a wide variety of epidemiological studies and disease surveillance. However, as it cannot detect noncircular, irregularly shaped clusters, many authors have proposed different spatial scan statistics, including the elliptic version of Kulldorff's scan statistic. The flexible spatial scan statistic proposed by Tango and Takahashi (2005) has also been used for detecting irregularly shaped clusters. However, this method sets a feasible limitation of a maximum of 30 nearest neighbors for searching candidate clusters because of heavy computational load. In this paper, we show a flexible spatial scan statistic implemented with a restricted likelihood ratio proposed by Tango (2008) to (1) eliminate the limitation of 30 nearest neighbors and (2) to have surprisingly much less computational time than the original flexible spatial scan statistic. As a side effect, it is shown to be able to detect clusters with any shape reasonably well as the relative risk of the cluster becomes large via Monte Carlo simulation. We illustrate the proposed spatial scan statistic with data on mortality from cerebrovascular disease in the Tokyo Metropolitan area, Japan. Copyright © 2012 John Wiley & Sons, Ltd.

Probability, statistics, and computational science.

PubMed

Beerenwinkel, Niko; Siebourg, Juliane

2012-01-01

In this chapter, we review basic concepts from probability theory and computational statistics that are fundamental to evolutionary genomics. We provide a very basic introduction to statistical modeling and discuss general principles, including maximum likelihood and Bayesian inference. Markov chains, hidden Markov models, and Bayesian network models are introduced in more detail as they occur frequently and in many variations in genomics applications. In particular, we discuss efficient inference algorithms and methods for learning these models from partially observed data. Several simple examples are given throughout the text, some of which point to models that are discussed in more detail in subsequent chapters.

Markov modulated Poisson process models incorporating covariates for rainfall intensity.

PubMed

Thayakaran, R; Ramesh, N I

2013-01-01

Time series of rainfall bucket tip times at the Beaufort Park station, Bracknell, in the UK are modelled by a class of Markov modulated Poisson processes (MMPP) which may be thought of as a generalization of the Poisson process. Our main focus in this paper is to investigate the effects of including covariate information into the MMPP model framework on statistical properties. In particular, we look at three types of time-varying covariates namely temperature, sea level pressure, and relative humidity that are thought to be affecting the rainfall arrival process. Maximum likelihood estimation is used to obtain the parameter estimates, and likelihood ratio tests are employed in model comparison. Simulated data from the fitted model are used to make statistical inferences about the accumulated rainfall in the discrete time interval. Variability of the daily Poisson arrival rates is studied.

L.U.St: a tool for approximated maximum likelihood supertree reconstruction.

PubMed

Akanni, Wasiu A; Creevey, Christopher J; Wilkinson, Mark; Pisani, Davide

2014-06-12

Supertrees combine disparate, partially overlapping trees to generate a synthesis that provides a high level perspective that cannot be attained from the inspection of individual phylogenies. Supertrees can be seen as meta-analytical tools that can be used to make inferences based on results of previous scientific studies. Their meta-analytical application has increased in popularity since it was realised that the power of statistical tests for the study of evolutionary trends critically depends on the use of taxon-dense phylogenies. Further to that, supertrees have found applications in phylogenomics where they are used to combine gene trees and recover species phylogenies based on genome-scale data sets. Here, we present the L.U.St package, a python tool for approximate maximum likelihood supertree inference and illustrate its application using a genomic data set for the placental mammals. L.U.St allows the calculation of the approximate likelihood of a supertree, given a set of input trees, performs heuristic searches to look for the supertree of highest likelihood, and performs statistical tests of two or more supertrees. To this end, L.U.St implements a winning sites test allowing ranking of a collection of a-priori selected hypotheses, given as a collection of input supertree topologies. It also outputs a file of input-tree-wise likelihood scores that can be used as input to CONSEL for calculation of standard tests of two trees (e.g. Kishino-Hasegawa, Shimidoara-Hasegawa and Approximately Unbiased tests). This is the first fully parametric implementation of a supertree method, it has clearly understood properties, and provides several advantages over currently available supertree approaches. It is easy to implement and works on any platform that has python installed. bitBucket page - https://afro-juju@bitbucket.org/afro-juju/l.u.st.git. Davide.Pisani@bristol.ac.uk.

A Comparison of Local Variance, Fractal Dimension, and Moran's I as Aids to Multispectral Image Classification

NASA Technical Reports Server (NTRS)

Emerson, Charles W.; Sig-NganLam, Nina; Quattrochi, Dale A.

2004-01-01

The accuracy of traditional multispectral maximum-likelihood image classification is limited by the skewed statistical distributions of reflectances from the complex heterogenous mixture of land cover types in urban areas. This work examines the utility of local variance, fractal dimension and Moran's I index of spatial autocorrelation in segmenting multispectral satellite imagery. Tools available in the Image Characterization and Modeling System (ICAMS) were used to analyze Landsat 7 imagery of Atlanta, Georgia. Although segmentation of panchromatic images is possible using indicators of spatial complexity, different land covers often yield similar values of these indices. Better results are obtained when a surface of local fractal dimension or spatial autocorrelation is combined as an additional layer in a supervised maximum-likelihood multispectral classification. The addition of fractal dimension measures is particularly effective at resolving land cover classes within urbanized areas, as compared to per-pixel spectral classification techniques.

Maximum Likelihood Reconstruction for Magnetic Resonance Fingerprinting

PubMed Central

Zhao, Bo; Setsompop, Kawin; Ye, Huihui; Cauley, Stephen; Wald, Lawrence L.

2017-01-01

This paper introduces a statistical estimation framework for magnetic resonance (MR) fingerprinting, a recently proposed quantitative imaging paradigm. Within this framework, we present a maximum likelihood (ML) formalism to estimate multiple parameter maps directly from highly undersampled, noisy k-space data. A novel algorithm, based on variable splitting, the alternating direction method of multipliers, and the variable projection method, is developed to solve the resulting optimization problem. Representative results from both simulations and in vivo experiments demonstrate that the proposed approach yields significantly improved accuracy in parameter estimation, compared to the conventional MR fingerprinting reconstruction. Moreover, the proposed framework provides new theoretical insights into the conventional approach. We show analytically that the conventional approach is an approximation to the ML reconstruction; more precisely, it is exactly equivalent to the first iteration of the proposed algorithm for the ML reconstruction, provided that a gridding reconstruction is used as an initialization. PMID:26915119

Maximum Likelihood Reconstruction for Magnetic Resonance Fingerprinting.

PubMed

Zhao, Bo; Setsompop, Kawin; Ye, Huihui; Cauley, Stephen F; Wald, Lawrence L

2016-08-01

This paper introduces a statistical estimation framework for magnetic resonance (MR) fingerprinting, a recently proposed quantitative imaging paradigm. Within this framework, we present a maximum likelihood (ML) formalism to estimate multiple MR tissue parameter maps directly from highly undersampled, noisy k-space data. A novel algorithm, based on variable splitting, the alternating direction method of multipliers, and the variable projection method, is developed to solve the resulting optimization problem. Representative results from both simulations and in vivo experiments demonstrate that the proposed approach yields significantly improved accuracy in parameter estimation, compared to the conventional MR fingerprinting reconstruction. Moreover, the proposed framework provides new theoretical insights into the conventional approach. We show analytically that the conventional approach is an approximation to the ML reconstruction; more precisely, it is exactly equivalent to the first iteration of the proposed algorithm for the ML reconstruction, provided that a gridding reconstruction is used as an initialization.

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.

High throughput nonparametric probability density estimation.

PubMed

Farmer, Jenny; Jacobs, Donald

2018-01-01

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference.

High throughput nonparametric probability density estimation

PubMed Central

Farmer, Jenny

2018-01-01

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference. PMID:29750803

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 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.

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.

Maximum-likelihood estimation of recent shared ancestry (ERSA).

PubMed

Huff, Chad D; Witherspoon, David J; Simonson, Tatum S; Xing, Jinchuan; Watkins, W Scott; Zhang, Yuhua; Tuohy, Therese M; Neklason, Deborah W; Burt, Randall W; Guthery, Stephen L; Woodward, Scott R; Jorde, Lynn B

2011-05-01

Accurate estimation of recent shared ancestry is important for genetics, evolution, medicine, conservation biology, and forensics. Established methods estimate kinship accurately for first-degree through third-degree relatives. We demonstrate that chromosomal segments shared by two individuals due to identity by descent (IBD) provide much additional information about shared ancestry. We developed a maximum-likelihood method for the estimation of recent shared ancestry (ERSA) from the number and lengths of IBD segments derived from high-density SNP or whole-genome sequence data. We used ERSA to estimate relationships from SNP genotypes in 169 individuals from three large, well-defined human pedigrees. ERSA is accurate to within one degree of relationship for 97% of first-degree through fifth-degree relatives and 80% of sixth-degree and seventh-degree relatives. We demonstrate that ERSA's statistical power approaches the maximum theoretical limit imposed by the fact that distant relatives frequently share no DNA through a common ancestor. ERSA greatly expands the range of relationships that can be estimated from genetic data and is implemented in a freely available software package.

Mapping grass communities based on multi-temporal Landsat TM imagery and environmental variables

NASA Astrophysics Data System (ADS)

Zeng, Yuandi; Liu, Yanfang; Liu, Yaolin; de Leeuw, Jan

2007-06-01

Information on the spatial distribution of grass communities in wetland is increasingly recognized as important for effective wetland management and biological conservation. Remote sensing techniques has been proved to be an effective alternative to intensive and costly ground surveys for mapping grass community. However, the mapping accuracy of grass communities in wetland is still not preferable. The aim of this paper is to develop an effective method to map grass communities in Poyang Lake Natural Reserve. Through statistic analysis, elevation is selected as an environmental variable for its high relationship with the distribution of grass communities; NDVI stacked from images of different months was used to generate Carex community map; the image in October was used to discriminate Miscanthus and Cynodon communities. Classifications were firstly performed with maximum likelihood classifier using single date satellite image with and without elevation; then layered classifications were performed using multi-temporal satellite imagery and elevation with maximum likelihood classifier, decision tree and artificial neural network separately. The results show that environmental variables can improve the mapping accuracy; and the classification with multitemporal imagery and elevation is significantly better than that with single date image and elevation (p=0.001). Besides, maximum likelihood (a=92.71%, k=0.90) and artificial neural network (a=94.79%, k=0.93) perform significantly better than decision tree (a=86.46%, k=0.83).

Load estimator (LOADEST): a FORTRAN program for estimating constituent loads in streams and rivers

USGS Publications Warehouse

Runkel, Robert L.; Crawford, Charles G.; Cohn, Timothy A.

2004-01-01

LOAD ESTimator (LOADEST) is a FORTRAN program for estimating constituent loads in streams and rivers. Given a time series of streamflow, additional data variables, and constituent concentration, LOADEST assists the user in developing a regression model for the estimation of constituent load (calibration). Explanatory variables within the regression model include various functions of streamflow, decimal time, and additional user-specified data variables. The formulated regression model then is used to estimate loads over a user-specified time interval (estimation). Mean load estimates, standard errors, and 95 percent confidence intervals are developed on a monthly and(or) seasonal basis. The calibration and estimation procedures within LOADEST are based on three statistical estimation methods. The first two methods, Adjusted Maximum Likelihood Estimation (AMLE) and Maximum Likelihood Estimation (MLE), are appropriate when the calibration model errors (residuals) are normally distributed. Of the two, AMLE is the method of choice when the calibration data set (time series of streamflow, additional data variables, and concentration) contains censored data. The third method, Least Absolute Deviation (LAD), is an alternative to maximum likelihood estimation when the residuals are not normally distributed. LOADEST output includes diagnostic tests and warnings to assist the user in determining the appropriate estimation method and in interpreting the estimated loads. This report describes the development and application of LOADEST. Sections of the report describe estimation theory, input/output specifications, sample applications, and installation instructions.

MultiPhyl: a high-throughput phylogenomics webserver using distributed computing

PubMed Central

Keane, Thomas M.; Naughton, Thomas J.; McInerney, James O.

2007-01-01

With the number of fully sequenced genomes increasing steadily, there is greater interest in performing large-scale phylogenomic analyses from large numbers of individual gene families. Maximum likelihood (ML) has been shown repeatedly to be one of the most accurate methods for phylogenetic construction. Recently, there have been a number of algorithmic improvements in maximum-likelihood-based tree search methods. However, it can still take a long time to analyse the evolutionary history of many gene families using a single computer. Distributed computing refers to a method of combining the computing power of multiple computers in order to perform some larger overall calculation. In this article, we present the first high-throughput implementation of a distributed phylogenetics platform, MultiPhyl, capable of using the idle computational resources of many heterogeneous non-dedicated machines to form a phylogenetics supercomputer. MultiPhyl allows a user to upload hundreds or thousands of amino acid or nucleotide alignments simultaneously and perform computationally intensive tasks such as model selection, tree searching and bootstrapping of each of the alignments using many desktop machines. The program implements a set of 88 amino acid models and 56 nucleotide maximum likelihood models and a variety of statistical methods for choosing between alternative models. A MultiPhyl webserver is available for public use at: http://www.cs.nuim.ie/distributed/multiphyl.php. PMID:17553837

Bayesian inference based on dual generalized order statistics from the exponentiated Weibull model

NASA Astrophysics Data System (ADS)

Al Sobhi, Mashail M.

2015-02-01

Bayesian estimation for the two parameters and the reliability function of the exponentiated Weibull model are obtained based on dual generalized order statistics (DGOS). Also, Bayesian prediction bounds for future DGOS from exponentiated Weibull model are obtained. The symmetric and asymmetric loss functions are considered for Bayesian computations. The Markov chain Monte Carlo (MCMC) methods are used for computing the Bayes estimates and prediction bounds. The results have been specialized to the lower record values. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.

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

Beaumier, Michael J.

This thesis discusses the process of extracting the longitudinal asymmetry, Amore » $$W±\\atop{L}$$ describing W → μ production in forward kinematic regimes. This asymmetry is used to constrain our understanding of the polarized parton distribution functions characterizing $$\\bar{u}$$ and $$\\bar{d}$$ sea quarks in the proton. This asymmetry will be used to constrain the overall contribution of the sea-quarks to the total proton spin. The asymmetry is evaluated over the pseudorapidity range of the PHENIX Muon Arms, 2.1 < |η| 2.6, for longitudinally polarized proton-proton collisions at 510 GeV √s. In particular, I will discuss the statistical methods used to characterize real muonic W decays and the various background processes is presented, including a discussion of likelihood event selection and the Extended Unbinned Maximum Likelihood t. These statistical methods serve estimate the yields of W muonic decays, which are used to calculate the longitudinal asymmetry.« less

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.

A likelihood-based time series modeling approach for application in dendrochronology to examine the growth-climate relations and forest disturbance history.

PubMed

Lee, E Henry; Wickham, Charlotte; Beedlow, Peter A; Waschmann, Ronald S; Tingey, David T

2017-10-01

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 climate and forest disturbances (i.e., pests, diseases, fire). The statistical method is illustrated with a tree-ring width time series for a mature closed-canopy Douglas-fir stand on the west slopes of the Cascade Mountains of Oregon, USA that is impacted by Swiss needle cast disease caused by the foliar fungus, Phaecryptopus gaeumannii (Rhode) Petrak. The likelihood-based TSIA method is proposed for the field of dendrochronology to understand the interaction of temperature, water, and forest disturbances that are important in forest ecology and climate change studies.

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.

GNSS Spoofing Detection and Mitigation Based on Maximum Likelihood Estimation

PubMed Central

Li, Hong; Lu, Mingquan

2017-01-01

Spoofing attacks are threatening the global navigation satellite system (GNSS). The maximum likelihood estimation (MLE)-based positioning technique is a direct positioning method originally developed for multipath rejection and weak signal processing. We find this method also has a potential ability for GNSS anti-spoofing since a spoofing attack that misleads the positioning and timing result will cause distortion to the MLE cost function. Based on the method, an estimation-cancellation approach is presented to detect spoofing attacks and recover the navigation solution. A statistic is derived for spoofing detection with the principle of the generalized likelihood ratio test (GLRT). Then, the MLE cost function is decomposed to further validate whether the navigation solution obtained by MLE-based positioning is formed by consistent signals. Both formulae and simulations are provided to evaluate the anti-spoofing performance. Experiments with recordings in real GNSS spoofing scenarios are also performed to validate the practicability of the approach. Results show that the method works even when the code phase differences between the spoofing and authentic signals are much less than one code chip, which can improve the availability of GNSS service greatly under spoofing attacks. PMID:28665318

GNSS Spoofing Detection and Mitigation Based on Maximum Likelihood Estimation.

PubMed

Wang, Fei; Li, Hong; Lu, Mingquan

2017-06-30

Spoofing attacks are threatening the global navigation satellite system (GNSS). The maximum likelihood estimation (MLE)-based positioning technique is a direct positioning method originally developed for multipath rejection and weak signal processing. We find this method also has a potential ability for GNSS anti-spoofing since a spoofing attack that misleads the positioning and timing result will cause distortion to the MLE cost function. Based on the method, an estimation-cancellation approach is presented to detect spoofing attacks and recover the navigation solution. A statistic is derived for spoofing detection with the principle of the generalized likelihood ratio test (GLRT). Then, the MLE cost function is decomposed to further validate whether the navigation solution obtained by MLE-based positioning is formed by consistent signals. Both formulae and simulations are provided to evaluate the anti-spoofing performance. Experiments with recordings in real GNSS spoofing scenarios are also performed to validate the practicability of the approach. Results show that the method works even when the code phase differences between the spoofing and authentic signals are much less than one code chip, which can improve the availability of GNSS service greatly under spoofing attacks.

Propagation of Statistical Noise Through a Two-Qubit Maximum Likelihood Tomography

DTIC Science & Technology

2018-04-01

University Daniel E Jones, Brian T Kirby, and Michael Brodsky Computational and Information Sciences Directorate, ARL Approved for...collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources...gathering and maintaining the data needed, and completing and reviewing the collection information . Send comments regarding this burden estimate or any other

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.

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.

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.

Detecting changes in ultrasound backscattered statistics by using Nakagami parameters: Comparisons of moment-based and maximum likelihood estimators.

PubMed

Lin, Jen-Jen; Cheng, Jung-Yu; Huang, Li-Fei; Lin, Ying-Hsiu; Wan, Yung-Liang; Tsui, Po-Hsiang

2017-05-01

The Nakagami distribution is an approximation useful to the statistics of ultrasound backscattered signals for tissue characterization. Various estimators may affect the Nakagami parameter in the detection of changes in backscattered statistics. In particular, the moment-based estimator (MBE) and maximum likelihood estimator (MLE) are two primary methods used to estimate the Nakagami parameters of ultrasound signals. This study explored the effects of the MBE and different MLE approximations on Nakagami parameter estimations. Ultrasound backscattered signals of different scatterer number densities were generated using a simulation model, and phantom experiments and measurements of human liver tissues were also conducted to acquire real backscattered echoes. Envelope signals were employed to estimate the Nakagami parameters by using the MBE, first- and second-order approximations of MLE (MLE 1 and MLE 2 , respectively), and Greenwood approximation (MLE gw ) for comparisons. The simulation results demonstrated that, compared with the MBE and MLE 1 , the MLE 2 and MLE gw enabled more stable parameter estimations with small sample sizes. Notably, the required data length of the envelope signal was 3.6 times the pulse length. The phantom and tissue measurement results also showed that the Nakagami parameters estimated using the MLE 2 and MLE gw could simultaneously differentiate various scatterer concentrations with lower standard deviations and reliably reflect physical meanings associated with the backscattered statistics. Therefore, the MLE 2 and MLE gw are suggested as estimators for the development of Nakagami-based methodologies for ultrasound tissue characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

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...

Maximum likelihood inference implies a high, not a low, ancestral haploid chromosome number in Araceae, with a critique of the bias introduced by ‘x’

PubMed Central

Cusimano, Natalie; Sousa, Aretuza; Renner, Susanne S.

2012-01-01

Background and Aims For 84 years, botanists have relied on calculating the highest common factor for series of haploid chromosome numbers to arrive at a so-called basic number, x. This was done without consistent (reproducible) reference to species relationships and frequencies of different numbers in a clade. Likelihood models that treat polyploidy, chromosome fusion and fission as events with particular probabilities now allow reconstruction of ancestral chromosome numbers in an explicit framework. We have used a modelling approach to reconstruct chromosome number change in the large monocot family Araceae and to test earlier hypotheses about basic numbers in the family. Methods Using a maximum likelihood approach and chromosome counts for 26 % of the 3300 species of Araceae and representative numbers for each of the other 13 families of Alismatales, polyploidization events and single chromosome changes were inferred on a genus-level phylogenetic tree for 113 of the 117 genera of Araceae. Key Results The previously inferred basic numbers x = 14 and x = 7 are rejected. Instead, maximum likelihood optimization revealed an ancestral haploid chromosome number of n = 16, Bayesian inference of n = 18. Chromosome fusion (loss) is the predominant inferred event, whereas polyploidization events occurred less frequently and mainly towards the tips of the tree. Conclusions The bias towards low basic numbers (x) introduced by the algebraic approach to inferring chromosome number changes, prevalent among botanists, may have contributed to an unrealistic picture of ancestral chromosome numbers in many plant clades. The availability of robust quantitative methods for reconstructing ancestral chromosome numbers on molecular phylogenetic trees (with or without branch length information), with confidence statistics, makes the calculation of x an obsolete approach, at least when applied to large clades. PMID:22210850

Maximum Likelihood Detection of Electro-Optic Moving Targets

DTIC Science & Technology

1992-01-16

indicates intensity. The Infrared Measurements Sensor (IRMS) is a scanning sensor that collects both long wave- length infrared ( LWIR , 8 to 12 fim...moving clutter. Nonstationary spatial statistics correspond to the nonuniform intensity of the background scene. An equivalent viewpoint is to...Figure 6 compares theory and experiment for 10 frames of the Longjump LWIR data obtained from the IRMS scanning sensor, which is looking at a background

Bayesian Monte Carlo and Maximum Likelihood Approach for ...

EPA Pesticide Factsheets

Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood estimation (BMCML) to calibrate a lake oxygen recovery model. We first derive an analytical solution of the differential equation governing lake-averaged oxygen dynamics as a function of time-variable wind speed. Statistical inferences on model parameters and predictive uncertainty are then drawn by Bayesian conditioning of the analytical solution on observed daily wind speed and oxygen concentration data obtained from an earlier study during two recovery periods on a eutrophic lake in upper state New York. The model is calibrated using oxygen recovery data for one year and statistical inferences were validated using recovery data for another year. Compared with essentially two-step, regression and optimization approach, the BMCML results are more comprehensive and performed relatively better in predicting the observed temporal dissolved oxygen levels (DO) in the lake. BMCML also produced comparable calibration and validation results with those obtained using popular Markov Chain Monte Carlo technique (MCMC) and is computationally simpler and easier to implement than the MCMC. Next, using the calibrated model, we derive an optimal relationship between liquid film-transfer coefficien

Automated thematic mapping and change detection of ERTS-A images. [farmlands, cities, and mountain identification in Utah, Washington, Arizona, and California

NASA Technical Reports Server (NTRS)

Gramenopoulos, N. (Principal Investigator)

1974-01-01

The author has identified the following significant results. A diffraction pattern analysis of MSS images led to the development of spatial signatures for farm land, urban areas and mountains. Four spatial features are employed to describe the spatial characteristics of image cells in the digital data. Three spectral features are combined with the spatial features to form a seven dimensional vector describing each cell. Then, the classification of the feature vectors is accomplished by using the maximum likelihood criterion. It was determined that the recognition accuracy with the maximum likelihood criterion depends on the statistics of the feature vectors. 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. Three ERTS-1 images from the Phoenix, Arizona area were processed, and recognition rates between 85% and 100% were obtained for the terrain classes of desert, farms, mountains, and urban areas. To eliminate the need for training data, a new clustering algorithm has been developed. Seven ERTS-1 images from four test sites have been processed through the clustering algorithm, and high recognition rates have been achieved for all terrain classes.

Maximum likelihood-based analysis of single-molecule photon arrival trajectories

NASA Astrophysics Data System (ADS)

Hajdziona, Marta; Molski, Andrzej

2011-02-01

In this work we explore the statistical properties of the maximum likelihood-based analysis of one-color photon arrival trajectories. This approach does not involve binning and, therefore, all of the information contained in an observed photon strajectory is used. We study the accuracy and precision of parameter estimates and the efficiency of the Akaike information criterion and the Bayesian information criterion (BIC) in selecting the true kinetic model. We focus on the low excitation regime where photon trajectories can be modeled as realizations of Markov modulated Poisson processes. The number of observed photons is the key parameter in determining model selection and parameter estimation. For example, the BIC can select the true three-state model from competing two-, three-, and four-state kinetic models even for relatively short trajectories made up of 2 × 103 photons. When the intensity levels are well-separated and 104 photons are observed, the two-state model parameters can be estimated with about 10% precision and those for a three-state model with about 20% precision.

How to Deal with Interval-Censored Data Practically while Assessing the Progression-Free Survival: A Step-by-Step Guide Using SAS and R Software.

PubMed

Dugué, Audrey Emmanuelle; Pulido, Marina; Chabaud, Sylvie; Belin, Lisa; Gal, Jocelyn

2016-12-01

We describe how to estimate progression-free survival while dealing with interval-censored data in the setting of clinical trials in oncology. Three procedures with SAS and R statistical software are described: one allowing for a nonparametric maximum likelihood estimation of the survival curve using the EM-ICM (Expectation and Maximization-Iterative Convex Minorant) algorithm as described by Wellner and Zhan in 1997; a sensitivity analysis procedure in which the progression time is assigned (i) at the midpoint, (ii) at the upper limit (reflecting the standard analysis when the progression time is assigned at the first radiologic exam showing progressive disease), or (iii) at the lower limit of the censoring interval; and finally, two multiple imputations are described considering a uniform or the nonparametric maximum likelihood estimation (NPMLE) distribution. Clin Cancer Res; 22(23); 5629-35. ©2016 AACR. ©2016 American Association for Cancer Research.

Extended maximum likelihood halo-independent analysis of dark matter direct detection data

DOE PAGES

Gelmini, Graciela B.; Georgescu, Andreea; Gondolo, Paolo; ...

2015-11-24

We extend and correct a recently proposed maximum-likelihood halo-independent method to analyze unbinned direct dark matter detection data. Instead of the recoil energy as independent variable we use the minimum speed a dark matter particle must have to impart a given recoil energy to a nucleus. This has the advantage of allowing us to apply the method to any type of target composition and interaction, e.g. with general momentum and velocity dependence, and with elastic or inelastic scattering. We prove the method and provide a rigorous statistical interpretation of the results. As first applications, we find that for dark mattermore » particles with elastic spin-independent interactions and neutron to proton coupling ratio f n/f p=-0.7, the WIMP interpretation of the signal observed by CDMS-II-Si is compatible with the constraints imposed by all other experiments with null results. We also find a similar compatibility for exothermic inelastic spin-independent interactions with f n/f p=-0.8.« less

Filtered maximum likelihood expectation maximization based global reconstruction for bioluminescence tomography.

PubMed

Yang, Defu; Wang, Lin; Chen, Dongmei; Yan, Chenggang; He, Xiaowei; Liang, Jimin; Chen, Xueli

2018-05-17

The reconstruction of bioluminescence tomography (BLT) is severely ill-posed due to the insufficient measurements and diffuses nature of the light propagation. Predefined permissible source region (PSR) combined with regularization terms is one common strategy to reduce such ill-posedness. However, the region of PSR is usually hard to determine and can be easily affected by subjective consciousness. Hence, we theoretically developed a filtered maximum likelihood expectation maximization (fMLEM) method for BLT. Our method can avoid predefining the PSR and provide a robust and accurate result for global reconstruction. In the method, the simplified spherical harmonics approximation (SP N ) was applied to characterize diffuse light propagation in medium, and the statistical estimation-based MLEM algorithm combined with a filter function was used to solve the inverse problem. We systematically demonstrated the performance of our method by the regular geometry- and digital mouse-based simulations and a liver cancer-based in vivo experiment. Graphical abstract The filtered MLEM-based global reconstruction method for BLT.

Sensing multiple ligands with single receptor

NASA Astrophysics Data System (ADS)

Singh, Vijay; Nemenman, Ilya

2015-03-01

Cells use surface receptors to measure concentrations of external ligand molecules. Limits on the accuracy of such sensing are well-known for the scenario where concentration of one molecular species is being determined by one receptor [Endres]. However, in more realistic scenarios, a cognate (high-affinity) ligand competes with many non-cognate (low-affinity) ligands for binding to the receptor. We analyze effects of this competition on the accuracy of sensing. We show that maximum-likelihood statistical inference allows determination of concentrations of multiple ligands, cognate and non-cognate, by the same receptor concurrently. While it is unclear if traditional biochemical circuitry downstream of the receptor can implement such inference exactly, we show that an approximate inference can be performed by coupling the receptor to a kinetic proofreading cascade. We characterize the accuracy of such kinetic proofreading sensing in comparison to the exact maximum-likelihood approach. We acknowledge the support from the James S. McDonnell Foundation and the Human Frontier Science Program.

Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states

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

Wu, Hao; Mey, Antonia S. J. S.; Noé, Frank

2014-12-07

We propose a discrete transition-based reweighting analysis method (dTRAM) for analyzing configuration-space-discretized simulation trajectories produced at different thermodynamic states (temperatures, Hamiltonians, etc.) dTRAM provides maximum-likelihood estimates of stationary quantities (probabilities, free energies, expectation values) at any thermodynamic state. In contrast to the weighted histogram analysis method (WHAM), dTRAM does not require data to be sampled from global equilibrium, and can thus produce superior estimates for enhanced sampling data such as parallel/simulated tempering, replica exchange, umbrella sampling, or metadynamics. In addition, dTRAM provides optimal estimates of Markov state models (MSMs) from the discretized state-space trajectories at all thermodynamic states. Under suitablemore » conditions, these MSMs can be used to calculate kinetic quantities (e.g., rates, timescales). In the limit of a single thermodynamic state, dTRAM estimates a maximum likelihood reversible MSM, while in the limit of uncorrelated sampling data, dTRAM is identical to WHAM. dTRAM is thus a generalization to both estimators.« less

Testing Multivariate Adaptive Regression Splines (MARS) as a Method of Land Cover Classification of TERRA-ASTER Satellite Images.

PubMed

Quirós, Elia; Felicísimo, Angel M; Cuartero, Aurora

2009-01-01

This work proposes a new method to classify multi-spectral satellite images based on multivariate adaptive regression splines (MARS) and compares this classification system with the more common parallelepiped and maximum likelihood (ML) methods. We apply the classification methods to the land cover classification of a test zone located in southwestern Spain. The basis of the MARS method and its associated procedures are explained in detail, and the area under the ROC curve (AUC) is compared for the three methods. The results show that the MARS method provides better results than the parallelepiped method in all cases, and it provides better results than the maximum likelihood method in 13 cases out of 17. These results demonstrate that the MARS method can be used in isolation or in combination with other methods to improve the accuracy of soil cover classification. The improvement is statistically significant according to the Wilcoxon signed rank test.

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.

Maximum Likelihood Analysis of Low Energy CDMS II Germanium Data

DOE PAGES

Agnese, R.

2015-03-30

We report on the results of a search for a Weakly Interacting Massive Particle (WIMP) signal in low-energy data of the Cryogenic Dark Matter Search experiment using a maximum likelihood analysis. A background model is constructed using GEANT4 to simulate the surface-event background from Pb210decay-chain events, while using independent calibration data to model the gamma background. Fitting this background model to the data results in no statistically significant WIMP component. In addition, we also perform fits using an analytic ad hoc background model proposed by Collar and Fields, who claimed to find a large excess of signal-like events in ourmore » data. Finally, we confirm the strong preference for a signal hypothesis in their analysis under these assumptions, but excesses are observed in both single- and multiple-scatter events, which implies the signal is not caused by WIMPs, but rather reflects the inadequacy of their background model.« less

Estimating contaminant loads in rivers: An application of adjusted maximum likelihood to type 1 censored data

USGS Publications Warehouse

Cohn, Timothy A.

2005-01-01

This paper presents an adjusted maximum likelihood estimator (AMLE) that can be used to estimate fluvial transport of contaminants, like phosphorus, that are subject to censoring because of analytical detection limits. The AMLE is a generalization of the widely accepted minimum variance unbiased estimator (MVUE), and Monte Carlo experiments confirm that it shares essentially all of the MVUE's desirable properties, including high efficiency and negligible bias. In particular, the AMLE exhibits substantially less bias than alternative censored‐data estimators such as the MLE (Tobit) or the MLE followed by a jackknife. As with the MLE and the MVUE the AMLE comes close to achieving the theoretical Frechet‐Cramér‐Rao bounds on its variance. This paper also presents a statistical framework, applicable to both censored and complete data, for understanding and estimating the components of uncertainty associated with load estimates. This can serve to lower the cost and improve the efficiency of both traditional and real‐time water quality monitoring.

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.

Model averaging techniques for quantifying conceptual model uncertainty.

PubMed

Singh, Abhishek; Mishra, Srikanta; Ruskauff, Greg

2010-01-01

In recent years a growing understanding has emerged regarding the need to expand the modeling paradigm to include conceptual model uncertainty for groundwater models. Conceptual model uncertainty is typically addressed by formulating alternative model conceptualizations and assessing their relative likelihoods using statistical model averaging approaches. Several model averaging techniques and likelihood measures have been proposed in the recent literature for this purpose with two broad categories--Monte Carlo-based techniques such as Generalized Likelihood Uncertainty Estimation or GLUE (Beven and Binley 1992) and criterion-based techniques that use metrics such as the Bayesian and Kashyap Information Criteria (e.g., the Maximum Likelihood Bayesian Model Averaging or MLBMA approach proposed by Neuman 2003) and Akaike Information Criterion-based model averaging (AICMA) (Poeter and Anderson 2005). These different techniques can often lead to significantly different relative model weights and ranks because of differences in the underlying statistical assumptions about the nature of model uncertainty. This paper provides a comparative assessment of the four model averaging techniques (GLUE, MLBMA with KIC, MLBMA with BIC, and AIC-based model averaging) mentioned above for the purpose of quantifying the impacts of model uncertainty on groundwater model predictions. Pros and cons of each model averaging technique are examined from a practitioner's perspective using two groundwater modeling case studies. Recommendations are provided regarding the use of these techniques in groundwater modeling practice.

Standard and goodness-of-fit parameter estimation methods for the three-parameter lognormal distribution

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

Kane, V.E.

1982-01-01

A class of goodness-of-fit estimators is found to provide a useful alternative in certain situations to the standard maximum likelihood method which has some undesirable estimation characteristics for estimation from the three-parameter lognormal distribution. The class of goodness-of-fit tests considered include the Shapiro-Wilk and Filliben tests which reduce to a weighted linear combination of the order statistics that can be maximized in estimation problems. The weighted order statistic estimators are compared to the standard procedures in Monte Carlo simulations. Robustness of the procedures are examined and example data sets analyzed.

A product Pearson-type VII density distribution

NASA Astrophysics Data System (ADS)

Nadarajah, Saralees; Kotz, Samuel

2008-01-01

The Pearson-type VII distributions (containing the Student's t distributions) are becoming increasing prominent and are being considered as competitors to the normal distribution. Motivated by real examples in decision sciences, Bayesian statistics, probability theory and Physics, a new Pearson-type VII distribution is introduced by taking the product of two Pearson-type VII pdfs. Various structural properties of this distribution are derived, including its cdf, moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix. Finally, an application to a Bayesian testing problem is illustrated.

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

Univariate and bivariate likelihood-based meta-analysis methods performed comparably when marginal sensitivity and specificity were the targets of inference.

PubMed

Dahabreh, Issa J; Trikalinos, Thomas A; Lau, Joseph; Schmid, Christopher H

2017-03-01

To compare statistical methods for meta-analysis of sensitivity and specificity of medical tests (e.g., diagnostic or screening tests). We constructed a database of PubMed-indexed meta-analyses of test performance from which 2 × 2 tables for each included study could be extracted. We reanalyzed the data using univariate and bivariate random effects models fit with inverse variance and maximum likelihood methods. Analyses were performed using both normal and binomial likelihoods to describe within-study variability. The bivariate model using the binomial likelihood was also fit using a fully Bayesian approach. We use two worked examples-thoracic computerized tomography to detect aortic injury and rapid prescreening of Papanicolaou smears to detect cytological abnormalities-to highlight that different meta-analysis approaches can produce different results. We also present results from reanalysis of 308 meta-analyses of sensitivity and specificity. Models using the normal approximation produced sensitivity and specificity estimates closer to 50% and smaller standard errors compared to models using the binomial likelihood; absolute differences of 5% or greater were observed in 12% and 5% of meta-analyses for sensitivity and specificity, respectively. Results from univariate and bivariate random effects models were similar, regardless of estimation method. Maximum likelihood and Bayesian methods produced almost identical summary estimates under the bivariate model; however, Bayesian analyses indicated greater uncertainty around those estimates. Bivariate models produced imprecise estimates of the between-study correlation of sensitivity and specificity. Differences between methods were larger with increasing proportion of studies that were small or required a continuity correction. The binomial likelihood should be used to model within-study variability. Univariate and bivariate models give similar estimates of the marginal distributions for sensitivity and specificity. Bayesian methods fully quantify uncertainty and their ability to incorporate external evidence may be useful for imprecisely estimated parameters. Copyright © 2017 Elsevier Inc. All rights reserved.

An evaluation of several different classification schemes - Their parameters and performance. [maximum likelihood decision for crop identification

NASA Technical Reports Server (NTRS)

Scholz, D.; Fuhs, N.; Hixson, M.

1979-01-01

The overall objective of this study was to apply and evaluate several of the currently available classification schemes for crop identification. The approaches examined were: (1) a per point Gaussian maximum likelihood classifier, (2) a per point sum of normal densities classifier, (3) a per point linear classifier, (4) a per point Gaussian maximum likelihood decision tree classifier, and (5) a texture sensitive per field Gaussian maximum likelihood classifier. Three agricultural data sets were used in the study: areas from Fayette County, Illinois, and Pottawattamie and Shelby Counties in Iowa. The segments were located in two distinct regions of the Corn Belt to sample variability in soils, climate, and agricultural practices.

Modelling maximum river flow by using Bayesian Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Cheong, R. Y.; Gabda, D.

2017-09-01

Analysis of flood trends is vital since flooding threatens human living in terms of financial, environment and security. The data of annual maximum river flows in Sabah were fitted into generalized extreme value (GEV) distribution. Maximum likelihood estimator (MLE) raised naturally when working with GEV distribution. However, previous researches showed that MLE provide unstable results especially in small sample size. In this study, we used different Bayesian Markov Chain Monte Carlo (MCMC) based on Metropolis-Hastings algorithm to estimate GEV parameters. Bayesian MCMC method is a statistical inference which studies the parameter estimation by using posterior distribution based on Bayes’ theorem. Metropolis-Hastings algorithm is used to overcome the high dimensional state space faced in Monte Carlo method. This approach also considers more uncertainty in parameter estimation which then presents a better prediction on maximum river flow in Sabah.

Inverse Ising problem in continuous time: A latent variable approach

NASA Astrophysics Data System (ADS)

Donner, Christian; Opper, Manfred

2017-12-01

We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.

Deterministic annealing for density estimation by multivariate normal mixtures

NASA Astrophysics Data System (ADS)

Kloppenburg, Martin; Tavan, Paul

1997-03-01

An approach to maximum-likelihood density estimation by mixtures of multivariate normal distributions for large high-dimensional data sets is presented. Conventionally that problem is tackled by notoriously unstable expectation-maximization (EM) algorithms. We remove these instabilities by the introduction of soft constraints, enabling deterministic annealing. Our developments are motivated by the proof that algorithmically stable fuzzy clustering methods that are derived from statistical physics analogs are special cases of EM procedures.

Spatial Statistics of Large Astronomical Databases: An Algorithmic Approach

NASA Technical Reports Server (NTRS)

Szapudi, Istvan

2004-01-01

In this AISRP, the we have demonstrated that the correlation function i) can be calculated for MAP in minutes (about 45 minutes for Planck) on a modest 500Mhz workstation ii) the corresponding method, although theoretically suboptimal, produces nearly optimal results for realistic noise and cut sky. This trillion fold improvement in speed over the standard maximum likelihood technique opens up tremendous new possibilities, which will be persued in the follow up.

Maximum-Likelihood Detection Of Noncoherent CPM

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Simon, Marvin K.

1993-01-01

Simplified detectors proposed for use in maximum-likelihood-sequence detection of symbols in alphabet of size M transmitted by uncoded, full-response continuous phase modulation over radio channel with additive white Gaussian noise. Structures of receivers derived from particular interpretation of maximum-likelihood metrics. Receivers include front ends, structures of which depends only on M, analogous to those in receivers of coherent CPM. Parts of receivers following front ends have structures, complexity of which would depend on N.

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

Framework for adaptive multiscale analysis of nonhomogeneous point processes.

PubMed

Helgason, Hannes; Bartroff, Jay; Abry, Patrice

2011-01-01

We develop the methodology for hypothesis testing and model selection in nonhomogeneous Poisson processes, with an eye toward the application of modeling and variability detection in heart beat data. Modeling the process' non-constant rate function using templates of simple basis functions, we develop the generalized likelihood ratio statistic for a given template and a multiple testing scheme to model-select from a family of templates. A dynamic programming algorithm inspired by network flows is used to compute the maximum likelihood template in a multiscale manner. In a numerical example, the proposed procedure is nearly as powerful as the super-optimal procedures that know the true template size and true partition, respectively. Extensions to general history-dependent point processes is discussed.

Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood

PubMed Central

Bondell, Howard D.; Stefanski, Leonard A.

2013-01-01

Large- and finite-sample efficiency and resistance to outliers are the key goals of robust statistics. Although often not simultaneously attainable, we develop and study a linear regression estimator that comes close. Efficiency obtains from the estimator’s close connection to generalized empirical likelihood, and its favorable robustness properties are obtained by constraining the associated sum of (weighted) squared residuals. We prove maximum attainable finite-sample replacement breakdown point, and full asymptotic efficiency for normal errors. Simulation evidence shows that compared to existing robust regression estimators, the new estimator has relatively high efficiency for small sample sizes, and comparable outlier resistance. The estimator is further illustrated and compared to existing methods via application to a real data set with purported outliers. PMID:23976805

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.

Stochastic control system parameter identifiability

NASA Technical Reports Server (NTRS)

Lee, C. H.; Herget, C. J.

1975-01-01

The parameter identification problem of general discrete time, nonlinear, multiple input/multiple output dynamic systems with Gaussian white distributed measurement errors is considered. The knowledge of the system parameterization was assumed to be known. Concepts of local parameter identifiability and local constrained maximum likelihood parameter identifiability were established. A set of sufficient conditions for the existence of a region of parameter identifiability was derived. A computation procedure employing interval arithmetic was provided for finding the regions of parameter identifiability. If the vector of the true parameters is locally constrained maximum likelihood (CML) identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the constrained maximum likelihood estimation sequence will converge to the vector of true parameters.

A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior

DOE PAGES

Ye, Xin; Garikapati, Venu M.; You, Daehyun; ...

2017-11-08

Most multinomial choice models (e.g., the multinomial logit model) adopted in practice assume an extreme-value Gumbel distribution for the random components (error terms) of utility functions. This distributional assumption offers a closed-form likelihood expression when the utility maximization principle is applied to model choice behaviors. As a result, model coefficients can be easily estimated using the standard maximum likelihood estimation method. However, maximum likelihood estimators are consistent and efficient only if distributional assumptions on the random error terms are valid. It is therefore critical to test the validity of underlying distributional assumptions on the error terms that form the basismore » of parameter estimation and policy evaluation. In this paper, a practical yet statistically rigorous method is proposed to test the validity of the distributional assumption on the random components of utility functions in both the multinomial logit (MNL) model and multiple discrete-continuous extreme value (MDCEV) model. Based on a semi-nonparametric approach, a closed-form likelihood function that nests the MNL or MDCEV model being tested is derived. The proposed method allows traditional likelihood ratio tests to be used to test violations of the standard Gumbel distribution assumption. Simulation experiments are conducted to demonstrate that the proposed test yields acceptable Type-I and Type-II error probabilities at commonly available sample sizes. The test is then applied to three real-world discrete and discrete-continuous choice models. For all three models, the proposed test rejects the validity of the standard Gumbel distribution in most utility functions, calling for the development of robust choice models that overcome adverse effects of violations of distributional assumptions on the error terms in random utility functions.« less

A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior

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

Ye, Xin; Garikapati, Venu M.; You, Daehyun

Most multinomial choice models (e.g., the multinomial logit model) adopted in practice assume an extreme-value Gumbel distribution for the random components (error terms) of utility functions. This distributional assumption offers a closed-form likelihood expression when the utility maximization principle is applied to model choice behaviors. As a result, model coefficients can be easily estimated using the standard maximum likelihood estimation method. However, maximum likelihood estimators are consistent and efficient only if distributional assumptions on the random error terms are valid. It is therefore critical to test the validity of underlying distributional assumptions on the error terms that form the basismore » of parameter estimation and policy evaluation. In this paper, a practical yet statistically rigorous method is proposed to test the validity of the distributional assumption on the random components of utility functions in both the multinomial logit (MNL) model and multiple discrete-continuous extreme value (MDCEV) model. Based on a semi-nonparametric approach, a closed-form likelihood function that nests the MNL or MDCEV model being tested is derived. The proposed method allows traditional likelihood ratio tests to be used to test violations of the standard Gumbel distribution assumption. Simulation experiments are conducted to demonstrate that the proposed test yields acceptable Type-I and Type-II error probabilities at commonly available sample sizes. The test is then applied to three real-world discrete and discrete-continuous choice models. For all three models, the proposed test rejects the validity of the standard Gumbel distribution in most utility functions, calling for the development of robust choice models that overcome adverse effects of violations of distributional assumptions on the error terms in random utility functions.« less

Challenges in Species Tree Estimation Under the Multispecies Coalescent Model

PubMed Central

Xu, Bo; Yang, Ziheng

2016-01-01

The multispecies coalescent (MSC) model has emerged as a powerful framework for inferring species phylogenies while accounting for ancestral polymorphism and gene tree-species tree conflict. A number of methods have been developed in the past few years to estimate the species tree under the MSC. The full likelihood methods (including maximum likelihood and Bayesian inference) average over the unknown gene trees and accommodate their uncertainties properly but involve intensive computation. The approximate or summary coalescent methods are computationally fast and are applicable to genomic datasets with thousands of loci, but do not make an efficient use of information in the multilocus data. Most of them take the two-step approach of reconstructing the gene trees for multiple loci by phylogenetic methods and then treating the estimated gene trees as observed data, without accounting for their uncertainties appropriately. In this article we review the statistical nature of the species tree estimation problem under the MSC, and explore the conceptual issues and challenges of species tree estimation by focusing mainly on simple cases of three or four closely related species. We use mathematical analysis and computer simulation to demonstrate that large differences in statistical performance may exist between the two classes of methods. We illustrate that several counterintuitive behaviors may occur with the summary methods but they are due to inefficient use of information in the data by summary methods and vanish when the data are analyzed using full-likelihood methods. These include (i) unidentifiability of parameters in the model, (ii) inconsistency in the so-called anomaly zone, (iii) singularity on the likelihood surface, and (iv) deterioration of performance upon addition of more data. We discuss the challenges and strategies of species tree inference for distantly related species when the molecular clock is violated, and highlight the need for improving the computational efficiency and model realism of the likelihood methods as well as the statistical efficiency of the summary methods. PMID:27927902

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.

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…

The Benefits of Maximum Likelihood Estimators in Predicting Bulk Permeability and Upscaling Fracture Networks

NASA Astrophysics Data System (ADS)

Emanuele Rizzo, Roberto; Healy, David; De Siena, Luca

2016-04-01

The success of any predictive model is largely dependent on the accuracy with which its parameters are known. When characterising fracture networks in fractured rock, one of the main issues is accurately scaling the parameters governing the distribution of fracture attributes. Optimal characterisation and analysis of fracture attributes (lengths, apertures, orientations and densities) is fundamental to the estimation of permeability and fluid flow, which are of primary importance in a number of contexts including: hydrocarbon production from fractured reservoirs; geothermal energy extraction; and deeper Earth systems, such as earthquakes and ocean floor hydrothermal venting. Our work links outcrop fracture data to modelled fracture networks in order to numerically predict bulk permeability. We collected outcrop data from a highly fractured upper Miocene biosiliceous mudstone formation, cropping out along the coastline north of Santa Cruz (California, USA). Using outcrop fracture networks as analogues for subsurface fracture systems has several advantages, because key fracture attributes such as spatial arrangements and lengths can be effectively measured only on outcrops [1]. However, a limitation when dealing with outcrop data is the relative sparseness of natural data due to the intrinsic finite size of the outcrops. We make use of a statistical approach for the overall workflow, starting from data collection with the Circular Windows Method [2]. Then we analyse the data statistically using Maximum Likelihood Estimators, which provide greater accuracy compared to the more commonly used Least Squares linear regression when investigating distribution of fracture attributes. Finally, we estimate the bulk permeability of the fractured rock mass using Oda's tensorial approach [3]. The higher quality of this statistical analysis is fundamental: better statistics of the fracture attributes means more accurate permeability estimation, since the fracture attributes feed directly into the permeability calculations. The application of Maximum Likelihood Estimators can have important consequences, especially when we aim to predict the tendency of fracture attributes towards smaller and larger scales than those observed, in order to build consistent, useable models from outcrop observations. The procedures presented here aim to understand whether the average permeability of a fracture network can be predicted, reducing its uncertainties; and if outcrop measurements of fracture attributes can be used directly to generate statistically identical fracture network models, which can then be easily up-scaled into larger areas or volumes. Gale et al. "Natural Fracture in shale: A review and new observations", AAPG Bulletin 98.11 (2014). Mauldon et al. "Circular scanlines and circular windows: new tools for characterizing the geometry of fracture traces", Journal of Structural Geology, 23 (2001). Oda "Permeability tensor for discontinuous rock masses", Geotechnique 35.4 (1985).

Statistical analysis of field data for aircraft warranties

NASA Astrophysics Data System (ADS)

Lakey, Mary J.

Air Force and Navy maintenance data collection systems were researched to determine their scientific applicability to the warranty process. New and unique algorithms were developed to extract failure distributions which were then used to characterize how selected families of equipment typically fails. Families of similar equipment were identified in terms of function, technology and failure patterns. Statistical analyses and applications such as goodness-of-fit test, maximum likelihood estimation and derivation of confidence intervals for the probability density function parameters were applied to characterize the distributions and their failure patterns. Statistical and reliability theory, with relevance to equipment design and operational failures were also determining factors in characterizing the failure patterns of the equipment families. Inferences about the families with relevance to warranty needs were then made.

Robust statistical reconstruction for charged particle tomography

DOEpatents

Schultz, Larry Joe; Klimenko, Alexei Vasilievich; Fraser, Andrew Mcleod; Morris, Christopher; Orum, John Christopher; Borozdin, Konstantin N; Sossong, Michael James; Hengartner, Nicolas W

2013-10-08

Systems and methods for charged particle detection including statistical reconstruction of object volume scattering density profiles from charged particle tomographic data to determine the probability distribution of charged particle scattering using a statistical multiple scattering model and determine a substantially maximum likelihood estimate of object volume scattering density using expectation maximization (ML/EM) algorithm to reconstruct the object volume scattering density. The presence of and/or type of object occupying the volume of interest can be identified from the reconstructed volume scattering density profile. The charged particle tomographic data can be cosmic ray muon tomographic data from a muon tracker for scanning packages, containers, vehicles or cargo. The method can be implemented using a computer program which is executable on a computer.

Statistical study of generalized nonlinear phase step estimation methods in phase-shifting interferometry.

PubMed

Langoju, Rajesh; Patil, Abhijit; Rastogi, Pramod

2007-11-20

Signal processing methods based on maximum-likelihood theory, discrete chirp Fourier transform, and spectral estimation methods have enabled accurate measurement of phase in phase-shifting interferometry in the presence of nonlinear response of the piezoelectric transducer to the applied voltage. We present the statistical study of these generalized nonlinear phase step estimation methods to identify the best method by deriving the Cramér-Rao bound. We also address important aspects of these methods for implementation in practical applications and compare the performance of the best-identified method with other bench marking algorithms in the presence of harmonics and noise.

Weak value amplification considered harmful

NASA Astrophysics Data System (ADS)

Ferrie, Christopher; Combes, Joshua

2014-03-01

We show using statistically rigorous arguments that the technique of weak value amplification does not perform better than standard statistical techniques for the tasks of parameter estimation and signal detection. We show that using all data and considering the joint distribution of all measurement outcomes yields the optimal estimator. Moreover, we show estimation using the maximum likelihood technique with weak values as small as possible produces better performance for quantum metrology. In doing so, we identify the optimal experimental arrangement to be the one which reveals the maximal eigenvalue of the square of system observables. We also show these conclusions do not change in the presence of technical noise.

Robust, Adaptive Radar Detection and Estimation

DTIC Science & Technology

2015-07-21

cost function is not a convex function in R, we apply a transformation variables i.e., let X = σ2R−1 and S′ = 1 σ2 S. Then, the revised cost function in...1 viv H i . We apply this inverse covariance matrix in computing the SINR as well as estimator variance. • Rank Constrained Maximum Likelihood: Our...even as almost all available training samples are corrupted. Probability of Detection vs. SNR We apply three test statistics, the normalized matched

Statistical modeling of ecosystem respiration using eddy covariance data: Maximum likelihood parameter estimation, and Monte Carlo simulation of model and parameter uncertainty, applied to three simple models

Treesearch

Andrew D. Richardson; David Y. Hollinger; David Y. Hollinger

2005-01-01

Whether the goal is to fill gaps in the flux record, or to extract physiological parameters from eddy covariance data, researchers are frequently interested in fitting simple models of ecosystem physiology to measured data. Presently, there is no consensus on the best models to use, or the ideal optimization criteria. We demonstrate that, given our estimates of the...

The Educational Consequences of Teen Childbearing

PubMed Central

Kane, Jennifer B.; Morgan, S. Philip; Harris, Kathleen Mullan; Guilkey, David K.

2013-01-01

A huge literature shows that teen mothers face a variety of detriments across the life course, including truncated educational attainment. To what extent is this association causal? The estimated effects of teen motherhood on schooling vary widely, ranging from no discernible difference to 2.6 fewer years among teen mothers. The magnitude of educational consequences is therefore uncertain, despite voluminous policy and prevention efforts that rest on the assumption of a negative and presumably causal effect. This study adjudicates between two potential sources of inconsistency in the literature—methodological differences or cohort differences—by using a single, high-quality data source: namely, The National Longitudinal Study of Adolescent Health. We replicate analyses across four different statistical strategies: ordinary least squares regression; propensity score matching; and parametric and semiparametric maximum likelihood estimation. Results demonstrate educational consequences of teen childbearing, with estimated effects between 0.7 and 1.9 fewer years of schooling among teen mothers. We select our preferred estimate (0.7), derived from semiparametric maximum likelihood estimation, on the basis of weighing the strengths and limitations of each approach. Based on the range of estimated effects observed in our study, we speculate that variable statistical methods are the likely source of inconsistency in the past. We conclude by discussing implications for future research and policy, and recommend that future studies employ a similar multimethod approach to evaluate findings. PMID:24078155

A Measurement of Gravitational Lensing of the Cosmic Microwave Background by Galaxy Clusters Using Data from the South Pole Telescope

DOE PAGES

Baxter, E. J.; Keisler, R.; Dodelson, S.; ...

2015-06-22

Clusters of galaxies are expected to gravitationally lens the cosmic microwave background (CMB) and thereby generate a distinct signal in the CMB on arcminute scales. Measurements of this effect can be used to constrain the masses of galaxy clusters with CMB data alone. Here we present a measurement of lensing of the CMB by galaxy clusters using data from the South Pole Telescope (SPT). We also develop a maximum likelihood approach to extract the CMB cluster lensing signal and validate the method on mock data. We quantify the effects on our analysis of several potential sources of systematic error andmore » find that they generally act to reduce the best-fit cluster mass. It is estimated that this bias to lower cluster mass is roughly 0.85σ in units of the statistical error bar, although this estimate should be viewed as an upper limit. Furthermore, we apply our maximum likelihood technique to 513 clusters selected via their Sunyaev–Zeldovich (SZ) signatures in SPT data, and rule out the null hypothesis of no lensing at 3.1σ. The lensing-derived mass estimate for the full cluster sample is consistent with that inferred from the SZ flux: M 200,lens = 0.83 +0.38 -0.37 M 200,SZ (68% C.L., statistical error only).« less

A Statistical Method of Identifying Interactions in Neuron–Glia Systems Based on Functional Multicell Ca2+ Imaging

PubMed Central

Nakae, Ken; Ikegaya, Yuji; Ishikawa, Tomoe; Oba, Shigeyuki; Urakubo, Hidetoshi; Koyama, Masanori; Ishii, Shin

2014-01-01

Crosstalk between neurons and glia may constitute a significant part of information processing in the brain. We present a novel method of statistically identifying interactions in a neuron–glia network. We attempted to identify neuron–glia interactions from neuronal and glial activities via maximum-a-posteriori (MAP)-based parameter estimation by developing a generalized linear model (GLM) of a neuron–glia network. The interactions in our interest included functional connectivity and response functions. We evaluated the cross-validated likelihood of GLMs that resulted from the addition or removal of connections to confirm the existence of specific neuron-to-glia or glia-to-neuron connections. We only accepted addition or removal when the modification improved the cross-validated likelihood. We applied the method to a high-throughput, multicellular in vitro Ca2+ imaging dataset obtained from the CA3 region of a rat hippocampus, and then evaluated the reliability of connectivity estimates using a statistical test based on a surrogate method. Our findings based on the estimated connectivity were in good agreement with currently available physiological knowledge, suggesting our method can elucidate undiscovered functions of neuron–glia systems. PMID:25393874

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…

Probabilistic models in human sensorimotor control

PubMed Central

Wolpert, Daniel M.

2009-01-01

Sensory and motor uncertainty form a fundamental constraint on human sensorimotor control. Bayesian decision theory (BDT) has emerged as a unifying framework to understand how the central nervous system performs optimal estimation and control in the face of such uncertainty. BDT has two components: Bayesian statistics and decision theory. Here we review Bayesian statistics and show how it applies to estimating the state of the world and our own body. Recent results suggest that when learning novel tasks we are able to learn the statistical properties of both the world and our own sensory apparatus so as to perform estimation using Bayesian statistics. We review studies which suggest that humans can combine multiple sources of information to form maximum likelihood estimates, can incorporate prior beliefs about possible states of the world so as to generate maximum a posteriori estimates and can use Kalman filter-based processes to estimate time-varying states. Finally, we review Bayesian decision theory in motor control and how the central nervous system processes errors to determine loss functions and optimal actions. We review results that suggest we plan movements based on statistics of our actions that result from signal-dependent noise on our motor outputs. Taken together these studies provide a statistical framework for how the motor system performs in the presence of uncertainty. PMID:17628731

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 likelihood-based analysis of single-molecule photon arrival trajectories.

