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…

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...

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.

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

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.

Climate reconstruction analysis using coexistence likelihood estimation (CRACLE): a method for the estimation of climate using vegetation.

PubMed

Harbert, Robert S; Nixon, Kevin C

2015-08-01

• Plant distributions have long been understood to be correlated with the environmental conditions to which species are adapted. Climate is one of the major components driving species distributions. Therefore, it is expected that the plants coexisting in a community are reflective of the local environment, particularly climate.• Presented here is a method for the estimation of climate from local plant species coexistence data. The method, Climate Reconstruction Analysis using Coexistence Likelihood Estimation (CRACLE), is a likelihood-based method that employs specimen collection data at a global scale for the inference of species climate tolerance. CRACLE calculates the maximum joint likelihood of coexistence given individual species climate tolerance characterization to estimate the expected climate.• Plant distribution data for more than 4000 species were used to show that this method accurately infers expected climate profiles for 165 sites with diverse climatic conditions. Estimates differ from the WorldClim global climate model by less than 1.5°C on average for mean annual temperature and less than ∼250 mm for mean annual precipitation. This is a significant improvement upon other plant-based climate-proxy methods.• CRACLE validates long hypothesized interactions between climate and local associations of plant species. Furthermore, CRACLE successfully estimates climate that is consistent with the widely used WorldClim model and therefore may be applied to the quantitative estimation of paleoclimate in future studies. © 2015 Botanical Society of America, Inc.

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.

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

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…

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…

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…

Method and system for diagnostics of apparatus

NASA Technical Reports Server (NTRS)

Gorinevsky, Dimitry (Inventor)

2012-01-01

Proposed is a method, implemented in software, for estimating fault state of an apparatus outfitted with sensors. At each execution period the method processes sensor data from the apparatus to obtain a set of parity parameters, which are further used for estimating fault state. The estimation method formulates a convex optimization problem for each fault hypothesis and employs a convex solver to compute fault parameter estimates and fault likelihoods for each fault hypothesis. The highest likelihoods and corresponding parameter estimates are transmitted to a display device or an automated decision and control system. The obtained accurate estimate of fault state can be used to improve safety, performance, or maintenance processes for the apparatus.

Cosmological parameter estimation using Particle Swarm Optimization

NASA Astrophysics Data System (ADS)

Prasad, J.; Souradeep, T.

2014-03-01

Constraining parameters of a theoretical model from observational data is an important exercise in cosmology. There are many theoretically motivated models, which demand greater number of cosmological parameters than the standard model of cosmology uses, and make the problem of parameter estimation challenging. It is a common practice to employ Bayesian formalism for parameter estimation for which, in general, likelihood surface is probed. For the standard cosmological model with six parameters, likelihood surface is quite smooth and does not have local maxima, and sampling based methods like Markov Chain Monte Carlo (MCMC) method are quite successful. However, when there are a large number of parameters or the likelihood surface is not smooth, other methods may be more effective. In this paper, we have demonstrated application of another method inspired from artificial intelligence, called Particle Swarm Optimization (PSO) for estimating cosmological parameters from Cosmic Microwave Background (CMB) data taken from the WMAP satellite.

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.

Rate of convergence of k-step Newton estimators to efficient likelihood estimators

Treesearch

Steve Verrill

2007-01-01

We make use of Cramer conditions together with the well-known local quadratic convergence of Newton?s method to establish the asymptotic closeness of k-step Newton estimators to efficient likelihood estimators. In Verrill and Johnson [2007. Confidence bounds and hypothesis tests for normal distribution coefficients of variation. USDA Forest Products Laboratory Research...

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.

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…

Estimation of brood and nest survival: Comparative methods in the presence of heterogeneity

USGS Publications Warehouse

Manly, Bryan F.J.; Schmutz, Joel A.

2001-01-01

The Mayfield method has been widely used for estimating survival of nests and young animals, especially when data are collected at irregular observation intervals. However, this method assumes survival is constant throughout the study period, which often ignores biologically relevant variation and may lead to biased survival estimates. We examined the bias and accuracy of 1 modification to the Mayfield method that allows for temporal variation in survival, and we developed and similarly tested 2 additional methods. One of these 2 new methods is simply an iterative extension of Klett and Johnson's method, which we refer to as the Iterative Mayfield method and bears similarity to Kaplan-Meier methods. The other method uses maximum likelihood techniques for estimation and is best applied to survival of animals in groups or families, rather than as independent individuals. We also examined how robust these estimators are to heterogeneity in the data, which can arise from such sources as dependent survival probabilities among siblings, inherent differences among families, and adoption. Testing of estimator performance with respect to bias, accuracy, and heterogeneity was done using simulations that mimicked a study of survival of emperor goose (Chen canagica) goslings. Assuming constant survival for inappropriately long periods of time or use of Klett and Johnson's methods resulted in large bias or poor accuracy (often >5% bias or root mean square error) compared to our Iterative Mayfield or maximum likelihood methods. Overall, estimator performance was slightly better with our Iterative Mayfield than our maximum likelihood method, but the maximum likelihood method provides a more rigorous framework for testing covariates and explicity models a heterogeneity factor. We demonstrated use of all estimators with data from emperor goose goslings. We advocate that future studies use the new methods outlined here rather than the traditional Mayfield method or its previous modifications.

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

Modeling of 2D diffusion processes based on microscopy data: parameter estimation and practical identifiability analysis.

PubMed

Hock, Sabrina; Hasenauer, Jan; Theis, Fabian J

2013-01-01

Diffusion is a key component of many biological processes such as chemotaxis, developmental differentiation and tissue morphogenesis. Since recently, the spatial gradients caused by diffusion can be assessed in-vitro and in-vivo using microscopy based imaging techniques. The resulting time-series of two dimensional, high-resolutions images in combination with mechanistic models enable the quantitative analysis of the underlying mechanisms. However, such a model-based analysis is still challenging due to measurement noise and sparse observations, which result in uncertainties of the model parameters. We introduce a likelihood function for image-based measurements with log-normal distributed noise. Based upon this likelihood function we formulate the maximum likelihood estimation problem, which is solved using PDE-constrained optimization methods. To assess the uncertainty and practical identifiability of the parameters we introduce profile likelihoods for diffusion processes. As proof of concept, we model certain aspects of the guidance of dendritic cells towards lymphatic vessels, an example for haptotaxis. Using a realistic set of artificial measurement data, we estimate the five kinetic parameters of this model and compute profile likelihoods. Our novel approach for the estimation of model parameters from image data as well as the proposed identifiability analysis approach is widely applicable to diffusion processes. The profile likelihood based method provides more rigorous uncertainty bounds in contrast to local approximation methods.

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)

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.

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

PubMed

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

2014-12-10

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

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

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.

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

PubMed

Bayar, Belhassen; Bouaynaya, Nidhal; Shterenberg, Roman

2017-03-01

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

A Penalized Likelihood Framework For High-Dimensional Phylogenetic Comparative Methods And An Application To New-World Monkeys Brain Evolution.

PubMed

Julien, Clavel; Leandro, Aristide; Hélène, Morlon

2018-06-19

Working with high-dimensional phylogenetic comparative datasets is challenging because likelihood-based multivariate methods suffer from low statistical performances as the number of traits p approaches the number of species n and because some computational complications occur when p exceeds n. Alternative phylogenetic comparative methods have recently been proposed to deal with the large p small n scenario but their use and performances are limited. Here we develop a penalized likelihood framework to deal with high-dimensional comparative datasets. We propose various penalizations and methods for selecting the intensity of the penalties. We apply this general framework to the estimation of parameters (the evolutionary trait covariance matrix and parameters of the evolutionary model) and model comparison for the high-dimensional multivariate Brownian (BM), Early-burst (EB), Ornstein-Uhlenbeck (OU) and Pagel's lambda models. We show using simulations that our penalized likelihood approach dramatically improves the estimation of evolutionary trait covariance matrices and model parameters when p approaches n, and allows for their accurate estimation when p equals or exceeds n. In addition, we show that penalized likelihood models can be efficiently compared using Generalized Information Criterion (GIC). We implement these methods, as well as the related estimation of ancestral states and the computation of phylogenetic PCA in the R package RPANDA and mvMORPH. Finally, we illustrate the utility of the new proposed framework by evaluating evolutionary models fit, analyzing integration patterns, and reconstructing evolutionary trajectories for a high-dimensional 3-D dataset of brain shape in the New World monkeys. We find a clear support for an Early-burst model suggesting an early diversification of brain morphology during the ecological radiation of the clade. Penalized likelihood offers an efficient way to deal with high-dimensional multivariate comparative data.

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

An alternative method to measure the likelihood of a financial crisis in an emerging market

NASA Astrophysics Data System (ADS)

Özlale, Ümit; Metin-Özcan, Kıvılcım

2007-07-01

This paper utilizes an early warning system in order to measure the likelihood of a financial crisis in an emerging market economy. We introduce a methodology, where we can both obtain a likelihood series and analyze the time-varying effects of several macroeconomic variables on this likelihood. Since the issue is analyzed in a non-linear state space framework, the extended Kalman filter emerges as the optimal estimation algorithm. Taking the Turkish economy as our laboratory, the results indicate that both the derived likelihood measure and the estimated time-varying parameters are meaningful and can successfully explain the path that the Turkish economy had followed between 2000 and 2006. The estimated parameters also suggest that overvalued domestic currency, current account deficit and the increase in the default risk increase the likelihood of having an economic crisis in the economy. Overall, the findings in this paper suggest that the estimation methodology introduced in this paper can also be applied to other emerging market economies as well.

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

Estimating Model Probabilities using Thermodynamic Markov Chain Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Ye, M.; Liu, P.; Beerli, P.; Lu, D.; Hill, M. C.

2014-12-01

Markov chain Monte Carlo (MCMC) methods are widely used to evaluate model probability for quantifying model uncertainty. In a general procedure, MCMC simulations are first conducted for each individual model, and MCMC parameter samples are then used to approximate marginal likelihood of the model by calculating the geometric mean of the joint likelihood of the model and its parameters. It has been found the method of evaluating geometric mean suffers from the numerical problem of low convergence rate. A simple test case shows that even millions of MCMC samples are insufficient to yield accurate estimation of the marginal likelihood. To resolve this problem, a thermodynamic method is used to have multiple MCMC runs with different values of a heating coefficient between zero and one. When the heating coefficient is zero, the MCMC run is equivalent to a random walk MC in the prior parameter space; when the heating coefficient is one, the MCMC run is the conventional one. For a simple case with analytical form of the marginal likelihood, the thermodynamic method yields more accurate estimate than the method of using geometric mean. This is also demonstrated for a case of groundwater modeling with consideration of four alternative models postulated based on different conceptualization of a confining layer. This groundwater example shows that model probabilities estimated using the thermodynamic method are more reasonable than those obtained using the geometric method. The thermodynamic method is general, and can be used for a wide range of environmental problem for model uncertainty quantification.

Maximum likelihood estimation of finite mixture model for economic data

NASA Astrophysics Data System (ADS)

Phoong, Seuk-Yen; Ismail, Mohd Tahir

2014-06-01

Finite mixture model is a mixture model with finite-dimension. This models are provides a natural representation of heterogeneity in a finite number of latent classes. In addition, finite mixture models also known as latent class models or unsupervised learning models. Recently, maximum likelihood estimation fitted finite mixture models has greatly drawn statistician's attention. The main reason is because maximum likelihood estimation is a powerful statistical method which provides consistent findings as the sample sizes increases to infinity. Thus, the application of maximum likelihood estimation is used to fit finite mixture model in the present paper in order to explore the relationship between nonlinear economic data. In this paper, a two-component normal mixture model is fitted by maximum likelihood estimation in order to investigate the relationship among stock market price and rubber price for sampled countries. Results described that there is a negative effect among rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia.

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.

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

Maximal likelihood correspondence estimation for face recognition across pose.

PubMed

Li, Shaoxin; Liu, Xin; Chai, Xiujuan; Zhang, Haihong; Lao, Shihong; Shan, Shiguang

2014-10-01

Due to the misalignment of image features, the performance of many conventional face recognition methods degrades considerably in across pose scenario. To address this problem, many image matching-based methods are proposed to estimate semantic correspondence between faces in different poses. In this paper, we aim to solve two critical problems in previous image matching-based correspondence learning methods: 1) fail to fully exploit face specific structure information in correspondence estimation and 2) fail to learn personalized correspondence for each probe image. To this end, we first build a model, termed as morphable displacement field (MDF), to encode face specific structure information of semantic correspondence from a set of real samples of correspondences calculated from 3D face models. Then, we propose a maximal likelihood correspondence estimation (MLCE) method to learn personalized correspondence based on maximal likelihood frontal face assumption. After obtaining the semantic correspondence encoded in the learned displacement, we can synthesize virtual frontal images of the profile faces for subsequent recognition. Using linear discriminant analysis method with pixel-intensity features, state-of-the-art performance is achieved on three multipose benchmarks, i.e., CMU-PIE, FERET, and MultiPIE databases. Owe to the rational MDF regularization and the usage of novel maximal likelihood objective, the proposed MLCE method can reliably learn correspondence between faces in different poses even in complex wild environment, i.e., labeled face in the wild database.

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

PubMed

Campos-Filho, N; Franco, E L

1989-02-01

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

Maximum Likelihood Estimation with Emphasis on Aircraft Flight Data

NASA Technical Reports Server (NTRS)

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

1985-01-01

Accurate modeling of flexible space structures is an important field that is currently under investigation. Parameter estimation, using methods such as maximum likelihood, is one of the ways that the model can be improved. The maximum likelihood estimator has been used to extract stability and control derivatives from flight data for many years. Most of the literature on aircraft estimation concentrates on new developments and applications, assuming familiarity with basic estimation concepts. Some of these basic concepts are presented. The maximum likelihood estimator and the aircraft equations of motion that the estimator uses are briefly discussed. The basic concepts of minimization and estimation are examined for a simple computed aircraft example. The cost functions that are to be minimized during estimation are defined and discussed. Graphic representations of the cost functions are given to help illustrate the minimization process. Finally, the basic concepts are generalized, and estimation from flight data is discussed. Specific examples of estimation of structural dynamics are included. Some of the major conclusions for the computed example are also developed for the analysis of flight data.

A Two-Stage Estimation Method for Random Coefficient Differential Equation Models with Application to Longitudinal HIV Dynamic Data.

PubMed

Fang, Yun; Wu, Hulin; Zhu, Li-Xing

2011-07-01

We propose a two-stage estimation method for random coefficient ordinary differential equation (ODE) models. A maximum pseudo-likelihood estimator (MPLE) is derived based on a mixed-effects modeling approach and its asymptotic properties for population parameters are established. The proposed method does not require repeatedly solving ODEs, and is computationally efficient although it does pay a price with the loss of some estimation efficiency. However, the method does offer an alternative approach when the exact likelihood approach fails due to model complexity and high-dimensional parameter space, and it can also serve as a method to obtain the starting estimates for more accurate estimation methods. In addition, the proposed method does not need to specify the initial values of state variables and preserves all the advantages of the mixed-effects modeling approach. The finite sample properties of the proposed estimator are studied via Monte Carlo simulations and the methodology is also illustrated with application to an AIDS clinical data set.

Quantum state estimation when qubits are lost: a no-data-left-behind approach

DOE PAGES

Williams, Brian P.; Lougovski, Pavel

2017-04-06

We present an approach to Bayesian mean estimation of quantum states using hyperspherical parametrization and an experiment-specific likelihood which allows utilization of all available data, even when qubits are lost. With this method, we report the first closed-form Bayesian mean and maximum likelihood estimates for the ideal single qubit. Due to computational constraints, we utilize numerical sampling to determine the Bayesian mean estimate for a photonic two-qubit experiment in which our novel analysis reduces burdens associated with experimental asymmetries and inefficiencies. This method can be applied to quantum states of any dimension and experimental complexity.

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

Pointwise nonparametric maximum likelihood estimator of stochastically ordered survivor functions

PubMed Central

Park, Yongseok; Taylor, Jeremy M. G.; Kalbfleisch, John D.