PubMed

Hajdziona, Marta; Molski, Andrzej

2011-02-07

In this work we explore the statistical properties of the maximum likelihood-based analysis of one-color photon arrival trajectories. This approach does not involve binning and, therefore, all of the information contained in an observed photon strajectory is used. We study the accuracy and precision of parameter estimates and the efficiency of the Akaike information criterion and the Bayesian information criterion (BIC) in selecting the true kinetic model. We focus on the low excitation regime where photon trajectories can be modeled as realizations of Markov modulated Poisson processes. The number of observed photons is the key parameter in determining model selection and parameter estimation. For example, the BIC can select the true three-state model from competing two-, three-, and four-state kinetic models even for relatively short trajectories made up of 2 × 10(3) photons. When the intensity levels are well-separated and 10(4) photons are observed, the two-state model parameters can be estimated with about 10% precision and those for a three-state model with about 20% precision.

Rating Movies and Rating the Raters Who Rate Them

PubMed Central

Zhou, Hua; Lange, Kenneth

2010-01-01

The movie distribution company Netflix has generated considerable buzz in the statistics community by offering a million dollar prize for improvements to its movie rating system. Among the statisticians and computer scientists who have disclosed their techniques, the emphasis has been on machine learning approaches. This article has the modest goal of discussing a simple model for movie rating and other forms of democratic rating. Because the model involves a large number of parameters, it is nontrivial to carry out maximum likelihood estimation. Here we derive a straightforward EM algorithm from the perspective of the more general MM algorithm. The algorithm is capable of finding the global maximum on a likelihood landscape littered with inferior modes. We apply two variants of the model to a dataset from the MovieLens archive and compare their results. Our model identifies quirky raters, redefines the raw rankings, and permits imputation of missing ratings. The model is intended to stimulate discussion and development of better theory rather than to win the prize. It has the added benefit of introducing readers to some of the issues connected with analyzing high-dimensional data. PMID:20802818

Rating Movies and Rating the Raters Who Rate Them.

PubMed

Zhou, Hua; Lange, Kenneth

2009-11-01

The movie distribution company Netflix has generated considerable buzz in the statistics community by offering a million dollar prize for improvements to its movie rating system. Among the statisticians and computer scientists who have disclosed their techniques, the emphasis has been on machine learning approaches. This article has the modest goal of discussing a simple model for movie rating and other forms of democratic rating. Because the model involves a large number of parameters, it is nontrivial to carry out maximum likelihood estimation. Here we derive a straightforward EM algorithm from the perspective of the more general MM algorithm. The algorithm is capable of finding the global maximum on a likelihood landscape littered with inferior modes. We apply two variants of the model to a dataset from the MovieLens archive and compare their results. Our model identifies quirky raters, redefines the raw rankings, and permits imputation of missing ratings. The model is intended to stimulate discussion and development of better theory rather than to win the prize. It has the added benefit of introducing readers to some of the issues connected with analyzing high-dimensional data.

Phylogeny of marattioid ferns (Marattiaceae): inferring a root in the absence of a closely related outgroup.

PubMed

Murdock, Andrew G

2008-05-01

Closely related outgroups are optimal for rooting phylogenetic trees; however, such ideal outgroups are not always available. A phylogeny of the marattioid ferns (Marattiaceae), an ancient lineage with no close relatives, was reconstructed using nucleotide sequences of multiple chloroplast regions (rps4 + rps4-trnS spacer, trnS-trnG spacer + trnG intron, rbcL, atpB), from 88 collections, selected to cover the broadest possible range of morphologies and geographic distributions within the extant taxa. Because marattioid ferns are phylogenetically isolated from other lineages, and internal branches are relatively short, rooting was problematic. Root placement was strongly affected by long-branch attraction under maximum parsimony and by model choice under maximum likelihood. A multifaceted approach to rooting was employed to isolate the sources of bias and produce a consensus root position. In a statistical comparison of all possible root positions with three different outgroups, most root positions were not significantly less optimal than the maximum likelihood root position, including the consensus root position. This phylogeny has several important taxonomic implications for marattioid ferns: Marattia in the broad sense is paraphyletic; the Hawaiian endemic Marattia douglasii is most closely related to tropical American taxa; and Angiopteris is monophyletic only if Archangiopteris and Macroglossum are included.

PyEvolve: a toolkit for statistical modelling of molecular evolution.

PubMed

Butterfield, Andrew; Vedagiri, Vivek; Lang, Edward; Lawrence, Cath; Wakefield, Matthew J; Isaev, Alexander; Huttley, Gavin A

2004-01-05

Examining the distribution of variation has proven an extremely profitable technique in the effort to identify sequences of biological significance. Most approaches in the field, however, evaluate only the conserved portions of sequences - ignoring the biological significance of sequence differences. A suite of sophisticated likelihood based statistical models from the field of molecular evolution provides the basis for extracting the information from the full distribution of sequence variation. The number of different problems to which phylogeny-based maximum likelihood calculations can be applied is extensive. Available software packages that can perform likelihood calculations suffer from a lack of flexibility and scalability, or employ error-prone approaches to model parameterisation. Here we describe the implementation of PyEvolve, a toolkit for the application of existing, and development of new, statistical methods for molecular evolution. We present the object architecture and design schema of PyEvolve, which includes an adaptable multi-level parallelisation schema. The approach for defining new methods is illustrated by implementing a novel dinucleotide model of substitution that includes a parameter for mutation of methylated CpG's, which required 8 lines of standard Python code to define. Benchmarking was performed using either a dinucleotide or codon substitution model applied to an alignment of BRCA1 sequences from 20 mammals, or a 10 species subset. Up to five-fold parallel performance gains over serial were recorded. Compared to leading alternative software, PyEvolve exhibited significantly better real world performance for parameter rich models with a large data set, reducing the time required for optimisation from approximately 10 days to approximately 6 hours. PyEvolve provides flexible functionality that can be used either for statistical modelling of molecular evolution, or the development of new methods in the field. The toolkit can be used interactively or by writing and executing scripts. The toolkit uses efficient processes for specifying the parameterisation of statistical models, and implements numerous optimisations that make highly parameter rich likelihood functions solvable within hours on multi-cpu hardware. PyEvolve can be readily adapted in response to changing computational demands and hardware configurations to maximise performance. PyEvolve is released under the GPL and can be downloaded from http://cbis.anu.edu.au/software.

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

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.

Statistical reconstruction for cosmic ray muon tomography.

PubMed

Schultz, Larry J; Blanpied, Gary S; Borozdin, Konstantin N; Fraser, Andrew M; Hengartner, Nicolas W; Klimenko, Alexei V; Morris, Christopher L; Orum, Chris; Sossong, Michael J

2007-08-01

Highly penetrating cosmic ray muons constantly shower the earth at a rate of about 1 muon per cm2 per minute. We have developed a technique which exploits the multiple Coulomb scattering of these particles to perform nondestructive inspection without the use of artificial radiation. In prior work [1]-[3], we have described heuristic methods for processing muon data to create reconstructed images. In this paper, we present a maximum likelihood/expectation maximization tomographic reconstruction algorithm designed for the technique. This algorithm borrows much from techniques used in medical imaging, particularly emission tomography, but the statistics of muon scattering dictates differences. We describe the statistical model for multiple scattering, derive the reconstruction algorithm, and present simulated examples. We also propose methods to improve the robustness of the algorithm to experimental errors and events departing from the statistical model.

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.

Low-complexity approximations to maximum likelihood MPSK modulation classification

NASA Technical Reports Server (NTRS)

Hamkins, Jon

2004-01-01

We present a new approximation to the maximum likelihood classifier to discriminate between M-ary and M'-ary phase-shift-keying transmitted on an additive white Gaussian noise (AWGN) channel and received noncoherentl, partially coherently, or coherently.

Demodulation of messages received with low signal to noise ratio

NASA Astrophysics Data System (ADS)

Marguinaud, A.; Quignon, T.; Romann, B.

The implementation of this all-digital demodulator is derived from maximum likelihood considerations applied to an analytical representation of the received signal. Traditional adapted filters and phase lock loops are replaced by minimum variance estimators and hypothesis tests. These statistical tests become very simple when working on phase signal. These methods, combined with rigorous control data representation allow significant computation savings as compared to conventional realizations. Nominal operation has been verified down to energetic signal over noise of -3 dB upon a QPSK demodulator.

Simulation and study of small numbers of random events

NASA Technical Reports Server (NTRS)

Shelton, R. D.

1986-01-01

Random events were simulated by computer and subjected to various statistical methods to extract important parameters. Various forms of curve fitting were explored, such as least squares, least distance from a line, maximum likelihood. Problems considered were dead time, exponential decay, and spectrum extraction from cosmic ray data using binned data and data from individual events. Computer programs, mostly of an iterative nature, were developed to do these simulations and extractions and are partially listed as appendices. The mathematical basis for the compuer programs is given.

Use of the Maximum Likelihood Method in the Analysis of Chamber Air Dives

DTIC Science & Technology

1988-01-01

the total gas pressure in compartment i, P0 is the current ambient pressure, 0 [ and A and B are constants (0.0026 min-’ -ATA- and 8.31 ATA...computer model (4), the Kidd- Stubbs 1971 decompression tables (11), and the current Defence and Civil Institute 20 of Environmental Medicine (DCIEM...it could be applied. Since the models are not suitable for this test, then within T ese no-deco current limits of statistical theory, the results can

Establishment of a center of excellence for applied mathematical and statistical research

NASA Technical Reports Server (NTRS)

Woodward, W. A.; Gray, H. L.

1983-01-01

The state of the art was assessed with regards to efforts in support of the crop production estimation problem and alternative generic proportion estimation techniques were investigated. Topics covered include modeling the greeness profile (Badhwarmos model), parameter estimation using mixture models such as CLASSY, and minimum distance estimation as an alternative to maximum likelihood estimation. Approaches to the problem of obtaining proportion estimates when the underlying distributions are asymmetric are examined including the properties of Weibull distribution.

A Regional Analysis of Non-Methane Hydrocarbons And Meteorology of The Rural Southeast United States

DTIC Science & Technology

1996-01-01

Zt is an ARIMA time series. This is a typical regression model , except that it allows for autocorrelation in the error term Z. In this work, an ARMA...data=folder; var residual; run; II Statistical output of 1992 regression model on 1993 ozone data ARIMA Procedure Maximum Likelihood Estimation Approx...at each of the sites, and to show the effect of synoptic meteorology on high ozone by examining NOAA daily weather maps and climatic data

Geological mapping in northwestern Saudi Arabia using LANDSAT multispectral techniques

NASA Technical Reports Server (NTRS)

Blodget, H. W.; Brown, G. F.; Moik, J. G.

1975-01-01

Various computer enhancement and data extraction systems using LANDSAT data were assessed and used to complement a continuing geologic mapping program. Interactive digital classification techniques using both the parallel-piped and maximum-likelihood statistical approaches achieve very limited success in areas of highly dissected terrain. Computer enhanced imagery developed by color compositing stretched MSS ratio data was constructed for a test site in northwestern Saudi Arabia. Initial results indicate that several igneous and sedimentary rock types can be discriminated.

Characterization of Cloud Water-Content Distribution

NASA Technical Reports Server (NTRS)

Lee, Seungwon

2010-01-01

The development of realistic cloud parameterizations for climate models requires accurate characterizations of subgrid distributions of thermodynamic variables. To this end, a software tool was developed to characterize cloud water-content distributions in climate-model sub-grid scales. This software characterizes distributions of cloud water content with respect to cloud phase, cloud type, precipitation occurrence, and geo-location using CloudSat radar measurements. It uses a statistical method called maximum likelihood estimation to estimate the probability density function of the cloud water content.

Transmuted of Rayleigh Distribution with Estimation and Application on Noise Signal

NASA Astrophysics Data System (ADS)

Ahmed, Suhad; Qasim, Zainab

2018-05-01

This paper deals with transforming one parameter Rayleigh distribution, into transmuted probability distribution through introducing a new parameter (λ), since this studied distribution is necessary in representing signal data distribution and failure data model the value of this transmuted parameter |λ| ≤ 1, is also estimated as well as the original parameter (⊖) by methods of moments and maximum likelihood using different sample size (n=25, 50, 75, 100) and comparing the results of estimation by statistical measure (mean square error, MSE).

Generalizing Terwilliger's likelihood approach: a new score statistic to test for genetic association.

PubMed

el Galta, Rachid; Uitte de Willige, Shirley; de Visser, Marieke C H; Helmer, Quinta; Hsu, Li; Houwing-Duistermaat, Jeanine J

2007-09-24

In this paper, we propose a one degree of freedom test for association between a candidate gene and a binary trait. This method is a generalization of Terwilliger's likelihood ratio statistic and is especially powerful for the situation of one associated haplotype. As an alternative to the likelihood ratio statistic, we derive a score statistic, which has a tractable expression. For haplotype analysis, we assume that phase is known. By means of a simulation study, we compare the performance of the score statistic to Pearson's chi-square statistic and the likelihood ratio statistic proposed by Terwilliger. We illustrate the method on three candidate genes studied in the Leiden Thrombophilia Study. We conclude that the statistic follows a chi square distribution under the null hypothesis and that the score statistic is more powerful than Terwilliger's likelihood ratio statistic when the associated haplotype has frequency between 0.1 and 0.4 and has a small impact on the studied disorder. With regard to Pearson's chi-square statistic, the score statistic has more power when the associated haplotype has frequency above 0.2 and the number of variants is above five.

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.

Maximum-likelihood block detection of noncoherent continuous phase modulation

NASA Technical Reports Server (NTRS)

Simon, Marvin K.; Divsalar, Dariush

1993-01-01

This paper examines maximum-likelihood block detection of uncoded full response CPM over an additive white Gaussian noise (AWGN) channel. Both the maximum-likelihood metrics and the bit error probability performances of the associated detection algorithms are considered. The special and popular case of minimum-shift-keying (MSK) corresponding to h = 0.5 and constant amplitude frequency pulse is treated separately. The many new receiver structures that result from this investigation can be compared to the traditional ones that have been used in the past both from the standpoint of simplicity of implementation and optimality of performance.

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.

Maximum likelihood clustering with dependent feature trees

NASA Technical Reports Server (NTRS)

Chittineni, C. B. (Principal Investigator)

1981-01-01

The decomposition of mixture density of the data into its normal component densities is considered. The densities are approximated with first order dependent feature trees using criteria of mutual information and distance measures. Expressions are presented for the criteria when the densities are Gaussian. By defining different typs of nodes in a general dependent feature tree, maximum likelihood equations are developed for the estimation of parameters using fixed point iterations. The field structure of the data is also taken into account in developing maximum likelihood equations. Experimental results from the processing of remotely sensed multispectral scanner imagery data are included.

Cleanroom certification model

NASA Technical Reports Server (NTRS)

Currit, P. A.

1983-01-01

The Cleanroom software development methodology is designed to take the gamble out of product releases for both suppliers and receivers of the software. The ingredients of this procedure are a life cycle of executable product increments, representative statistical testing, and a standard estimate of the MTTF (Mean Time To Failure) of the product at the time of its release. A statistical approach to software product testing using randomly selected samples of test cases is considered. A statistical model is defined for the certification process which uses the timing data recorded during test. A reasonableness argument for this model is provided that uses previously published data on software product execution. Also included is a derivation of the certification model estimators and a comparison of the proposed least squares technique with the more commonly used maximum likelihood estimators.

Comparison of 2- and 10-micron coherent Doppler lidar performance

NASA Technical Reports Server (NTRS)

Frehlich, Rod

1995-01-01

The performance of 2- and 10-micron coherent Doppler lidar is presented in terms of the statistical distribution of the maximum-likelihood velocity estimator from simulations for fixed range resolution and fixed velocity search space as a function of the number of coherent photoelectrons per estimate. The wavelength dependence of the aerosol backscatter coefficient, the detector quantum efficiency, and the atmospheric extinction produce a simple shift of the performance curves. Results are presented for a typical boundary layer measurement and a space-based measurement for two regimes: the pulse-dominated regime where the signal statistics are determined by the transmitted pulse, and the atmospheric-dominated regime where the signal statistics are determined by the velocity fluctuations over the range gate. The optimal choice of wavelength depends on the problem under 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…

Stage-structured transmission of phocine distemper virus in the Dutch 2002 outbreak

PubMed Central

Klepac, Petra; Pomeroy, Laura W.; Bjørnstad, Ottar N.; Kuiken, Thijs; Osterhaus, Albert D.M.E.; Rijks, Jolianne M.

2009-01-01

Heterogeneities in transmission among hosts can be very important in shaping infectious disease dynamics. In mammals with strong social organization, such heterogeneities are often structured by functional stage: juveniles, subadults and adults. We investigate the importance of such stage-related heterogeneities in shaping the 2002 phocine distemper virus (PDV) outbreak in the Dutch Wadden Sea, when more than 40 per cent of the harbour seals were killed. We do this by comparing the statistical fit of a hierarchy of models with varying transmission complexity: homogeneous versus heterogeneous mixing and density- versus frequency-dependent transmission. We use the stranding data as a proxy for incidence and use Poisson likelihoods to estimate the ‘who acquires infection from whom’ (WAIFW) matrix. Statistically, the model with strong heterogeneous mixing and density-dependent transmission was found to best describe the transmission dynamics. However, patterns of incidence support a model of frequency-dependent transmission among adults and juveniles. Based on the maximum-likelihood WAIFW matrix estimates, we use the next-generation formalism to calculate an R0 between 2 and 2.5 for the Dutch 2002 PDV epidemic. PMID:19364743

Statistical methods for astronomical data with upper limits. I - Univariate distributions

NASA Technical Reports Server (NTRS)

Feigelson, E. D.; Nelson, P. I.

1985-01-01

The statistical treatment of univariate censored data is discussed. A heuristic derivation of the Kaplan-Meier maximum-likelihood estimator from first principles is presented which results in an expression amenable to analytic error analysis. Methods for comparing two or more censored samples are given along with simple computational examples, stressing the fact that most astronomical problems involve upper limits while the standard mathematical methods require lower limits. The application of univariate survival analysis to six data sets in the recent astrophysical literature is described, and various aspects of the use of survival analysis in astronomy, such as the limitations of various two-sample tests and the role of parametric modelling, are discussed.

The evolution of autodigestion in the mushroom family Psathyrellaceae (Agaricales) inferred from Maximum Likelihood and Bayesian methods.

PubMed

Nagy, László G; Urban, Alexander; Orstadius, Leif; Papp, Tamás; Larsson, Ellen; Vágvölgyi, Csaba

2010-12-01

Recently developed comparative phylogenetic methods offer a wide spectrum of applications in evolutionary biology, although it is generally accepted that their statistical properties are incompletely known. Here, we examine and compare the statistical power of the ML and Bayesian methods with regard to selection of best-fit models of fruiting-body evolution and hypothesis testing of ancestral states on a real-life data set of a physiological trait (autodigestion) in the family Psathyrellaceae. Our phylogenies are based on the first multigene data set generated for the family. Two different coding regimes (binary and multistate) and two data sets differing in taxon sampling density are examined. The Bayesian method outperformed Maximum Likelihood with regard to statistical power in all analyses. This is particularly evident if the signal in the data is weak, i.e. in cases when the ML approach does not provide support to choose among competing hypotheses. Results based on binary and multistate coding differed only modestly, although it was evident that multistate analyses were less conclusive in all cases. It seems that increased taxon sampling density has favourable effects on inference of ancestral states, while model parameters are influenced to a smaller extent. The model best fitting our data implies that the rate of losses of deliquescence equals zero, although model selection in ML does not provide proper support to reject three of the four candidate models. The results also support the hypothesis that non-deliquescence (lack of autodigestion) has been ancestral in Psathyrellaceae, and that deliquescent fruiting bodies represent the preferred state, having evolved independently several times during evolution. Copyright © 2010 Elsevier Inc. All rights reserved.

Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data.

PubMed

Rhodes, Kirsty M; Turner, Rebecca M; White, Ian R; Jackson, Dan; Spiegelhalter, David J; Higgins, Julian P T

2016-12-20

Many meta-analyses combine results from only a small number of studies, a situation in which the between-study variance is imprecisely estimated when standard methods are applied. Bayesian meta-analysis allows incorporation of external evidence on heterogeneity, providing the potential for more robust inference on the effect size of interest. We present a method for performing Bayesian meta-analysis using data augmentation, in which we represent an informative conjugate prior for between-study variance by pseudo data and use meta-regression for estimation. To assist in this, we derive predictive inverse-gamma distributions for the between-study variance expected in future meta-analyses. These may serve as priors for heterogeneity in new meta-analyses. In a simulation study, we compare approximate Bayesian methods using meta-regression and pseudo data against fully Bayesian approaches based on importance sampling techniques and Markov chain Monte Carlo (MCMC). We compare the frequentist properties of these Bayesian methods with those of the commonly used frequentist DerSimonian and Laird procedure. The method is implemented in standard statistical software and provides a less complex alternative to standard MCMC approaches. An importance sampling approach produces almost identical results to standard MCMC approaches, and results obtained through meta-regression and pseudo data are very similar. On average, data augmentation provides closer results to MCMC, if implemented using restricted maximum likelihood estimation rather than DerSimonian and Laird or maximum likelihood estimation. The methods are applied to real datasets, and an extension to network meta-analysis is described. The proposed method facilitates Bayesian meta-analysis in a way that is accessible to applied researchers. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Statistical analyses support power law distributions found in neuronal avalanches.

PubMed

Klaus, Andreas; Yu, Shan; Plenz, Dietmar

2011-01-01

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.

Maximum-likelihood curve-fitting scheme for experiments with pulsed lasers subject to intensity fluctuations.

PubMed

Metz, Thomas; Walewski, Joachim; Kaminski, Clemens F

2003-03-20

Evaluation schemes, e.g., least-squares fitting, are not generally applicable to any types of experiments. If the evaluation schemes were not derived from a measurement model that properly described the experiment to be evaluated, poorer precision or accuracy than attainable from the measured data could result. We outline ways in which statistical data evaluation schemes should be derived for all types of experiment, and we demonstrate them for laser-spectroscopic experiments, in which pulse-to-pulse fluctuations of the laser power cause correlated variations of laser intensity and generated signal intensity. The method of maximum likelihood is demonstrated in the derivation of an appropriate fitting scheme for this type of experiment. Statistical data evaluation contains the following steps. First, one has to provide a measurement model that considers statistical variation of all enclosed variables. Second, an evaluation scheme applicable to this particular model has to be derived or provided. Third, the scheme has to be characterized in terms of accuracy and precision. A criterion for accepting an evaluation scheme is that it have accuracy and precision as close as possible to the theoretical limit. The fitting scheme derived for experiments with pulsed lasers is compared to well-established schemes in terms of fitting power and rational functions. The precision is found to be as much as three timesbetter than for simple least-squares fitting. Our scheme also suppresses the bias on the estimated model parameters that other methods may exhibit if they are applied in an uncritical fashion. We focus on experiments in nonlinear spectroscopy, but the fitting scheme derived is applicable in many scientific disciplines.

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.

Statistical alignment: computational properties, homology testing and goodness-of-fit.

PubMed

Hein, J; Wiuf, C; Knudsen, B; Møller, M B; Wibling, G

2000-09-08

The model of insertions and deletions in biological sequences, first formulated by Thorne, Kishino, and Felsenstein in 1991 (the TKF91 model), provides a basis for performing alignment within a statistical framework. Here we investigate this model.Firstly, we show how to accelerate the statistical alignment algorithms several orders of magnitude. The main innovations are to confine likelihood calculations to a band close to the similarity based alignment, to get good initial guesses of the evolutionary parameters and to apply an efficient numerical optimisation algorithm for finding the maximum likelihood estimate. In addition, the recursions originally presented by Thorne, Kishino and Felsenstein can be simplified. Two proteins, about 1500 amino acids long, can be analysed with this method in less than five seconds on a fast desktop computer, which makes this method practical for actual data analysis.Secondly, we propose a new homology test based on this model, where homology means that an ancestor to a sequence pair can be found finitely far back in time. This test has statistical advantages relative to the traditional shuffle test for proteins.Finally, we describe a goodness-of-fit test, that allows testing the proposed insertion-deletion (indel) process inherent to this model and find that real sequences (here globins) probably experience indels longer than one, contrary to what is assumed by the model. Copyright 2000 Academic Press.

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

Auto- and cross-power spectral analysis of dual trap optical tweezer experiments using Bayesian inference.

PubMed

von Hansen, Yann; Mehlich, Alexander; Pelz, Benjamin; Rief, Matthias; Netz, Roland R

2012-09-01

The thermal fluctuations of micron-sized beads in dual trap optical tweezer experiments contain complete dynamic information about the viscoelastic properties of the embedding medium and-if present-macromolecular constructs connecting the two beads. To quantitatively interpret the spectral properties of the measured signals, a detailed understanding of the instrumental characteristics is required. To this end, we present a theoretical description of the signal processing in a typical dual trap optical tweezer experiment accounting for polarization crosstalk and instrumental noise and discuss the effect of finite statistics. To infer the unknown parameters from experimental data, a maximum likelihood method based on the statistical properties of the stochastic signals is derived. In a first step, the method can be used for calibration purposes: We propose a scheme involving three consecutive measurements (both traps empty, first one occupied and second empty, and vice versa), by which all instrumental and physical parameters of the setup are determined. We test our approach for a simple model system, namely a pair of unconnected, but hydrodynamically interacting spheres. The comparison to theoretical predictions based on instantaneous as well as retarded hydrodynamics emphasizes the importance of hydrodynamic retardation effects due to vorticity diffusion in the fluid. For more complex experimental scenarios, where macromolecular constructs are tethered between the two beads, the same maximum likelihood method in conjunction with dynamic deconvolution theory will in a second step allow one to determine the viscoelastic properties of the tethered element connecting the two beads.

Maximum likelihood pedigree reconstruction using integer linear programming.

PubMed

Cussens, James; Bartlett, Mark; Jones, Elinor M; Sheehan, Nuala A

2013-01-01

Large population biobanks of unrelated individuals have been highly successful in detecting common genetic variants affecting diseases of public health concern. However, they lack the statistical power to detect more modest gene-gene and gene-environment interaction effects or the effects of rare variants for which related individuals are ideally required. In reality, most large population studies will undoubtedly contain sets of undeclared relatives, or pedigrees. Although a crude measure of relatedness might sometimes suffice, having a good estimate of the true pedigree would be much more informative if this could be obtained efficiently. Relatives are more likely to share longer haplotypes around disease susceptibility loci and are hence biologically more informative for rare variants than unrelated cases and controls. Distant relatives are arguably more useful for detecting variants with small effects because they are less likely to share masking environmental effects. Moreover, the identification of relatives enables appropriate adjustments of statistical analyses that typically assume unrelatedness. We propose to exploit an integer linear programming optimisation approach to pedigree learning, which is adapted to find valid pedigrees by imposing appropriate constraints. Our method is not restricted to small pedigrees and is guaranteed to return a maximum likelihood pedigree. With additional constraints, we can also search for multiple high-probability pedigrees and thus account for the inherent uncertainty in any particular pedigree reconstruction. The true pedigree is found very quickly by comparison with other methods when all individuals are observed. Extensions to more complex problems seem feasible. © 2012 Wiley Periodicals, Inc.

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

Safe semi-supervised learning based on weighted likelihood.

PubMed

Kawakita, Masanori; Takeuchi, Jun'ichi

2014-05-01

We are interested in developing a safe semi-supervised learning that works in any situation. Semi-supervised learning postulates that n(') unlabeled data are available in addition to n labeled data. However, almost all of the previous semi-supervised methods require additional assumptions (not only unlabeled data) to make improvements on supervised learning. If such assumptions are not met, then the methods possibly perform worse than supervised learning. Sokolovska, Cappé, and Yvon (2008) proposed a semi-supervised method based on a weighted likelihood approach. They proved that this method asymptotically never performs worse than supervised learning (i.e., it is safe) without any assumption. Their method is attractive because it is easy to implement and is potentially general. Moreover, it is deeply related to a certain statistical paradox. However, the method of Sokolovska et al. (2008) assumes a very limited situation, i.e., classification, discrete covariates, n(')→∞ and a maximum likelihood estimator. In this paper, we extend their method by modifying the weight. We prove that our proposal is safe in a significantly wide range of situations as long as n≤n('). Further, we give a geometrical interpretation of the proof of safety through the relationship with the above-mentioned statistical paradox. Finally, we show that the above proposal is asymptotically safe even when n(')

On the Spike Train Variability Characterized by Variance-to-Mean Power Relationship.

PubMed

Koyama, Shinsuke

2015-07-01

We propose a statistical method for modeling the non-Poisson variability of spike trains observed in a wide range of brain regions. Central to our approach is the assumption that the variance and the mean of interspike intervals are related by a power function characterized by two parameters: the scale factor and exponent. It is shown that this single assumption allows the variability of spike trains to have an arbitrary scale and various dependencies on the firing rate in the spike count statistics, as well as in the interval statistics, depending on the two parameters of the power function. We also propose a statistical model for spike trains that exhibits the variance-to-mean power relationship. Based on this, a maximum likelihood method is developed for inferring the parameters from rate-modulated spike trains. The proposed method is illustrated on simulated and experimental spike trains.

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.

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.

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.

Effect of formal and informal likelihood functions on uncertainty assessment in a single event rainfall-runoff model

NASA Astrophysics Data System (ADS)

Nourali, Mahrouz; Ghahraman, Bijan; Pourreza-Bilondi, Mohsen; Davary, Kamran

2016-09-01

In the present study, DREAM(ZS), Differential Evolution Adaptive Metropolis combined with both formal and informal likelihood functions, is used to investigate uncertainty of parameters of the HEC-HMS model in Tamar watershed, Golestan province, Iran. In order to assess the uncertainty of 24 parameters used in HMS, three flood events were used to calibrate and one flood event was used to validate the posterior distributions. Moreover, performance of seven different likelihood functions (L1-L7) was assessed by means of DREAM(ZS)approach. Four likelihood functions, L1-L4, Nash-Sutcliffe (NS) efficiency, Normalized absolute error (NAE), Index of agreement (IOA), and Chiew-McMahon efficiency (CM), is considered as informal, whereas remaining (L5-L7) is represented in formal category. L5 focuses on the relationship between the traditional least squares fitting and the Bayesian inference, and L6, is a hetereoscedastic maximum likelihood error (HMLE) estimator. Finally, in likelihood function L7, serial dependence of residual errors is accounted using a first-order autoregressive (AR) model of the residuals. According to the results, sensitivities of the parameters strongly depend on the likelihood function, and vary for different likelihood functions. Most of the parameters were better defined by formal likelihood functions L5 and L7 and showed a high sensitivity to model performance. Posterior cumulative distributions corresponding to the informal likelihood functions L1, L2, L3, L4 and the formal likelihood function L6 are approximately the same for most of the sub-basins, and these likelihood functions depict almost a similar effect on sensitivity of parameters. 95% total prediction uncertainty bounds bracketed most of the observed data. Considering all the statistical indicators and criteria of uncertainty assessment, including RMSE, KGE, NS, P-factor and R-factor, results showed that DREAM(ZS) algorithm performed better under formal likelihood functions L5 and L7, but likelihood function L5 may result in biased and unreliable estimation of parameters due to violation of the residualerror assumptions. Thus, likelihood function L7 provides posterior distribution of model parameters credibly and therefore can be employed for further applications.

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.

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…

Estimating population genetic parameters and comparing model goodness-of-fit using DNA sequences with error

PubMed Central

Liu, Xiaoming; Fu, Yun-Xin; Maxwell, Taylor J.; Boerwinkle, Eric

2010-01-01

It is known that sequencing error can bias estimation of evolutionary or population genetic parameters. This problem is more prominent in deep resequencing studies because of their large sample size n, and a higher probability of error at each nucleotide site. We propose a new method based on the composite likelihood of the observed SNP configurations to infer population mutation rate θ = 4Neμ, population exponential growth rate R, and error rate ɛ, simultaneously. Using simulation, we show the combined effects of the parameters, θ, n, ɛ, and R on the accuracy of parameter estimation. We compared our maximum composite likelihood estimator (MCLE) of θ with other θ estimators that take into account the error. The results show the MCLE performs well when the sample size is large or the error rate is high. Using parametric bootstrap, composite likelihood can also be used as a statistic for testing the model goodness-of-fit of the observed DNA sequences. The MCLE method is applied to sequence data on the ANGPTL4 gene in 1832 African American and 1045 European American individuals. PMID:19952140

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.

Genetic variance of tolerance and the toxicant threshold model.

PubMed

Tanaka, Yoshinari; Mano, Hiroyuki; Tatsuta, Haruki

2012-04-01

A statistical genetics method is presented for estimating the genetic variance (heritability) of tolerance to pollutants on the basis of a standard acute toxicity test conducted on several isofemale lines of cladoceran species. To analyze the genetic variance of tolerance in the case when the response is measured as a few discrete states (quantal endpoints), the authors attempted to apply the threshold character model in quantitative genetics to the threshold model separately developed in ecotoxicology. The integrated threshold model (toxicant threshold model) assumes that the response of a particular individual occurs at a threshold toxicant concentration and that the individual tolerance characterized by the individual's threshold value is determined by genetic and environmental factors. As a case study, the heritability of tolerance to p-nonylphenol in the cladoceran species Daphnia galeata was estimated by using the maximum likelihood method and nested analysis of variance (ANOVA). Broad-sense heritability was estimated to be 0.199 ± 0.112 by the maximum likelihood method and 0.184 ± 0.089 by ANOVA; both results implied that the species examined had the potential to acquire tolerance to this substance by evolutionary change. Copyright © 2012 SETAC.

Estimating unbiased magnitudes for the announced DPRK nuclear tests, 2006-2016

NASA Astrophysics Data System (ADS)

Peacock, Sheila; Bowers, David

2017-04-01

The seismic disturbances generated from the five (2006-2016) announced nuclear test explosions by the Democratic People's Republic of Korea (DPRK) are of moderate magnitude (body-wave magnitude mb 4-5) by global earthquake standards. An upward bias of network mean mb of low- to moderate-magnitude events is long established, and is caused by the censoring of readings from stations where the signal was below noise level at the time of the predicted arrival. This sampling bias can be overcome by maximum-likelihood methods using station thresholds at detecting (and non-detecting) stations. Bias in the mean mb can also be introduced by differences in the network of stations recording each explosion - this bias can reduced by using station corrections. We apply a maximum-likelihood (JML) inversion that jointly estimates station corrections and unbiased network mb for the five DPRK explosions recorded by the CTBTO International Monitoring Network (IMS) of seismic stations. The thresholds can either be directly measured from the noise preceding the observed signal, or determined by statistical analysis of bulletin amplitudes. The network mb of the first and smallest explosion is reduced significantly relative to the mean mb (to < 4.0 mb) by removal of the censoring bias.

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.

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.

Modularity-like objective function in annotated networks

NASA Astrophysics Data System (ADS)

Xie, Jia-Rong; Wang, Bing-Hong

2017-12-01

We ascertain the modularity-like objective function whose optimization is equivalent to the maximum likelihood in annotated networks. We demonstrate that the modularity-like objective function is a linear combination of modularity and conditional entropy. In contrast with statistical inference methods, in our method, the influence of the metadata is adjustable; when its influence is strong enough, the metadata can be recovered. Conversely, when it is weak, the detection may correspond to another partition. Between the two, there is a transition. This paper provides a concept for expanding the scope of modularity methods.

An unsupervised classification technique for multispectral remote sensing data.

NASA Technical Reports Server (NTRS)

Su, M. Y.; Cummings, R. E.

1973-01-01

Description of a two-part clustering technique consisting of (a) a sequential statistical clustering, which is essentially a sequential variance analysis, and (b) a generalized K-means clustering. In this composite clustering technique, the output of (a) is a set of initial clusters which are input to (b) for further improvement by an iterative scheme. This unsupervised composite technique was employed for automatic classification of two sets of remote multispectral earth resource observations. The classification accuracy by the unsupervised technique is found to be comparable to that by traditional supervised maximum-likelihood classification techniques.

F-8C adaptive control law refinement and software development

NASA Technical Reports Server (NTRS)

Hartmann, G. L.; Stein, G.

1981-01-01

An explicit adaptive control algorithm based on maximum likelihood estimation of parameters was designed. To avoid iterative calculations, the algorithm uses parallel channels of Kalman filters operating at fixed locations in parameter space. This algorithm was implemented in NASA/DFRC's Remotely Augmented Vehicle (RAV) facility. Real-time sensor outputs (rate gyro, accelerometer, surface position) are telemetered to a ground computer which sends new gain values to an on-board system. Ground test data and flight records were used to establish design values of noise statistics and to verify the ground-based adaptive software.

Statistics of some atmospheric turbulence records relevant to aircraft response calculations

NASA Technical Reports Server (NTRS)

Mark, W. D.; Fischer, R. W.

1981-01-01

Methods for characterizing atmospheric turbulence are described. The methods illustrated include maximum likelihood estimation of the integral scale and intensity of records obeying the von Karman transverse power spectral form, constrained least-squares estimation of the parameters of a parametric representation of autocorrelation functions, estimation of the power spectra density of the instantaneous variance of a record with temporally fluctuating variance, and estimation of the probability density functions of various turbulence components. Descriptions of the computer programs used in the computations are given, and a full listing of these programs is included.

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.

Efficient estimation of Pareto model: Some modified percentile estimators.

PubMed

Bhatti, Sajjad Haider; Hussain, Shahzad; Ahmad, Tanvir; Aslam, Muhammad; Aftab, Muhammad; Raza, Muhammad Ali

2018-01-01

The article proposes three modified percentile estimators for parameter estimation of the Pareto distribution. These modifications are based on median, geometric mean and expectation of empirical cumulative distribution function of first-order statistic. The proposed modified estimators are compared with traditional percentile estimators through a Monte Carlo simulation for different parameter combinations with varying sample sizes. Performance of different estimators is assessed in terms of total mean square error and total relative deviation. It is determined that modified percentile estimator based on expectation of empirical cumulative distribution function of first-order statistic provides efficient and precise parameter estimates compared to other estimators considered. The simulation results were further confirmed using two real life examples where maximum likelihood and moment estimators were also considered.

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.

The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction

PubMed Central

Williamson, Ross S.; Sahani, Maneesh; Pillow, Jonathan W.

2015-01-01

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron’s probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as “single-spike information” to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex. PMID:25831448

Exponential series approaches for nonparametric graphical models

NASA Astrophysics Data System (ADS)

Janofsky, Eric

Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of exponential series which approximates the log density by a finite-dimensional exponential family with the number of sufficient statistics increasing with the sample size. We consider two approaches to estimating these models. The first is regularized maximum likelihood. This involves optimizing the sum of the log-likelihood of the data and a sparsity-inducing regularizer. We then propose a variational approximation to the likelihood based on tree-reweighted, nonparametric message passing. This approximation allows for upper bounds on risk estimates, leverages parallelization and is scalable to densities on hundreds of nodes. We show how the regularized variational MLE may be estimated using a proximal gradient algorithm. We then consider estimation using regularized score matching. This approach uses an alternative scoring rule to the log-likelihood, which obviates the need to compute the normalizing constant of the distribution. For general continuous-valued exponential families, we provide parameter and edge consistency results. As a special case we detail a new approach to sparse precision matrix estimation which has statistical performance competitive with the graphical lasso and computational performance competitive with the state-of-the-art glasso algorithm. We then describe results for model selection in the nonparametric pairwise model using exponential series. The regularized score matching problem is shown to be a convex program; we provide scalable algorithms based on consensus alternating direction method of multipliers (ADMM) and coordinate-wise descent. We use simulations to compare our method to others in the literature as well as the aforementioned TRW estimator.

Gaussian process inference for estimating pharmacokinetic parameters of dynamic contrast-enhanced MR images.

PubMed

Wang, Shijun; Liu, Peter; Turkbey, Baris; Choyke, Peter; Pinto, Peter; Summers, Ronald M

2012-01-01

In this paper, we propose a new pharmacokinetic model for parameter estimation of dynamic contrast-enhanced (DCE) MRI by using Gaussian process inference. Our model is based on the Tofts dual-compartment model for the description of tracer kinetics and the observed time series from DCE-MRI is treated as a Gaussian stochastic process. The parameter estimation is done through a maximum likelihood approach and we propose a variant of the coordinate descent method to solve this likelihood maximization problem. The new model was shown to outperform a baseline method on simulated data. Parametric maps generated on prostate DCE data with the new model also provided better enhancement of tumors, lower intensity on false positives, and better boundary delineation when compared with the baseline method. New statistical parameter maps from the process model were also found to be informative, particularly when paired with the PK parameter maps.

Testing the causality of Hawkes processes with time reversal

NASA Astrophysics Data System (ADS)

Cordi, Marcus; Challet, Damien; Muni Toke, Ioane

2018-03-01

We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, tests of goodness of parametric fit unambiguously reject backward event times, which implies that inferring kernels from time-symmetric quantities, such as the autocovariance of the event rate, only rarely produce statistically significant fits. Finally, we find that fitting financial data with many-parameter kernels may yield significant fits for both arrows of time for the same event time vector, sometimes favouring the backward time direction. This goes to show that a significant fit of Hawkes processes to real data with flexible kernels does not imply a definite arrow of time unless one tests it.

Maximum likelihood methods for investigating reporting rates of rings on hunter-shot birds

USGS Publications Warehouse

Conroy, M.J.; Morgan, B.J.T.; North, P.M.

1985-01-01

It is well known that hunters do not report 100% of the rings that they find on shot birds. Reward studies can be used to estimate what this reporting rate is, by comparison of recoveries of rings offering a monetary reward, to ordinary rings. A reward study of American Black Ducks (Anas rubripes) is used to illustrate the design, and to motivate the development of statistical models for estimation and for testing hypotheses of temporal and geographic variation in reporting rates. The method involves indexing the data (recoveries) and parameters (reporting, harvest, and solicitation rates) by geographic and temporal strata. Estimates are obtained under unconstrained (e.g., allowing temporal variability in reporting rates) and constrained (e.g., constant reporting rates) models, and hypotheses are tested by likelihood ratio. A FORTRAN program, available from the author, is used to perform the computations.

Halo-independence with quantified maximum entropy at DAMA/LIBRA

NASA Astrophysics Data System (ADS)

Fowlie, Andrew

2017-10-01

Using the DAMA/LIBRA anomaly as an example, we formalise the notion of halo-independence in the context of Bayesian statistics and quantified maximum entropy. We consider an infinite set of possible profiles, weighted by an entropic prior and constrained by a likelihood describing noisy measurements of modulated moments by DAMA/LIBRA. Assuming an isotropic dark matter (DM) profile in the galactic rest frame, we find the most plausible DM profiles and predictions for unmodulated signal rates at DAMA/LIBRA. The entropic prior contains an a priori unknown regularisation factor, β, that describes the strength of our conviction that the profile is approximately Maxwellian. By varying β, we smoothly interpolate between a halo-independent and a halo-dependent analysis, thus exploring the impact of prior information about the DM profile.

Bayesian Image Segmentations by Potts Prior and Loopy Belief Propagation

NASA Astrophysics Data System (ADS)

Tanaka, Kazuyuki; Kataoka, Shun; Yasuda, Muneki; Waizumi, Yuji; Hsu, Chiou-Ting

2014-12-01

This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms are often referred to as hyperparameters in statistical machine learning theory. In order to determine these hyperparameters, we propose a new scheme for hyperparameter estimation based on conditional maximization of entropy in the Potts prior. The algorithm is given based on loopy belief propagation. In addition, we compare our conditional maximum entropy framework with the conventional maximum likelihood framework, and also clarify how the first order phase transitions in loopy belief propagations for Potts models influence our hyperparameter estimation procedures.

A maximum likelihood approach to diffeomorphic speckle tracking for 3D strain estimation in echocardiography.

PubMed

Curiale, Ariel H; Vegas-Sánchez-Ferrero, Gonzalo; Bosch, Johan G; Aja-Fernández, Santiago

2015-08-01

The strain and strain-rate measures are commonly used for the analysis and assessment of regional myocardial function. In echocardiography (EC), the strain analysis became possible using Tissue Doppler Imaging (TDI). Unfortunately, this modality shows an important limitation: the angle between the myocardial movement and the ultrasound beam should be small to provide reliable measures. This constraint makes it difficult to provide strain measures of the entire myocardium. Alternative non-Doppler techniques such as Speckle Tracking (ST) can provide strain measures without angle constraints. However, the spatial resolution and the noisy appearance of speckle still make the strain estimation a challenging task in EC. Several maximum likelihood approaches have been proposed to statistically characterize the behavior of speckle, which results in a better performance of speckle tracking. However, those models do not consider common transformations to achieve the final B-mode image (e.g. interpolation). This paper proposes a new maximum likelihood approach for speckle tracking which effectively characterizes speckle of the final B-mode image. Its formulation provides a diffeomorphic scheme than can be efficiently optimized with a second-order method. The novelty of the method is threefold: First, the statistical characterization of speckle generalizes conventional speckle models (Rayleigh, Nakagami and Gamma) to a more versatile model for real data. Second, the formulation includes local correlation to increase the efficiency of frame-to-frame speckle tracking. Third, a probabilistic myocardial tissue characterization is used to automatically identify more reliable myocardial motions. The accuracy and agreement assessment was evaluated on a set of 16 synthetic image sequences for three different scenarios: normal, acute ischemia and acute dyssynchrony. The proposed method was compared to six speckle tracking methods. Results revealed that the proposed method is the most accurate method to measure the motion and strain with an average median motion error of 0.42 mm and a median strain error of 2.0 ± 0.9%, 2.1 ± 1.3% and 7.1 ± 4.9% for circumferential, longitudinal and radial strain respectively. It also showed its capability to identify abnormal segments with reduced cardiac function and timing differences for the dyssynchrony cases. These results indicate that the proposed diffeomorphic speckle tracking method provides robust and accurate motion and strain estimation. Copyright © 2015. Published by Elsevier B.V.

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.

Mapping quantitative trait loci for binary trait in the F2:3 design.

PubMed

Zhu, Chengsong; Zhang, Yuan-Ming; Guo, Zhigang

2008-12-01

In the analysis of inheritance of quantitative traits with low heritability, an F(2:3) design that genotypes plants in F(2) and phenotypes plants in F(2:3) progeny is often used in plant genetics. Although statistical approaches for mapping quantitative trait loci (QTL) in the F(2:3) design have been well developed, those for binary traits of biological interest and economic importance are seldom addressed. In this study, an attempt was made to map binary trait loci (BTL) in the F(2:3) design. The fundamental idea was: the F(2) plants were genotyped, all phenotypic values of each F(2:3) progeny were measured for binary trait, and these binary trait values and the marker genotype informations were used to detect BTL under the penetrance and liability models. The proposed method was verified by a series of Monte-Carlo simulation experiments. These results showed that maximum likelihood approaches under the penetrance and liability models provide accurate estimates for the effects and the locations of BTL with high statistical power, even under of low heritability. Moreover, the penetrance model is as efficient as the liability model, and the F(2:3) design is more efficient than classical F(2) design, even though only a single progeny is collected from each F(2:3) family. With the maximum likelihood approaches under the penetrance and the liability models developed in this study, we can map binary traits as we can do for quantitative trait in the F(2:3) design.

Using Maximum Likelihood Statistical Methods and Pigment Flux Data to Constrain Particle Exchange and Organic Matter Remineralization Rate Constants in the Mediterranean Sea

NASA Astrophysics Data System (ADS)

Wang, W.; Lee, C.; Cochran, K. K.; Armstrong, R. A.

2016-02-01

Sinking particles play a pivotal role transferring material from the surface to the deeper ocean via the "biological pump". To quantify the extent to which these particles aggregate and disaggregate, and thus affect particle settling velocity, we constructed a box model to describe organic matter cycling. The box model was fit to chloropigment data sampled in the 2005 MedFlux project using Indented Rotating Sphere sediment traps operating in Settling Velocity (SV) mode. Because of the very different pigment compositions of phytoplankton and fecal pellets, chloropigments are useful as proxies to record particle exchange. The maximum likelihood statistical method was used to estimate particle aggregation, disaggregation, and organic matter remineralization rate constants. Eleven settling velocity categories collected by SV sediment traps were grouped into two sinking velocity classes (fast- and slow-sinking) to decrease the number of parameters that needed to be estimated. Organic matter degradation rate constants were estimated to be 1.2, 1.6, and 1.1 y^-1, which are equivalent to degradation half-lives of 0.60, 0.45, and 0.62 y^-1, at 313, 524, and 1918 m, respectively. Rate constants of chlorophyll a degradation to pheopigments (pheophorbide, pheophytin, and pyropheophorbide) were estimated to be 0.88, 0.93, and 1.2 y^-1, at 313, 524, and 1918 m, respectively. Aggregation rate constants varied little with depth, with the highest value being 0.07 y^-1 at 524 m. Disaggregation rate constants were highest at 524 m (14 y^-1) and lowest at 1918 m (9.6 y^-1)

Predicting bulk permeability using outcrop fracture attributes: The benefits of a Maximum Likelihood Estimator

NASA Astrophysics Data System (ADS)

Rizzo, R. E.; Healy, D.; De Siena, L.

2015-12-01

The success of any model prediction is largely dependent on the accuracy with which its parameters are known. In characterising fracture networks in naturally fractured rocks, the main issues are related with the difficulties in accurately up- and down-scaling the parameters governing the distribution of fracture attributes. Optimal characterisation and analysis of fracture attributes (fracture lengths, apertures, orientations and densities) represents a fundamental step which can aid the estimation of permeability and fluid flow, which are of primary importance in a number of contexts ranging from hydrocarbon production in fractured reservoirs and reservoir stimulation by hydrofracturing, to geothermal energy extraction and deeper Earth systems, such as earthquakes and ocean floor hydrothermal venting. This work focuses on linking fracture data collected directly from outcrops to permeability estimation and fracture network modelling. Outcrop studies can supplement the limited data inherent to natural fractured systems in the subsurface. The study area is a highly fractured upper Miocene biosiliceous mudstone formation cropping out along the coastline north of Santa Cruz (California, USA). These unique outcrops exposes a recently active bitumen-bearing formation representing a geological analogue of a fractured top seal. In order to validate field observations as useful analogues of subsurface reservoirs, we describe a methodology of statistical analysis for more accurate probability distribution of fracture attributes, using Maximum Likelihood Estimators. These procedures aim to understand whether the average permeability of a fracture network can be predicted reducing its uncertainties, and if outcrop measurements of fracture attributes can be used directly to generate statistically identical fracture network models.

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.

Using genetic data to estimate diffusion rates in heterogeneous landscapes.

PubMed

Roques, L; Walker, E; Franck, P; Soubeyrand, S; Klein, E K

2016-08-01

Having a precise knowledge of the dispersal ability of a population in a heterogeneous environment is of critical importance in agroecology and conservation biology as it can provide management tools to limit the effects of pests or to increase the survival of endangered species. In this paper, we propose a mechanistic-statistical method to estimate space-dependent diffusion parameters of spatially-explicit models based on stochastic differential equations, using genetic data. Dividing the total population into subpopulations corresponding to different habitat patches with known allele frequencies, the expected proportions of individuals from each subpopulation at each position is computed by solving a system of reaction-diffusion equations. Modelling the capture and genotyping of the individuals with a statistical approach, we derive a numerically tractable formula for the likelihood function associated with the diffusion parameters. In a simulated environment made of three types of regions, each associated with a different diffusion coefficient, we successfully estimate the diffusion parameters with a maximum-likelihood approach. Although higher genetic differentiation among subpopulations leads to more accurate estimations, once a certain level of differentiation has been reached, the finite size of the genotyped population becomes the limiting factor for accurate estimation.

Robustness of fit indices to outliers and leverage observations in structural equation modeling.

PubMed

Yuan, Ke-Hai; Zhong, Xiaoling

2013-06-01

Normal-distribution-based maximum likelihood (NML) is the most widely used method in structural equation modeling (SEM), although practical data tend to be nonnormally distributed. The effect of nonnormally distributed data or data contamination on the normal-distribution-based likelihood ratio (LR) statistic is well understood due to many analytical and empirical studies. In SEM, fit indices are used as widely as the LR statistic. In addition to NML, robust procedures have been developed for more efficient and less biased parameter estimates with practical data. This article studies the effect of outliers and leverage observations on fit indices following NML and two robust methods. Analysis and empirical results indicate that good leverage observations following NML and one of the robust methods lead most fit indices to give more support to the substantive model. While outliers tend to make a good model superficially bad according to many fit indices following NML, they have little effect on those following the two robust procedures. Implications of the results to data analysis are discussed, and recommendations are provided regarding the use of estimation methods and interpretation of fit indices. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

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.

How much to trust the senses: Likelihood learning

PubMed Central

Sato, Yoshiyuki; Kording, Konrad P.

2014-01-01

Our brain often needs to estimate unknown variables from imperfect information. Our knowledge about the statistical distributions of quantities in our environment (called priors) and currently available information from sensory inputs (called likelihood) are the basis of all Bayesian models of perception and action. While we know that priors are learned, most studies of prior-likelihood integration simply assume that subjects know about the likelihood. However, as the quality of sensory inputs change over time, we also need to learn about new likelihoods. Here, we show that human subjects readily learn the distribution of visual cues (likelihood function) in a way that can be predicted by models of statistically optimal learning. Using a likelihood that depended on color context, we found that a learned likelihood generalized to new priors. Thus, we conclude that subjects learn about likelihood. PMID:25398975

Testing the non-unity of rate ratio under inverse sampling.

PubMed

Tang, Man-Lai; Liao, Yi Jie; Ng, Hong Keung Tony; Chan, Ping Shing

2007-08-01

Inverse sampling is considered to be a more appropriate sampling scheme than the usual binomial sampling scheme when subjects arrive sequentially, when the underlying response of interest is acute, and when maximum likelihood estimators of some epidemiologic indices are undefined. In this article, we study various statistics for testing non-unity rate ratios in case-control studies under inverse sampling. These include the Wald, unconditional score, likelihood ratio and conditional score statistics. Three methods (the asymptotic, conditional exact, and Mid-P methods) are adopted for P-value calculation. We evaluate the performance of different combinations of test statistics and P-value calculation methods in terms of their empirical sizes and powers via Monte Carlo simulation. In general, asymptotic score and conditional score tests are preferable for their actual type I error rates are well controlled around the pre-chosen nominal level, and their powers are comparatively the largest. The exact version of Wald test is recommended if one wants to control the actual type I error rate at or below the pre-chosen nominal level. If larger power is expected and fluctuation of sizes around the pre-chosen nominal level are allowed, then the Mid-P version of Wald test is a desirable alternative. We illustrate the methodologies with a real example from a heart disease study. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Variability of space climate and its extremes with successive solar cycles

NASA Astrophysics Data System (ADS)

Chapman, Sandra; Hush, Phillip; Tindale, Elisabeth; Dunlop, Malcolm; Watkins, Nicholas

2016-04-01

Auroral geomagnetic indices coupled with in situ solar wind monitors provide a comprehensive data set, spanning several solar cycles. Space climate can be considered as the distribution of space weather. We can then characterize these observations in terms of changing space climate by quantifying how the statistical properties of ensembles of these observed variables vary between different phases of the solar cycle. We first consider the AE index burst distribution. Bursts are constructed by thresholding the AE time series; the size of a burst is the sum of the excess in the time series for each time interval over which the threshold is exceeded. The distribution of burst sizes is two component with a crossover in behaviour at thresholds ≈ 1000 nT. Above this threshold, we find[1] a range over which the mean burst size is almost constant with threshold for both solar maxima and minima. The burst size distribution of the largest events has a functional form which is exponential. The relative likelihood of these large events varies from one solar maximum and minimum to the next. If the relative overall activity of a solar maximum/minimum can be estimated, these results then constrain the likelihood of extreme events of a given size for that solar maximum/minimum. We next develop and apply a methodology to quantify how the full distribution of geomagnetic indices and upstream solar wind observables are changing between and across different solar cycles. This methodology[2] estimates how different quantiles of the distribution, or equivalently, how the return times of events of a given size, are changing. [1] Hush, P., S. C. Chapman, M. W. Dunlop, and N. W. Watkins (2015), Robust statistical properties of the size of large burst events in AE, Geophys. Res. Lett.,42 doi:10.1002/2015GL066277 [2] Chapman, S. C., D. A. Stainforth, N. W. Watkins, (2013) On estimating long term local climate trends , Phil. Trans. Royal Soc., A,371 20120287 DOI:10.1098/rsta.2012.0287

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.

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)

PlanetPack: A radial-velocity time-series analysis tool facilitating exoplanets detection, characterization, and dynamical simulations

NASA Astrophysics Data System (ADS)

Baluev, Roman V.

2013-08-01

We present PlanetPack, a new software tool that we developed to facilitate and standardize the advanced analysis of radial velocity (RV) data for the goal of exoplanets detection, characterization, and basic dynamical N-body simulations. PlanetPack is a command-line interpreter, that can run either in an interactive mode or in a batch mode of automatic script interpretation. Its major abilities include: (i) advanced RV curve fitting with the proper maximum-likelihood treatment of unknown RV jitter; (ii) user-friendly multi-Keplerian as well as Newtonian N-body RV fits; (iii) use of more efficient maximum-likelihood periodograms that involve the full multi-planet fitting (sometimes called as “residual” or “recursive” periodograms); (iv) easily calculatable parametric 2D likelihood function level contours, reflecting the asymptotic confidence regions; (v) fitting under some useful functional constraints is user-friendly; (vi) basic tasks of short- and long-term planetary dynamical simulation using a fast Everhart-type integrator based on Gauss-Legendre spacings; (vii) fitting the data with red noise (auto-correlated errors); (viii) various analytical and numerical methods for the tasks of determining the statistical significance. It is planned that further functionality may be added to PlanetPack in the future. During the development of this software, a lot of effort was made to improve the calculational speed, especially for CPU-demanding tasks. PlanetPack was written in pure C++ (standard of 1998/2003), and is expected to be compilable and useable on a wide range of platforms.

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.