2012-01-01

In this paper, we consider estimation of survivor functions from groups of observations with right-censored data when the groups are subject to a stochastic ordering constraint. Many methods and algorithms have been proposed to estimate distribution functions under such restrictions, but none have completely satisfactory properties when the observations are censored. We propose a pointwise constrained nonparametric maximum likelihood estimator, which is defined at each time t by the estimates of the survivor functions subject to constraints applied at time t only. We also propose an efficient method to obtain the estimator. The estimator of each constrained survivor function is shown to be nonincreasing in t, and its consistency and asymptotic distribution are established. A simulation study suggests better small and large sample properties than for alternative estimators. An example using prostate cancer data illustrates the method. PMID:23843661

Modified Maxium Likelihood Estimation Method for Completely Separated and Quasi-Completely Separated Data for a Dose-Response Model

DTIC Science & Technology

2015-08-01

McCullagh, P.; Nelder, J.A. Generalized Linear Model , 2nd ed.; Chapman and Hall: London, 1989. 7. Johnston, J. Econometric Methods, 3rd ed.; McGraw...FOR A DOSE-RESPONSE MODEL ECBC-TN-068 Kyong H. Park Steven J. Lagan RESEARCH AND TECHNOLOGY DIRECTORATE August 2015 Approved for public release...Likelihood Estimation Method for Completely Separated and Quasi-Completely Separated Data for a Dose-Response Model 5a. CONTRACT NUMBER 5b. GRANT

Effect of sampling rate and record length on the determination of stability and control derivatives

NASA Technical Reports Server (NTRS)

Brenner, M. J.; Iliff, K. W.; Whitman, R. K.

1978-01-01

Flight data from five aircraft were used to assess the effects of sampling rate and record length reductions on estimates of stability and control derivatives produced by a maximum likelihood estimation method. Derivatives could be extracted from flight data with the maximum likelihood estimation method even if there were considerable reductions in sampling rate and/or record length. Small amplitude pulse maneuvers showed greater degradation of the derivative maneuvers than large amplitude pulse maneuvers when these reductions were made. Reducing the sampling rate was found to be more desirable than reducing the record length as a method of lessening the total computation time required without greatly degrading the quantity of the estimates.

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.

Technical Note: Approximate Bayesian parameterization of a process-based tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2014-02-01

Inverse parameter estimation of process-based models is a long-standing problem in many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to the data. This metric can be expressed by general cost or objective functions, but statistical inversion methods require a particular metric, the probability of observing the data given the model parameters, known as the likelihood. For technical and computational reasons, likelihoods for process-based stochastic models are usually based on general assumptions about variability in the observed data, and not on the stochasticity generated by the model. Only in recent years have new methods become available that allow the generation of likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional Markov chain Monte Carlo (MCMC) sampler, performs well in retrieving known parameter values from virtual inventory data generated by the forest model. We analyze the results of the parameter estimation, examine its sensitivity to the choice and aggregation of model outputs and observed data (summary statistics), and demonstrate the application of this method by fitting the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss how this approach differs from approximate Bayesian computation (ABC), another method commonly used to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can be successfully applied to process-based models of high complexity. The methodology is particularly suitable for heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models.

Species delimitation using Bayes factors: simulations and application to the Sceloporus scalaris species group (Squamata: Phrynosomatidae).

PubMed

Grummer, Jared A; Bryson, Robert W; Reeder, Tod W

2014-03-01

Current molecular methods of species delimitation are limited by the types of species delimitation models and scenarios that can be tested. Bayes factors allow for more flexibility in testing non-nested species delimitation models and hypotheses of individual assignment to alternative lineages. Here, we examined the efficacy of Bayes factors in delimiting species through simulations and empirical data from the Sceloporus scalaris species group. Marginal-likelihood scores of competing species delimitation models, from which Bayes factor values were compared, were estimated with four different methods: harmonic mean estimation (HME), smoothed harmonic mean estimation (sHME), path-sampling/thermodynamic integration (PS), and stepping-stone (SS) analysis. We also performed model selection using a posterior simulation-based analog of the Akaike information criterion through Markov chain Monte Carlo analysis (AICM). Bayes factor species delimitation results from the empirical data were then compared with results from the reversible-jump MCMC (rjMCMC) coalescent-based species delimitation method Bayesian Phylogenetics and Phylogeography (BP&P). Simulation results show that HME and sHME perform poorly compared with PS and SS marginal-likelihood estimators when identifying the true species delimitation model. Furthermore, Bayes factor delimitation (BFD) of species showed improved performance when species limits are tested by reassigning individuals between species, as opposed to either lumping or splitting lineages. In the empirical data, BFD through PS and SS analyses, as well as the rjMCMC method, each provide support for the recognition of all scalaris group taxa as independent evolutionary lineages. Bayes factor species delimitation and BP&P also support the recognition of three previously undescribed lineages. In both simulated and empirical data sets, harmonic and smoothed harmonic mean marginal-likelihood estimators provided much higher marginal-likelihood estimates than PS and SS estimators. The AICM displayed poor repeatability in both simulated and empirical data sets, and produced inconsistent model rankings across replicate runs with the empirical data. Our results suggest that species delimitation through the use of Bayes factors with marginal-likelihood estimates via PS or SS analyses provide a useful and complementary alternative to existing species delimitation methods.

Comparisons of Four Methods for Estimating a Dynamic Factor Model

ERIC Educational Resources Information Center

Zhang, Zhiyong; Hamaker, Ellen L.; Nesselroade, John R.

2008-01-01

Four methods for estimating a dynamic factor model, the direct autoregressive factor score (DAFS) model, are evaluated and compared. The first method estimates the DAFS model using a Kalman filter algorithm based on its state space model representation. The second one employs the maximum likelihood estimation method based on the construction of a…

Estimation Methods for One-Parameter Testlet Models

ERIC Educational Resources Information Center

Jiao, Hong; Wang, Shudong; He, Wei

2013-01-01

This study demonstrated the equivalence between the Rasch testlet model and the three-level one-parameter testlet model and explored the Markov Chain Monte Carlo (MCMC) method for model parameter estimation in WINBUGS. The estimation accuracy from the MCMC method was compared with those from the marginalized maximum likelihood estimation (MMLE)…

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

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

Beer, M.

1980-12-01

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

A simulation study on Bayesian Ridge regression models for several collinearity levels

NASA Astrophysics Data System (ADS)

Efendi, Achmad; Effrihan

2017-12-01

When analyzing data with multiple regression model if there are collinearities, then one or several predictor variables are usually omitted from the model. However, there sometimes some reasons, for instance medical or economic reasons, the predictors are all important and should be included in the model. Ridge regression model is not uncommon in some researches to use to cope with collinearity. Through this modeling, weights for predictor variables are used for estimating parameters. The next estimation process could follow the concept of likelihood. Furthermore, for the estimation nowadays the Bayesian version could be an alternative. This estimation method does not match likelihood one in terms of popularity due to some difficulties; computation and so forth. Nevertheless, with the growing improvement of computational methodology recently, this caveat should not at the moment become a problem. This paper discusses about simulation process for evaluating the characteristic of Bayesian Ridge regression parameter estimates. There are several simulation settings based on variety of collinearity levels and sample sizes. The results show that Bayesian method gives better performance for relatively small sample sizes, and for other settings the method does perform relatively similar to the likelihood method.

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.

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.

Estimation of submarine mass failure probability from a sequence of deposits with age dates

USGS Publications Warehouse

Geist, Eric L.; Chaytor, Jason D.; Parsons, Thomas E.; ten Brink, Uri S.

2013-01-01

The empirical probability of submarine mass failure is quantified from a sequence of dated mass-transport deposits. Several different techniques are described to estimate the parameters for a suite of candidate probability models. The techniques, previously developed for analyzing paleoseismic data, include maximum likelihood and Type II (Bayesian) maximum likelihood methods derived from renewal process theory and Monte Carlo methods. The estimated mean return time from these methods, unlike estimates from a simple arithmetic mean of the center age dates and standard likelihood methods, includes the effects of age-dating uncertainty and of open time intervals before the first and after the last event. The likelihood techniques are evaluated using Akaike’s Information Criterion (AIC) and Akaike’s Bayesian Information Criterion (ABIC) to select the optimal model. The techniques are applied to mass transport deposits recorded in two Integrated Ocean Drilling Program (IODP) drill sites located in the Ursa Basin, northern Gulf of Mexico. Dates of the deposits were constrained by regional bio- and magnetostratigraphy from a previous study. Results of the analysis indicate that submarine mass failures in this location occur primarily according to a Poisson process in which failures are independent and return times follow an exponential distribution. However, some of the model results suggest that submarine mass failures may occur quasiperiodically at one of the sites (U1324). The suite of techniques described in this study provides quantitative probability estimates of submarine mass failure occurrence, for any number of deposits and age uncertainty distributions.

Zero-inflated Poisson model based likelihood ratio test for drug safety signal detection.

PubMed

Huang, Lan; Zheng, Dan; Zalkikar, Jyoti; Tiwari, Ram

2017-02-01

In recent decades, numerous methods have been developed for data mining of large drug safety databases, such as Food and Drug Administration's (FDA's) Adverse Event Reporting System, where data matrices are formed by drugs such as columns and adverse events as rows. Often, a large number of cells in these data matrices have zero cell counts and some of them are "true zeros" indicating that the drug-adverse event pairs cannot occur, and these zero counts are distinguished from the other zero counts that are modeled zero counts and simply indicate that the drug-adverse event pairs have not occurred yet or have not been reported yet. In this paper, a zero-inflated Poisson model based likelihood ratio test method is proposed to identify drug-adverse event pairs that have disproportionately high reporting rates, which are also called signals. The maximum likelihood estimates of the model parameters of zero-inflated Poisson model based likelihood ratio test are obtained using the expectation and maximization algorithm. The zero-inflated Poisson model based likelihood ratio test is also modified to handle the stratified analyses for binary and categorical covariates (e.g. gender and age) in the data. The proposed zero-inflated Poisson model based likelihood ratio test method is shown to asymptotically control the type I error and false discovery rate, and its finite sample performance for signal detection is evaluated through a simulation study. The simulation results show that the zero-inflated Poisson model based likelihood ratio test method performs similar to Poisson model based likelihood ratio test method when the estimated percentage of true zeros in the database is small. Both the zero-inflated Poisson model based likelihood ratio test and likelihood ratio test methods are applied to six selected drugs, from the 2006 to 2011 Adverse Event Reporting System database, with varying percentages of observed zero-count cells.

Approximate likelihood calculation on a phylogeny for Bayesian estimation of divergence times.

PubMed

dos Reis, Mario; Yang, Ziheng

2011-07-01

The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.

Effects of time-shifted data on flight determined stability and control derivatives

NASA Technical Reports Server (NTRS)

Steers, S. T.; Iliff, K. W.

1975-01-01

Flight data were shifted in time by various increments to assess the effects of time shifts on estimates of stability and control derivatives produced by a maximum likelihood estimation method. Derivatives could be extracted from flight data with the maximum likelihood estimation method even if there was a considerable time shift in the data. Time shifts degraded the estimates of the derivatives, but the degradation was in a consistent rather than a random pattern. Time shifts in the control variables caused the most degradation, and the lateral-directional rotary derivatives were affected the most by time shifts in any variable.

Robust Methods for Moderation Analysis with a Two-Level Regression Model.

PubMed

Yang, Miao; Yuan, Ke-Hai

2016-01-01

Moderation analysis has many applications in social sciences. Most widely used estimation methods for moderation analysis assume that errors are normally distributed and homoscedastic. When these assumptions are not met, the results from a classical moderation analysis can be misleading. For more reliable moderation analysis, this article proposes two robust methods with a two-level regression model when the predictors do not contain measurement error. One method is based on maximum likelihood with Student's t distribution and the other is based on M-estimators with Huber-type weights. An algorithm for obtaining the robust estimators is developed. Consistent estimates of standard errors of the robust estimators are provided. The robust approaches are compared against normal-distribution-based maximum likelihood (NML) with respect to power and accuracy of parameter estimates through a simulation study. Results show that the robust approaches outperform NML under various distributional conditions. Application of the robust methods is illustrated through a real data example. An R program is developed and documented to facilitate the application of the robust methods.

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…

Technical Note: Approximate Bayesian parameterization of a complex tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2013-08-01

Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics), and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC), another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can successfully be applied to process-based models of high complexity. The methodology is particularly suited to heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models in ecology and evolution.

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

Multiple-hit parameter estimation in monolithic detectors.

PubMed

Hunter, William C J; Barrett, Harrison H; Lewellen, Tom K; Miyaoka, Robert S

2013-02-01

We examine a maximum-a-posteriori method for estimating the primary interaction position of gamma rays with multiple interaction sites (hits) in a monolithic detector. In assessing the performance of a multiple-hit estimator over that of a conventional one-hit estimator, we consider a few different detector and readout configurations of a 50-mm-wide square cerium-doped lutetium oxyorthosilicate block. For this study, we use simulated data from SCOUT, a Monte-Carlo tool for photon tracking and modeling scintillation- camera output. With this tool, we determine estimate bias and variance for a multiple-hit estimator and compare these with similar metrics for a one-hit maximum-likelihood estimator, which assumes full energy deposition in one hit. We also examine the effect of event filtering on these metrics; for this purpose, we use a likelihood threshold to reject signals that are not likely to have been produced under the assumed likelihood model. Depending on detector design, we observe a 1%-12% improvement of intrinsic resolution for a 1-or-2-hit estimator as compared with a 1-hit estimator. We also observe improved differentiation of photopeak events using a 1-or-2-hit estimator as compared with the 1-hit estimator; more than 6% of photopeak events that were rejected by likelihood filtering for the 1-hit estimator were accurately identified as photopeak events and positioned without loss of resolution by a 1-or-2-hit estimator; for PET, this equates to at least a 12% improvement in coincidence-detection efficiency with likelihood filtering applied.

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.

A comparison of abundance estimates from extended batch-marking and Jolly–Seber-type experiments

PubMed Central

Cowen, Laura L E; Besbeas, Panagiotis; Morgan, Byron J T; Schwarz, Carl J

2014-01-01

Little attention has been paid to the use of multi-sample batch-marking studies, as it is generally assumed that an individual's capture history is necessary for fully efficient estimates. However, recently, Huggins et al. (2010) present a pseudo-likelihood for a multi-sample batch-marking study where they used estimating equations to solve for survival and capture probabilities and then derived abundance estimates using a Horvitz–Thompson-type estimator. We have developed and maximized the likelihood for batch-marking studies. We use data simulated from a Jolly–Seber-type study and convert this to what would have been obtained from an extended batch-marking study. We compare our abundance estimates obtained from the Crosbie–Manly–Arnason–Schwarz (CMAS) model with those of the extended batch-marking model to determine the efficiency of collecting and analyzing batch-marking data. We found that estimates of abundance were similar for all three estimators: CMAS, Huggins, and our likelihood. Gains are made when using unique identifiers and employing the CMAS model in terms of precision; however, the likelihood typically had lower mean square error than the pseudo-likelihood method of Huggins et al. (2010). When faced with designing a batch-marking study, researchers can be confident in obtaining unbiased abundance estimators. Furthermore, they can design studies in order to reduce mean square error by manipulating capture probabilities and sample size. PMID:24558576

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

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…

Empirical Likelihood in Nonignorable Covariate-Missing Data Problems.