Statistical modeling of optical attenuation measurements in continental fog conditions

NASA Astrophysics Data System (ADS)

Khan, Muhammad Saeed; Amin, Muhammad; Awan, Muhammad Saleem; Minhas, Abid Ali; Saleem, Jawad; Khan, Rahimdad

2017-03-01

Free-space optics is an innovative technology that uses atmosphere as a propagation medium to provide higher data rates. These links are heavily affected by atmospheric channel mainly because of fog and clouds that act to scatter and even block the modulated beam of light from reaching the receiver end, hence imposing severe attenuation. A comprehensive statistical study of the fog effects and deep physical understanding of the fog phenomena are very important for suggesting improvements (reliability and efficiency) in such communication systems. In this regard, 6-months real-time measured fog attenuation data are considered and statistically investigated. A detailed statistical analysis related to each fog event for that period is presented; the best probability density functions are selected on the basis of Akaike information criterion, while the estimates of unknown parameters are computed by maximum likelihood estimation technique. The results show that most fog attenuation events follow normal mixture distribution and some follow the Weibull distribution.

Identifying irregularly shaped crime hot-spots using a multiobjective evolutionary algorithm

NASA Astrophysics Data System (ADS)

Wu, Xiaolan; Grubesic, Tony H.

2010-12-01

Spatial cluster detection techniques are widely used in criminology, geography, epidemiology, and other fields. In particular, spatial scan statistics are popular and efficient techniques for detecting areas of elevated crime or disease events. The majority of spatial scan approaches attempt to delineate geographic zones by evaluating the significance of clusters using likelihood ratio statistics tested with the Poisson distribution. While this can be effective, many scan statistics give preference to circular clusters, diminishing their ability to identify elongated and/or irregular shaped clusters. Although adjusting the shape of the scan window can mitigate some of these problems, both the significance of irregular clusters and their spatial structure must be accounted for in a meaningful way. This paper utilizes a multiobjective evolutionary algorithm to find clusters with maximum significance while quantitatively tracking their geographic structure. Crime data for the city of Cincinnati are utilized to demonstrate the advantages of the new approach and highlight its benefits versus more traditional scan statistics.

Fitting and Modeling in the ASC Data Analysis Environment

NASA Astrophysics Data System (ADS)

Doe, S.; Siemiginowska, A.; Joye, W.; McDowell, J.

As part of the AXAF Science Center (ASC) Data Analysis Environment, we will provide to the astronomical community a Fitting Application. We present a design of the application in this paper. Our design goal is to give the user the flexibility to use a variety of optimization techniques (Levenberg-Marquardt, maximum entropy, Monte Carlo, Powell, downhill simplex, CERN-Minuit, and simulated annealing) and fit statistics (chi (2) , Cash, variance, and maximum likelihood); our modular design allows the user easily to add their own optimization techniques and/or fit statistics. We also present a comparison of the optimization techniques to be provided by the Application. The high spatial and spectral resolutions that will be obtained with AXAF instruments require a sophisticated data modeling capability. We will provide not only a suite of astronomical spatial and spectral source models, but also the capability of combining these models into source models of up to four data dimensions (i.e., into source functions f(E,x,y,t)). We will also provide tools to create instrument response models appropriate for each observation.

A method for classification of multisource data using interval-valued probabilities and its application to HIRIS data

NASA Technical Reports Server (NTRS)

Kim, H.; Swain, P. H.

1991-01-01

A method of classifying multisource data in remote sensing is presented. The proposed method considers each data source as an information source providing a body of evidence, represents statistical evidence by interval-valued probabilities, and uses Dempster's rule to integrate information based on multiple data source. The method is applied to the problems of ground-cover classification of multispectral data combined with digital terrain data such as elevation, slope, and aspect. Then this method is applied to simulated 201-band High Resolution Imaging Spectrometer (HIRIS) data by dividing the dimensionally huge data source into smaller and more manageable pieces based on the global statistical correlation information. It produces higher classification accuracy than the Maximum Likelihood (ML) classification method when the Hughes phenomenon is apparent.

Fitting a three-parameter lognormal distribution with applications to hydrogeochemical data from the National Uranium Resource Evaluation Program

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

Kane, V.E.

1979-10-01

The standard maximum likelihood and moment estimation procedures are shown to have some undesirable characteristics for estimating the parameters in a three-parameter lognormal distribution. A class of goodness-of-fit estimators is found which provides a useful alternative to the standard methods. The class of goodness-of-fit tests considered include the Shapiro-Wilk and Shapiro-Francia tests which reduce to a weighted linear combination of the order statistics that can be maximized in estimation problems. The weighted-order statistic estimators are compared to the standard procedures in Monte Carlo simulations. Bias and robustness of the procedures are examined and example data sets analyzed including geochemical datamore » from the National Uranium Resource Evaluation Program.« less

Land use/land cover mapping (1:25000) of Taiwan, Republic of China by automated multispectral interpretation of LANDSAT imagery

NASA Technical Reports Server (NTRS)

Sung, Q. C.; Miller, L. D.

1977-01-01

Three methods were tested for collection of the training sets needed to establish the spectral signatures of the land uses/land covers sought due to the difficulties of retrospective collection of representative ground control data. Computer preprocessing techniques applied to the digital images to improve the final classification results were geometric corrections, spectral band or image ratioing and statistical cleaning of the representative training sets. A minimal level of statistical verification was made based upon the comparisons between the airphoto estimates and the classification results. The verifications provided a further support to the selection of MSS band 5 and 7. It also indicated that the maximum likelihood ratioing technique can achieve more agreeable classification results with the airphoto estimates than the stepwise discriminant analysis.

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

Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra

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

Hock, Kiel; Earle, Keith

2016-02-06

In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the optimum parameter set and to estimate parameter uncertainties. In conclusion, the posterior distribution allows us to define a metric on parameter space that induces a geometry with negative curvature that affects the parameter uncertainty estimates, particularly for spectra with low signal to noise.

Constrained Stochastic Extended Redundancy Analysis.

PubMed

DeSarbo, Wayne S; Hwang, Heungsun; Stadler Blank, Ashley; Kappe, Eelco

2015-06-01

We devise a new statistical methodology called constrained stochastic extended redundancy analysis (CSERA) to examine the comparative impact of various conceptual factors, or drivers, as well as the specific predictor variables that contribute to each driver on designated dependent variable(s). The technical details of the proposed methodology, the maximum likelihood estimation algorithm, and model selection heuristics are discussed. A sports marketing consumer psychology application is provided in a Major League Baseball (MLB) context where the effects of six conceptual drivers of game attendance and their defining predictor variables are estimated. Results compare favorably to those obtained using traditional extended redundancy analysis (ERA).

The CLASSY clustering algorithm: Description, evaluation, and comparison with the iterative self-organizing clustering system (ISOCLS). [used for LACIE data

NASA Technical Reports Server (NTRS)

Lennington, R. K.; Malek, H.

1978-01-01

A clustering method, CLASSY, was developed, which alternates maximum likelihood iteration with a procedure for splitting, combining, and eliminating the resulting statistics. The method maximizes the fit of a mixture of normal distributions to the observed first through fourth central moments of the data and produces an estimate of the proportions, means, and covariances in this mixture. The mathematical model which is the basic for CLASSY and the actual operation of the algorithm is described. Data comparing the performances of CLASSY and ISOCLS on simulated and actual LACIE data are presented.

The application of signal detection theory to optics

NASA Technical Reports Server (NTRS)

Helstrom, C. W.

1971-01-01

The restoration of images focused on a photosensitive surface is treated from the standpoint of maximum likelihood estimation, taking into account the Poisson distributions of the observed data, which are the numbers of photoelectrons from various elements of the surface. A detector of an image focused on such a surface utilizes a certain linear combination of those numbers as the optimum detection statistic. Methods for calculating the false alarm and detection probabilities are proposed. It is shown that measuring noncommuting observables in an ideal quantum receiver cannot yield a lower Bayes cost than that attainable by a system measuring only commuting observables.

Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme

NASA Astrophysics Data System (ADS)

Bakoban, Rana A.

2017-08-01

The coefficient of variation [CV] has several applications in applied statistics. So in this paper, we adopt Bayesian and non-Bayesian approaches for the estimation of CV under type-II censored data from extension exponential distribution [EED]. The point and interval estimate of the CV are obtained for each of the maximum likelihood and parametric bootstrap techniques. Also the Bayesian approach with the help of MCMC method is presented. A real data set is presented and analyzed, hence the obtained results are used to assess the obtained theoretical results.

The concordance index C and the Mann-Whitney parameter Pr(X>Y) with randomly censored data.

PubMed

Koziol, James A; Jia, Zhenyu

2009-06-01

Harrell's c-index or concordance C has been widely used as a measure of separation of two survival distributions. In the absence of censored data, the c-index estimates the Mann-Whitney parameter Pr(X>Y), which has been repeatedly utilized in various statistical contexts. In the presence of randomly censored data, the c-index no longer estimates Pr(X>Y); rather, a parameter that involves the underlying censoring distributions. This is in contrast to Efron's maximum likelihood estimator of the Mann-Whitney parameter, which is recommended in the setting of random censorship.

The admixture maximum likelihood test to test for association between rare variants and disease phenotypes.

PubMed

Tyrer, Jonathan P; Guo, Qi; Easton, Douglas F; Pharoah, Paul D P

2013-06-06

The development of genotyping arrays containing hundreds of thousands of rare variants across the genome and advances in high-throughput sequencing technologies have made feasible empirical genetic association studies to search for rare disease susceptibility alleles. As single variant testing is underpowered to detect associations, the development of statistical methods to combine analysis across variants - so-called "burden tests" - is an area of active research interest. We previously developed a method, the admixture maximum likelihood test, to test multiple, common variants for association with a trait of interest. We have extended this method, called the rare admixture maximum likelihood test (RAML), for the analysis of rare variants. In this paper we compare the performance of RAML with six other burden tests designed to test for association of rare variants. We used simulation testing over a range of scenarios to test the power of RAML compared to the other rare variant association testing methods. These scenarios modelled differences in effect variability, the average direction of effect and the proportion of associated variants. We evaluated the power for all the different scenarios. RAML tended to have the greatest power for most scenarios where the proportion of associated variants was small, whereas SKAT-O performed a little better for the scenarios with a higher proportion of associated variants. The RAML method makes no assumptions about the proportion of variants that are associated with the phenotype of interest or the magnitude and direction of their effect. The method is flexible and can be applied to both dichotomous and quantitative traits and allows for the inclusion of covariates in the underlying regression model. The RAML method performed well compared to the other methods over a wide range of scenarios. Generally power was moderate in most of the scenarios, underlying the need for large sample sizes in any form of association testing.

Constrained Maximum Likelihood Estimation for Model Calibration Using Summary-level Information from External Big Data Sources

PubMed Central

Chatterjee, Nilanjan; Chen, Yi-Hau; Maas, Paige; Carroll, Raymond J.

2016-01-01

Information from various public and private data sources of extremely large sample sizes are now increasingly available for research purposes. Statistical methods are needed for utilizing information from such big data sources while analyzing data from individual studies that may collect more detailed information required for addressing specific hypotheses of interest. In this article, we consider the problem of building regression models based on individual-level data from an “internal” study while utilizing summary-level information, such as information on parameters for reduced models, from an “external” big data source. We identify a set of very general constraints that link internal and external models. These constraints are used to develop a framework for semiparametric maximum likelihood inference that allows the distribution of covariates to be estimated using either the internal sample or an external reference sample. We develop extensions for handling complex stratified sampling designs, such as case-control sampling, for the internal study. Asymptotic theory and variance estimators are developed for each case. We use simulation studies and a real data application to assess the performance of the proposed methods in contrast to the generalized regression (GR) calibration methodology that is popular in the sample survey literature. PMID:27570323

Application of maximum-likelihood estimation in optical coherence tomography for nanometer-class thickness estimation

NASA Astrophysics Data System (ADS)

Huang, Jinxin; Yuan, Qun; Tankam, Patrice; Clarkson, Eric; Kupinski, Matthew; Hindman, Holly B.; Aquavella, James V.; Rolland, Jannick P.

2015-03-01

In biophotonics imaging, one important and quantitative task is layer-thickness estimation. In this study, we investigate the approach of combining optical coherence tomography and a maximum-likelihood (ML) estimator for layer thickness estimation in the context of tear film imaging. The motivation of this study is to extend our understanding of tear film dynamics, which is the prerequisite to advance the management of Dry Eye Disease, through the simultaneous estimation of the thickness of the tear film lipid and aqueous layers. The estimator takes into account the different statistical processes associated with the imaging chain. We theoretically investigated the impact of key system parameters, such as the axial point spread functions (PSF) and various sources of noise on measurement uncertainty. Simulations show that an OCT system with a 1 μm axial PSF (FWHM) allows unbiased estimates down to nanometers with nanometer precision. In implementation, we built a customized Fourier domain OCT system that operates in the 600 to 1000 nm spectral window and achieves 0.93 micron axial PSF in corneal epithelium. We then validated the theoretical framework with physical phantoms made of custom optical coatings, with layer thicknesses from tens of nanometers to microns. Results demonstrate unbiased nanometer-class thickness estimates in three different physical phantoms.

Application of change-point problem to the detection of plant patches.

PubMed

López, I; Gámez, M; Garay, J; Standovár, T; Varga, Z

2010-03-01

In ecology, if the considered area or space is large, the spatial distribution of individuals of a given plant species is never homogeneous; plants form different patches. The homogeneity change in space or in time (in particular, the related change-point problem) is an important research subject in mathematical statistics. In the paper, for a given data system along a straight line, two areas are considered, where the data of each area come from different discrete distributions, with unknown parameters. In the paper a method is presented for the estimation of the distribution change-point between both areas and an estimate is given for the distributions separated by the obtained change-point. The solution of this problem will be based on the maximum likelihood method. Furthermore, based on an adaptation of the well-known bootstrap resampling, a method for the estimation of the so-called change-interval is also given. The latter approach is very general, since it not only applies in the case of the maximum-likelihood estimation of the change-point, but it can be also used starting from any other change-point estimation known in the ecological literature. The proposed model is validated against typical ecological situations, providing at the same time a verification of the applied algorithms.

Maximum likelihood bolometric tomography for the determination of the uncertainties in the radiation emission on JET TOKAMAK

NASA Astrophysics Data System (ADS)

Craciunescu, Teddy; Peluso, Emmanuele; Murari, Andrea; Gelfusa, Michela; JET Contributors

2018-05-01

The total emission of radiation is a crucial quantity to calculate the power balances and to understand the physics of any Tokamak. Bolometric systems are the main tool to measure this important physical quantity through quite sophisticated tomographic inversion methods. On the Joint European Torus, the coverage of the bolometric diagnostic, due to the availability of basically only two projection angles, is quite limited, rendering the inversion a very ill-posed mathematical problem. A new approach, based on the maximum likelihood, has therefore been developed and implemented to alleviate one of the major weaknesses of traditional tomographic techniques: the difficulty to determine routinely the confidence intervals in the results. The method has been validated by numerical simulations with phantoms to assess the quality of the results and to optimise the configuration of the parameters for the main types of emissivity encountered experimentally. The typical levels of statistical errors, which may significantly influence the quality of the reconstructions, have been identified. The systematic tests with phantoms indicate that the errors in the reconstructions are quite limited and their effect on the total radiated power remains well below 10%. A comparison with other approaches to the inversion and to the regularization has also been performed.

Design and analysis of three-arm trials with negative binomially distributed endpoints.

PubMed

Mütze, Tobias; Munk, Axel; Friede, Tim

2016-02-20

A three-arm clinical trial design with an experimental treatment, an active control, and a placebo control, commonly referred to as the gold standard design, enables testing of non-inferiority or superiority of the experimental treatment compared with the active control. In this paper, we propose methods for designing and analyzing three-arm trials with negative binomially distributed endpoints. In particular, we develop a Wald-type test with a restricted maximum-likelihood variance estimator for testing non-inferiority or superiority. For this test, sample size and power formulas as well as optimal sample size allocations will be derived. The performance of the proposed test will be assessed in an extensive simulation study with regard to type I error rate, power, sample size, and sample size allocation. For the purpose of comparison, Wald-type statistics with a sample variance estimator and an unrestricted maximum-likelihood estimator are included in the simulation study. We found that the proposed Wald-type test with a restricted variance estimator performed well across the considered scenarios and is therefore recommended for application in clinical trials. The methods proposed are motivated and illustrated by a recent clinical trial in multiple sclerosis. The R package ThreeArmedTrials, which implements the methods discussed in this paper, is available on CRAN. Copyright © 2015 John Wiley & Sons, Ltd.

Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: statistical and systematic error budgets for future experiments

NASA Astrophysics Data System (ADS)

Raghunathan, Srinivasan; Patil, Sanjaykumar; Baxter, Eric J.; Bianchini, Federico; Bleem, Lindsey E.; Crawford, Thomas M.; Holder, Gilbert P.; Manzotti, Alessandro; Reichardt, Christian L.

2017-08-01

We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential systematic errors. Using realistic simulations, we examine the cluster mass uncertainties from CMB-cluster lensing as a function of an experiment's beam size and noise level. We predict the cluster mass uncertainties will be 3 - 6% for SPT-3G, AdvACT, and Simons Array experiments with 10,000 clusters and less than 1% for the CMB-S4 experiment with a sample containing 100,000 clusters. The mass constraints from CMB polarization are very sensitive to the experimental beam size and map noise level: for a factor of three reduction in either the beam size or noise level, the lensing signal-to-noise improves by roughly a factor of two.

Halo-independence with quantified maximum entropy at DAMA/LIBRA

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

Fowlie, Andrew, E-mail: andrew.j.fowlie@googlemail.com

2017-10-01

Using the DAMA/LIBRA anomaly as an example, we formalise the notion of halo-independence in the context of Bayesian statistics and quantified maximum entropy. We consider an infinite set of possible profiles, weighted by an entropic prior and constrained by a likelihood describing noisy measurements of modulated moments by DAMA/LIBRA. Assuming an isotropic dark matter (DM) profile in the galactic rest frame, we find the most plausible DM profiles and predictions for unmodulated signal rates at DAMA/LIBRA. The entropic prior contains an a priori unknown regularisation factor, β, that describes the strength of our conviction that the profile is approximately Maxwellian.more » By varying β, we smoothly interpolate between a halo-independent and a halo-dependent analysis, thus exploring the impact of prior information about the DM profile.« less

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…

A smoothed stochastic earthquake rate model considering seismicity and fault moment release for Europe

NASA Astrophysics Data System (ADS)

Hiemer, S.; Woessner, J.; Basili, R.; Danciu, L.; Giardini, D.; Wiemer, S.

2014-08-01

We present a time-independent gridded earthquake rate forecast for the European region including Turkey. The spatial component of our model is based on kernel density estimation techniques, which we applied to both past earthquake locations and fault moment release on mapped crustal faults and subduction zone interfaces with assigned slip rates. Our forecast relies on the assumption that the locations of past seismicity is a good guide to future seismicity, and that future large-magnitude events occur more likely in the vicinity of known faults. We show that the optimal weighted sum of the corresponding two spatial densities depends on the magnitude range considered. The kernel bandwidths and density weighting function are optimized using retrospective likelihood-based forecast experiments. We computed earthquake activity rates (a- and b-value) of the truncated Gutenberg-Richter distribution separately for crustal and subduction seismicity based on a maximum likelihood approach that considers the spatial and temporal completeness history of the catalogue. The final annual rate of our forecast is purely driven by the maximum likelihood fit of activity rates to the catalogue data, whereas its spatial component incorporates contributions from both earthquake and fault moment-rate densities. Our model constitutes one branch of the earthquake source model logic tree of the 2013 European seismic hazard model released by the EU-FP7 project `Seismic HAzard haRmonization in Europe' (SHARE) and contributes to the assessment of epistemic uncertainties in earthquake activity rates. We performed retrospective and pseudo-prospective likelihood consistency tests to underline the reliability of our model and SHARE's area source model (ASM) using the testing algorithms applied in the collaboratory for the study of earthquake predictability (CSEP). We comparatively tested our model's forecasting skill against the ASM and find a statistically significant better performance for testing periods of 10-20 yr. The testing results suggest that our model is a viable candidate model to serve for long-term forecasting on timescales of years to decades for the European region.

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.

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.

Marginal Structural Models with Counterfactual Effect Modifiers.

PubMed

Zheng, Wenjing; Luo, Zhehui; van der Laan, Mark J

2018-06-08

In health and social sciences, research questions often involve systematic assessment of the modification of treatment causal effect by patient characteristics. In longitudinal settings, time-varying or post-intervention effect modifiers are also of interest. In this work, we investigate the robust and efficient estimation of the Counterfactual-History-Adjusted Marginal Structural Model (van der Laan MJ, Petersen M. Statistical learning of origin-specific statically optimal individualized treatment rules. Int J Biostat. 2007;3), which models the conditional intervention-specific mean outcome given a counterfactual modifier history in an ideal experiment. We establish the semiparametric efficiency theory for these models, and present a substitution-based, semiparametric efficient and doubly robust estimator using the targeted maximum likelihood estimation methodology (TMLE, e.g. van der Laan MJ, Rubin DB. Targeted maximum likelihood learning. Int J Biostat. 2006;2, van der Laan MJ, Rose S. Targeted learning: causal inference for observational and experimental data, 1st ed. Springer Series in Statistics. Springer, 2011). To facilitate implementation in applications where the effect modifier is high dimensional, our third contribution is a projected influence function (and the corresponding projected TMLE estimator), which retains most of the robustness of its efficient peer and can be easily implemented in applications where the use of the efficient influence function becomes taxing. We compare the projected TMLE estimator with an Inverse Probability of Treatment Weighted estimator (e.g. Robins JM. Marginal structural models. In: Proceedings of the American Statistical Association. Section on Bayesian Statistical Science, 1-10. 1997a, Hernan MA, Brumback B, Robins JM. Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. 2000;11:561-570), and a non-targeted G-computation estimator (Robins JM. A new approach to causal inference in mortality studies with sustained exposure periods - application to control of the healthy worker survivor effect. Math Modell. 1986;7:1393-1512.). The comparative performance of these estimators is assessed in a simulation study. The use of the projected TMLE estimator is illustrated in a secondary data analysis for the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) trial where effect modifiers are subject to missing at random.

Which Statistic Should Be Used to Detect Item Preknowledge When the Set of Compromised Items Is Known?

PubMed

Sinharay, Sandip

2017-09-01

Benefiting from item preknowledge is a major type of fraudulent behavior during educational assessments. Belov suggested the posterior shift statistic for detection of item preknowledge and showed its performance to be better on average than that of seven other statistics for detection of item preknowledge for a known set of compromised items. Sinharay suggested a statistic based on the likelihood ratio test for detection of item preknowledge; the advantage of the statistic is that its null distribution is known. Results from simulated and real data and adaptive and nonadaptive tests are used to demonstrate that the Type I error rate and power of the statistic based on the likelihood ratio test are very similar to those of the posterior shift statistic. Thus, the statistic based on the likelihood ratio test appears promising in detecting item preknowledge when the set of compromised items is known.

Ensemble classification for identifying neighbourhood sources of fugitive dust and associations with observed PM10

NASA Astrophysics Data System (ADS)

Khuluse-Makhanya, Sibusisiwe; Stein, Alfred; Breytenbach, André; Gxumisa, Athi; Dudeni-Tlhone, Nontembeko; Debba, Pravesh

2017-10-01

In urban areas the deterioration of air quality as a result of fugitive dust receives less attention than the more prominent traffic and industrial emissions. We assessed whether fugitive dust emission sources in the neighbourhood of an air quality monitor are predictors of ambient PM10 concentrations on days characterized by strong local winds. An ensemble maximum likelihood method is developed for land cover mapping in the vicinity of an air quality station using SPOT 6 multi-spectral images. The ensemble maximum likelihood classifier is developed through multiple training iterations for improved accuracy of the bare soil class. Five primary land cover classes are considered, namely built-up areas, vegetation, bare soil, water and 'mixed bare soil' which denotes areas where soil is mixed with either vegetation or synthetic materials. Preliminary validation of the ensemble classifier for the bare soil class results in an accuracy range of 65-98%. Final validation of all classes results in an overall accuracy of 78%. Next, cluster analysis and a varying intercepts regression model are used to assess the statistical association between land cover, a fugitive dust emissions proxy and observed PM10. We found that land cover patterns in the neighbourhood of an air quality station are significant predictors of observed average PM10 concentrations on days when wind speeds are conducive for dust emissions. This study concludes that in the absence of an emissions inventory for ambient particulate matter, PM10 emitted from dust reservoirs can be statistically accounted for by land cover characteristics. This supports the use of land cover data for improved prediction of PM10 at locations without air quality monitoring stations.

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

NASA Technical Reports Server (NTRS)

Howell, L. W., Jr.

2003-01-01

A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.

Bayesian comparison of conceptual models of abrupt climate changes during the last glacial period

NASA Astrophysics Data System (ADS)

Boers, Niklas; Ghil, Michael; Rousseau, Denis-Didier

2017-04-01

Records of oxygen isotope ratios and dust concentrations from the North Greenland Ice Core Project (NGRIP) provide accurate proxies for the evolution of Arctic temperature and atmospheric circulation during the last glacial period (12ka to 100ka b2k) [1]. The most distinctive feature of these records are sudden transitions, called Dansgaard-Oeschger (DO) events, during which Arctic temperatures increased by up to 10 K within a few decades. These warming events are consistently followed by more gradual cooling in Antarctica [2]. The physical mechanisms responsible for these transitions and their out-of-phase relationship between the northern and southern hemisphere remain unclear. Substantial evidence hints at variations of the Atlantic Meridional Overturning Circulation as a key mechanism [2,3], but also other mechanisms, such as variations of sea ice extent [4] or ice shelf coverage [5] may play an important role. Here, we intend to shed more light on the relevance of the different mechanisms suggested to explain the abrupt climate changes and their inter-hemispheric coupling. For this purpose, several conceptual differential equation models are developed that represent the suggested physical mechanisms. Optimal parameters for each model candidate are then determined via maximum likelihood estimation with respect to the observed paleoclimatic data. Our approach is thus semi-empirical: While a model's general form is deduced from physical arguments about relevant climatic mechanisms — oceanic and atmospheric — its specific parameters are obtained by training the model on observed data. The distinct model candidates are evaluated by comparing statistical properties of time series simulated with these models to the observed statistics. In particular, Bayesian model selection criteria like Maximum Likelihood Ratio tests are used to obtain a hierarchy of the different candidates in terms of their likelihood, given the observed oxygen isotope and dust time series. [1] Kindler et al., Clim. Past (2014) [2] WAIS, Nature (2015) [3] Henry et al., Science (2016) [4] Gildor and Tziperman, Phil. Trans. R. Soc. (2003) [5] Petersen et al., Paleoceanography (2013)

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…

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.

Scaled test statistics and robust standard errors for non-normal data in covariance structure analysis: a Monte Carlo study.

PubMed

Chou, C P; Bentler, P M; Satorra, A

1991-11-01

Research studying robustness of maximum likelihood (ML) statistics in covariance structure analysis has concluded that test statistics and standard errors are biased under severe non-normality. An estimation procedure known as asymptotic distribution free (ADF), making no distributional assumption, has been suggested to avoid these biases. Corrections to the normal theory statistics to yield more adequate performance have also been proposed. This study compares the performance of a scaled test statistic and robust standard errors for two models under several non-normal conditions and also compares these with the results from ML and ADF methods. Both ML and ADF test statistics performed rather well in one model and considerably worse in the other. In general, the scaled test statistic seemed to behave better than the ML test statistic and the ADF statistic performed the worst. The robust and ADF standard errors yielded more appropriate estimates of sampling variability than the ML standard errors, which were usually downward biased, in both models under most of the non-normal conditions. ML test statistics and standard errors were found to be quite robust to the violation of the normality assumption when data had either symmetric and platykurtic distributions, or non-symmetric and zero kurtotic distributions.

Change-in-ratio estimators for populations with more than two subclasses

USGS Publications Warehouse

Udevitz, Mark S.; Pollock, Kenneth H.

1991-01-01

Change-in-ratio methods have been developed to estimate the size of populations with two or three population subclasses. Most of these methods require the often unreasonable assumption of equal sampling probabilities for individuals in all subclasses. This paper presents new models based on the weaker assumption that ratios of sampling probabilities are constant over time for populations with three or more subclasses. Estimation under these models requires that a value be assumed for one of these ratios when there are two samples. Explicit expressions are given for the maximum likelihood estimators under models for two samples with three or more subclasses and for three samples with two subclasses. A numerical method using readily available statistical software is described for obtaining the estimators and their standard errors under all of the models. Likelihood ratio tests that can be used in model selection are discussed. Emphasis is on the two-sample, three-subclass models for which Monte-Carlo simulation results and an illustrative example are presented.

Application of multispectral scanner data to the study of an abandoned surface coal mine

NASA Technical Reports Server (NTRS)

Spisz, E. W.

1978-01-01

The utility of aircraft multispectral scanner data for describing the land cover features of an abandoned contour-mined coal mine is considered. The data were obtained with an 11 band multispectral scanner at an altitude of 1.2 kilometers. Supervised, maximum-likelihood statistical classifications of the data were made to establish land-cover classes and also to describe in more detail the barren surface features as they may pertain to the reclamation or restoration of the area. The scanner data for the surface-water areas were studied to establish the variability and range of the spectral signatures. Both day and night thermal images of the area are presented. The results of the study show that a high degree of statistical separation can be obtained from the multispectral scanner data for the various land-cover features.

Non-convex Statistical Optimization for Sparse Tensor Graphical Model

PubMed Central

Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang

2016-01-01

We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies. PMID:28316459

Comparison of algebraic and analytical approaches to the formulation of the statistical model-based reconstruction problem for X-ray computed tomography.