PubMed

Xie, Yanmei; Zhang, Biao

2017-04-20

Missing covariate data occurs often in regression analysis, which frequently arises in the health and social sciences as well as in survey sampling. We study methods for the analysis of a nonignorable covariate-missing data problem in an assumed conditional mean function when some covariates are completely observed but other covariates are missing for some subjects. We adopt the semiparametric perspective of Bartlett et al. (Improving upon the efficiency of complete case analysis when covariates are MNAR. Biostatistics 2014;15:719-30) on regression analyses with nonignorable missing covariates, in which they have introduced the use of two working models, the working probability model of missingness and the working conditional score model. In this paper, we study an empirical likelihood approach to nonignorable covariate-missing data problems with the objective of effectively utilizing the two working models in the analysis of covariate-missing data. We propose a unified approach to constructing a system of unbiased estimating equations, where there are more equations than unknown parameters of interest. One useful feature of these unbiased estimating equations is that they naturally incorporate the incomplete data into the data analysis, making it possible to seek efficient estimation of the parameter of interest even when the working regression function is not specified to be the optimal regression function. We apply the general methodology of empirical likelihood to optimally combine these unbiased estimating equations. We propose three maximum empirical likelihood estimators of the underlying regression parameters and compare their efficiencies with other existing competitors. We present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. The proposed empirical likelihood method is also illustrated by an analysis of a data set from the US National Health and Nutrition Examination Survey (NHANES).

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.

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

Estimation of parameters of dose volume models and their confidence limits

NASA Astrophysics Data System (ADS)

van Luijk, P.; Delvigne, T. C.; Schilstra, C.; Schippers, J. M.

2003-07-01

Predictions of the normal-tissue complication probability (NTCP) for the ranking of treatment plans are based on fits of dose-volume models to clinical and/or experimental data. In the literature several different fit methods are used. In this work frequently used methods and techniques to fit NTCP models to dose response data for establishing dose-volume effects, are discussed. The techniques are tested for their usability with dose-volume data and NTCP models. Different methods to estimate the confidence intervals of the model parameters are part of this study. From a critical-volume (CV) model with biologically realistic parameters a primary dataset was generated, serving as the reference for this study and describable by the NTCP model. The CV model was fitted to this dataset. From the resulting parameters and the CV model, 1000 secondary datasets were generated by Monte Carlo simulation. All secondary datasets were fitted to obtain 1000 parameter sets of the CV model. Thus the 'real' spread in fit results due to statistical spreading in the data is obtained and has been compared with estimates of the confidence intervals obtained by different methods applied to the primary dataset. The confidence limits of the parameters of one dataset were estimated using the methods, employing the covariance matrix, the jackknife method and directly from the likelihood landscape. These results were compared with the spread of the parameters, obtained from the secondary parameter sets. For the estimation of confidence intervals on NTCP predictions, three methods were tested. Firstly, propagation of errors using the covariance matrix was used. Secondly, the meaning of the width of a bundle of curves that resulted from parameters that were within the one standard deviation region in the likelihood space was investigated. Thirdly, many parameter sets and their likelihood were used to create a likelihood-weighted probability distribution of the NTCP. It is concluded that for the type of dose response data used here, only a full likelihood analysis will produce reliable results. The often-used approximations, such as the usage of the covariance matrix, produce inconsistent confidence limits on both the parameter sets and the resulting NTCP values.

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

NASA Astrophysics Data System (ADS)

Sumarjaya, I. W.

2017-10-01

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

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,…

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

INFERRING THE ECCENTRICITY DISTRIBUTION

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

Hogg, David W.; Bovy, Jo; Myers, Adam D., E-mail: david.hogg@nyu.ed

2010-12-20

Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observables, a simple histogram of estimated eccentricities is not a good estimate of the true eccentricity distribution. Here, we develop and test a hierarchical probabilistic method for performing the relevant meta-analysis, that is, inferring the true eccentricity distribution, taking as input the likelihood functions for the individual star eccentricities, or samplings of the posterior probability distributions for the eccentricities (under a given, uninformative prior). The method is a simple implementationmore » of a hierarchical Bayesian model; it can also be seen as a kind of heteroscedastic deconvolution. It can be applied to any quantity measured with finite precision-other orbital parameters, or indeed any astronomical measurements of any kind, including magnitudes, distances, or photometric redshifts-so long as the measurements have been communicated as a likelihood function or a posterior sampling.« less

Improving and Evaluating Nested Sampling Algorithm for Marginal Likelihood Estimation

NASA Astrophysics Data System (ADS)

Ye, M.; Zeng, X.; Wu, J.; Wang, D.; Liu, J.

2016-12-01

With the growing impacts of climate change and human activities on the cycle of water resources, an increasing number of researches focus on the quantification of modeling uncertainty. Bayesian model averaging (BMA) provides a popular framework for quantifying conceptual model and parameter uncertainty. The ensemble prediction is generated by combining each plausible model's prediction, and each model is attached with a model weight which is determined by model's prior weight and marginal likelihood. Thus, the estimation of model's marginal likelihood is crucial for reliable and accurate BMA prediction. Nested sampling estimator (NSE) is a new proposed method for marginal likelihood estimation. The process of NSE is accomplished by searching the parameters' space from low likelihood area to high likelihood area gradually, and this evolution is finished iteratively via local sampling procedure. Thus, the efficiency of NSE is dominated by the strength of local sampling procedure. Currently, Metropolis-Hasting (M-H) algorithm is often used for local sampling. However, M-H is not an efficient sampling algorithm for high-dimensional or complicated parameter space. For improving the efficiency of NSE, it could be ideal to incorporate the robust and efficient sampling algorithm - DREAMzs into the local sampling of NSE. The comparison results demonstrated that the improved NSE could improve the efficiency of marginal likelihood estimation significantly. However, both improved and original NSEs suffer from heavy instability. In addition, the heavy computation cost of huge number of model executions is overcome by using an adaptive sparse grid surrogates.

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.

Multiple-Hit Parameter Estimation in Monolithic Detectors

PubMed Central

Barrett, Harrison H.; Lewellen, Tom K.; Miyaoka, Robert S.

2014-01-01

We examine a maximum-a-posteriori method for estimating the primary interaction position of gamma rays with multiple interaction sites (hits) in a monolithic detector. In assessing the performance of a multiple-hit estimator over that of a conventional one-hit estimator, we consider a few different detector and readout configurations of a 50-mm-wide square cerium-doped lutetium oxyorthosilicate block. For this study, we use simulated data from SCOUT, a Monte-Carlo tool for photon tracking and modeling scintillation- camera output. With this tool, we determine estimate bias and variance for a multiple-hit estimator and compare these with similar metrics for a one-hit maximum-likelihood estimator, which assumes full energy deposition in one hit. We also examine the effect of event filtering on these metrics; for this purpose, we use a likelihood threshold to reject signals that are not likely to have been produced under the assumed likelihood model. Depending on detector design, we observe a 1%–12% improvement of intrinsic resolution for a 1-or-2-hit estimator as compared with a 1-hit estimator. We also observe improved differentiation of photopeak events using a 1-or-2-hit estimator as compared with the 1-hit estimator; more than 6% of photopeak events that were rejected by likelihood filtering for the 1-hit estimator were accurately identified as photopeak events and positioned without loss of resolution by a 1-or-2-hit estimator; for PET, this equates to at least a 12% improvement in coincidence-detection efficiency with likelihood filtering applied. PMID:23193231

Maximum likelihood method for estimating airplane stability and control parameters from flight data in frequency domain

NASA Technical Reports Server (NTRS)

Klein, V.

1980-01-01

A frequency domain maximum likelihood method is developed for the estimation of airplane stability and control parameters from measured data. The model of an airplane is represented by a discrete-type steady state Kalman filter with time variables replaced by their Fourier series expansions. The likelihood function of innovations is formulated, and by its maximization with respect to unknown parameters the estimation algorithm is obtained. This algorithm is then simplified to the output error estimation method with the data in the form of transformed time histories, frequency response curves, or spectral and cross-spectral densities. The development is followed by a discussion on the equivalence of the cost function in the time and frequency domains, and on advantages and disadvantages of the frequency domain approach. The algorithm developed is applied in four examples to the estimation of longitudinal parameters of a general aviation airplane using computer generated and measured data in turbulent and still air. The cost functions in the time and frequency domains are shown to be equivalent; therefore, both approaches are complementary and not contradictory. Despite some computational advantages of parameter estimation in the frequency domain, this approach is limited to linear equations of motion with constant coefficients.

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

An Improved Nested Sampling Algorithm for Model Selection and Assessment

NASA Astrophysics Data System (ADS)

Zeng, X.; Ye, M.; Wu, J.; WANG, D.

2017-12-01

Multimodel strategy is a general approach for treating model structure uncertainty in recent researches. The unknown groundwater system is represented by several plausible conceptual models. Each alternative conceptual model is attached with a weight which represents the possibility of this model. In Bayesian framework, the posterior model weight is computed as the product of model prior weight and marginal likelihood (or termed as model evidence). As a result, estimating marginal likelihoods is crucial for reliable model selection and assessment in multimodel analysis. Nested sampling estimator (NSE) is a new proposed algorithm for marginal likelihood estimation. The implementation of NSE comprises searching the parameters' space from low likelihood area to high likelihood area gradually, and this evolution is finished iteratively via local sampling procedure. Thus, the efficiency of NSE is dominated by the strength of local sampling procedure. Currently, Metropolis-Hasting (M-H) algorithm and its variants are often used for local sampling in NSE. However, M-H is not an efficient sampling algorithm for high-dimensional or complex likelihood function. For improving the performance of NSE, it could be feasible to integrate more efficient and elaborated sampling algorithm - DREAMzs into the local sampling. In addition, in order to overcome the computation burden problem of large quantity of repeating model executions in marginal likelihood estimation, an adaptive sparse grid stochastic collocation method is used to build the surrogates for original groundwater model.

An Empirical Comparison of Heterogeneity Variance Estimators in 12,894 Meta-Analyses

ERIC Educational Resources Information Center

Langan, Dean; Higgins, Julian P. T.; Simmonds, Mark

2015-01-01

Heterogeneity in meta-analysis is most commonly estimated using a moment-based approach described by DerSimonian and Laird. However, this method has been shown to produce biased estimates. Alternative methods to estimate heterogeneity include the restricted maximum likelihood approach and those proposed by Paule and Mandel, Sidik and Jonkman, and…

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

NASA Astrophysics Data System (ADS)

Pan, Zhen; Anderes, Ethan; Knox, Lloyd

2018-05-01

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

Performance and separation occurrence of binary probit regression estimator using maximum likelihood method and Firths approach under different sample size

NASA Astrophysics Data System (ADS)

Lusiana, Evellin Dewi

2017-12-01

The parameters of binary probit regression model are commonly estimated by using Maximum Likelihood Estimation (MLE) method. However, MLE method has limitation if the binary data contains separation. Separation is the condition where there are one or several independent variables that exactly grouped the categories in binary response. It will result the estimators of MLE method become non-convergent, so that they cannot be used in modeling. One of the effort to resolve the separation is using Firths approach instead. This research has two aims. First, to identify the chance of separation occurrence in binary probit regression model between MLE method and Firths approach. Second, to compare the performance of binary probit regression model estimator that obtained by MLE method and Firths approach using RMSE criteria. Those are performed using simulation method and under different sample size. The results showed that the chance of separation occurrence in MLE method for small sample size is higher than Firths approach. On the other hand, for larger sample size, the probability decreased and relatively identic between MLE method and Firths approach. Meanwhile, Firths estimators have smaller RMSE than MLEs especially for smaller sample sizes. But for larger sample sizes, the RMSEs are not much different. It means that Firths estimators outperformed MLE estimator.

Using local multiplicity to improve effect estimation from a hypothesis-generating pharmacogenetics study.

PubMed

Zou, W; Ouyang, H

2016-02-01

We propose a multiple estimation adjustment (MEA) method to correct effect overestimation due to selection bias from a hypothesis-generating study (HGS) in pharmacogenetics. MEA uses a hierarchical Bayesian approach to model individual effect estimates from maximal likelihood estimation (MLE) in a region jointly and shrinks them toward the regional effect. Unlike many methods that model a fixed selection scheme, MEA capitalizes on local multiplicity independent of selection. We compared mean square errors (MSEs) in simulated HGSs from naive MLE, MEA and a conditional likelihood adjustment (CLA) method that model threshold selection bias. We observed that MEA effectively reduced MSE from MLE on null effects with or without selection, and had a clear advantage over CLA on extreme MLE estimates from null effects under lenient threshold selection in small samples, which are common among 'top' associations from a pharmacogenetics HGS.

A New Online Calibration Method Based on Lord's Bias-Correction.

PubMed

He, Yinhong; Chen, Ping; Li, Yong; Zhang, Shumei

2017-09-01

Online calibration technique has been widely employed to calibrate new items due to its advantages. Method A is the simplest online calibration method and has attracted many attentions from researchers recently. However, a key assumption of Method A is that it treats person-parameter estimates θ ^ s (obtained by maximum likelihood estimation [MLE]) as their true values θ s , thus the deviation of the estimated θ ^ s from their true values might yield inaccurate item calibration when the deviation is nonignorable. To improve the performance of Method A, a new method, MLE-LBCI-Method A, is proposed. This new method combines a modified Lord's bias-correction method (named as maximum likelihood estimation-Lord's bias-correction with iteration [MLE-LBCI]) with the original Method A in an effort to correct the deviation of θ ^ s which may adversely affect the item calibration precision. Two simulation studies were carried out to explore the performance of both MLE-LBCI and MLE-LBCI-Method A under several scenarios. Simulation results showed that MLE-LBCI could make a significant improvement over the ML ability estimates, and MLE-LBCI-Method A did outperform Method A in almost all experimental conditions.

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.

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.

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

Combining Ratio Estimation for Low Density Parity Check (LDPC) Coding

NASA Technical Reports Server (NTRS)

Mahmoud, Saad; Hi, Jianjun

2012-01-01

The Low Density Parity Check (LDPC) Code decoding algorithm make use of a scaled receive signal derived from maximizing the log-likelihood ratio of the received signal. The scaling factor (often called the combining ratio) in an AWGN channel is a ratio between signal amplitude and noise variance. Accurately estimating this ratio has shown as much as 0.6 dB decoding performance gain. This presentation briefly describes three methods for estimating the combining ratio: a Pilot-Guided estimation method, a Blind estimation method, and a Simulation-Based Look-Up table. The Pilot Guided Estimation method has shown that the maximum likelihood estimates of signal amplitude is the mean inner product of the received sequence and the known sequence, the attached synchronization marker (ASM) , and signal variance is the difference of the mean of the squared received sequence and the square of the signal amplitude. This method has the advantage of simplicity at the expense of latency since several frames worth of ASMs. The Blind estimation method s maximum likelihood estimator is the average of the product of the received signal with the hyperbolic tangent of the product combining ratio and the received signal. The root of this equation can be determined by an iterative binary search between 0 and 1 after normalizing the received sequence. This method has the benefit of requiring one frame of data to estimate the combining ratio which is good for faster changing channels compared to the previous method, however it is computationally expensive. The final method uses a look-up table based on prior simulated results to determine signal amplitude and noise variance. In this method the received mean signal strength is controlled to a constant soft decision value. The magnitude of the deviation is averaged over a predetermined number of samples. This value is referenced in a look up table to determine the combining ratio that prior simulation associated with the average magnitude of the deviation. This method is more complicated than the Pilot-Guided Method due to the gain control circuitry, but does not have the real-time computation complexity of the Blind Estimation method. Each of these methods can be used to provide an accurate estimation of the combining ratio, and the final selection of the estimation method depends on other design constraints.

Estimation of Time-Varying Pilot Model Parameters

NASA Technical Reports Server (NTRS)

Zaal, Peter M. T.; Sweet, Barbara T.

2011-01-01

Human control behavior is rarely completely stationary over time due to fatigue or loss of attention. In addition, there are many control tasks for which human operators need to adapt their control strategy to vehicle dynamics that vary in time. In previous studies on the identification of time-varying pilot control behavior wavelets were used to estimate the time-varying frequency response functions. However, the estimation of time-varying pilot model parameters was not considered. Estimating these parameters can be a valuable tool for the quantification of different aspects of human time-varying manual control. This paper presents two methods for the estimation of time-varying pilot model parameters, a two-step method using wavelets and a windowed maximum likelihood estimation method. The methods are evaluated using simulations of a closed-loop control task with time-varying pilot equalization and vehicle dynamics. Simulations are performed with and without remnant. Both methods give accurate results when no pilot remnant is present. The wavelet transform is very sensitive to measurement noise, resulting in inaccurate parameter estimates when considerable pilot remnant is present. Maximum likelihood estimation is less sensitive to pilot remnant, but cannot detect fast changes in pilot control behavior.

Local Intrinsic Dimension Estimation by Generalized Linear Modeling.

PubMed

Hino, Hideitsu; Fujiki, Jun; Akaho, Shotaro; Murata, Noboru

2017-07-01

We propose a method for intrinsic dimension estimation. By fitting the power of distance from an inspection point and the number of samples included inside a ball with a radius equal to the distance, to a regression model, we estimate the goodness of fit. Then, by using the maximum likelihood method, we estimate the local intrinsic dimension around the inspection point. The proposed method is shown to be comparable to conventional methods in global intrinsic dimension estimation experiments. Furthermore, we experimentally show that the proposed method outperforms a conventional local dimension estimation method.

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.

A New Monte Carlo Method for Estimating Marginal Likelihoods.

PubMed

Wang, Yu-Bo; Chen, Ming-Hui; Kuo, Lynn; Lewis, Paul O

2018-06-01

Evaluating the marginal likelihood in Bayesian analysis is essential for model selection. Estimators based on a single Markov chain Monte Carlo sample from the posterior distribution include the harmonic mean estimator and the inflated density ratio estimator. We propose a new class of Monte Carlo estimators based on this single Markov chain Monte Carlo sample. This class can be thought of as a generalization of the harmonic mean and inflated density ratio estimators using a partition weighted kernel (likelihood times prior). We show that our estimator is consistent and has better theoretical properties than the harmonic mean and inflated density ratio estimators. In addition, we provide guidelines on choosing optimal weights. Simulation studies were conducted to examine the empirical performance of the proposed estimator. We further demonstrate the desirable features of the proposed estimator with two real data sets: one is from a prostate cancer study using an ordinal probit regression model with latent variables; the other is for the power prior construction from two Eastern Cooperative Oncology Group phase III clinical trials using the cure rate survival model with similar objectives.

GRID-BASED EXPLORATION OF COSMOLOGICAL PARAMETER SPACE WITH SNAKE

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

Mikkelsen, K.; Næss, S. K.; Eriksen, H. K., E-mail: kristin.mikkelsen@astro.uio.no

2013-11-10

We present a fully parallelized grid-based parameter estimation algorithm for investigating multidimensional likelihoods called Snake, and apply it to cosmological parameter estimation. The basic idea is to map out the likelihood grid-cell by grid-cell according to decreasing likelihood, and stop when a certain threshold has been reached. This approach improves vastly on the 'curse of dimensionality' problem plaguing standard grid-based parameter estimation simply by disregarding grid cells with negligible likelihood. The main advantages of this method compared to standard Metropolis-Hastings Markov Chain Monte Carlo methods include (1) trivial extraction of arbitrary conditional distributions; (2) direct access to Bayesian evidences; (3)more » better sampling of the tails of the distribution; and (4) nearly perfect parallelization scaling. The main disadvantage is, as in the case of brute-force grid-based evaluation, a dependency on the number of parameters, N{sub par}. One of the main goals of the present paper is to determine how large N{sub par} can be, while still maintaining reasonable computational efficiency; we find that N{sub par} = 12 is well within the capabilities of the method. The performance of the code is tested by comparing cosmological parameters estimated using Snake and the WMAP-7 data with those obtained using CosmoMC, the current standard code in the field. We find fully consistent results, with similar computational expenses, but shorter wall time due to the perfect parallelization scheme.« less

Fast Component Pursuit for Large-Scale Inverse Covariance Estimation.

PubMed

Han, Lei; Zhang, Yu; Zhang, Tong

2016-08-01

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

Likelihood-based confidence intervals for estimating floods with given return periods

NASA Astrophysics Data System (ADS)

Martins, Eduardo Sávio P. R.; Clarke, Robin T.

1993-06-01

This paper discusses aspects of the calculation of likelihood-based confidence intervals for T-year floods, with particular reference to (1) the two-parameter gamma distribution; (2) the Gumbel distribution; (3) the two-parameter log-normal distribution, and other distributions related to the normal by Box-Cox transformations. Calculation of the confidence limits is straightforward using the Nelder-Mead algorithm with a constraint incorporated, although care is necessary to ensure convergence either of the Nelder-Mead algorithm, or of the Newton-Raphson calculation of maximum-likelihood estimates. Methods are illustrated using records from 18 gauging stations in the basin of the River Itajai-Acu, State of Santa Catarina, southern Brazil. A small and restricted simulation compared likelihood-based confidence limits with those given by use of the central limit theorem; for the same confidence probability, the confidence limits of the simulation were wider than those of the central limit theorem, which failed more frequently to contain the true quantile being estimated. The paper discusses possible applications of likelihood-based confidence intervals in other areas of hydrological analysis.

A matrix-based method of moments for fitting the multivariate random effects model for meta-analysis and meta-regression

PubMed Central

Jackson, Dan; White, Ian R; Riley, Richard D

2013-01-01

Multivariate meta-analysis is becoming more commonly used. Methods for fitting the multivariate random effects model include maximum likelihood, restricted maximum likelihood, Bayesian estimation and multivariate generalisations of the standard univariate method of moments. Here, we provide a new multivariate method of moments for estimating the between-study covariance matrix with the properties that (1) it allows for either complete or incomplete outcomes and (2) it allows for covariates through meta-regression. Further, for complete data, it is invariant to linear transformations. Our method reduces to the usual univariate method of moments, proposed by DerSimonian and Laird, in a single dimension. We illustrate our method and compare it with some of the alternatives using a simulation study and a real example. PMID:23401213

WEIGHTED LIKELIHOOD ESTIMATION UNDER TWO-PHASE SAMPLING

PubMed Central

Saegusa, Takumi; Wellner, Jon A.

2013-01-01

We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process tools are developed including a Glivenko–Cantelli theorem, a theorem for rates of convergence of M-estimators, and a Donsker theorem for the inverse probability weighted empirical processes under two-phase sampling and sampling without replacement at the second phase. Using these general results, we derive asymptotic distributions of the WLE of a finite-dimensional parameter in a general semiparametric model where an estimator of a nuisance parameter is estimable either at regular or nonregular rates. We illustrate these results and methods in the Cox model with right censoring and interval censoring. We compare the methods via their asymptotic variances under both sampling without replacement and the more usual (and easier to analyze) assumption of Bernoulli sampling at the second phase. PMID:24563559

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.

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.

Proportion estimation using prior cluster purities

NASA Technical Reports Server (NTRS)

Terrell, G. R. (Principal Investigator)

1980-01-01

The prior distribution of CLASSY component purities is studied, and this information incorporated into maximum likelihood crop proportion estimators. The method is tested on Transition Year spring small grain segments.

An alternative empirical likelihood method in missing response problems and causal inference.

PubMed

Ren, Kaili; Drummond, Christopher A; Brewster, Pamela S; Haller, Steven T; Tian, Jiang; Cooper, Christopher J; Zhang, Biao

2016-11-30

Missing responses are common problems in medical, social, and economic studies. When responses are missing at random, a complete case data analysis may result in biases. A popular debias method is inverse probability weighting proposed by Horvitz and Thompson. To improve efficiency, Robins et al. proposed an augmented inverse probability weighting method. The augmented inverse probability weighting estimator has a double-robustness property and achieves the semiparametric efficiency lower bound when the regression model and propensity score model are both correctly specified. In this paper, we introduce an empirical likelihood-based estimator as an alternative to Qin and Zhang (2007). Our proposed estimator is also doubly robust and locally efficient. Simulation results show that the proposed estimator has better performance when the propensity score is correctly modeled. Moreover, the proposed method can be applied in the estimation of average treatment effect in observational causal inferences. Finally, we apply our method to an observational study of smoking, using data from the Cardiovascular Outcomes in Renal Atherosclerotic Lesions clinical trial. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Comparing Three Estimation Methods for the Three-Parameter Logistic IRT Model

ERIC Educational Resources Information Center

Lamsal, Sunil

2015-01-01

Different estimation procedures have been developed for the unidimensional three-parameter item response theory (IRT) model. These techniques include the marginal maximum likelihood estimation, the fully Bayesian estimation using Markov chain Monte Carlo simulation techniques, and the Metropolis-Hastings Robbin-Monro estimation. With each…

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

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

Quantitative PET Imaging in Drug Development: Estimation of Target Occupancy.

PubMed

Naganawa, Mika; Gallezot, Jean-Dominique; Rossano, Samantha; Carson, Richard E

2017-12-11

Positron emission tomography, an imaging tool using radiolabeled tracers in humans and preclinical species, has been widely used in recent years in drug development, particularly in the central nervous system. One important goal of PET in drug development is assessing the occupancy of various molecular targets (e.g., receptors, transporters, enzymes) by exogenous drugs. The current linear mathematical approaches used to determine occupancy using PET imaging experiments are presented. These algorithms use results from multiple regions with different target content in two scans, a baseline (pre-drug) scan and a post-drug scan. New mathematical estimation approaches to determine target occupancy, using maximum likelihood, are presented. A major challenge in these methods is the proper definition of the covariance matrix of the regional binding measures, accounting for different variance of the individual regional measures and their nonzero covariance, factors that have been ignored by conventional methods. The novel methods are compared to standard methods using simulation and real human occupancy data. The simulation data showed the expected reduction in variance and bias using the proper maximum likelihood methods, when the assumptions of the estimation method matched those in simulation. Between-method differences for data from human occupancy studies were less obvious, in part due to small dataset sizes. These maximum likelihood methods form the basis for development of improved PET covariance models, in order to minimize bias and variance in PET occupancy studies.

Genealogical Working Distributions for Bayesian Model Testing with Phylogenetic Uncertainty

PubMed Central

Baele, Guy; Lemey, Philippe; Suchard, Marc A.

2016-01-01

Marginal likelihood estimates to compare models using Bayes factors frequently accompany Bayesian phylogenetic inference. Approaches to estimate marginal likelihoods have garnered increased attention over the past decade. In particular, the introduction of path sampling (PS) and stepping-stone sampling (SS) into Bayesian phylogenetics has tremendously improved the accuracy of model selection. These sampling techniques are now used to evaluate complex evolutionary and population genetic models on empirical data sets, but considerable computational demands hamper their widespread adoption. Further, when very diffuse, but proper priors are specified for model parameters, numerical issues complicate the exploration of the priors, a necessary step in marginal likelihood estimation using PS or SS. To avoid such instabilities, generalized SS (GSS) has recently been proposed, introducing the concept of “working distributions” to facilitate—or shorten—the integration process that underlies marginal likelihood estimation. However, the need to fix the tree topology currently limits GSS in a coalescent-based framework. Here, we extend GSS by relaxing the fixed underlying tree topology assumption. To this purpose, we introduce a “working” distribution on the space of genealogies, which enables estimating marginal likelihoods while accommodating phylogenetic uncertainty. We propose two different “working” distributions that help GSS to outperform PS and SS in terms of accuracy when comparing demographic and evolutionary models applied to synthetic data and real-world examples. Further, we show that the use of very diffuse priors can lead to a considerable overestimation in marginal likelihood when using PS and SS, while still retrieving the correct marginal likelihood using both GSS approaches. The methods used in this article are available in BEAST, a powerful user-friendly software package to perform Bayesian evolutionary analyses. PMID:26526428

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.

Generalized Likelihood Uncertainty Estimation (GLUE) Using Multi-Optimization Algorithm as Sampling Method

NASA Astrophysics Data System (ADS)

Wang, Z.

2015-12-01

For decades, distributed and lumped hydrological models have furthered our understanding of hydrological system. The development of hydrological simulation in large scale and high precision elaborated the spatial descriptions and hydrological behaviors. Meanwhile, the new trend is also followed by the increment of model complexity and number of parameters, which brings new challenges of uncertainty quantification. Generalized Likelihood Uncertainty Estimation (GLUE) has been widely used in uncertainty analysis for hydrological models referring to Monte Carlo method coupled with Bayesian estimation. However, the stochastic sampling method of prior parameters adopted by GLUE appears inefficient, especially in high dimensional parameter space. The heuristic optimization algorithms utilizing iterative evolution show better convergence speed and optimality-searching performance. In light of the features of heuristic optimization algorithms, this study adopted genetic algorithm, differential evolution, shuffled complex evolving algorithm to search the parameter space and obtain the parameter sets of large likelihoods. Based on the multi-algorithm sampling, hydrological model uncertainty analysis is conducted by the typical GLUE framework. To demonstrate the superiority of the new method, two hydrological models of different complexity are examined. The results shows the adaptive method tends to be efficient in sampling and effective in uncertainty analysis, providing an alternative path for uncertainty quantilization.

MrBayes tgMC3++: A High Performance and Resource-Efficient GPU-Oriented Phylogenetic Analysis Method.

PubMed

Ling, Cheng; Hamada, Tsuyoshi; Gao, Jingyang; Zhao, Guoguang; Sun, Donghong; Shi, Weifeng

2016-01-01

MrBayes is a widespread phylogenetic inference tool harnessing empirical evolutionary models and Bayesian statistics. However, the computational cost on the likelihood estimation is very expensive, resulting in undesirably long execution time. Although a number of multi-threaded optimizations have been proposed to speed up MrBayes, there are bottlenecks that severely limit the GPU thread-level parallelism of likelihood estimations. This study proposes a high performance and resource-efficient method for GPU-oriented parallelization of likelihood estimations. Instead of having to rely on empirical programming, the proposed novel decomposition storage model implements high performance data transfers implicitly. In terms of performance improvement, a speedup factor of up to 178 can be achieved on the analysis of simulated datasets by four Tesla K40 cards. In comparison to the other publicly available GPU-oriented MrBayes, the tgMC 3 ++ method (proposed herein) outperforms the tgMC 3 (v1.0), nMC 3 (v2.1.1) and oMC 3 (v1.00) methods by speedup factors of up to 1.6, 1.9 and 2.9, respectively. Moreover, tgMC 3 ++ supports more evolutionary models and gamma categories, which previous GPU-oriented methods fail to take into analysis.

Objectively combining AR5 instrumental period and paleoclimate climate sensitivity evidence

NASA Astrophysics Data System (ADS)

Lewis, Nicholas; Grünwald, Peter

2018-03-01

Combining instrumental period evidence regarding equilibrium climate sensitivity with largely independent paleoclimate proxy evidence should enable a more constrained sensitivity estimate to be obtained. Previous, subjective Bayesian approaches involved selection of a prior probability distribution reflecting the investigators' beliefs about climate sensitivity. Here a recently developed approach employing two different statistical methods—objective Bayesian and frequentist likelihood-ratio—is used to combine instrumental period and paleoclimate evidence based on data presented and assessments made in the IPCC Fifth Assessment Report. Probabilistic estimates from each source of evidence are represented by posterior probability density functions (PDFs) of physically-appropriate form that can be uniquely factored into a likelihood function and a noninformative prior distribution. The three-parameter form is shown accurately to fit a wide range of estimated climate sensitivity PDFs. The likelihood functions relating to the probabilistic estimates from the two sources are multiplicatively combined and a prior is derived that is noninformative for inference from the combined evidence. A posterior PDF that incorporates the evidence from both sources is produced using a single-step approach, which avoids the order-dependency that would arise if Bayesian updating were used. Results are compared with an alternative approach using the frequentist signed root likelihood ratio method. Results from these two methods are effectively identical, and provide a 5-95% range for climate sensitivity of 1.1-4.05 K (median 1.87 K).

Nonlinear phase noise tolerance for coherent optical systems using soft-decision-aided ML carrier phase estimation enhanced with constellation partitioning

NASA Astrophysics Data System (ADS)

Li, Yan; Wu, Mingwei; Du, Xinwei; Xu, Zhuoran; Gurusamy, Mohan; Yu, Changyuan; Kam, Pooi-Yuen

2018-02-01

A novel soft-decision-aided maximum likelihood (SDA-ML) carrier phase estimation method and its simplified version, the decision-aided and soft-decision-aided maximum likelihood (DA-SDA-ML) methods are tested in a nonlinear phase noise-dominant channel. The numerical performance results show that both the SDA-ML and DA-SDA-ML methods outperform the conventional DA-ML in systems with constant-amplitude modulation formats. In addition, modified algorithms based on constellation partitioning are proposed. With partitioning, the modified SDA-ML and DA-SDA-ML are shown to be useful for compensating the nonlinear phase noise in multi-level modulation systems.