PubMed

Cierniak, Robert; Lorent, Anna

2016-09-01

The main aim of this paper is to investigate properties of our originally formulated statistical model-based iterative approach applied to the image reconstruction from projections problem which are related to its conditioning, and, in this manner, to prove a superiority of this approach over ones recently used by other authors. The reconstruction algorithm based on this conception uses a maximum likelihood estimation with an objective adjusted to the probability distribution of measured signals obtained from an X-ray computed tomography system with parallel beam geometry. The analysis and experimental results presented here show that our analytical approach outperforms the referential algebraic methodology which is explored widely in the literature and exploited in various commercial implementations. Copyright © 2016 Elsevier Ltd. All rights reserved.

TDRS orbit determination by radio interferometry

NASA Technical Reports Server (NTRS)

Pavloff, Michael S.

1994-01-01

In support of a NASA study on the application of radio interferometry to satellite orbit determination, MITRE developed a simulation tool for assessing interferometry tracking accuracy. The Orbit Determination Accuracy Estimator (ODAE) models the general batch maximum likelihood orbit determination algorithms of the Goddard Trajectory Determination System (GTDS) with the group and phase delay measurements from radio interferometry. ODAE models the statistical properties of tracking error sources, including inherent observable imprecision, atmospheric delays, clock offsets, station location uncertainty, and measurement biases, and through Monte Carlo simulation, ODAE calculates the statistical properties of errors in the predicted satellites state vector. This paper presents results from ODAE application to orbit determination of the Tracking and Data Relay Satellite (TDRS) by radio interferometry. Conclusions about optimal ground station locations for interferometric tracking of TDRS are presented, along with a discussion of operational advantages of radio interferometry.

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.

Density-based empirical likelihood procedures for testing symmetry of data distributions and K-sample comparisons.

PubMed

Vexler, Albert; Tanajian, Hovig; Hutson, Alan D

In practice, parametric likelihood-ratio techniques are powerful statistical tools. In this article, we propose and examine novel and simple distribution-free test statistics that efficiently approximate parametric likelihood ratios to analyze and compare distributions of K groups of observations. Using the density-based empirical likelihood methodology, we develop a Stata package that applies to a test for symmetry of data distributions and compares K -sample distributions. Recognizing that recent statistical software packages do not sufficiently address K -sample nonparametric comparisons of data distributions, we propose a new Stata command, vxdbel, to execute exact density-based empirical likelihood-ratio tests using K samples. To calculate p -values of the proposed tests, we use the following methods: 1) a classical technique based on Monte Carlo p -value evaluations; 2) an interpolation technique based on tabulated critical values; and 3) a new hybrid technique that combines methods 1 and 2. The third, cutting-edge method is shown to be very efficient in the context of exact-test p -value computations. This Bayesian-type method considers tabulated critical values as prior information and Monte Carlo generations of test statistic values as data used to depict the likelihood function. In this case, a nonparametric Bayesian method is proposed to compute critical values of exact tests.

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.

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.

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.

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

Exclusion probabilities and likelihood ratios with applications to kinship problems.

PubMed

Slooten, Klaas-Jan; Egeland, Thore

2014-05-01

In forensic genetics, DNA profiles are compared in order to make inferences, paternity cases being a standard example. The statistical evidence can be summarized and reported in several ways. For example, in a paternity case, the likelihood ratio (LR) and the probability of not excluding a random man as father (RMNE) are two common summary statistics. There has been a long debate on the merits of the two statistics, also in the context of DNA mixture interpretation, and no general consensus has been reached. In this paper, we show that the RMNE is a certain weighted average of inverse likelihood ratios. This is true in any forensic context. We show that the likelihood ratio in favor of the correct hypothesis is, in expectation, bigger than the reciprocal of the RMNE probability. However, with the exception of pathological cases, it is also possible to obtain smaller likelihood ratios. We illustrate this result for paternity cases. Moreover, some theoretical properties of the likelihood ratio for a large class of general pairwise kinship cases, including expected value and variance, are derived. The practical implications of the findings are discussed and exemplified.

Identifying the Source of Misfit in Item Response Theory Models.

PubMed

Liu, Yang; Maydeu-Olivares, Alberto

2014-01-01

When an item response theory model fails to fit adequately, the items for which the model provides a good fit and those for which it does not must be determined. To this end, we compare the performance of several fit statistics for item pairs with known asymptotic distributions under maximum likelihood estimation of the item parameters: (a) a mean and variance adjustment to bivariate Pearson's X(2), (b) a bivariate subtable analog to Reiser's (1996) overall goodness-of-fit test, (c) a z statistic for the bivariate residual cross product, and (d) Maydeu-Olivares and Joe's (2006) M2 statistic applied to bivariate subtables. The unadjusted Pearson's X(2) with heuristically determined degrees of freedom is also included in the comparison. For binary and ordinal data, our simulation results suggest that the z statistic has the best Type I error and power behavior among all the statistics under investigation when the observed information matrix is used in its computation. However, if one has to use the cross-product information, the mean and variance adjusted X(2) is recommended. We illustrate the use of pairwise fit statistics in 2 real-data examples and discuss possible extensions of the current research in various directions.

Handling Big Data in Medical Imaging: Iterative Reconstruction with Large-Scale Automated Parallel Computation

PubMed Central

Lee, Jae H.; Yao, Yushu; Shrestha, Uttam; Gullberg, Grant T.; Seo, Youngho

2014-01-01

The primary goal of this project is to implement the iterative statistical image reconstruction algorithm, in this case maximum likelihood expectation maximum (MLEM) used for dynamic cardiac single photon emission computed tomography, on Spark/GraphX. This involves porting the algorithm to run on large-scale parallel computing systems. Spark is an easy-to- program software platform that can handle large amounts of data in parallel. GraphX is a graph analytic system running on top of Spark to handle graph and sparse linear algebra operations in parallel. The main advantage of implementing MLEM algorithm in Spark/GraphX is that it allows users to parallelize such computation without any expertise in parallel computing or prior knowledge in computer science. In this paper we demonstrate a successful implementation of MLEM in Spark/GraphX and present the performance gains with the goal to eventually make it useable in clinical setting. PMID:27081299

Handling Big Data in Medical Imaging: Iterative Reconstruction with Large-Scale Automated Parallel Computation.

PubMed

Lee, Jae H; Yao, Yushu; Shrestha, Uttam; Gullberg, Grant T; Seo, Youngho

2014-11-01

The primary goal of this project is to implement the iterative statistical image reconstruction algorithm, in this case maximum likelihood expectation maximum (MLEM) used for dynamic cardiac single photon emission computed tomography, on Spark/GraphX. This involves porting the algorithm to run on large-scale parallel computing systems. Spark is an easy-to- program software platform that can handle large amounts of data in parallel. GraphX is a graph analytic system running on top of Spark to handle graph and sparse linear algebra operations in parallel. The main advantage of implementing MLEM algorithm in Spark/GraphX is that it allows users to parallelize such computation without any expertise in parallel computing or prior knowledge in computer science. In this paper we demonstrate a successful implementation of MLEM in Spark/GraphX and present the performance gains with the goal to eventually make it useable in clinical setting.

Methods for flexible sample-size design in clinical trials: Likelihood, weighted, dual test, and promising zone approaches.

PubMed

Shih, Weichung Joe; Li, Gang; Wang, Yining

2016-03-01

Sample size plays a crucial role in clinical trials. Flexible sample-size designs, as part of the more general category of adaptive designs that utilize interim data, have been a popular topic in recent years. In this paper, we give a comparative review of four related methods for such a design. The likelihood method uses the likelihood ratio test with an adjusted critical value. The weighted method adjusts the test statistic with given weights rather than the critical value. The dual test method requires both the likelihood ratio statistic and the weighted statistic to be greater than the unadjusted critical value. The promising zone approach uses the likelihood ratio statistic with the unadjusted value and other constraints. All four methods preserve the type-I error rate. In this paper we explore their properties and compare their relationships and merits. We show that the sample size rules for the dual test are in conflict with the rules of the promising zone approach. We delineate what is necessary to specify in the study protocol to ensure the validity of the statistical procedure and what can be kept implicit in the protocol so that more flexibility can be attained for confirmatory phase III trials in meeting regulatory requirements. We also prove that under mild conditions, the likelihood ratio test still preserves the type-I error rate when the actual sample size is larger than the re-calculated one. Copyright © 2015 Elsevier Inc. All rights reserved.

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…

Assessing market uncertainty by means of a time-varying intermittency parameter for asset price fluctuations

NASA Astrophysics Data System (ADS)

Rypdal, Martin; Sirnes, Espen; Løvsletten, Ola; Rypdal, Kristoffer

2013-08-01

Maximum likelihood estimation techniques for multifractal processes are applied to high-frequency data in order to quantify intermittency in the fluctuations of asset prices. From time records as short as one month these methods permit extraction of a meaningful intermittency parameter λ characterising the degree of volatility clustering. We can therefore study the time evolution of volatility clustering and test the statistical significance of this variability. By analysing data from the Oslo Stock Exchange, and comparing the results with the investment grade spread, we find that the estimates of λ are lower at times of high market uncertainty.

Stochastic modelling of the monthly average maximum and minimum temperature patterns in India 1981-2015

NASA Astrophysics Data System (ADS)

Narasimha Murthy, K. V.; Saravana, R.; Vijaya Kumar, K.

2018-04-01

The paper investigates the stochastic modelling and forecasting of monthly average maximum and minimum temperature patterns through suitable seasonal auto regressive integrated moving average (SARIMA) model for the period 1981-2015 in India. The variations and distributions of monthly maximum and minimum temperatures are analyzed through Box plots and cumulative distribution functions. The time series plot indicates that the maximum temperature series contain sharp peaks in almost all the years, while it is not true for the minimum temperature series, so both the series are modelled separately. The possible SARIMA model has been chosen based on observing autocorrelation function (ACF), partial autocorrelation function (PACF), and inverse autocorrelation function (IACF) of the logarithmic transformed temperature series. The SARIMA (1, 0, 0) × (0, 1, 1)12 model is selected for monthly average maximum and minimum temperature series based on minimum Bayesian information criteria. The model parameters are obtained using maximum-likelihood method with the help of standard error of residuals. The adequacy of the selected model is determined using correlation diagnostic checking through ACF, PACF, IACF, and p values of Ljung-Box test statistic of residuals and using normal diagnostic checking through the kernel and normal density curves of histogram and Q-Q plot. Finally, the forecasting of monthly maximum and minimum temperature patterns of India for the next 3 years has been noticed with the help of selected model.

Calculation of Weibull strength parameters, Batdorf flaw density constants and related statistical quantities using PC-CARES

NASA Technical Reports Server (NTRS)

Szatmary, Steven A.; Gyekenyesi, John P.; Nemeth, Noel N.

1990-01-01

This manual describes the operation and theory of the PC-CARES (Personal Computer-Ceramic Analysis and Reliability Evaluation of Structures) computer program for the IBM PC and compatibles running PC-DOS/MS-DOR OR IBM/MS-OS/2 (version 1.1 or higher) operating systems. The primary purpose of this code is to estimate Weibull material strength parameters, the Batdorf crack density coefficient, and other related statistical quantities. Included in the manual is the description of the calculation of shape and scale parameters of the two-parameter Weibull distribution using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. The methods for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull line, as well as the techniques for calculating the Batdorf flaw-density constants are also described.

An Adaptive Buddy Check for Observational Quality Control

NASA Technical Reports Server (NTRS)

Dee, Dick P.; Rukhovets, Leonid; Todling, Ricardo; DaSilva, Arlindo M.; Larson, Jay W.; Einaudi, Franco (Technical Monitor)

2000-01-01

An adaptive buddy check algorithm is presented that adjusts tolerances for outlier observations based on the variability of surrounding data. The algorithm derives from a statistical hypothesis test combined with maximum-likelihood covariance estimation. Its stability is shown to depend on the initial identification of outliers by a simple background check. The adaptive feature ensures that the final quality control decisions are not very sensitive to prescribed statistics of first-guess and observation errors, nor on other approximations introduced into the algorithm. The implementation of the algorithm in a global atmospheric data assimilation is described. Its performance is contrasted with that of a non-adaptive buddy check, for the surface analysis of an extreme storm that took place in Europe on 27 December 1999. The adaptive algorithm allowed the inclusion of many important observations that differed greatly from the first guess and that would have been excluded on the basis of prescribed statistics. The analysis of the storm development was much improved as a result of these additional observations.

Noncentral Chi-Square versus Normal Distributions in Describing the Likelihood Ratio Statistic: The Univariate Case and Its Multivariate Implication

ERIC Educational Resources Information Center

Yuan, Ke-Hai

2008-01-01

In the literature of mean and covariance structure analysis, noncentral chi-square distribution is commonly used to describe the behavior of the likelihood ratio (LR) statistic under alternative hypothesis. Due to the inaccessibility of the rather technical literature for the distribution of the LR statistic, it is widely believed that the…

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.

Estimation of the geochemical threshold and its statistical significance

USGS Publications Warehouse

Miesch, A.T.

1981-01-01

A statistic is proposed for estimating the geochemical threshold and its statistical significance, or it may be used to identify a group of extreme values that can be tested for significance by other means. The statistic is the maximum gap between adjacent values in an ordered array after each gap has been adjusted for the expected frequency. The values in the ordered array are geochemical values transformed by either ln(?? - ??) or ln(?? - ??) and then standardized so that the mean is zero and the variance is unity. The expected frequency is taken from a fitted normal curve with unit area. The midpoint of an adjusted gap that exceeds the corresponding critical value may be taken as an estimate of the geochemical threshold, and the associated probability indicates the likelihood that the threshold separates two geochemical populations. The adjusted gap test may fail to identify threshold values if the variation tends to be continuous from background values to the higher values that reflect mineralized ground. However, the test will serve to identify other anomalies that may be too subtle to have been noted by other means. ?? 1981.

Testing homogeneity of proportion ratios for stratified correlated bilateral data in two-arm randomized clinical trials.

PubMed

Pei, Yanbo; Tian, Guo-Liang; Tang, Man-Lai

2014-11-10

Stratified data analysis is an important research topic in many biomedical studies and clinical trials. In this article, we develop five test statistics for testing the homogeneity of proportion ratios for stratified correlated bilateral binary data based on an equal correlation model assumption. Bootstrap procedures based on these test statistics are also considered. To evaluate the performance of these statistics and procedures, we conduct Monte Carlo simulations to study their empirical sizes and powers under various scenarios. Our results suggest that the procedure based on score statistic performs well generally and is highly recommended. When the sample size is large, procedures based on the commonly used weighted least square estimate and logarithmic transformation with Mantel-Haenszel estimate are recommended as they do not involve any computation of maximum likelihood estimates requiring iterative algorithms. We also derive approximate sample size formulas based on the recommended test procedures. Finally, we apply the proposed methods to analyze a multi-center randomized clinical trial for scleroderma patients. Copyright © 2014 John Wiley & Sons, Ltd.

Investigation of optimal parameters for penalized maximum-likelihood reconstruction applied to iodinated contrast-enhanced breast CT

NASA Astrophysics Data System (ADS)

Makeev, Andrey; Ikejimba, Lynda; Lo, Joseph Y.; Glick, Stephen J.

2016-03-01

Although digital mammography has reduced breast cancer mortality by approximately 30%, sensitivity and specificity are still far from perfect. In particular, the performance of mammography is especially limited for women with dense breast tissue. Two out of every three biopsies performed in the U.S. are unnecessary, thereby resulting in increased patient anxiety, pain, and possible complications. One promising tomographic breast imaging method that has recently been approved by the FDA is dedicated breast computed tomography (BCT). However, visualizing lesions with BCT can still be challenging for women with dense breast tissue due to the minimal contrast for lesions surrounded by fibroglandular tissue. In recent years there has been renewed interest in improving lesion conspicuity in x-ray breast imaging by administration of an iodinated contrast agent. Due to the fully 3-D imaging nature of BCT, as well as sub-optimal contrast enhancement while the breast is under compression with mammography and breast tomosynthesis, dedicated BCT of the uncompressed breast is likely to offer the best solution for injected contrast-enhanced x-ray breast imaging. It is well known that use of statistically-based iterative reconstruction in CT results in improved image quality at lower radiation dose. Here we investigate possible improvements in image reconstruction for BCT, by optimizing free regularization parameter in method of maximum likelihood and comparing its performance with clinical cone-beam filtered backprojection (FBP) algorithm.

Dynamic Financial Constraints: Distinguishing Mechanism Design from Exogenously Incomplete Regimes*

PubMed Central

Karaivanov, Alexander; Townsend, Robert M.

2014-01-01

We formulate and solve a range of dynamic models of constrained credit/insurance that allow for moral hazard and limited commitment. We compare them to full insurance and exogenously incomplete financial regimes (autarky, saving only, borrowing and lending in a single asset). We develop computational methods based on mechanism design, linear programming, and maximum likelihood to estimate, compare, and statistically test these alternative dynamic models with financial/information constraints. Our methods can use both cross-sectional and panel data and allow for measurement error and unobserved heterogeneity. We estimate the models using data on Thai households running small businesses from two separate samples. We find that in the rural sample, the exogenously incomplete saving only and borrowing regimes provide the best fit using data on consumption, business assets, investment, and income. Family and other networks help consumption smoothing there, as in a moral hazard constrained regime. In contrast, in urban areas, we find mechanism design financial/information regimes that are decidedly less constrained, with the moral hazard model fitting best combined business and consumption data. We perform numerous robustness checks in both the Thai data and in Monte Carlo simulations and compare our maximum likelihood criterion with results from other metrics and data not used in the estimation. A prototypical counterfactual policy evaluation exercise using the estimation results is also featured. PMID:25246710

Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: statistical and systematic error budgets for future experiments

DOE PAGES

Raghunathan, Srinivasan; Patil, Sanjaykumar; Baxter, Eric J.; ...

2017-08-25

We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential systematic errors. Using realistic simulations, wemore » examine the cluster mass uncertainties from CMB-cluster lensing as a function of an experiment’s beam size and noise level. We predict the cluster mass uncertainties will be 3 - 6% for SPT-3G, AdvACT, and Simons Array experiments with 10,000 clusters and less than 1% for the CMB-S4 experiment with a sample containing 100,000 clusters. The mass constraints from CMB polarization are very sensitive to the experimental beam size and map noise level: for a factor of three reduction in either the beam size or noise level, the lensing signal-to-noise improves by roughly a factor of two.« less

Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: statistical and systematic error budgets for future experiments

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

Raghunathan, Srinivasan; Patil, Sanjaykumar; Baxter, Eric J.

We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential systematic errors. Using realistic simulations, wemore » examine the cluster mass uncertainties from CMB-cluster lensing as a function of an experiment’s beam size and noise level. We predict the cluster mass uncertainties will be 3 - 6% for SPT-3G, AdvACT, and Simons Array experiments with 10,000 clusters and less than 1% for the CMB-S4 experiment with a sample containing 100,000 clusters. The mass constraints from CMB polarization are very sensitive to the experimental beam size and map noise level: for a factor of three reduction in either the beam size or noise level, the lensing signal-to-noise improves by roughly a factor of two.« less

Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: statistical and systematic error budgets for future experiments

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

Raghunathan, Srinivasan; Patil, Sanjaykumar; Bianchini, Federico

We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential systematic errors. Using realistic simulations, wemore » examine the cluster mass uncertainties from CMB-cluster lensing as a function of an experiment's beam size and noise level. We predict the cluster mass uncertainties will be 3 - 6% for SPT-3G, AdvACT, and Simons Array experiments with 10,000 clusters and less than 1% for the CMB-S4 experiment with a sample containing 100,000 clusters. The mass constraints from CMB polarization are very sensitive to the experimental beam size and map noise level: for a factor of three reduction in either the beam size or noise level, the lensing signal-to-noise improves by roughly a factor of two.« less

A comparative review of methods for comparing means using partially paired data.

PubMed

Guo, Beibei; Yuan, Ying

2017-06-01

In medical experiments with the objective of testing the equality of two means, data are often partially paired by design or because of missing data. The partially paired data represent a combination of paired and unpaired observations. In this article, we review and compare nine methods for analyzing partially paired data, including the two-sample t-test, paired t-test, corrected z-test, weighted t-test, pooled t-test, optimal pooled t-test, multiple imputation method, mixed model approach, and the test based on a modified maximum likelihood estimate. We compare the performance of these methods through extensive simulation studies that cover a wide range of scenarios with different effect sizes, sample sizes, and correlations between the paired variables, as well as true underlying distributions. The simulation results suggest that when the sample size is moderate, the test based on the modified maximum likelihood estimator is generally superior to the other approaches when the data is normally distributed and the optimal pooled t-test performs the best when the data is not normally distributed, with well-controlled type I error rates and high statistical power; when the sample size is small, the optimal pooled t-test is to be recommended when both variables have missing data and the paired t-test is to be recommended when only one variable has missing data.

Modelling average maximum daily temperature using r largest order statistics: An application to South African data

PubMed Central

2018-01-01

Natural hazards (events that may cause actual disasters) are established in the literature as major causes of various massive and destructive problems worldwide. The occurrences of earthquakes, floods and heat waves affect millions of people through several impacts. These include cases of hospitalisation, loss of lives and economic challenges. The focus of this study was on the risk reduction of the disasters that occur because of extremely high temperatures and heat waves. Modelling average maximum daily temperature (AMDT) guards against the disaster risk and may also help countries towards preparing for extreme heat. This study discusses the use of the r largest order statistics approach of extreme value theory towards modelling AMDT over the period of 11 years, that is, 2000–2010. A generalised extreme value distribution for r largest order statistics is fitted to the annual maxima. This is performed in an effort to study the behaviour of the r largest order statistics. The method of maximum likelihood is used in estimating the target parameters and the frequency of occurrences of the hottest days is assessed. The study presents a case study of South Africa in which the data for the non-winter season (September–April of each year) are used. The meteorological data used are the AMDT that are collected by the South African Weather Service and provided by Eskom. The estimation of the shape parameter reveals evidence of a Weibull class as an appropriate distribution for modelling AMDT in South Africa. The extreme quantiles for specified return periods are estimated using the quantile function and the best model is chosen through the use of the deviance statistic with the support of the graphical diagnostic tools. The Entropy Difference Test (EDT) is used as a specification test for diagnosing the fit of the models to the data.

Efficient Maximum Likelihood Estimation for Pedigree Data with the Sum-Product Algorithm.

PubMed

Engelhardt, Alexander; Rieger, Anna; Tresch, Achim; Mansmann, Ulrich

2016-01-01

We analyze data sets consisting of pedigrees with age at onset of colorectal cancer (CRC) as phenotype. The occurrence of familial clusters of CRC suggests the existence of a latent, inheritable risk factor. We aimed to compute the probability of a family possessing this risk factor as well as the hazard rate increase for these risk factor carriers. Due to the inheritability of this risk factor, the estimation necessitates a costly marginalization of the likelihood. We propose an improved EM algorithm by applying factor graphs and the sum-product algorithm in the E-step. This reduces the computational complexity from exponential to linear in the number of family members. Our algorithm is as precise as a direct likelihood maximization in a simulation study and a real family study on CRC risk. For 250 simulated families of size 19 and 21, the runtime of our algorithm is faster by a factor of 4 and 29, respectively. On the largest family (23 members) in the real data, our algorithm is 6 times faster. We introduce a flexible and runtime-efficient tool for statistical inference in biomedical event data with latent variables that opens the door for advanced analyses of pedigree data. © 2017 S. Karger AG, Basel.

Estimating Divergence Parameters With Small Samples From a Large Number of Loci

PubMed Central

Wang, Yong; Hey, Jody

2010-01-01

Most methods for studying divergence with gene flow rely upon data from many individuals at few loci. Such data can be useful for inferring recent population history but they are unlikely to contain sufficient information about older events. However, the growing availability of genome sequences suggests a different kind of sampling scheme, one that may be more suited to studying relatively ancient divergence. Data sets extracted from whole-genome alignments may represent very few individuals but contain a very large number of loci. To take advantage of such data we developed a new maximum-likelihood method for genomic data under the isolation-with-migration model. Unlike many coalescent-based likelihood methods, our method does not rely on Monte Carlo sampling of genealogies, but rather provides a precise calculation of the likelihood by numerical integration over all genealogies. We demonstrate that the method works well on simulated data sets. We also consider two models for accommodating mutation rate variation among loci and find that the model that treats mutation rates as random variables leads to better estimates. We applied the method to the divergence of Drosophila melanogaster and D. simulans and detected a low, but statistically significant, signal of gene flow from D. simulans to D. melanogaster. PMID:19917765

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

BEAGLE: an application programming interface and high-performance computing library for statistical phylogenetics.

PubMed

Ayres, Daniel L; Darling, Aaron; Zwickl, Derrick J; Beerli, Peter; Holder, Mark T; Lewis, Paul O; Huelsenbeck, John P; Ronquist, Fredrik; Swofford, David L; Cummings, Michael P; Rambaut, Andrew; Suchard, Marc A

2012-01-01

Phylogenetic inference is fundamental to our understanding of most aspects of the origin and evolution of life, and in recent years, there has been a concentration of interest in statistical approaches such as Bayesian inference and maximum likelihood estimation. Yet, for large data sets and realistic or interesting models of evolution, these approaches remain computationally demanding. High-throughput sequencing can yield data for thousands of taxa, but scaling to such problems using serial computing often necessitates the use of nonstatistical or approximate approaches. The recent emergence of graphics processing units (GPUs) provides an opportunity to leverage their excellent floating-point computational performance to accelerate statistical phylogenetic inference. A specialized library for phylogenetic calculation would allow existing software packages to make more effective use of available computer hardware, including GPUs. Adoption of a common library would also make it easier for other emerging computing architectures, such as field programmable gate arrays, to be used in the future. We present BEAGLE, an application programming interface (API) and library for high-performance statistical phylogenetic inference. The API provides a uniform interface for performing phylogenetic likelihood calculations on a variety of compute hardware platforms. The library includes a set of efficient implementations and can currently exploit hardware including GPUs using NVIDIA CUDA, central processing units (CPUs) with Streaming SIMD Extensions and related processor supplementary instruction sets, and multicore CPUs via OpenMP. To demonstrate the advantages of a common API, we have incorporated the library into several popular phylogenetic software packages. The BEAGLE library is free open source software licensed under the Lesser GPL and available from http://beagle-lib.googlecode.com. An example client program is available as public domain software.

BEAGLE: An Application Programming Interface and High-Performance Computing Library for Statistical Phylogenetics

PubMed Central

Ayres, Daniel L.; Darling, Aaron; Zwickl, Derrick J.; Beerli, Peter; Holder, Mark T.; Lewis, Paul O.; Huelsenbeck, John P.; Ronquist, Fredrik; Swofford, David L.; Cummings, Michael P.; Rambaut, Andrew; Suchard, Marc A.

2012-01-01

Abstract Phylogenetic inference is fundamental to our understanding of most aspects of the origin and evolution of life, and in recent years, there has been a concentration of interest in statistical approaches such as Bayesian inference and maximum likelihood estimation. Yet, for large data sets and realistic or interesting models of evolution, these approaches remain computationally demanding. High-throughput sequencing can yield data for thousands of taxa, but scaling to such problems using serial computing often necessitates the use of nonstatistical or approximate approaches. The recent emergence of graphics processing units (GPUs) provides an opportunity to leverage their excellent floating-point computational performance to accelerate statistical phylogenetic inference. A specialized library for phylogenetic calculation would allow existing software packages to make more effective use of available computer hardware, including GPUs. Adoption of a common library would also make it easier for other emerging computing architectures, such as field programmable gate arrays, to be used in the future. We present BEAGLE, an application programming interface (API) and library for high-performance statistical phylogenetic inference. The API provides a uniform interface for performing phylogenetic likelihood calculations on a variety of compute hardware platforms. The library includes a set of efficient implementations and can currently exploit hardware including GPUs using NVIDIA CUDA, central processing units (CPUs) with Streaming SIMD Extensions and related processor supplementary instruction sets, and multicore CPUs via OpenMP. To demonstrate the advantages of a common API, we have incorporated the library into several popular phylogenetic software packages. The BEAGLE library is free open source software licensed under the Lesser GPL and available from http://beagle-lib.googlecode.com. An example client program is available as public domain software. PMID:21963610

Multivariate Meta-Analysis of Heterogeneous Studies Using Only Summary Statistics: Efficiency and Robustness

PubMed Central

Liu, Dungang; Liu, Regina; Xie, Minge

2014-01-01

Meta-analysis has been widely used to synthesize evidence from multiple studies for common hypotheses or parameters of interest. However, it has not yet been fully developed for incorporating heterogeneous studies, which arise often in applications due to different study designs, populations or outcomes. For heterogeneous studies, the parameter of interest may not be estimable for certain studies, and in such a case, these studies are typically excluded from conventional meta-analysis. The exclusion of part of the studies can lead to a non-negligible loss of information. This paper introduces a metaanalysis for heterogeneous studies by combining the confidence density functions derived from the summary statistics of individual studies, hence referred to as the CD approach. It includes all the studies in the analysis and makes use of all information, direct as well as indirect. Under a general likelihood inference framework, this new approach is shown to have several desirable properties, including: i) it is asymptotically as efficient as the maximum likelihood approach using individual participant data (IPD) from all studies; ii) unlike the IPD analysis, it suffices to use summary statistics to carry out the CD approach. Individual-level data are not required; and iii) it is robust against misspecification of the working covariance structure of the parameter estimates. Besides its own theoretical significance, the last property also substantially broadens the applicability of the CD approach. All the properties of the CD approach are further confirmed by data simulated from a randomized clinical trials setting as well as by real data on aircraft landing performance. Overall, one obtains an unifying approach for combining summary statistics, subsuming many of the existing meta-analysis methods as special cases. PMID:26190875

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.

Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

PubMed

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik

2009-06-01

The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

An index-flood model for deficit volumes assessment

NASA Astrophysics Data System (ADS)

Strnad, Filip; Moravec, Vojtěch; Hanel, Martin

2017-04-01

The estimation of return periods of hydrological extreme events and the evaluation of risks related to such events are objectives of many water resources studies. The aim of this study is to develop statistical model for drought indices using extreme value theory and index-flood method and to use this model for estimation of return levels of maximum deficit volumes of total runoff and baseflow. Deficit volumes for hundred and thirty-three catchments in the Czech Republic for the period 1901-2015 simulated by a hydrological model Bilan are considered. The characteristics of simulated deficit periods (severity, intensity and length) correspond well to those based on observed data. It is assumed that annual maximum deficit volumes in each catchment follow the generalized extreme value (GEV) distribution. The catchments are divided into three homogeneous regions considering long term mean runoff, potential evapotranspiration and base flow. In line with the index-flood method it is further assumed that the deficit volumes within each homogeneous region are identically distributed after scaling with a site-specific factor. The goodness-of-fit of the statistical model is assessed by Anderson-Darling statistics. For the estimation of critical values of the test several resampling strategies allowing for appropriate handling of years without drought are presented. Finally the significance of the trends in the deficit volumes is assessed by a likelihood ratio test.

pplacer: linear time maximum-likelihood and Bayesian phylogenetic placement of sequences onto a fixed reference tree

PubMed Central

2010-01-01

Background Likelihood-based phylogenetic inference is generally considered to be the most reliable classification method for unknown sequences. However, traditional likelihood-based phylogenetic methods cannot be applied to large volumes of short reads from next-generation sequencing due to computational complexity issues and lack of phylogenetic signal. "Phylogenetic placement," where a reference tree is fixed and the unknown query sequences are placed onto the tree via a reference alignment, is a way to bring the inferential power offered by likelihood-based approaches to large data sets. Results This paper introduces pplacer, a software package for phylogenetic placement and subsequent visualization. The algorithm can place twenty thousand short reads on a reference tree of one thousand taxa per hour per processor, has essentially linear time and memory complexity in the number of reference taxa, and is easy to run in parallel. Pplacer features calculation of the posterior probability of a placement on an edge, which is a statistically rigorous way of quantifying uncertainty on an edge-by-edge basis. It also can inform the user of the positional uncertainty for query sequences by calculating expected distance between placement locations, which is crucial in the estimation of uncertainty with a well-sampled reference tree. The software provides visualizations using branch thickness and color to represent number of placements and their uncertainty. A simulation study using reads generated from 631 COG alignments shows a high level of accuracy for phylogenetic placement over a wide range of alignment diversity, and the power of edge uncertainty estimates to measure placement confidence. Conclusions Pplacer enables efficient phylogenetic placement and subsequent visualization, making likelihood-based phylogenetics methodology practical for large collections of reads; it is freely available as source code, binaries, and a web service. PMID:21034504

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.

Simulation program for estimating statistical power of Cox's proportional hazards model assuming no specific distribution for the survival time.

PubMed

Akazawa, K; Nakamura, T; Moriguchi, S; Shimada, M; Nose, Y

1991-07-01

Small sample properties of the maximum partial likelihood estimates for Cox's proportional hazards model depend on the sample size, the true values of regression coefficients, covariate structure, censoring pattern and possibly baseline hazard functions. Therefore, it would be difficult to construct a formula or table to calculate the exact power of a statistical test for the treatment effect in any specific clinical trial. The simulation program, written in SAS/IML, described in this paper uses Monte-Carlo methods to provide estimates of the exact power for Cox's proportional hazards model. For illustrative purposes, the program was applied to real data obtained from a clinical trial performed in Japan. Since the program does not assume any specific function for the baseline hazard, it is, in principle, applicable to any censored survival data as long as they follow Cox's proportional hazards model.

Incorporating spatial context into statistical classification of multidimensional image data

NASA Technical Reports Server (NTRS)

Bauer, M. E. (Principal Investigator); Tilton, J. C.; Swain, P. H.

1981-01-01

Compound decision theory is employed to develop a general statistical model for classifying image data using spatial context. The classification algorithm developed from this model exploits the tendency of certain ground-cover classes to occur more frequently in some spatial contexts than in others. A key input to this contextural classifier is a quantitative characterization of this tendency: the context function. Several methods for estimating the context function are explored, and two complementary methods are recommended. The contextural classifier is shown to produce substantial improvements in classification accuracy compared to the accuracy produced by a non-contextural uniform-priors maximum likelihood classifier when these methods of estimating the context function are used. An approximate algorithm, which cuts computational requirements by over one-half, is presented. The search for an optimal implementation is furthered by an exploration of the relative merits of using spectral classes or information classes for classification and/or context function estimation.

Detecting Anomalies in Process Control Networks

NASA Astrophysics Data System (ADS)

Rrushi, Julian; Kang, Kyoung-Don

This paper presents the estimation-inspection algorithm, a statistical algorithm for anomaly detection in process control networks. The algorithm determines if the payload of a network packet that is about to be processed by a control system is normal or abnormal based on the effect that the packet will have on a variable stored in control system memory. The estimation part of the algorithm uses logistic regression integrated with maximum likelihood estimation in an inductive machine learning process to estimate a series of statistical parameters; these parameters are used in conjunction with logistic regression formulas to form a probability mass function for each variable stored in control system memory. The inspection part of the algorithm uses the probability mass functions to estimate the normalcy probability of a specific value that a network packet writes to a variable. Experimental results demonstrate that the algorithm is very effective at detecting anomalies in process control networks.

RAD-ADAPT: Software for modelling clonogenic assay data in radiation biology.

PubMed

Zhang, Yaping; Hu, Kaiqiang; Beumer, Jan H; Bakkenist, Christopher J; D'Argenio, David Z

2017-04-01

We present a comprehensive software program, RAD-ADAPT, for the quantitative analysis of clonogenic assays in radiation biology. Two commonly used models for clonogenic assay analysis, the linear-quadratic model and single-hit multi-target model, are included in the software. RAD-ADAPT uses maximum likelihood estimation method to obtain parameter estimates with the assumption that cell colony count data follow a Poisson distribution. The program has an intuitive interface, generates model prediction plots, tabulates model parameter estimates, and allows automatic statistical comparison of parameters between different groups. The RAD-ADAPT interface is written using the statistical software R and the underlying computations are accomplished by the ADAPT software system for pharmacokinetic/pharmacodynamic systems analysis. The use of RAD-ADAPT is demonstrated using an example that examines the impact of pharmacologic ATM and ATR kinase inhibition on human lung cancer cell line A549 after ionizing radiation. Copyright © 2017 Elsevier B.V. All rights reserved.

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.

Sunyaev-Zel'dovich Effect Derived Distance to the High Redshift Clusters MS 0451.6-0305 and CL 0016+16

NASA Technical Reports Server (NTRS)

Reese, E. D.; Mohr, J. J.; Carlstrom, J. E.; Grego, L.; Holder, G. P.; Holzapfel, W. L.; Hughes, J. P.; Patel, S. K.

2000-01-01

We determine the distances to the z approximately equal to 0.55 galaxy clusters MS 0451.6-0305 and CL 0016+16 from a maximum likelihood joint fit to interferometric Sunyaev-Zel'dovich effect (SZE) and X-ray observations. We model the intracluster medium (ICM) using a spherical isothermal beta-model. We quantify the statistical and systematic uncertainties inherent to these direct distance measurements, and we determine constraints on the Hubble parameter for three different cosmologies. For an OmegaM = 0.3, OmegaL = 0.7 cosmology, these distances imply a Hubble constant of 63(exp 12)(sub -9)(exp +21)(sub -21) km/s/Mpc, where the uncertainties correspond to statistical followed by systematic at 68% confidence. The best fit H(sub o) is 57 km/sec/Mpc for an open OmegaM = 0.3 universe and 52 km/s/Mpc for a flat Omega = 1 universe.

Sunyaev-Zeldovich Effect-Derived Distances to the High-Redshift Clusters

NASA Technical Reports Server (NTRS)

Reese, Erik D.; Mohr, Joseph J.; Carlstrom, John E.; Joy, Marshall; Grego, Laura; Holder, Gilbert P.; Holzapfel, William L.; Hughes, John P.; Patel, Sandeep K.; Donahue, Megan

2000-01-01

We determine the distances to the z approximately equals 0.55 galaxy clusters MS 0451.6 - 0305 and Cl 0016 + 16 from a maximum-likelihood joint fit to interferometric Sunyaev-Zeldovich effect (SZE) and X-ray observations. We model the intracluster medium (ICM) using a spherical isothermal beta model. We quantify the statistical and systematic uncertainties inherent to these direct distance measurements, and we determine constraints on the Hubble parameter for three different cosmologies. For an Omega(sub M) = 0.3, Omega(sub lambda) = 0.7 cosmology, these distances imply a Hubble constant of 63(sup +12) (sub -9) (sup + 21) (sub -21) km/s Mp/c, where the uncertainties correspond to statistical followed by systematic at 68% confidence. The best-fit H(sub 0) is 57 km/s Mp/c for an open (Omega(sub M) = 0.3) universe and 52 km/s Mp/c for a flat (Omega(sub M) = 1) universe.

Dark Matter interpretation of low energy IceCube MESE excess

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

Chianese, M.; Miele, G.; Morisi, S., E-mail: chianese@na.infn.it, E-mail: miele@na.infn.it, E-mail: stefano.morisi@na.infn.it

2017-01-01

The 2-years MESE IceCube events show a slightly excess in the energy range 10–100 TeV with a maximum local statistical significance of 2.3σ, once a hard astrophysical power-law is assumed. A spectral index smaller than 2.2 is indeed suggested by multi-messenger studies related to p - p sources and by the recent IceCube analysis regarding 6-years up-going muon neutrinos. In the present paper, we propose a two-components scenario where the extraterrestrial neutrinos are explained in terms of an astrophysical power-law and a Dark Matter signal. We consider both decaying and annihilating Dark Matter candidates with different final states (quarks andmore » leptons) and different halo density profiles. We perform a likelihood-ratio analysis that provides a statistical significance up to 3.9σ for a Dark Matter interpretation of the IceCube low energy excess.« less

Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology

NASA Astrophysics Data System (ADS)

Alsing, Justin; Wandelt, Benjamin; Feeney, Stephen

2018-07-01

Many statistical models in cosmology can be simulated forwards but have intractable likelihood functions. Likelihood-free inference methods allow us to perform Bayesian inference from these models using only forward simulations, free from any likelihood assumptions or approximations. Likelihood-free inference generically involves simulating mock data and comparing to the observed data; this comparison in data space suffers from the curse of dimensionality and requires compression of the data to a small number of summary statistics to be tractable. In this paper, we use massive asymptotically optimal data compression to reduce the dimensionality of the data space to just one number per parameter, providing a natural and optimal framework for summary statistic choice for likelihood-free inference. Secondly, we present the first cosmological application of Density Estimation Likelihood-Free Inference (DELFI), which learns a parametrized model for joint distribution of data and parameters, yielding both the parameter posterior and the model evidence. This approach is conceptually simple, requires less tuning than traditional Approximate Bayesian Computation approaches to likelihood-free inference and can give high-fidelity posteriors from orders of magnitude fewer forward simulations. As an additional bonus, it enables parameter inference and Bayesian model comparison simultaneously. We demonstrate DELFI with massive data compression on an analysis of the joint light-curve analysis supernova data, as a simple validation case study. We show that high-fidelity posterior inference is possible for full-scale cosmological data analyses with as few as ˜104 simulations, with substantial scope for further improvement, demonstrating the scalability of likelihood-free inference to large and complex cosmological data sets.

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.

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.

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.

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.

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.

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.

Incidence of childhood leukaemia and non-Hodgkin's lymphoma in the vicinity of nuclear sites in Scotland, 1968-93.

PubMed Central

Sharp, L; Black, R J; Harkness, E F; McKinney, P A

1996-01-01

OBJECTIVES: The primary aims were to investigate the incidence of leukaemia and non-Hodgkin's lymphoma in children resident near seven nuclear sites in Scotland and to determine whether there was any evidence of a gradient in risk with distance of residence from a nuclear site. A secondary aim was to assess the power of statistical tests for increased risk of disease near a point source when applied in the context of census data for Scotland. METHODS: The study data set comprised 1287 cases of leukaemia and non-Hodgkin's lymphoma diagnosed in children aged under 15 years in the period 1968-93, validated for accuracy and completeness. A study zone around each nuclear site was constructed from enumeration districts within 25 km. Expected numbers were calculated, adjusting for sex, age, and indices of deprivation and urban-rural residence. Six statistical tests were evaluated. Stone's maximum likelihood ratio (unconditional application) was applied as the main test for general increased incidence across a study zone. The linear risk score based on enumeration districts (conditional application) was used as a secondary test for declining risk with distance from each site. RESULTS: More cases were observed (O) than expected (E) in the study zones around Rosyth naval base (O/E 1.02), Chapelcross electricity generating station (O/E 1.08), and Dounreay reprocessing plant (O/E 1.99). The maximum likelihood ratio test reached significance only for Dounreay (P = 0.030). The linear risk score test did not indicate a trend in risk with distance from any of the seven sites, including Dounreay. CONCLUSIONS: There was no evidence of a generally increased risk of childhood leukaemia and non-Hodgkin's lymphoma around nuclear sites in Scotland, nor any evidence of a trend of decreasing risk with distance from any of the sites. There was a significant excess risk in the zone around Dounreay, which was only partially accounted for by the sociodemographic characteristics of the area. The statistical power of tests for localised increased risk of disease around a point source should be assessed in each new setting in which they are applied. PMID:8994402

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.

The composite sequential clustering technique for analysis of multispectral scanner data

NASA Technical Reports Server (NTRS)

Su, M. Y.

1972-01-01

The clustering technique consists of two parts: (1) a sequential statistical clustering which is essentially a sequential variance analysis, and (2) a generalized K-means clustering. In this composite clustering technique, the output of (1) is a set of initial clusters which are input to (2) for further improvement by an iterative scheme. This unsupervised composite technique was employed for automatic classification of two sets of remote multispectral earth resource observations. The classification accuracy by the unsupervised technique is found to be comparable to that by traditional supervised maximum likelihood classification techniques. The mathematical algorithms for the composite sequential clustering program and a detailed computer program description with job setup are given.

Image statistics decoding for convolutional codes

NASA Technical Reports Server (NTRS)

Pitt, G. H., III; Swanson, L.; Yuen, J. H.

1987-01-01

It is a fact that adjacent pixels in a Voyager image are very similar in grey level. This fact can be used in conjunction with the Maximum-Likelihood Convolutional Decoder (MCD) to decrease the error rate when decoding a picture from Voyager. Implementing this idea would require no changes in the Voyager spacecraft and could be used as a backup to the current system without too much expenditure, so the feasibility of it and the possible gains for Voyager were investigated. Simulations have shown that the gain could be as much as 2 dB at certain error rates, and experiments with real data inspired new ideas on ways to get the most information possible out of the received symbol stream.

Survival Data and Regression Models

NASA Astrophysics Data System (ADS)

Grégoire, G.

2014-12-01

We start this chapter by introducing some basic elements for the analysis of censored survival data. Then we focus on right censored data and develop two types of regression models. The first one concerns the so-called accelerated failure time models (AFT), which are parametric models where a function of a parameter depends linearly on the covariables. The second one is a semiparametric model, where the covariables enter in a multiplicative form in the expression of the hazard rate function. The main statistical tool for analysing these regression models is the maximum likelihood methodology and, in spite we recall some essential results about the ML theory, we refer to the chapter "Logistic Regression" for a more detailed presentation.

Flight data processing with the F-8 adaptive algorithm

NASA Technical Reports Server (NTRS)

Hartmann, G.; Stein, G.; Petersen, K.

1977-01-01

An explicit adaptive control algorithm based on maximum likelihood estimation of parameters has been designed for NASA's DFBW F-8 aircraft. To avoid iterative calculations, the algorithm uses parallel channels of Kalman filters operating at fixed locations in parameter space. This algorithm has been implemented in NASA/DFRC's Remotely Augmented Vehicle (RAV) facility. Real-time sensor outputs (rate gyro, accelerometer and surface position) are telemetered to a ground computer which sends new gain values to an on-board system. Ground test data and flight records were used to establish design values of noise statistics and to verify the ground-based adaptive software. The software and its performance evaluation based on flight data are described

On locating steganographic payload using residuals

NASA Astrophysics Data System (ADS)

Quach, Tu-Thach

2011-02-01

Locating steganographic payload usingWeighted Stego-image (WS) residuals has been proven successful provided a large number of stego images are available. In this paper, we revisit this topic with two goals. First, we argue that it is a promising approach to locate payload by showing that in the ideal scenario where the cover images are available, the expected number of stego images needed to perfectly locate all load-carrying pixels is the logarithm of the payload size. Second, we generalize cover estimation to a maximum likelihood decoding problem and demonstrate that a second-order statistical cover model can be used to compute residuals to locate payload embedded by both LSB replacement and LSB matching steganography.

Soft context clustering for F0 modeling in HMM-based speech synthesis

NASA Astrophysics Data System (ADS)

Khorram, Soheil; Sameti, Hossein; King, Simon

2015-12-01

This paper proposes the use of a new binary decision tree, which we call a soft decision tree, to improve generalization performance compared to the conventional `hard' decision tree method that is used to cluster context-dependent model parameters in statistical parametric speech synthesis. We apply the method to improve the modeling of fundamental frequency, which is an important factor in synthesizing natural-sounding high-quality speech. Conventionally, hard decision tree-clustered hidden Markov models (HMMs) are used, in which each model parameter is assigned to a single leaf node. However, this `divide-and-conquer' approach leads to data sparsity, with the consequence that it suffers from poor generalization, meaning that it is unable to accurately predict parameters for models of unseen contexts: the hard decision tree is a weak function approximator. To alleviate this, we propose the soft decision tree, which is a binary decision tree with soft decisions at the internal nodes. In this soft clustering method, internal nodes select both their children with certain membership degrees; therefore, each node can be viewed as a fuzzy set with a context-dependent membership function. The soft decision tree improves model generalization and provides a superior function approximator because it is able to assign each context to several overlapped leaves. In order to use such a soft decision tree to predict the parameters of the HMM output probability distribution, we derive the smoothest (maximum entropy) distribution which captures all partial first-order moments and a global second-order moment of the training samples. Employing such a soft decision tree architecture with maximum entropy distributions, a novel speech synthesis system is trained using maximum likelihood (ML) parameter re-estimation and synthesis is achieved via maximum output probability parameter generation. In addition, a soft decision tree construction algorithm optimizing a log-likelihood measure is developed. Both subjective and objective evaluations were conducted and indicate a considerable improvement over the conventional method.

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

Flood Frequency Curves - Use of information on the likelihood of extreme floods

NASA Astrophysics Data System (ADS)

Faber, B.

2011-12-01

Investment in the infrastructure that reduces flood risk for flood-prone communities must incorporate information on the magnitude and frequency of flooding in that area. Traditionally, that information has been a probability distribution of annual maximum streamflows developed from the historical gaged record at a stream site. Practice in the United States fits a Log-Pearson type3 distribution to the annual maximum flows of an unimpaired streamflow record, using the method of moments to estimate distribution parameters. The procedure makes the assumptions that annual peak streamflow events are (1) independent, (2) identically distributed, and (3) form a representative sample of the overall probability distribution. Each of these assumptions can be challenged. We rarely have enough data to form a representative sample, and therefore must compute and display the uncertainty in the estimated flood distribution. But, is there a wet/dry cycle that makes precipitation less than independent between successive years? Are the peak flows caused by different types of events from different statistical populations? How does the watershed or climate changing over time (non-stationarity) affect the probability distribution floods? Potential approaches to avoid these assumptions vary from estimating trend and shift and removing them from early data (and so forming a homogeneous data set), to methods that estimate statistical parameters that vary with time. A further issue in estimating a probability distribution of flood magnitude (the flood frequency curve) is whether a purely statistical approach can accurately capture the range and frequency of floods that are of interest. A meteorologically-based analysis produces "probable maximum precipitation" (PMP) and subsequently a "probable maximum flood" (PMF) that attempts to describe an upper bound on flood magnitude in a particular watershed. This analysis can help constrain the upper tail of the probability distribution, well beyond the range of gaged data or even historical or paleo-flood data, which can be very important in risk analyses performed for flood risk management and dam and levee safety studies.

What influences the choice of assessment methods in health technology assessments? Statistical analysis of international health technology assessments from 1989 to 2002.

PubMed

Draborg, Eva; Andersen, Christian Kronborg

2006-01-01

Health technology assessment (HTA) has been used as input in decision making worldwide for more than 25 years. However, no uniform definition of HTA or agreement on assessment methods exists, leaving open the question of what influences the choice of assessment methods in HTAs. The objective of this study is to analyze statistically a possible relationship between methods of assessment used in practical HTAs, type of assessed technology, type of assessors, and year of publication. A sample of 433 HTAs published by eleven leading institutions or agencies in nine countries was reviewed and analyzed by multiple logistic regression. The study shows that outsourcing of HTA reports to external partners is associated with a higher likelihood of using assessment methods, such as meta-analysis, surveys, economic evaluations, and randomized controlled trials; and with a lower likelihood of using assessment methods, such as literature reviews and "other methods". The year of publication was statistically related to the inclusion of economic evaluations and shows a decreasing likelihood during the year span. The type of assessed technology was related to economic evaluations with a decreasing likelihood, to surveys, and to "other methods" with a decreasing likelihood when pharmaceuticals were the assessed type of technology. During the period from 1989 to 2002, no major developments in assessment methods used in practical HTAs were shown statistically in a sample of 433 HTAs worldwide. Outsourcing to external assessors has a statistically significant influence on choice of assessment methods.

A scan statistic for binary outcome based on hypergeometric probability model, with an application to detecting spatial clusters of Japanese encephalitis.

PubMed

Zhao, Xing; Zhou, Xiao-Hua; Feng, Zijian; Guo, Pengfei; He, Hongyan; Zhang, Tao; Duan, Lei; Li, Xiaosong

2013-01-01

As a useful tool for geographical cluster detection of events, the spatial scan statistic is widely applied in many fields and plays an increasingly important role. The classic version of the spatial scan statistic for the binary outcome is developed by Kulldorff, based on the Bernoulli or the Poisson probability model. In this paper, we apply the Hypergeometric probability model to construct the likelihood function under the null hypothesis. Compared with existing methods, the likelihood function under the null hypothesis is an alternative and indirect method to identify the potential cluster, and the test statistic is the extreme value of the likelihood function. Similar with Kulldorff's methods, we adopt Monte Carlo test for the test of significance. Both methods are applied for detecting spatial clusters of Japanese encephalitis in Sichuan province, China, in 2009, and the detected clusters are identical. Through a simulation to independent benchmark data, it is indicated that the test statistic based on the Hypergeometric model outweighs Kulldorff's statistics for clusters of high population density or large size; otherwise Kulldorff's statistics are superior.

Validation of the alternating conditional estimation algorithm for estimation of flexible extensions of Cox's proportional hazards model with nonlinear constraints on the parameters.

PubMed

Wynant, Willy; Abrahamowicz, Michal

2016-11-01

Standard optimization algorithms for maximizing likelihood may not be applicable to the estimation of those flexible multivariable models that are nonlinear in their parameters. For applications where the model's structure permits separating estimation of mutually exclusive subsets of parameters into distinct steps, we propose the alternating conditional estimation (ACE) algorithm. We validate the algorithm, in simulations, for estimation of two flexible extensions of Cox's proportional hazards model where the standard maximum partial likelihood estimation does not apply, with simultaneous modeling of (1) nonlinear and time-dependent effects of continuous covariates on the hazard, and (2) nonlinear interaction and main effects of the same variable. We also apply the algorithm in real-life analyses to estimate nonlinear and time-dependent effects of prognostic factors for mortality in colon cancer. Analyses of both simulated and real-life data illustrate good statistical properties of the ACE algorithm and its ability to yield new potentially useful insights about the data structure. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Generalized Full-Information Item Bifactor Analysis

PubMed Central

Cai, Li; Yang, Ji Seung; Hansen, Mark

2011-01-01

Full-information item bifactor analysis is an important statistical method in psychological and educational measurement. Current methods are limited to single group analysis and inflexible in the types of item response models supported. We propose a flexible multiple-group item bifactor analysis framework that supports a variety of multidimensional item response theory models for an arbitrary mixing of dichotomous, ordinal, and nominal items. The extended item bifactor model also enables the estimation of latent variable means and variances when data from more than one group are present. Generalized user-defined parameter restrictions are permitted within or across groups. We derive an efficient full-information maximum marginal likelihood estimator. Our estimation method achieves substantial computational savings by extending Gibbons and Hedeker’s (1992) bifactor dimension reduction method so that the optimization of the marginal log-likelihood only requires two-dimensional integration regardless of the dimensionality of the latent variables. We use simulation studies to demonstrate the flexibility and accuracy of the proposed methods. We apply the model to study cross-country differences, including differential item functioning, using data from a large international education survey on mathematics literacy. PMID:21534682

Modeling, estimation and identification methods for static shape determination of flexible structures. [for large space structure design

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Scheid, R. E., Jr.

1986-01-01

This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.

Parametric Model Based On Imputations Techniques for Partly Interval Censored Data

NASA Astrophysics Data System (ADS)

Zyoud, Abdallah; Elfaki, F. A. M.; Hrairi, Meftah

2017-12-01

The term ‘survival analysis’ has been used in a broad sense to describe collection of statistical procedures for data analysis. In this case, outcome variable of interest is time until an event occurs where the time to failure of a specific experimental unit might be censored which can be right, left, interval, and Partly Interval Censored data (PIC). In this paper, analysis of this model was conducted based on parametric Cox model via PIC data. Moreover, several imputation techniques were used, which are: midpoint, left & right point, random, mean, and median. Maximum likelihood estimate was considered to obtain the estimated survival function. These estimations were then compared with the existing model, such as: Turnbull and Cox model based on clinical trial data (breast cancer data), for which it showed the validity of the proposed model. Result of data set indicated that the parametric of Cox model proved to be more superior in terms of estimation of survival functions, likelihood ratio tests, and their P-values. Moreover, based on imputation techniques; the midpoint, random, mean, and median showed better results with respect to the estimation of survival function.

Statistical Signal Processing and the Motor Cortex

PubMed Central

Brockwell, A.E.; Kass, R.E.; Schwartz, A.B.

2011-01-01

Over the past few decades, developments in technology have significantly improved the ability to measure activity in the brain. This has spurred a great deal of research into brain function and its relation to external stimuli, and has important implications in medicine and other fields. As a result of improved understanding of brain function, it is now possible to build devices that provide direct interfaces between the brain and the external world. We describe some of the current understanding of function of the motor cortex region. We then discuss a typical likelihood-based state-space model and filtering based approach to address the problems associated with building a motor cortical-controlled cursor or robotic prosthetic device. As a variation on previous work using this approach, we introduce the idea of using Markov chain Monte Carlo methods for parameter estimation in this context. By doing this instead of performing maximum likelihood estimation, it is possible to expand the range of possible models that can be explored, at a cost in terms of computational load. We demonstrate results obtained applying this methodology to experimental data gathered from a monkey. PMID:21765538

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

Likelihoods for fixed rank nomination networks

PubMed Central

HOFF, PETER; FOSDICK, BAILEY; VOLFOVSKY, ALEX; STOVEL, KATHERINE

2014-01-01

Many studies that gather social network data use survey methods that lead to censored, missing, or otherwise incomplete information. For example, the popular fixed rank nomination (FRN) scheme, often used in studies of schools and businesses, asks study participants to nominate and rank at most a small number of contacts or friends, leaving the existence of other relations uncertain. However, most statistical models are formulated in terms of completely observed binary networks. Statistical analyses of FRN data with such models ignore the censored and ranked nature of the data and could potentially result in misleading statistical inference. To investigate this possibility, we compare Bayesian parameter estimates obtained from a likelihood for complete binary networks with those obtained from likelihoods that are derived from the FRN scheme, and therefore accommodate the ranked and censored nature of the data. We show analytically and via simulation that the binary likelihood can provide misleading inference, particularly for certain model parameters that relate network ties to characteristics of individuals and pairs of individuals. We also compare these different likelihoods in a data analysis of several adolescent social networks. For some of these networks, the parameter estimates from the binary and FRN likelihoods lead to different conclusions, indicating the importance of analyzing FRN data with a method that accounts for the FRN survey design. PMID:25110586

Multivariate meta-analysis: a robust approach based on the theory of U-statistic.

PubMed

Ma, Yan; Mazumdar, Madhu

2011-10-30

Meta-analysis is the methodology for combining findings from similar research studies asking the same question. When the question of interest involves multiple outcomes, multivariate meta-analysis is used to synthesize the outcomes simultaneously taking into account the correlation between the outcomes. Likelihood-based approaches, in particular restricted maximum likelihood (REML) method, are commonly utilized in this context. REML assumes a multivariate normal distribution for the random-effects model. This assumption is difficult to verify, especially for meta-analysis with small number of component studies. The use of REML also requires iterative estimation between parameters, needing moderately high computation time, especially when the dimension of outcomes is large. A multivariate method of moments (MMM) is available and is shown to perform equally well to REML. However, there is a lack of information on the performance of these two methods when the true data distribution is far from normality. In this paper, we propose a new nonparametric and non-iterative method for multivariate meta-analysis on the basis of the theory of U-statistic and compare the properties of these three procedures under both normal and skewed data through simulation studies. It is shown that the effect on estimates from REML because of non-normal data distribution is marginal and that the estimates from MMM and U-statistic-based approaches are very similar. Therefore, we conclude that for performing multivariate meta-analysis, the U-statistic estimation procedure is a viable alternative to REML and MMM. Easy implementation of all three methods are illustrated by their application to data from two published meta-analysis from the fields of hip fracture and periodontal disease. We discuss ideas for future research based on U-statistic for testing significance of between-study heterogeneity and for extending the work to meta-regression setting. Copyright © 2011 John Wiley & Sons, Ltd.