Effects of Content Balancing and Item Selection Method on Ability Estimation in Computerized Adaptive Tests

ERIC Educational Resources Information Center

Sahin, Alper; Ozbasi, Durmus

2017-01-01

Purpose: This study aims to reveal effects of content balancing and item selection method on ability estimation in computerized adaptive tests by comparing Fisher's maximum information (FMI) and likelihood weighted information (LWI) methods. Research Methods: Four groups of examinees (250, 500, 750, 1000) and a bank of 500 items with 10 different…

Practical aspects of a maximum likelihood estimation method to extract stability and control derivatives from flight data

NASA Technical Reports Server (NTRS)

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

1976-01-01

A maximum likelihood estimation method was applied to flight data and procedures to facilitate the routine analysis of a large amount of flight data were described. Techniques that can be used to obtain stability and control derivatives from aircraft maneuvers that are less than ideal for this purpose are described. The techniques involve detecting and correcting the effects of dependent or nearly dependent variables, structural vibration, data drift, inadequate instrumentation, and difficulties with the data acquisition system and the mathematical model. The use of uncertainty levels and multiple maneuver analysis also proved to be useful in improving the quality of the estimated coefficients. The procedures used for editing the data and for overall analysis are also discussed.

The Least-Squares Estimation of Latent Trait Variables.

ERIC Educational Resources Information Center

Tatsuoka, Kikumi

This paper presents a new method for estimating a given latent trait variable by the least-squares approach. The beta weights are obtained recursively with the help of Fourier series and expressed as functions of item parameters of response curves. The values of the latent trait variable estimated by this method and by maximum likelihood method…

Empirical Likelihood-Based Estimation of the Treatment Effect in a Pretest-Posttest Study.

PubMed

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

2008-09-01

The pretest-posttest study design is commonly used in medical and social science research to assess the effect of a treatment or an intervention. Recently, interest has been rising in developing inference procedures that improve efficiency while relaxing assumptions used in the pretest-posttest data analysis, especially when the posttest measurement might be missing. In this article we propose a semiparametric estimation procedure based on empirical likelihood (EL) that incorporates the common baseline covariate information to improve efficiency. The proposed method also yields an asymptotically unbiased estimate of the response distribution. Thus functions of the response distribution, such as the median, can be estimated straightforwardly, and the EL method can provide a more appealing estimate of the treatment effect for skewed data. We show that, compared with existing methods, the proposed EL estimator has appealing theoretical properties, especially when the working model for the underlying relationship between the pretest and posttest measurements is misspecified. A series of simulation studies demonstrates that the EL-based estimator outperforms its competitors when the working model is misspecified and the data are missing at random. We illustrate the methods by analyzing data from an AIDS clinical trial (ACTG 175).

Empirical Likelihood-Based Estimation of the Treatment Effect in a Pretest–Posttest Study

PubMed Central

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

2013-01-01

The pretest–posttest study design is commonly used in medical and social science research to assess the effect of a treatment or an intervention. Recently, interest has been rising in developing inference procedures that improve efficiency while relaxing assumptions used in the pretest–posttest data analysis, especially when the posttest measurement might be missing. In this article we propose a semiparametric estimation procedure based on empirical likelihood (EL) that incorporates the common baseline covariate information to improve efficiency. The proposed method also yields an asymptotically unbiased estimate of the response distribution. Thus functions of the response distribution, such as the median, can be estimated straightforwardly, and the EL method can provide a more appealing estimate of the treatment effect for skewed data. We show that, compared with existing methods, the proposed EL estimator has appealing theoretical properties, especially when the working model for the underlying relationship between the pretest and posttest measurements is misspecified. A series of simulation studies demonstrates that the EL-based estimator outperforms its competitors when the working model is misspecified and the data are missing at random. We illustrate the methods by analyzing data from an AIDS clinical trial (ACTG 175). PMID:23729942

New method to incorporate Type B uncertainty into least-squares procedures in radionuclide metrology.

PubMed

Han, Jubong; Lee, K B; Lee, Jong-Man; Park, Tae Soon; Oh, J S; Oh, Pil-Jei

2016-03-01

We discuss a new method to incorporate Type B uncertainty into least-squares procedures. The new method is based on an extension of the likelihood function from which a conventional least-squares function is derived. The extended likelihood function is the product of the original likelihood function with additional PDFs (Probability Density Functions) that characterize the Type B uncertainties. The PDFs are considered to describe one's incomplete knowledge on correction factors being called nuisance parameters. We use the extended likelihood function to make point and interval estimations of parameters in the basically same way as the least-squares function used in the conventional least-squares method is derived. Since the nuisance parameters are not of interest and should be prevented from appearing in the final result, we eliminate such nuisance parameters by using the profile likelihood. As an example, we present a case study for a linear regression analysis with a common component of Type B uncertainty. In this example we compare the analysis results obtained from using our procedure with those from conventional methods. Copyright © 2015. Published by Elsevier Ltd.

Evaluation of a mark-recapture method for estimating mortality and migration rates of stratified populations

USGS Publications Warehouse

Dorazio, R.M.; Rago, P.J.

1991-01-01

We simulated mark–recapture experiments to evaluate a method for estimating fishing mortality and migration rates of populations stratified at release and recovery. When fish released in two or more strata were recovered from different recapture strata in nearly the same proportions, conditional recapture probabilities were estimated outside the [0, 1] interval. The maximum likelihood estimates tended to be biased and imprecise when the patterns of recaptures produced extremely "flat" likelihood surfaces. Absence of bias was not guaranteed, however, in experiments where recapture rates could be estimated within the [0, 1] interval. Inadequate numbers of tag releases and recoveries also produced biased estimates, although the bias was easily detected by the high sampling variability of the estimates. A stratified tag–recapture experiment with sockeye salmon (Oncorhynchus nerka) was used to demonstrate procedures for analyzing data that produce biased estimates of recapture probabilities. An estimator was derived to examine the sensitivity of recapture rate estimates to assumed differences in natural and tagging mortality, tag loss, and incomplete reporting of tag recoveries.

Multifrequency InSAR height reconstruction through maximum likelihood estimation of local planes parameters.

PubMed

Pascazio, Vito; Schirinzi, Gilda

2002-01-01

In this paper, a technique that is able to reconstruct highly sloped and discontinuous terrain height profiles, starting from multifrequency wrapped phase acquired by interferometric synthetic aperture radar (SAR) systems, is presented. We propose an innovative unwrapping method, based on a maximum likelihood estimation technique, which uses multifrequency independent phase data, obtained by filtering the interferometric SAR raw data pair through nonoverlapping band-pass filters, and approximating the unknown surface by means of local planes. Since the method does not exploit the phase gradient, it assures the uniqueness of the solution, even in the case of highly sloped or piecewise continuous elevation patterns with strong discontinuities.

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics.

PubMed

Arampatzis, Georgios; Katsoulakis, Markos A; Rey-Bellet, Luc

2016-03-14

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

NASA Astrophysics Data System (ADS)

Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc

2016-03-01

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

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

Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc

2016-03-14

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systemsmore » with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.« less

Paule‐Mandel estimators for network meta‐analysis with random inconsistency effects

PubMed Central

Veroniki, Areti Angeliki; Law, Martin; Tricco, Andrea C.; Baker, Rose

2017-01-01

Network meta‐analysis is used to simultaneously compare multiple treatments in a single analysis. However, network meta‐analyses may exhibit inconsistency, where direct and different forms of indirect evidence are not in agreement with each other, even after allowing for between‐study heterogeneity. Models for network meta‐analysis with random inconsistency effects have the dual aim of allowing for inconsistencies and estimating average treatment effects across the whole network. To date, two classical estimation methods for fitting this type of model have been developed: a method of moments that extends DerSimonian and Laird's univariate method and maximum likelihood estimation. However, the Paule and Mandel estimator is another recommended classical estimation method for univariate meta‐analysis. In this paper, we extend the Paule and Mandel method so that it can be used to fit models for network meta‐analysis with random inconsistency effects. We apply all three estimation methods to a variety of examples that have been used previously and we also examine a challenging new dataset that is highly heterogenous. We perform a simulation study based on this new example. We find that the proposed Paule and Mandel method performs satisfactorily and generally better than the previously proposed method of moments because it provides more accurate inferences. Furthermore, the Paule and Mandel method possesses some advantages over likelihood‐based methods because it is both semiparametric and requires no convergence diagnostics. Although restricted maximum likelihood estimation remains the gold standard, the proposed methodology is a fully viable alternative to this and other estimation methods. PMID:28585257

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.

Estimating the Parameters of the Beta-Binomial Distribution.

ERIC Educational Resources Information Center

Wilcox, Rand R.

1979-01-01

For some situations the beta-binomial distribution might be used to describe the marginal distribution of test scores for a particular population of examinees. Several different methods of approximating the maximum likelihood estimate were investigated, and it was found that the Newton-Raphson method should be used when it yields admissable…

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.…

On Correlated-noise Analyses Applied to Exoplanet Light Curves

NASA Astrophysics Data System (ADS)

Cubillos, Patricio; Harrington, Joseph; Loredo, Thomas J.; Lust, Nate B.; Blecic, Jasmina; Stemm, Madison

2017-01-01

Time-correlated noise is a significant source of uncertainty when modeling exoplanet light-curve data. A correct assessment of correlated noise is fundamental to determine the true statistical significance of our findings. Here, we review three of the most widely used correlated-noise estimators in the exoplanet field, the time-averaging, residual-permutation, and wavelet-likelihood methods. We argue that the residual-permutation method is unsound in estimating the uncertainty of parameter estimates. We thus recommend to refrain from this method altogether. We characterize the behavior of the time averaging’s rms-versus-bin-size curves at bin sizes similar to the total observation duration, which may lead to underestimated uncertainties. For the wavelet-likelihood method, we note errors in the published equations and provide a list of corrections. We further assess the performance of these techniques by injecting and retrieving eclipse signals into synthetic and real Spitzer light curves, analyzing the results in terms of the relative-accuracy and coverage-fraction statistics. Both the time-averaging and wavelet-likelihood methods significantly improve the estimate of the eclipse depth over a white-noise analysis (a Markov-chain Monte Carlo exploration assuming uncorrelated noise). However, the corrections are not perfect when retrieving the eclipse depth from Spitzer data sets, these methods covered the true (injected) depth within the 68% credible region in only ˜45%-65% of the trials. Lastly, we present our open-source model-fitting tool, Multi-Core Markov-Chain Monte Carlo (MC3). This package uses Bayesian statistics to estimate the best-fitting values and the credible regions for the parameters for a (user-provided) model. MC3 is a Python/C code, available at https://github.com/pcubillos/MCcubed.

Semiparametric time-to-event modeling in the presence of a latent progression event.

PubMed

Rice, John D; Tsodikov, Alex

2017-06-01

In cancer research, interest frequently centers on factors influencing a latent event that must precede a terminal event. In practice it is often impossible to observe the latent event precisely, making inference about this process difficult. To address this problem, we propose a joint model for the unobserved time to the latent and terminal events, with the two events linked by the baseline hazard. Covariates enter the model parametrically as linear combinations that multiply, respectively, the hazard for the latent event and the hazard for the terminal event conditional on the latent one. We derive the partial likelihood estimators for this problem assuming the latent event is observed, and propose a profile likelihood-based method for estimation when the latent event is unobserved. The baseline hazard in this case is estimated nonparametrically using the EM algorithm, which allows for closed-form Breslow-type estimators at each iteration, bringing improved computational efficiency and stability compared with maximizing the marginal likelihood directly. We present simulation studies to illustrate the finite-sample properties of the method; its use in practice is demonstrated in the analysis of a prostate cancer data set. © 2016, The International Biometric Society.

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

An architecture for efficient gravitational wave parameter estimation with multimodal linear surrogate models

NASA Astrophysics Data System (ADS)

O'Shaughnessy, Richard; Blackman, Jonathan; Field, Scott E.

2017-07-01

The recent direct observation of gravitational waves has further emphasized the desire for fast, low-cost, and accurate methods to infer the parameters of gravitational wave sources. Due to expense in waveform generation and data handling, the cost of evaluating the likelihood function limits the computational performance of these calculations. Building on recently developed surrogate models and a novel parameter estimation pipeline, we show how to quickly generate the likelihood function as an analytic, closed-form expression. Using a straightforward variant of a production-scale parameter estimation code, we demonstrate our method using surrogate models of effective-one-body and numerical relativity waveforms. Our study is the first time these models have been used for parameter estimation and one of the first ever parameter estimation calculations with multi-modal numerical relativity waveforms, which include all \\ell ≤slant 4 modes. Our grid-free method enables rapid parameter estimation for any waveform with a suitable reduced-order model. The methods described in this paper may also find use in other data analysis studies, such as vetting coincident events or the computation of the coalescing-compact-binary detection statistic.

Improving estimates of genetic maps: a meta-analysis-based approach.

PubMed

Stewart, William C L

2007-07-01

Inaccurate genetic (or linkage) maps can reduce the power to detect linkage, increase type I error, and distort haplotype and relationship inference. To improve the accuracy of existing maps, I propose a meta-analysis-based method that combines independent map estimates into a single estimate of the linkage map. The method uses the variance of each independent map estimate to combine them efficiently, whether the map estimates use the same set of markers or not. As compared with a joint analysis of the pooled genotype data, the proposed method is attractive for three reasons: (1) it has comparable efficiency to the maximum likelihood map estimate when the pooled data are homogeneous; (2) relative to existing map estimation methods, it can have increased efficiency when the pooled data are heterogeneous; and (3) it avoids the practical difficulties of pooling human subjects data. On the basis of simulated data modeled after two real data sets, the proposed method can reduce the sampling variation of linkage maps commonly used in whole-genome linkage scans. Furthermore, when the independent map estimates are also maximum likelihood estimates, the proposed method performs as well as or better than when they are estimated by the program CRIMAP. Since variance estimates of maps may not always be available, I demonstrate the feasibility of three different variance estimators. Overall, the method should prove useful to investigators who need map positions for markers not contained in publicly available maps, and to those who wish to minimize the negative effects of inaccurate maps. Copyright 2007 Wiley-Liss, Inc.

A parametric method for determining the number of signals in narrow-band direction finding

NASA Astrophysics Data System (ADS)

Wu, Qiang; Fuhrmann, Daniel R.

1991-08-01

A novel and more accurate method to determine the number of signals in the multisource direction finding problem is developed. The information-theoretic criteria of Yin and Krishnaiah (1988) are applied to a set of quantities which are evaluated from the log-likelihood function. Based on proven asymptotic properties of the maximum likelihood estimation, these quantities have the properties required by the criteria. Since the information-theoretic criteria use these quantities instead of the eigenvalues of the estimated correlation matrix, this approach possesses the advantage of not requiring a subjective threshold, and also provides higher performance than when eigenvalues are used. Simulation results are presented and compared to those obtained from the nonparametric method given by Wax and Kailath (1985).

Systems identification using a modified Newton-Raphson method: A FORTRAN program

NASA Technical Reports Server (NTRS)

Taylor, L. W., Jr.; Iliff, K. W.

1972-01-01

A FORTRAN program is offered which computes a maximum likelihood estimate of the parameters of any linear, constant coefficient, state space model. For the case considered, the maximum likelihood estimate can be identical to that which minimizes simultaneously the weighted mean square difference between the computed and measured response of a system and the weighted square of the difference between the estimated and a priori parameter values. A modified Newton-Raphson or quasilinearization method is used to perform the minimization which typically requires several iterations. A starting technique is used which insures convergence for any initial values of the unknown parameters. The program and its operation are described in sufficient detail to enable the user to apply the program to his particular problem with a minimum of difficulty.

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.

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.

The Relation between Factor Score Estimates, Image Scores, and Principal Component Scores

ERIC Educational Resources Information Center

Velicer, Wayne F.

1976-01-01

Investigates the relation between factor score estimates, principal component scores, and image scores. The three methods compared are maximum likelihood factor analysis, principal component analysis, and a variant of rescaled image analysis. (RC)

Score Estimating Equations from Embedded Likelihood Functions under Accelerated Failure Time Model

PubMed Central

NING, JING; QIN, JING; SHEN, YU

2014-01-01

SUMMARY The semiparametric accelerated failure time (AFT) model is one of the most popular models for analyzing time-to-event outcomes. One appealing feature of the AFT model is that the observed failure time data can be transformed to identically independent distributed random variables without covariate effects. We describe a class of estimating equations based on the score functions for the transformed data, which are derived from the full likelihood function under commonly used semiparametric models such as the proportional hazards or proportional odds model. The methods of estimating regression parameters under the AFT model can be applied to traditional right-censored survival data as well as more complex time-to-event data subject to length-biased sampling. We establish the asymptotic properties and evaluate the small sample performance of the proposed estimators. We illustrate the proposed methods through applications in two examples. PMID:25663727

Methods for fitting a parametric probability distribution to most probable number data.

PubMed

Williams, Michael S; Ebel, Eric D

2012-07-02

Every year hundreds of thousands, if not millions, of samples are collected and analyzed to assess microbial contamination in food and water. The concentration of pathogenic organisms at the end of the production process is low for most commodities, so a highly sensitive screening test is used to determine whether the organism of interest is present in a sample. In some applications, samples that test positive are subjected to quantitation. The most probable number (MPN) technique is a common method to quantify the level of contamination in a sample because it is able to provide estimates at low concentrations. This technique uses a series of dilution count experiments to derive estimates of the concentration of the microorganism of interest. An application for these data is food-safety risk assessment, where the MPN concentration estimates can be fitted to a parametric distribution to summarize the range of potential exposures to the contaminant. Many different methods (e.g., substitution methods, maximum likelihood and regression on order statistics) have been proposed to fit microbial contamination data to a distribution, but the development of these methods rarely considers how the MPN technique influences the choice of distribution function and fitting method. An often overlooked aspect when applying these methods is whether the data represent actual measurements of the average concentration of microorganism per milliliter or the data are real-valued estimates of the average concentration, as is the case with MPN data. In this study, we propose two methods for fitting MPN data to a probability distribution. The first method uses a maximum likelihood estimator that takes average concentration values as the data inputs. The second is a Bayesian latent variable method that uses the counts of the number of positive tubes at each dilution to estimate the parameters of the contamination distribution. The performance of the two fitting methods is compared for two data sets that represent Salmonella and Campylobacter concentrations on chicken carcasses. The results demonstrate a bias in the maximum likelihood estimator that increases with reductions in average concentration. The Bayesian method provided unbiased estimates of the concentration distribution parameters for all data sets. We provide computer code for the Bayesian fitting method. Published by Elsevier B.V.

An Investigation of the Standard Errors of Expected A Posteriori Ability Estimates.

ERIC Educational Resources Information Center

De Ayala, R. J.; And Others

Expected a posteriori has a number of advantages over maximum likelihood estimation or maximum a posteriori (MAP) estimation methods. These include ability estimates (thetas) for all response patterns, less regression towards the mean than MAP ability estimates, and a lower average squared error. R. D. Bock and R. J. Mislevy (1982) state that the…

Determining the accuracy of maximum likelihood parameter estimates with colored residuals

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.; Klein, Vladislav

1994-01-01

An important part of building high fidelity mathematical models based on measured data is calculating the accuracy associated with statistical estimates of the model parameters. Indeed, without some idea of the accuracy of parameter estimates, the estimates themselves have limited value. In this work, an expression based on theoretical analysis was developed to properly compute parameter accuracy measures for maximum likelihood estimates with colored residuals. This result is important because experience from the analysis of measured data reveals that the residuals from maximum likelihood estimation are almost always colored. The calculations involved can be appended to conventional maximum likelihood estimation algorithms. Simulated data runs were used to show that the parameter accuracy measures computed with this technique accurately reflect the quality of the parameter estimates from maximum likelihood estimation without the need for analysis of the output residuals in the frequency domain or heuristically determined multiplication factors. The result is general, although the application studied here is maximum likelihood estimation of aerodynamic model parameters from flight test data.

Two new methods to fit models for network meta-analysis with random inconsistency effects.

PubMed

Law, Martin; Jackson, Dan; Turner, Rebecca; Rhodes, Kirsty; Viechtbauer, Wolfgang

2016-07-28

Meta-analysis is a valuable tool for combining evidence from multiple studies. Network meta-analysis is becoming more widely used as a means to compare multiple treatments in the same analysis. However, a network meta-analysis may exhibit inconsistency, whereby the treatment effect estimates do not agree across all trial designs, even after taking between-study heterogeneity into account. We propose two new estimation methods for network meta-analysis models with random inconsistency effects. The model we consider is an extension of the conventional random-effects model for meta-analysis to the network meta-analysis setting and allows for potential inconsistency using random inconsistency effects. Our first new estimation method uses a Bayesian framework with empirically-based prior distributions for both the heterogeneity and the inconsistency variances. We fit the model using importance sampling and thereby avoid some of the difficulties that might be associated with using Markov Chain Monte Carlo (MCMC). However, we confirm the accuracy of our importance sampling method by comparing the results to those obtained using MCMC as the gold standard. The second new estimation method we describe uses a likelihood-based approach, implemented in the metafor package, which can be used to obtain (restricted) maximum-likelihood estimates of the model parameters and profile likelihood confidence intervals of the variance components. We illustrate the application of the methods using two contrasting examples. The first uses all-cause mortality as an outcome, and shows little evidence of between-study heterogeneity or inconsistency. The second uses "ear discharge" as an outcome, and exhibits substantial between-study heterogeneity and inconsistency. Both new estimation methods give results similar to those obtained using MCMC. The extent of heterogeneity and inconsistency should be assessed and reported in any network meta-analysis. Our two new methods can be used to fit models for network meta-analysis with random inconsistency effects. They are easily implemented using the accompanying R code in the Additional file 1. Using these estimation methods, the extent of inconsistency can be assessed and reported.

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.

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.

Scanning linear estimation: improvements over region of interest (ROI) methods

NASA Astrophysics Data System (ADS)

Kupinski, Meredith K.; Clarkson, Eric W.; Barrett, Harrison H.

2013-03-01

In tomographic medical imaging, a signal activity is typically estimated by summing voxels from a reconstructed image. We introduce an alternative estimation scheme that operates on the raw projection data and offers a substantial improvement, as measured by the ensemble mean-square error (EMSE), when compared to using voxel values from a maximum-likelihood expectation-maximization (MLEM) reconstruction. The scanning-linear (SL) estimator operates on the raw projection data and is derived as a special case of maximum-likelihood estimation with a series of approximations to make the calculation tractable. The approximated likelihood accounts for background randomness, measurement noise and variability in the parameters to be estimated. When signal size and location are known, the SL estimate of signal activity is unbiased, i.e. the average estimate equals the true value. By contrast, unpredictable bias arising from the null functions of the imaging system affect standard algorithms that operate on reconstructed data. The SL method is demonstrated for two different tasks: (1) simultaneously estimating a signal’s size, location and activity; (2) for a fixed signal size and location, estimating activity. Noisy projection data are realistically simulated using measured calibration data from the multi-module multi-resolution small-animal SPECT imaging system. For both tasks, the same set of images is reconstructed using the MLEM algorithm (80 iterations), and the average and maximum values within the region of interest (ROI) are calculated for comparison. This comparison shows dramatic improvements in EMSE for the SL estimates. To show that the bias in ROI estimates affects not only absolute values but also relative differences, such as those used to monitor the response to therapy, the activity estimation task is repeated for three different signal sizes.

Methods for estimating drought streamflow probabilities for Virginia streams

USGS Publications Warehouse

Austin, Samuel H.

2014-01-01

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

Robust Gaussian Graphical Modeling via l1 Penalization

PubMed Central

Sun, Hokeun; Li, Hongzhe

2012-01-01

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

Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes.

PubMed

Hudson, H M; Ma, J; Green, P

1994-01-01

Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fisher's method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.

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…

Using an EM Covariance Matrix to Estimate Structural Equation Models with Missing Data: Choosing an Adjusted Sample Size to Improve the Accuracy of Inferences

ERIC Educational Resources Information Center

Enders, Craig K.; Peugh, James L.

2004-01-01

Two methods, direct maximum likelihood (ML) and the expectation maximization (EM) algorithm, can be used to obtain ML parameter estimates for structural equation models with missing data (MD). Although the 2 methods frequently produce identical parameter estimates, it may be easier to satisfy missing at random assumptions using EM. However, no…

Model selection and parameter estimation in structural dynamics using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Ben Abdessalem, Anis; Dervilis, Nikolaos; Wagg, David; Worden, Keith

2018-01-01

This paper will introduce the use of the approximate Bayesian computation (ABC) algorithm for model selection and parameter estimation in structural dynamics. ABC is a likelihood-free method typically used when the likelihood function is either intractable or cannot be approached in a closed form. To circumvent the evaluation of the likelihood function, simulation from a forward model is at the core of the ABC algorithm. The algorithm offers the possibility to use different metrics and summary statistics representative of the data to carry out Bayesian inference. The efficacy of the algorithm in structural dynamics is demonstrated through three different illustrative examples of nonlinear system identification: cubic and cubic-quintic models, the Bouc-Wen model and the Duffing oscillator. The obtained results suggest that ABC is a promising alternative to deal with model selection and parameter estimation issues, specifically for systems with complex behaviours.

Determination of stability and control parameters of a light airplane from flight data using two estimation methods. [equation error and maximum likelihood methods

NASA Technical Reports Server (NTRS)

Klein, V.

1979-01-01

Two identification methods, the equation error method and the output error method, are used to estimate stability and control parameter values from flight data for a low-wing, single-engine, general aviation airplane. The estimated parameters from both methods are in very good agreement primarily because of sufficient accuracy of measured data. The estimated static parameters also agree with the results from steady flights. The effect of power different input forms are demonstrated. Examination of all results available gives the best values of estimated parameters and specifies their accuracies.

Mapping Quantitative Traits in Unselected Families: Algorithms and Examples

PubMed Central

Dupuis, Josée; Shi, Jianxin; Manning, Alisa K.; Benjamin, Emelia J.; Meigs, James B.; Cupples, L. Adrienne; Siegmund, David

2009-01-01

Linkage analysis has been widely used to identify from family data genetic variants influencing quantitative traits. Common approaches have both strengths and limitations. Likelihood ratio tests typically computed in variance component analysis can accommodate large families but are highly sensitive to departure from normality assumptions. Regression-based approaches are more robust but their use has primarily been restricted to nuclear families. In this paper, we develop methods for mapping quantitative traits in moderately large pedigrees. Our methods are based on the score statistic which in contrast to the likelihood ratio statistic, can use nonparametric estimators of variability to achieve robustness of the false positive rate against departures from the hypothesized phenotypic model. Because the score statistic is easier to calculate than the likelihood ratio statistic, our basic mapping methods utilize relatively simple computer code that performs statistical analysis on output from any program that computes estimates of identity-by-descent. This simplicity also permits development and evaluation of methods to deal with multivariate and ordinal phenotypes, and with gene-gene and gene-environment interaction. We demonstrate our methods on simulated data and on fasting insulin, a quantitative trait measured in the Framingham Heart Study. PMID:19278016

Usual Physical Activity and Hip Fracture in Older Men: An Application of Semiparametric Methods to Observational Data

PubMed Central

Mackey, Dawn C.; Hubbard, Alan E.; Cawthon, Peggy M.; Cauley, Jane A.; Cummings, Steven R.; Tager, Ira B.

2011-01-01

Few studies have examined the relation between usual physical activity level and rate of hip fracture in older men or applied semiparametric methods from the causal inference literature that estimate associations without assuming a particular parametric model. Using the Physical Activity Scale for the Elderly, the authors measured usual physical activity level at baseline (2000–2002) in 5,682 US men ≥65 years of age who were enrolled in the Osteoporotic Fractures in Men Study. Physical activity levels were classified as low (bottom quartile of Physical Activity Scale for the Elderly score), moderate (middle quartiles), or high (top quartile). Hip fractures were confirmed by central review. Marginal associations between physical activity and hip fracture were estimated with 3 estimation methods: inverse probability-of-treatment weighting, G-computation, and doubly robust targeted maximum likelihood estimation. During 6.5 years of follow-up, 95 men (1.7%) experienced a hip fracture. The unadjusted risk of hip fracture was lower in men with a high physical activity level versus those with a low physical activity level (relative risk = 0.51, 95% confidence interval: 0.28, 0.92). In semiparametric analyses that controlled confounding, hip fracture risk was not lower with moderate (e.g., targeted maximum likelihood estimation relative risk = 0.92, 95% confidence interval: 0.62, 1.44) or high (e.g., targeted maximum likelihood estimation relative risk = 0.88, 95% confidence interval: 0.53, 2.03) physical activity relative to low. This study does not support a protective effect of usual physical activity on hip fracture in older men. PMID:21303805

Use of empirical likelihood to calibrate auxiliary information in partly linear monotone regression models.

PubMed

Chen, Baojiang; Qin, Jing

2014-05-10

In statistical analysis, a regression model is needed if one is interested in finding the relationship between a response variable and covariates. When the response depends on the covariate, then it may also depend on the function of this covariate. If one has no knowledge of this functional form but expect for monotonic increasing or decreasing, then the isotonic regression model is preferable. Estimation of parameters for isotonic regression models is based on the pool-adjacent-violators algorithm (PAVA), where the monotonicity constraints are built in. With missing data, people often employ the augmented estimating method to improve estimation efficiency by incorporating auxiliary information through a working regression model. However, under the framework of the isotonic regression model, the PAVA does not work as the monotonicity constraints are violated. In this paper, we develop an empirical likelihood-based method for isotonic regression model to incorporate the auxiliary information. Because the monotonicity constraints still hold, the PAVA can be used for parameter estimation. Simulation studies demonstrate that the proposed method can yield more efficient estimates, and in some situations, the efficiency improvement is substantial. We apply this method to a dementia study. Copyright © 2013 John Wiley & Sons, Ltd.

Why Might Relative Fit Indices Differ between Estimators?

ERIC Educational Resources Information Center

Weng, Li-Jen; Cheng, Chung-Ping

1997-01-01

Relative fit indices using the null model as the reference point in computation may differ across estimation methods, as this article illustrates by comparing maximum likelihood, ordinary least squares, and generalized least squares estimation in structural equation modeling. The illustration uses a covariance matrix for six observed variables…

Characterization of a maximum-likelihood nonparametric density estimator of kernel type

NASA Technical Reports Server (NTRS)

Geman, S.; Mcclure, D. E.

1982-01-01

Kernel type density estimators calculated by the method of sieves. Proofs are presented for the characterization theorem: Let x(1), x(2),...x(n) be a random sample from a population with density f(0). Let sigma 0 and consider estimators f of f(0) defined by (1).

Numerical Demons in Monte Carlo Estimation of Bayesian Model Evidence with Application to Soil Respiration Models

NASA Astrophysics Data System (ADS)

Elshall, A. S.; Ye, M.; Niu, G. Y.; Barron-Gafford, G.