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.

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.

An Evaluation of Statistical Strategies for Making Equating Function Selections. Research Report. ETS RR-08-60

ERIC Educational Resources Information Center

Moses, Tim

2008-01-01

Nine statistical strategies for selecting equating functions in an equivalent groups design were evaluated. The strategies of interest were likelihood ratio chi-square tests, regression tests, Kolmogorov-Smirnov tests, and significance tests for equated score differences. The most accurate strategies in the study were the likelihood ratio tests…

Rapid radiation events in the family Ursidae indicated by likelihood phylogenetic estimation from multiple fragments of mtDNA.

PubMed

Waits, L P; Sullivan, J; O'Brien, S J; Ward, R H

1999-10-01

The bear family (Ursidae) presents a number of phylogenetic ambiguities as the evolutionary relationships of the six youngest members (ursine bears) are largely unresolved. Recent mitochondrial DNA analyses have produced conflicting results with respect to the phylogeny of ursine bears. In an attempt to resolve these issues, we obtained 1916 nucleotides of mitochondrial DNA sequence data from six gene segments for all eight bear species and conducted maximum likelihood and maximum parsimony analyses on all fragments separately and combined. All six single-region gene trees gave different phylogenetic estimates; however, only for control region data was this significantly incongruent with the results from the combined data. The optimal phylogeny for the combined data set suggests that the giant panda is most basal followed by the spectacled bear. The sloth bear is the basal ursine bear, and there is weak support for a sister taxon relationship of the American and Asiatic black bears. The sun bear is sister taxon to the youngest clade containing brown bears and polar bears. Statistical analyses of alternate hypotheses revealed a lack of strong support for many of the relationships. We suggest that the difficulties surrounding the resolution of the evolutionary relationships of the Ursidae are linked to the existence of sequential rapid radiation events in bear evolution. Thus, unresolved branching orders during these time periods may represent an accurate representation of the evolutionary history of bear species. Copyright 1999 Academic Press.

Phylogenetic relationships of the endangered Shenandoah salamander (Plethodon shenandoah) and other salamanders of the Plethodon cinereus group (Caudata : Plethodontidae)

USGS Publications Warehouse

Sites, J.W.; Morando, M.; Highton, R.; Huber, F.; Jung, R.E.

2004-01-01

The Shenandoah salamander (Plethodon shenandoah), known from isolated talus slopes on three of the highest mountains in Shenandoah National Park, is listed as state-endangered in Virginia and federally endangered under the U.S. Endangered Species Act. A 1999 paper by G. R. Thurow described P. shenandoah-like salamanders from three localities further south in the Blue Ridge Physiographic Province, which, if confirmed, would represent a range extension for P. shenandoah of approximately 90 km from its nearest known locality. Samples collected from two of these three localities were included in a molecular phylogenetic study of the known populations of P. shenandoah, and all other recognized species in the Plethodon cinereus group, using a 792 bp region of the mitochondrial cytochrome-b gene. Phylogenetic estimates were based on Bayesian, maximum likelihood, and maximum parsimony methods and topologies examined for placement of the new P. shenandoah-like samples relative to all others. All topologies recovered all haplotypes of the P. shenandoah-like animals nested within P. cinereus, and a statistical comparison of the best likelihood tree topology with one with an enforced (Thurow + Shenandoah P. shenandoah) clade revealed that the unconstrained tree had a significantly lower -In L score (P < 0.05, using the Shimodaira-Hasegawa test) than the constraint tree. This result and other anecdotal information give us no solid reason to consider the Thurow report valid. The current recovery program for P. shenandoah should remain focused on populations in Shenandoah National Park.

APPROXIMATION AND ESTIMATION OF s-CONCAVE DENSITIES VIA RÉNYI DIVERGENCES.

PubMed

Han, Qiyang; Wellner, Jon A

2016-01-01

In this paper, we study the approximation and estimation of s -concave densities via Rényi divergence. We first show that the approximation of a probability measure Q by an s -concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [ Ann. Statist. 38 (2010) 2998-3027] if and only if Q admits full-dimensional support and a first moment. We also show continuity of the divergence functional in Q : if Q n → Q in the Wasserstein metric, then the projected densities converge in weighted L 1 metrics and uniformly on closed subsets of the continuity set of the limit. Moreover, directional derivatives of the projected densities also enjoy local uniform convergence. This contains both on-the-model and off-the-model situations, and entails strong consistency of the divergence estimator of an s -concave density under mild conditions. One interesting and important feature for the Rényi divergence estimator of an s -concave density is that the estimator is intrinsically related with the estimation of log-concave densities via maximum likelihood methods. In fact, we show that for d = 1 at least, the Rényi divergence estimators for s -concave densities converge to the maximum likelihood estimator of a log-concave density as s ↗ 0. The Rényi divergence estimator shares similar characterizations as the MLE for log-concave distributions, which allows us to develop pointwise asymptotic distribution theory assuming that the underlying density is s -concave.

APPROXIMATION AND ESTIMATION OF s-CONCAVE DENSITIES VIA RÉNYI DIVERGENCES

PubMed Central

Han, Qiyang; Wellner, Jon A.

2017-01-01

In this paper, we study the approximation and estimation of s-concave densities via Rényi divergence. We first show that the approximation of a probability measure Q by an s-concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [Ann. Statist. 38 (2010) 2998–3027] if and only if Q admits full-dimensional support and a first moment. We also show continuity of the divergence functional in Q: if Qn → Q in the Wasserstein metric, then the projected densities converge in weighted L1 metrics and uniformly on closed subsets of the continuity set of the limit. Moreover, directional derivatives of the projected densities also enjoy local uniform convergence. This contains both on-the-model and off-the-model situations, and entails strong consistency of the divergence estimator of an s-concave density under mild conditions. One interesting and important feature for the Rényi divergence estimator of an s-concave density is that the estimator is intrinsically related with the estimation of log-concave densities via maximum likelihood methods. In fact, we show that for d = 1 at least, the Rényi divergence estimators for s-concave densities converge to the maximum likelihood estimator of a log-concave density as s ↗ 0. The Rényi divergence estimator shares similar characterizations as the MLE for log-concave distributions, which allows us to develop pointwise asymptotic distribution theory assuming that the underlying density is s-concave. PMID:28966410

Reduction of Metal Artifact in Single Photon-Counting Computed Tomography by Spectral-Driven Iterative Reconstruction Technique

PubMed Central

Nasirudin, Radin A.; Mei, Kai; Panchev, Petar; Fehringer, Andreas; Pfeiffer, Franz; Rummeny, Ernst J.; Fiebich, Martin; Noël, Peter B.

2015-01-01

Purpose The exciting prospect of Spectral CT (SCT) using photon-counting detectors (PCD) will lead to new techniques in computed tomography (CT) that take advantage of the additional spectral information provided. We introduce a method to reduce metal artifact in X-ray tomography by incorporating knowledge obtained from SCT into a statistical iterative reconstruction scheme. We call our method Spectral-driven Iterative Reconstruction (SPIR). Method The proposed algorithm consists of two main components: material decomposition and penalized maximum likelihood iterative reconstruction. In this study, the spectral data acquisitions with an energy-resolving PCD were simulated using a Monte-Carlo simulator based on EGSnrc C++ class library. A jaw phantom with a dental implant made of gold was used as an object in this study. A total of three dental implant shapes were simulated separately to test the influence of prior knowledge on the overall performance of the algorithm. The generated projection data was first decomposed into three basis functions: photoelectric absorption, Compton scattering and attenuation of gold. A pseudo-monochromatic sinogram was calculated and used as input in the reconstruction, while the spatial information of the gold implant was used as a prior. The results from the algorithm were assessed and benchmarked with state-of-the-art reconstruction methods. Results Decomposition results illustrate that gold implant of any shape can be distinguished from other components of the phantom. Additionally, the result from the penalized maximum likelihood iterative reconstruction shows that artifacts are significantly reduced in SPIR reconstructed slices in comparison to other known techniques, while at the same time details around the implant are preserved. Quantitatively, the SPIR algorithm best reflects the true attenuation value in comparison to other algorithms. Conclusion It is demonstrated that the combination of the additional information from Spectral CT and statistical reconstruction can significantly improve image quality, especially streaking artifacts caused by the presence of materials with high atomic numbers. PMID:25955019

A state space approach for piecewise-linear recurrent neural networks for identifying computational dynamics from neural measurements.

PubMed

Durstewitz, Daniel

2017-06-01

The computational and cognitive properties of neural systems are often thought to be implemented in terms of their (stochastic) network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit recordings or neuroimaging data, is an important step toward understanding its computations. Ideally, one would not only seek a (lower-dimensional) state space representation of the dynamics, but would wish to have access to its statistical properties and their generative equations for in-depth analysis. Recurrent neural networks (RNNs) are a computationally powerful and dynamically universal formal framework which has been extensively studied from both the computational and the dynamical systems perspective. Here we develop a semi-analytical maximum-likelihood estimation scheme for piecewise-linear RNNs (PLRNNs) within the statistical framework of state space models, which accounts for noise in both the underlying latent dynamics and the observation process. The Expectation-Maximization algorithm is used to infer the latent state distribution, through a global Laplace approximation, and the PLRNN parameters iteratively. After validating the procedure on toy examples, and using inference through particle filters for comparison, the approach is applied to multiple single-unit recordings from the rodent anterior cingulate cortex (ACC) obtained during performance of a classical working memory task, delayed alternation. Models estimated from kernel-smoothed spike time data were able to capture the essential computational dynamics underlying task performance, including stimulus-selective delay activity. The estimated models were rarely multi-stable, however, but rather were tuned to exhibit slow dynamics in the vicinity of a bifurcation point. In summary, the present work advances a semi-analytical (thus reasonably fast) maximum-likelihood estimation framework for PLRNNs that may enable to recover relevant aspects of the nonlinear dynamics underlying observed neuronal time series, and directly link these to computational properties.

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.

Differing Interpretations of Report Terminology Between Primary Care Physicians and Radiologists.

PubMed

Gunn, Andrew J; Tuttle, Mitch C; Flores, Efren J; Mangano, Mark D; Bennett, Susan E; Sahani, Dushyant V; Choy, Garry; Boland, Giles W

2016-12-01

The lexicons of the radiologist and the referring physician may not be synonymous, which could cause confusion with radiology reporting. To further explore this possibility, we surveyed radiologists and primary care physicians (PCPs) regarding their respective interpretations of report terminology. A survey was distributed to radiologists and PCPs through an internal listserv. Respondents were asked to provide an interpretation of the statistical likelihood of the presence of metastatic disease based upon the terminology used within a hypothetical radiology report. Ten common modifying terms were evaluated. Potential responses for the statistical likelihoods included 0%-25%, 26%-50%, 51%-75%, 76%-99%, and 100%. Differences between the groups were evaluated using either a χ 2 test or Fisher exact test, as appropriate. The phrases "diagnostic for metastatic disease" and "represents metastatic disease" were selected by a high percentage of both groups as conferring a 100% likelihood of "true metastatic disease." The phrases "cannot exclude metastatic disease" and "may represent metastatic disease" were selected by a high proportion of both groups as conferring a 0% likelihood of "true metastatic disease." Radiologists assigned a higher statistical likelihood to the terms "diagnostic for metastatic disease" (P = .016), "represents metastatic disease" (P = .004), "suspicious for metastatic disease" (P = .04), "consistent with metastatic disease" (P < .0001), and "compatible with metastatic disease" (P = .003). A qualitative agreement among radiologists and PCPs exists concerning the significance of the evaluated terminology, although radiologists assigned a higher statistical likelihood than PCPs for several phrases. Copyright © 2016 American College of Radiology. Published by Elsevier Inc. All rights reserved.

Changes in seasonal streamflow extremes experienced in rivers of Northwestern South America (Colombia)

NASA Astrophysics Data System (ADS)

Pierini, J. O.; Restrepo, J. C.; Aguirre, J.; Bustamante, A. M.; Velásquez, G. J.

2017-04-01

A measure of the variability in seasonal extreme streamflow was estimated for the Colombian Caribbean coast, using monthly time series of freshwater discharge from ten watersheds. The aim was to detect modifications in the streamflow monthly distribution, seasonal trends, variance and extreme monthly values. A 20-year length time moving window, with 1-year successive shiftments, was applied to the monthly series to analyze the seasonal variability of streamflow. The seasonal-windowed data were statistically fitted through the Gamma distribution function. Scale and shape parameters were computed using the Maximum Likelihood Estimation (MLE) and the bootstrap method for 1000 resample. A trend analysis was performed for each windowed-serie, allowing to detect the window of maximum absolute values for trends. Significant temporal shifts in seasonal streamflow distribution and quantiles (QT), were obtained for different frequencies. Wet and dry extremes periods increased significantly in the last decades. Such increase did not occur simultaneously through the region. Some locations exhibited continuous increases only at minimum QT.

Trajectory Dispersed Vehicle Process for Space Launch System

NASA Technical Reports Server (NTRS)

Statham, Tamara; Thompson, Seth

2017-01-01

The Space Launch System (SLS) vehicle is part of NASA's deep space exploration plans that includes manned missions to Mars. Manufacturing uncertainties in design parameters are key considerations throughout SLS development as they have significant effects on focus parameters such as lift-off-thrust-to-weight, vehicle payload, maximum dynamic pressure, and compression loads. This presentation discusses how the SLS program captures these uncertainties by utilizing a 3 degree of freedom (DOF) process called Trajectory Dispersed (TD) analysis. This analysis biases nominal trajectories to identify extremes in the design parameters for various potential SLS configurations and missions. This process utilizes a Design of Experiments (DOE) and response surface methodologies (RSM) to statistically sample uncertainties, and develop resulting vehicles using a Maximum Likelihood Estimate (MLE) process for targeting uncertainties bias. These vehicles represent various missions and configurations which are used as key inputs into a variety of analyses in the SLS design process, including 6 DOF dispersions, separation clearances, and engine out failure studies.

On the Computation of the RMSEA and CFI from the Mean-And-Variance Corrected Test Statistic with Nonnormal Data in SEM.

PubMed

Savalei, Victoria

2018-01-01

A new type of nonnormality correction to the RMSEA has recently been developed, which has several advantages over existing corrections. In particular, the new correction adjusts the sample estimate of the RMSEA for the inflation due to nonnormality, while leaving its population value unchanged, so that established cutoff criteria can still be used to judge the degree of approximate fit. A confidence interval (CI) for the new robust RMSEA based on the mean-corrected ("Satorra-Bentler") test statistic has also been proposed. Follow up work has provided the same type of nonnormality correction for the CFI (Brosseau-Liard & Savalei, 2014). These developments have recently been implemented in lavaan. This note has three goals: a) to show how to compute the new robust RMSEA and CFI from the mean-and-variance corrected test statistic; b) to offer a new CI for the robust RMSEA based on the mean-and-variance corrected test statistic; and c) to caution that the logic of the new nonnormality corrections to RMSEA and CFI is most appropriate for the maximum likelihood (ML) estimator, and cannot easily be generalized to the most commonly used categorical data estimators.

Valid statistical inference methods for a case-control study with missing data.

PubMed

Tian, Guo-Liang; Zhang, Chi; Jiang, Xuejun

2018-04-01

The main objective of this paper is to derive the valid sampling distribution of the observed counts in a case-control study with missing data under the assumption of missing at random by employing the conditional sampling method and the mechanism augmentation method. The proposed sampling distribution, called the case-control sampling distribution, can be used to calculate the standard errors of the maximum likelihood estimates of parameters via the Fisher information matrix and to generate independent samples for constructing small-sample bootstrap confidence intervals. Theoretical comparisons of the new case-control sampling distribution with two existing sampling distributions exhibit a large difference. Simulations are conducted to investigate the influence of the three different sampling distributions on statistical inferences. One finding is that the conclusion by the Wald test for testing independency under the two existing sampling distributions could be completely different (even contradictory) from the Wald test for testing the equality of the success probabilities in control/case groups under the proposed distribution. A real cervical cancer data set is used to illustrate the proposed statistical methods.

A scan statistic for identifying optimal risk windows in vaccine safety studies using self-controlled case series design.

PubMed

Xu, Stanley; Hambidge, Simon J; McClure, David L; Daley, Matthew F; Glanz, Jason M

2013-08-30

In the examination of the association between vaccines and rare adverse events after vaccination in postlicensure observational studies, it is challenging to define appropriate risk windows because prelicensure RCTs provide little insight on the timing of specific adverse events. Past vaccine safety studies have often used prespecified risk windows based on prior publications, biological understanding of the vaccine, and expert opinion. Recently, a data-driven approach was developed to identify appropriate risk windows for vaccine safety studies that use the self-controlled case series design. This approach employs both the maximum incidence rate ratio and the linear relation between the estimated incidence rate ratio and the inverse of average person time at risk, given a specified risk window. In this paper, we present a scan statistic that can identify appropriate risk windows in vaccine safety studies using the self-controlled case series design while taking into account the dependence of time intervals within an individual and while adjusting for time-varying covariates such as age and seasonality. This approach uses the maximum likelihood ratio test based on fixed-effects models, which has been used for analyzing data from self-controlled case series design in addition to conditional Poisson models. Copyright © 2013 John Wiley & Sons, Ltd.

Maximum entropy approach to statistical inference for an ocean acoustic waveguide.

PubMed

Knobles, D P; Sagers, J D; Koch, R A

2012-02-01

A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations. © 2012 Acoustical Society of America

Leishmania Infection: Laboratory Diagnosing in the Absence of a “Gold Standard”

PubMed Central

Rodríguez-Cortés, Alhelí; Ojeda, Ana; Francino, Olga; López-Fuertes, Laura; Timón, Marcos; Alberola, Jordi

2010-01-01

There is no gold standard for diagnosing leishmaniases. Our aim was to assess the operative validity of tests used in detecting Leishmania infection using samples from experimental infections, a reliable equivalent to the classic definition of gold standard. Without statistical differences, the highest sensitivity was achieved by protein A (ProtA), immunoglobulin (Ig)G2, indirect fluorescenece antibody test (IFAT), lymphocyte proliferation assay, quantitative real-time polymerase chain reaction of bone marrow (qPCR-BM), qPCR-Blood, and IgG; and the highest specificity by IgG1, IgM, IgA, qPCR-Blood, IgG, IgG2, and qPCR-BM. Maximum positive predictive value was obtained simultaneously by IgG2, qPCR-Blood, and IgG; and maximum negative predictive value by qPCR-BM. Best positive and negative likelihood ratios were obtained by IgG2. The test having the greatest, statistically significant, area under the receiver operating characteristics curve was IgG2 enzyme-linked immunosorbent assay (ELISA). Thus, according to the gold standard used, IFAT and qPCR are far from fulfilling the requirements to be considered gold standards, and the test showing the highest potential to detect Leishmania infection is Leishmania-specific ELISA IgG2. PMID:20134001

Leishmania infection: laboratory diagnosing in the absence of a "gold standard".

PubMed

Rodríguez-Cortés, Alhelí; Ojeda, Ana; Francino, Olga; López-Fuertes, Laura; Timón, Marcos; Alberola, Jordi

2010-02-01

There is no gold standard for diagnosing leishmaniases. Our aim was to assess the operative validity of tests used in detecting Leishmania infection using samples from experimental infections, a reliable equivalent to the classic definition of gold standard. Without statistical differences, the highest sensitivity was achieved by protein A (ProtA), immunoglobulin (Ig)G2, indirect fluorescenece antibody test (IFAT), lymphocyte proliferation assay, quantitative real-time polymerase chain reaction of bone marrow (qPCR-BM), qPCR-Blood, and IgG; and the highest specificity by IgG1, IgM, IgA, qPCR-Blood, IgG, IgG2, and qPCR-BM. Maximum positive predictive value was obtained simultaneously by IgG2, qPCR-Blood, and IgG; and maximum negative predictive value by qPCR-BM. Best positive and negative likelihood ratios were obtained by IgG2. The test having the greatest, statistically significant, area under the receiver operating characteristics curve was IgG2 enzyme-linked immunosorbent assay (ELISA). Thus, according to the gold standard used, IFAT and qPCR are far from fulfilling the requirements to be considered gold standards, and the test showing the highest potential to detect Leishmania infection is Leishmania-specific ELISA IgG2.

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.

A Selective Overview of Variable Selection in High Dimensional Feature Space

PubMed Central

Fan, Jianqing

2010-01-01

High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional idea of best subset selection methods, which can be regarded as a specific form of penalized likelihood, is computationally too expensive for many modern statistical applications. Other forms of penalized likelihood methods have been successfully developed over the last decade to cope with high dimensionality. They have been widely applied for simultaneously selecting important variables and estimating their effects in high dimensional statistical inference. In this article, we present a brief account of the recent developments of theory, methods, and implementations for high dimensional variable selection. What limits of the dimensionality such methods can handle, what the role of penalty functions is, and what the statistical properties are rapidly drive the advances of the field. The properties of non-concave penalized likelihood and its roles in high dimensional statistical modeling are emphasized. We also review some recent advances in ultra-high dimensional variable selection, with emphasis on independence screening and two-scale methods. PMID:21572976

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.

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

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.

Statistical methods for the beta-binomial model in teratology.

PubMed Central

Yamamoto, E; Yanagimoto, T

1994-01-01

The beta-binomial model is widely used for analyzing teratological data involving littermates. Recent developments in statistical analyses of teratological data are briefly reviewed with emphasis on the model. For statistical inference of the parameters in the beta-binomial distribution, separation of the likelihood introduces an likelihood inference. This leads to reducing biases of estimators and also to improving accuracy of empirical significance levels of tests. Separate inference of the parameters can be conducted in a unified way. PMID:8187716

Statistical parsimony networks and species assemblages in Cephalotrichid nemerteans (nemertea).

PubMed

Chen, Haixia; Strand, Malin; Norenburg, Jon L; Sun, Shichun; Kajihara, Hiroshi; Chernyshev, Alexey V; Maslakova, Svetlana A; Sundberg, Per

2010-09-21

It has been suggested that statistical parsimony network analysis could be used to get an indication of species represented in a set of nucleotide data, and the approach has been used to discuss species boundaries in some taxa. Based on 635 base pairs of the mitochondrial protein-coding gene cytochrome c oxidase I (COI), we analyzed 152 nemertean specimens using statistical parsimony network analysis with the connection probability set to 95%. The analysis revealed 15 distinct networks together with seven singletons. Statistical parsimony yielded three networks supporting the species status of Cephalothrix rufifrons, C. major and C. spiralis as they currently have been delineated by morphological characters and geographical location. Many other networks contained haplotypes from nearby geographical locations. Cladistic structure by maximum likelihood analysis overall supported the network analysis, but indicated a false positive result where subnetworks should have been connected into one network/species. This probably is caused by undersampling of the intraspecific haplotype diversity. Statistical parsimony network analysis provides a rapid and useful tool for detecting possible undescribed/cryptic species among cephalotrichid nemerteans based on COI gene. It should be combined with phylogenetic analysis to get indications of false positive results, i.e., subnetworks that would have been connected with more extensive haplotype sampling.

Empirical likelihood-based tests for stochastic ordering

PubMed Central

BARMI, HAMMOU EL; MCKEAGUE, IAN W.

2013-01-01

This paper develops an empirical likelihood approach to testing for the presence of stochastic ordering among univariate distributions based on independent random samples from each distribution. The proposed test statistic is formed by integrating a localized empirical likelihood statistic with respect to the empirical distribution of the pooled sample. The asymptotic null distribution of this test statistic is found to have a simple distribution-free representation in terms of standard Brownian bridge processes. The approach is used to compare the lengths of rule of Roman Emperors over various historical periods, including the “decline and fall” phase of the empire. In a simulation study, the power of the proposed test is found to improve substantially upon that of a competing test due to El Barmi and Mukerjee. PMID:23874142

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.

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

The Theory and Practice of Estimating the Accuracy of Dynamic Flight-Determined Coefficients

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1981-01-01

Means of assessing the accuracy of maximum likelihood parameter estimates obtained from dynamic flight data are discussed. The most commonly used analytical predictors of accuracy are derived and compared from both statistical and simplified geometrics standpoints. The accuracy predictions are evaluated with real and simulated data, with an emphasis on practical considerations, such as modeling error. Improved computations of the Cramer-Rao bound to correct large discrepancies due to colored noise and modeling error are presented. The corrected Cramer-Rao bound is shown to be the best available analytical predictor of accuracy, and several practical examples of the use of the Cramer-Rao bound are given. Engineering judgement, aided by such analytical tools, is the final arbiter of accuracy estimation.

Increasing power-law range in avalanche amplitude and energy distributions

NASA Astrophysics Data System (ADS)

Navas-Portella, Víctor; Serra, Isabel; Corral, Álvaro; Vives, Eduard

2018-02-01

Power-law-type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constraints that limit the range of truncated power-law distributions. By considering catalogs of events that cover different observation windows, the maximum likelihood estimation of a global power-law exponent is computed. This methodology is applied to amplitude and energy distributions of acoustic emission avalanches in failure-under-compression experiments of a nanoporous silica glass, finding in some cases global exponents in an unprecedented broad range: 4.5 decades for amplitudes and 9.5 decades for energies. In the latter case, however, strict statistical analysis suggests experimental limitations might alter the power-law behavior.

Multi-gene phylogeny of jacks and pompanos (Carangidae), including placement of monotypic vadigo Campogramma glaycos.

PubMed

Damerau, M; Freese, M; Hanel, R

2018-01-01

In this study, the phylogenetic trees of jacks and pompanos (Carangidae), an ecologically and morphologically diverse, globally distributed fish family, are inferred from a complete, concatenated data set of two mitochondrial (cytochrome c oxidase I, cytochrome b) loci and one nuclear (myosin heavy chain 6) locus. Maximum likelihood and Bayesian inferences are largely congruent and show a clear separation of Carangidae into the four subfamilies: Scomberoidinae, Trachinotinae, Naucratinae and Caranginae. The inclusion of the carangid sister lineages Coryphaenidae (dolphinfishes) and Rachycentridae (cobia), however, render Carangidae paraphyletic. The phylogenetic trees also show with high statistical support that the monotypic vadigo Campogramma glaycos is the sister to all other species within the Naucratinae. © 2017 The Fisheries Society of the British Isles.

A step-up test procedure to find the minimum effective dose.

PubMed

Wang, Weizhen; Peng, Jianan

2015-01-01

It is of great interest to find the minimum effective dose (MED) in dose-response studies. A sequence of decreasing null hypotheses to find the MED is formulated under the assumption of nondecreasing dose response means. A step-up multiple test procedure that controls the familywise error rate (FWER) is constructed based on the maximum likelihood estimators for the monotone normal means. When the MED is equal to one, the proposed test is uniformly more powerful than Hsu and Berger's test (1999). Also, a simulation study shows a substantial power improvement for the proposed test over four competitors. Three R-codes are provided in Supplemental Materials for this article. Go to the publishers online edition of Journal of Biopharmaceutical Statistics to view the files.

Increasing power-law range in avalanche amplitude and energy distributions.

PubMed

Navas-Portella, Víctor; Serra, Isabel; Corral, Álvaro; Vives, Eduard

2018-02-01

Power-law-type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constraints that limit the range of truncated power-law distributions. By considering catalogs of events that cover different observation windows, the maximum likelihood estimation of a global power-law exponent is computed. This methodology is applied to amplitude and energy distributions of acoustic emission avalanches in failure-under-compression experiments of a nanoporous silica glass, finding in some cases global exponents in an unprecedented broad range: 4.5 decades for amplitudes and 9.5 decades for energies. In the latter case, however, strict statistical analysis suggests experimental limitations might alter the power-law behavior.

Detection of low-contrast images in film-grain noise.

PubMed

Naderi, F; Sawchuk, A A

1978-09-15

When low contrast photographic images are digitized by a very small aperture, extreme film-grain noise almost completely obliterates the image information. Using a large aperture to average out the noise destroys the fine details of the image. In these situations conventional statistical restoration techniques have little effect, and well chosen heuristic algorithms have yielded better results. In this paper we analyze the noisecheating algorithm of Zweig et al. [J. Opt. Soc. Am. 65, 1347 (1975)] and show that it can be justified by classical maximum-likelihood detection theory. A more general algorithm applicable to a broader class of images is then developed by considering the signal-dependent nature of film-grain noise. Finally, a Bayesian detection algorithm with improved performance is presented.

Statistical inferences with jointly type-II censored samples from two Pareto distributions

NASA Astrophysics Data System (ADS)

Abu-Zinadah, Hanaa H.

2017-08-01

In the several fields of industries the product comes from more than one production line, which is required to work the comparative life tests. This problem requires sampling of the different production lines, then the joint censoring scheme is appeared. In this article we consider the life time Pareto distribution with jointly type-II censoring scheme. The maximum likelihood estimators (MLE) and the corresponding approximate confidence intervals as well as the bootstrap confidence intervals of the model parameters are obtained. Also Bayesian point and credible intervals of the model parameters are presented. The life time data set is analyzed for illustrative purposes. Monte Carlo results from simulation studies are presented to assess the performance of our proposed method.

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.…