2016-12-01

Bayesian multimodel inference is increasingly being used in hydrology. Estimating Bayesian model evidence (BME) is of central importance in many Bayesian multimodel analysis such as Bayesian model averaging and model selection. BME is the overall probability of the model in reproducing the data, accounting for the trade-off between the goodness-of-fit and the model complexity. Yet estimating BME is challenging, especially for high dimensional problems with complex sampling space. Estimating BME using the Monte Carlo numerical methods is preferred, as the methods yield higher accuracy than semi-analytical solutions (e.g. Laplace approximations, BIC, KIC, etc.). However, numerical methods are prone the numerical demons arising from underflow of round off errors. Although few studies alluded to this issue, to our knowledge this is the first study that illustrates these numerical demons. We show that the precision arithmetic can become a threshold on likelihood values and Metropolis acceptance ratio, which results in trimming parameter regions (when likelihood function is less than the smallest floating point number that a computer can represent) and corrupting of the empirical measures of the random states of the MCMC sampler (when using log-likelihood function). We consider two of the most powerful numerical estimators of BME that are the path sampling method of thermodynamic integration (TI) and the importance sampling method of steppingstone sampling (SS). We also consider the two most widely used numerical estimators, which are the prior sampling arithmetic mean (AS) and posterior sampling harmonic mean (HM). We investigate the vulnerability of these four estimators to the numerical demons. Interesting, the most biased estimator, namely the HM, turned out to be the least vulnerable. While it is generally assumed that AM is a bias-free estimator that will always approximate the true BME by investing in computational effort, we show that arithmetic underflow can hamper AM resulting in severe underestimation of BME. TI turned out to be the most vulnerable, resulting in BME overestimation. Finally, we show how SS can be largely invariant to rounding errors, yielding the most accurate and computational efficient results. These research results are useful for MC simulations to estimate Bayesian model evidence.

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

A Review of System Identification Methods Applied to Aircraft

NASA Technical Reports Server (NTRS)

Klein, V.

1983-01-01

Airplane identification, equation error method, maximum likelihood method, parameter estimation in frequency domain, extended Kalman filter, aircraft equations of motion, aerodynamic model equations, criteria for the selection of a parsimonious model, and online aircraft identification are addressed.

MCMC multilocus lod scores: application of a new approach.

PubMed

George, Andrew W; Wijsman, Ellen M; Thompson, Elizabeth A

2005-01-01

On extended pedigrees with extensive missing data, the calculation of multilocus likelihoods for linkage analysis is often beyond the computational bounds of exact methods. Growing interest therefore surrounds the implementation of Monte Carlo estimation methods. In this paper, we demonstrate the speed and accuracy of a new Markov chain Monte Carlo method for the estimation of linkage likelihoods through an analysis of real data from a study of early-onset Alzheimer's disease. For those data sets where comparison with exact analysis is possible, we achieved up to a 100-fold increase in speed. Our approach is implemented in the program lm_bayes within the framework of the freely available MORGAN 2.6 package for Monte Carlo genetic analysis (http://www.stat.washington.edu/thompson/Genepi/MORGAN/Morgan.shtml).

Simulation-Based Evaluation of Hybridization Network Reconstruction Methods in the Presence of Incomplete Lineage Sorting

PubMed Central

Kamneva, Olga K; Rosenberg, Noah A

2017-01-01

Hybridization events generate reticulate species relationships, giving rise to species networks rather than species trees. We report a comparative study of consensus, maximum parsimony, and maximum likelihood methods of species network reconstruction using gene trees simulated assuming a known species history. We evaluate the role of the divergence time between species involved in a hybridization event, the relative contributions of the hybridizing species, and the error in gene tree estimation. When gene tree discordance is mostly due to hybridization and not due to incomplete lineage sorting (ILS), most of the methods can detect even highly skewed hybridization events between highly divergent species. For recent divergences between hybridizing species, when the influence of ILS is sufficiently high, likelihood methods outperform parsimony and consensus methods, which erroneously identify extra hybridizations. The more sophisticated likelihood methods, however, are affected by gene tree errors to a greater extent than are consensus and parsimony. PMID:28469378

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

A real-time digital program for estimating aircraft stability and control parameters from flight test data by using the maximum likelihood method

NASA Technical Reports Server (NTRS)

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

1973-01-01

A computer program (Langley program C1123) has been developed for estimating aircraft stability and control parameters from flight test data. These parameters are estimated by the maximum likelihood estimation procedure implemented on a real-time digital simulation system, which uses the Control Data 6600 computer. This system allows the investigator to interact with the program in order to obtain satisfactory results. Part of this system, the control and display capabilities, is described for this program. This report also describes the computer program by presenting the program variables, subroutines, flow charts, listings, and operational features. Program usage is demonstrated with a test case using pseudo or simulated flight data.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Updated logistic regression equations for the calculation of post-fire debris-flow likelihood in the western United States

USGS Publications Warehouse

Staley, Dennis M.; Negri, Jacquelyn A.; Kean, Jason W.; Laber, Jayme L.; Tillery, Anne C.; Youberg, Ann M.

2016-06-30

Wildfire can significantly alter the hydrologic response of a watershed to the extent that even modest rainstorms can generate dangerous flash floods and debris flows. To reduce public exposure to hazard, the U.S. Geological Survey produces post-fire debris-flow hazard assessments for select fires in the western United States. We use publicly available geospatial data describing basin morphology, burn severity, soil properties, and rainfall characteristics to estimate the statistical likelihood that debris flows will occur in response to a storm of a given rainfall intensity. Using an empirical database and refined geospatial analysis methods, we defined new equations for the prediction of debris-flow likelihood using logistic regression methods. We showed that the new logistic regression model outperformed previous models used to predict debris-flow likelihood.

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

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.

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

Item Response Theory with Estimation of the Latent Density Using Davidian Curves

ERIC Educational Resources Information Center

Woods, Carol M.; Lin, Nan

2009-01-01

Davidian-curve item response theory (DC-IRT) is introduced, evaluated with simulations, and illustrated using data from the Schedule for Nonadaptive and Adaptive Personality Entitlement scale. DC-IRT is a method for fitting unidimensional IRT models with maximum marginal likelihood estimation, in which the latent density is estimated,…

Small area estimation for estimating the number of infant mortality in West Java, Indonesia

NASA Astrophysics Data System (ADS)

Anggreyani, Arie; Indahwati, Kurnia, Anang

2016-02-01

Demographic and Health Survey Indonesia (DHSI) is a national designed survey to provide information regarding birth rate, mortality rate, family planning and health. DHSI was conducted by BPS in cooperation with National Population and Family Planning Institution (BKKBN), Indonesia Ministry of Health (KEMENKES) and USAID. Based on the publication of DHSI 2012, the infant mortality rate for a period of five years before survey conducted is 32 for 1000 birth lives. In this paper, Small Area Estimation (SAE) is used to estimate the number of infant mortality in districts of West Java. SAE is a special model of Generalized Linear Mixed Models (GLMM). In this case, the incidence of infant mortality is a Poisson distribution which has equdispersion assumption. The methods to handle overdispersion are binomial negative and quasi-likelihood model. Based on the results of analysis, quasi-likelihood model is the best model to overcome overdispersion problem. The basic model of the small area estimation used basic area level model. Mean square error (MSE) which based on resampling method is used to measure the accuracy of small area estimates.

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.

A Comparative Study of Co-Channel Interference Suppression Techniques

NASA Technical Reports Server (NTRS)

Hamkins, Jon; Satorius, Ed; Paparisto, Gent; Polydoros, Andreas

1997-01-01

We describe three methods of combatting co-channel interference (CCI): a cross-coupled phase-locked loop (CCPLL); a phase-tracking circuit (PTC), and joint Viterbi estimation based on the maximum likelihood principle. In the case of co-channel FM-modulated voice signals, the CCPLL and PTC methods typically outperform the maximum likelihood estimators when the modulation parameters are dissimilar. However, as the modulation parameters become identical, joint Viterbi estimation provides for a more robust estimate of the co-channel signals and does not suffer as much from "signal switching" which especially plagues the CCPLL approach. Good performance for the PTC requires both dissimilar modulation parameters and a priori knowledge of the co-channel signal amplitudes. The CCPLL and joint Viterbi estimators, on the other hand, incorporate accurate amplitude estimates. In addition, application of the joint Viterbi algorithm to demodulating co-channel digital (BPSK) signals in a multipath environment is also discussed. It is shown in this case that if the interference is sufficiently small, a single trellis model is most effective in demodulating the co-channel signals.

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.

Empirical likelihood inference in randomized clinical trials.

PubMed

Zhang, Biao

2017-01-01

In individually randomized controlled trials, in addition to the primary outcome, information is often available on a number of covariates prior to randomization. This information is frequently utilized to undertake adjustment for baseline characteristics in order to increase precision of the estimation of average treatment effects; such adjustment is usually performed via covariate adjustment in outcome regression models. Although the use of covariate adjustment is widely seen as desirable for making treatment effect estimates more precise and the corresponding hypothesis tests more powerful, there are considerable concerns that objective inference in randomized clinical trials can potentially be compromised. In this paper, we study an empirical likelihood approach to covariate adjustment and propose two unbiased estimating functions that automatically decouple evaluation of average treatment effects from regression modeling of covariate-outcome relationships. The resulting empirical likelihood estimator of the average treatment effect is as efficient as the existing efficient adjusted estimators 1 when separate treatment-specific working regression models are correctly specified, yet are at least as efficient as the existing efficient adjusted estimators 1 for any given treatment-specific working regression models whether or not they coincide with the true treatment-specific covariate-outcome relationships. We present a simulation study to compare the finite sample performance of various methods along with some results on analysis of a data set from an HIV clinical trial. The simulation results indicate that the proposed empirical likelihood approach is more efficient and powerful than its competitors when the working covariate-outcome relationships by treatment status are misspecified.

Case-Deletion Diagnostics for Maximum Likelihood Multipoint Quantitative Trait Locus Linkage Analysis

PubMed Central

Mendoza, Maria C.B.; Burns, Trudy L.; Jones, Michael P.

2009-01-01

Objectives Case-deletion diagnostic methods are tools that allow identification of influential observations that may affect parameter estimates and model fitting conclusions. The goal of this paper was to develop two case-deletion diagnostics, the exact case deletion (ECD) and the empirical influence function (EIF), for detecting outliers that can affect results of sib-pair maximum likelihood quantitative trait locus (QTL) linkage analysis. Methods Subroutines to compute the ECD and EIF were incorporated into the maximum likelihood QTL variance estimation components of the linkage analysis program MAPMAKER/SIBS. Performance of the diagnostics was compared in simulation studies that evaluated the proportion of outliers correctly identified (sensitivity), and the proportion of non-outliers correctly identified (specificity). Results Simulations involving nuclear family data sets with one outlier showed EIF sensitivities approximated ECD sensitivities well for outlier-affected parameters. Sensitivities were high, indicating the outlier was identified a high proportion of the time. Simulations also showed the enormous computational time advantage of the EIF. Diagnostics applied to body mass index in nuclear families detected observations influential on the lod score and model parameter estimates. Conclusions The EIF is a practical diagnostic tool that has the advantages of high sensitivity and quick computation. PMID:19172086

Accuracy of maximum likelihood and least-squares estimates in the lidar slope method with noisy data.

PubMed

Eberhard, Wynn L

2017-04-01

The maximum likelihood estimator (MLE) is derived for retrieving the extinction coefficient and zero-range intercept in the lidar slope method in the presence of random and independent Gaussian noise. Least-squares fitting, weighted by the inverse of the noise variance, is equivalent to the MLE. Monte Carlo simulations demonstrate that two traditional least-squares fitting schemes, which use different weights, are less accurate. Alternative fitting schemes that have some positive attributes are introduced and evaluated. The principal factors governing accuracy of all these schemes are elucidated. Applying these schemes to data with Poisson rather than Gaussian noise alters accuracy little, even when the signal-to-noise ratio is low. Methods to estimate optimum weighting factors in actual data are presented. Even when the weighting estimates are coarse, retrieval accuracy declines only modestly. Mathematical tools are described for predicting retrieval accuracy. Least-squares fitting with inverse variance weighting has optimum accuracy for retrieval of parameters from single-wavelength lidar measurements when noise, errors, and uncertainties are Gaussian distributed, or close to optimum when only approximately Gaussian.

New algorithms and methods to estimate maximum-likelihood phylogenies: assessing the performance of PhyML 3.0.

PubMed

Guindon, Stéphane; Dufayard, Jean-François; Lefort, Vincent; Anisimova, Maria; Hordijk, Wim; Gascuel, Olivier

2010-05-01

PhyML is a phylogeny software based on the maximum-likelihood principle. Early PhyML versions used a fast algorithm performing nearest neighbor interchanges to improve a reasonable starting tree topology. Since the original publication (Guindon S., Gascuel O. 2003. A simple, fast and accurate algorithm to estimate large phylogenies by maximum likelihood. Syst. Biol. 52:696-704), PhyML has been widely used (>2500 citations in ISI Web of Science) because of its simplicity and a fair compromise between accuracy and speed. In the meantime, research around PhyML has continued, and this article describes the new algorithms and methods implemented in the program. First, we introduce a new algorithm to search the tree space with user-defined intensity using subtree pruning and regrafting topological moves. The parsimony criterion is used here to filter out the least promising topology modifications with respect to the likelihood function. The analysis of a large collection of real nucleotide and amino acid data sets of various sizes demonstrates the good performance of this method. Second, we describe a new test to assess the support of the data for internal branches of a phylogeny. This approach extends the recently proposed approximate likelihood-ratio test and relies on a nonparametric, Shimodaira-Hasegawa-like procedure. A detailed analysis of real alignments sheds light on the links between this new approach and the more classical nonparametric bootstrap method. Overall, our tests show that the last version (3.0) of PhyML is fast, accurate, stable, and ready to use. A Web server and binary files are available from http://www.atgc-montpellier.fr/phyml/.

Multivariate normal maximum likelihood with both ordinal and continuous variables, and data missing at random.

PubMed

Pritikin, Joshua N; Brick, Timothy R; Neale, Michael C

2018-04-01

A novel method for the maximum likelihood estimation of structural equation models (SEM) with both ordinal and continuous indicators is introduced using a flexible multivariate probit model for the ordinal indicators. A full information approach ensures unbiased estimates for data missing at random. Exceeding the capability of prior methods, up to 13 ordinal variables can be included before integration time increases beyond 1 s per row. The method relies on the axiom of conditional probability to split apart the distribution of continuous and ordinal variables. Due to the symmetry of the axiom, two similar methods are available. A simulation study provides evidence that the two similar approaches offer equal accuracy. A further simulation is used to develop a heuristic to automatically select the most computationally efficient approach. Joint ordinal continuous SEM is implemented in OpenMx, free and open-source software.

Estimation of a Ramsay-Curve Item Response Theory Model by the Metropolis-Hastings Robbins-Monro Algorithm. CRESST Report 834

ERIC Educational Resources Information Center

Monroe, Scott; Cai, Li

2013-01-01

In Ramsay curve item response theory (RC-IRT, Woods & Thissen, 2006) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's (1981) EM algorithm, which yields maximum marginal likelihood estimates. This method, however,…

Estimation of a Ramsay-Curve Item Response Theory Model by the Metropolis-Hastings Robbins-Monro Algorithm

ERIC Educational Resources Information Center

Monroe, Scott; Cai, Li

2014-01-01

In Ramsay curve item response theory (RC-IRT) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's EM algorithm, which yields maximum marginal likelihood estimates. This method, however, does not produce the…

A Computer Program for Solving a Set of Conditional Maximum Likelihood Equations Arising in the Rasch Model for Questionnaires.

ERIC Educational Resources Information Center

Andersen, Erling B.

A computer program for solving the conditional likelihood equations arising in the Rasch model for questionnaires is described. The estimation method and the computational problems involved are described in a previous research report by Andersen, but a summary of those results are given in two sections of this paper. A working example is also…

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

PubMed

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

2017-11-01

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

Likelihood-Based Random-Effect Meta-Analysis of Binary Events.

PubMed

Amatya, Anup; Bhaumik, Dulal K; Normand, Sharon-Lise; Greenhouse, Joel; Kaizar, Eloise; Neelon, Brian; Gibbons, Robert D

2015-01-01

Meta-analysis has been used extensively for evaluation of efficacy and safety of medical interventions. Its advantages and utilities are well known. However, recent studies have raised questions about the accuracy of the commonly used moment-based meta-analytic methods in general and for rare binary outcomes in particular. The issue is further complicated for studies with heterogeneous effect sizes. Likelihood-based mixed-effects modeling provides an alternative to moment-based methods such as inverse-variance weighted fixed- and random-effects estimators. In this article, we compare and contrast different mixed-effect modeling strategies in the context of meta-analysis. Their performance in estimation and testing of overall effect and heterogeneity are evaluated when combining results from studies with a binary outcome. Models that allow heterogeneity in both baseline rate and treatment effect across studies have low type I and type II error rates, and their estimates are the least biased among the models considered.

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.

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.

Cross-validation to select Bayesian hierarchical models in phylogenetics.

PubMed

Duchêne, Sebastián; Duchêne, David A; Di Giallonardo, Francesca; Eden, John-Sebastian; Geoghegan, Jemma L; Holt, Kathryn E; Ho, Simon Y W; Holmes, Edward C

2016-05-26

Recent developments in Bayesian phylogenetic models have increased the range of inferences that can be drawn from molecular sequence data. Accordingly, model selection has become an important component of phylogenetic analysis. Methods of model selection generally consider the likelihood of the data under the model in question. In the context of Bayesian phylogenetics, the most common approach involves estimating the marginal likelihood, which is typically done by integrating the likelihood across model parameters, weighted by the prior. Although this method is accurate, it is sensitive to the presence of improper priors. We explored an alternative approach based on cross-validation that is widely used in evolutionary analysis. This involves comparing models according to their predictive performance. We analysed simulated data and a range of viral and bacterial data sets using a cross-validation approach to compare a variety of molecular clock and demographic models. Our results show that cross-validation can be effective in distinguishing between strict- and relaxed-clock models and in identifying demographic models that allow growth in population size over time. In most of our empirical data analyses, the model selected using cross-validation was able to match that selected using marginal-likelihood estimation. The accuracy of cross-validation appears to improve with longer sequence data, particularly when distinguishing between relaxed-clock models. Cross-validation is a useful method for Bayesian phylogenetic model selection. This method can be readily implemented even when considering complex models where selecting an appropriate prior for all parameters may be difficult.

Simulated maximum likelihood method for estimating kinetic rates in gene expression.

PubMed

Tian, Tianhai; Xu, Songlin; Gao, Junbin; Burrage, Kevin

2007-01-01

Kinetic rate in gene expression is a key measurement of the stability of gene products and gives important information for the reconstruction of genetic regulatory networks. Recent developments in experimental technologies have made it possible to measure the numbers of transcripts and protein molecules in single cells. Although estimation methods based on deterministic models have been proposed aimed at evaluating kinetic rates from experimental observations, these methods cannot tackle noise in gene expression that may arise from discrete processes of gene expression, small numbers of mRNA transcript, fluctuations in the activity of transcriptional factors and variability in the experimental environment. In this paper, we develop effective methods for estimating kinetic rates in genetic regulatory networks. The simulated maximum likelihood method is used to evaluate parameters in stochastic models described by either stochastic differential equations or discrete biochemical reactions. Different types of non-parametric density functions are used to measure the transitional probability of experimental observations. For stochastic models described by biochemical reactions, we propose to use the simulated frequency distribution to evaluate the transitional density based on the discrete nature of stochastic simulations. The genetic optimization algorithm is used as an efficient tool to search for optimal reaction rates. Numerical results indicate that the proposed methods can give robust estimations of kinetic rates with good accuracy.

LS-APC v1.0: a tuning-free method for the linear inverse problem and its application to source-term determination

NASA Astrophysics Data System (ADS)

Tichý, Ondřej; Šmídl, Václav; Hofman, Radek; Stohl, Andreas

2016-11-01

Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values) as a product of the source-receptor sensitivity (SRS) matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX) where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.

Generalized Ordinary Differential Equation Models 1

PubMed Central

Miao, Hongyu; Wu, Hulin; Xue, Hongqi

2014-01-01

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method. PMID:25544787

Generalized Ordinary Differential Equation Models.

PubMed

Miao, Hongyu; Wu, Hulin; Xue, Hongqi

2014-10-01

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method.

Spatial hydrological drought characteristics in Karkheh River basin, southwest Iran using copulas

NASA Astrophysics Data System (ADS)

Dodangeh, Esmaeel; Shahedi, Kaka; Shiau, Jenq-Tzong; MirAkbari, Maryam

2017-08-01

Investigation on drought characteristics such as severity, duration, and frequency is crucial for water resources planning and management in a river basin. While the methodology for multivariate drought frequency analysis is well established by applying the copulas, the estimation on the associated parameters by various parameter estimation methods and the effects on the obtained results have not yet been investigated. This research aims at conducting a comparative analysis between the maximum likelihood parametric and non-parametric method of the Kendall τ estimation method for copulas parameter estimation. The methods were employed to study joint severity-duration probability and recurrence intervals in Karkheh River basin (southwest Iran) which is facing severe water-deficit problems. Daily streamflow data at three hydrological gauging stations (Tang Sazbon, Huleilan and Polchehr) near the Karkheh dam were used to draw flow duration curves (FDC) of these three stations. The Q_{75} index extracted from the FDC were set as threshold level to abstract drought characteristics such as drought duration and severity on the basis of the run theory. Drought duration and severity were separately modeled using the univariate probabilistic distributions and gamma-GEV, LN2-exponential, and LN2-gamma were selected as the best paired drought severity-duration inputs for copulas according to the Akaike Information Criteria (AIC), Kolmogorov-Smirnov and chi-square tests. Archimedean Clayton, Frank, and extreme value Gumbel copulas were employed to construct joint cumulative distribution functions (JCDF) of droughts for each station. Frank copula at Tang Sazbon and Gumbel at Huleilan and Polchehr stations were identified as the best copulas based on the performance evaluation criteria including AIC, BIC, log-likelihood and root mean square error (RMSE) values. Based on the RMSE values, nonparametric Kendall-τ is preferred to the parametric maximum likelihood estimation method. The results showed greater drought return periods by the parametric ML method in comparison to the nonparametric Kendall τ estimation method. The results also showed that stations located in tributaries (Huleilan and Polchehr) have close return periods, while the station along the main river (Tang Sazbon) has the smaller return periods for the drought events with identical drought duration and severity.

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.

Nonparametric Discrete Survival Function Estimation with Uncertain Endpoints Using an Internal Validation Subsample

PubMed Central

Zee, Jarcy; Xie, Sharon X.

2015-01-01

Summary When a true survival endpoint cannot be assessed for some subjects, an alternative endpoint that measures the true endpoint with error may be collected, which often occurs when obtaining the true endpoint is too invasive or costly. We develop an estimated likelihood function for the situation where we have both uncertain endpoints for all participants and true endpoints for only a subset of participants. We propose a nonparametric maximum estimated likelihood estimator of the discrete survival function of time to the true endpoint. We show that the proposed estimator is consistent and asymptotically normal. We demonstrate through extensive simulations that the proposed estimator has little bias compared to the naïve Kaplan-Meier survival function estimator, which uses only uncertain endpoints, and more efficient with moderate missingness compared to the complete-case Kaplan-Meier survival function estimator, which uses only available true endpoints. Finally, we apply the proposed method to a dataset for estimating the risk of developing Alzheimer's disease from the Alzheimer's Disease Neuroimaging Initiative. PMID:25916510

Estimating multilevel logistic regression models when the number of clusters is low: a comparison of different statistical software procedures.

PubMed

Austin, Peter C

2010-04-22

Multilevel logistic regression models are increasingly being used to analyze clustered data in medical, public health, epidemiological, and educational research. Procedures for estimating the parameters of such models are available in many statistical software packages. There is currently little evidence on the minimum number of clusters necessary to reliably fit multilevel regression models. We conducted a Monte Carlo study to compare the performance of different statistical software procedures for estimating multilevel logistic regression models when the number of clusters was low. We examined procedures available in BUGS, HLM, R, SAS, and Stata. We found that there were qualitative differences in the performance of different software procedures for estimating multilevel logistic models when the number of clusters was low. Among the likelihood-based procedures, estimation methods based on adaptive Gauss-Hermite approximations to the likelihood (glmer in R and xtlogit in Stata) or adaptive Gaussian quadrature (Proc NLMIXED in SAS) tended to have superior performance for estimating variance components when the number of clusters was small, compared to software procedures based on penalized quasi-likelihood. However, only Bayesian estimation with BUGS allowed for accurate estimation of variance components when there were fewer than 10 clusters. For all statistical software procedures, estimation of variance components tended to be poor when there were only five subjects per cluster, regardless of the number of clusters.

Vehicle Sprung Mass Estimation for Rough Terrain

DTIC Science & Technology

2011-03-01

distributions are greater than zero. The multivariate polynomials are functions of the Legendre polynomials (Poularikas (1999...developed methods based on polynomial chaos theory and on the maximum likelihood approach to estimate the most likely value of the vehicle sprung...mass. The polynomial chaos estimator is compared to benchmark algorithms including recursive least squares, recursive total least squares, extended

Marginal Maximum A Posteriori Item Parameter Estimation for the Generalized Graded Unfolding Model

ERIC Educational Resources Information Center

Roberts, James S.; Thompson, Vanessa M.

2011-01-01

A marginal maximum a posteriori (MMAP) procedure was implemented to estimate item parameters in the generalized graded unfolding model (GGUM). Estimates from the MMAP method were compared with those derived from marginal maximum likelihood (MML) and Markov chain Monte Carlo (MCMC) procedures in a recovery simulation that varied sample size,…

dPIRPLE: a joint estimation framework for deformable registration and penalized-likelihood CT image reconstruction using prior images

NASA Astrophysics Data System (ADS)

Dang, H.; Wang, A. S.; Sussman, Marc S.; Siewerdsen, J. H.; Stayman, J. W.

2014-09-01

Sequential imaging studies are conducted in many clinical scenarios. Prior images from previous studies contain a great deal of patient-specific anatomical information and can be used in conjunction with subsequent imaging acquisitions to maintain image quality while enabling radiation dose reduction (e.g., through sparse angular sampling, reduction in fluence, etc). However, patient motion between images in such sequences results in misregistration between the prior image and current anatomy. Existing prior-image-based approaches often include only a simple rigid registration step that can be insufficient for capturing complex anatomical motion, introducing detrimental effects in subsequent image reconstruction. In this work, we propose a joint framework that estimates the 3D deformation between an unregistered prior image and the current anatomy (based on a subsequent data acquisition) and reconstructs the current anatomical image using a model-based reconstruction approach that includes regularization based on the deformed prior image. This framework is referred to as deformable prior image registration, penalized-likelihood estimation (dPIRPLE). Central to this framework is the inclusion of a 3D B-spline-based free-form-deformation model into the joint registration-reconstruction objective function. The proposed framework is solved using a maximization strategy whereby alternating updates to the registration parameters and image estimates are applied allowing for improvements in both the registration and reconstruction throughout the optimization process. Cadaver experiments were conducted on a cone-beam CT testbench emulating a lung nodule surveillance scenario. Superior reconstruction accuracy and image quality were demonstrated using the dPIRPLE algorithm as compared to more traditional reconstruction methods including filtered backprojection, penalized-likelihood estimation (PLE), prior image penalized-likelihood estimation (PIPLE) without registration, and prior image penalized-likelihood estimation with rigid registration of a prior image (PIRPLE) over a wide range of sampling sparsity and exposure levels.

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.

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.

Bias correction for estimated QTL effects using the penalized maximum likelihood method.

PubMed

Zhang, J; Yue, C; Zhang, Y-M

2012-04-01

A penalized maximum likelihood method has been proposed as an important approach to the detection of epistatic quantitative trait loci (QTL). However, this approach is not optimal in two special situations: (1) closely linked QTL with effects in opposite directions and (2) small-effect QTL, because the method produces downwardly biased estimates of QTL effects. The present study aims to correct the bias by using correction coefficients and shifting from the use of a uniform prior on the variance parameter of a QTL effect to that of a scaled inverse chi-square prior. The results of Monte Carlo simulation experiments show that the improved method increases the power from 25 to 88% in the detection of two closely linked QTL of equal size in opposite directions and from 60 to 80% in the identification of QTL with small effects (0.5% of the total phenotypic variance). We used the improved method to detect QTL responsible for the barley kernel weight trait using 145 doubled haploid lines developed in the North American Barley Genome Mapping Project. Application of the proposed method to other shrinkage estimation of QTL effects is discussed.

Likelihood-based methods for evaluating principal surrogacy in augmented vaccine trials.

PubMed

Liu, Wei; Zhang, Bo; Zhang, Hui; Zhang, Zhiwei

2017-04-01

There is growing interest in assessing immune biomarkers, which are quick to measure and potentially predictive of long-term efficacy, as surrogate endpoints in randomized, placebo-controlled vaccine trials. This can be done under a principal stratification approach, with principal strata defined using a subject's potential immune responses to vaccine and placebo (the latter may be assumed to be zero). In this context, principal surrogacy refers to the extent to which vaccine efficacy varies across principal strata. Because a placebo recipient's potential immune response to vaccine is unobserved in a standard vaccine trial, augmented vaccine trials have been proposed to produce the information needed to evaluate principal surrogacy. This article reviews existing methods based on an estimated likelihood and a pseudo-score (PS) and proposes two new methods based on a semiparametric likelihood (SL) and a pseudo-likelihood (PL), for analyzing augmented vaccine trials. Unlike the PS method, the SL method does not require a model for missingness, which can be advantageous when immune response data are missing by happenstance. The SL method is shown to be asymptotically efficient, and it performs similarly to the PS and PL methods in simulation experiments. The PL method appears to have a computational advantage over the PS and SL methods.

A phase match based frequency estimation method for sinusoidal signals

NASA Astrophysics Data System (ADS)

Shen, Yan-Lin; Tu, Ya-Qing; Chen, Lin-Jun; Shen, Ting-Ao

2015-04-01

Accurate frequency estimation affects the ranging precision of linear frequency modulated continuous wave (LFMCW) radars significantly. To improve the ranging precision of LFMCW radars, a phase match based frequency estimation method is proposed. To obtain frequency estimation, linear prediction property, autocorrelation, and cross correlation of sinusoidal signals are utilized. The analysis of computational complex shows that the computational load of the proposed method is smaller than those of two-stage autocorrelation (TSA) and maximum likelihood. Simulations and field experiments are performed to validate the proposed method, and the results demonstrate the proposed method has better performance in terms of frequency estimation precision than methods of Pisarenko harmonic decomposition, modified covariance, and TSA, which contribute to improving the precision of LFMCW radars effectively.

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.

Estimation of rank correlation for clustered data.

PubMed

Rosner, Bernard; Glynn, Robert J

2017-06-30

It is well known that the sample correlation coefficient (R xy ) is the maximum likelihood estimator of the Pearson correlation (ρ xy ) for independent and identically distributed (i.i.d.) bivariate normal data. However, this is not true for ophthalmologic data where X (e.g., visual acuity) and Y (e.g., visual field) are available for each eye and there is positive intraclass correlation for both X and Y in fellow eyes. In this paper, we provide a regression-based approach for obtaining the maximum likelihood estimator of ρ xy for clustered data, which can be implemented using standard mixed effects model software. This method is also extended to allow for estimation of partial correlation by controlling both X and Y for a vector U_ of other covariates. In addition, these methods can be extended to allow for estimation of rank correlation for clustered data by (i) converting ranks of both X and Y to the probit scale, (ii) estimating the Pearson correlation between probit scores for X and Y, and (iii) using the relationship between Pearson and rank correlation for bivariate normally distributed data. The validity of the methods in finite-sized samples is supported by simulation studies. Finally, two examples from ophthalmology and analgesic abuse are used to illustrate the methods. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

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.

An Efficient Acoustic Density Estimation Method with Human Detectors Applied to Gibbons in Cambodia.

PubMed

Kidney, Darren; Rawson, Benjamin M; Borchers, David L; Stevenson, Ben C; Marques, Tiago A; Thomas, Len

2016-01-01

Some animal species are hard to see but easy to hear. Standard visual methods for estimating population density for such species are often ineffective or inefficient, but methods based on passive acoustics show more promise. We develop spatially explicit capture-recapture (SECR) methods for territorial vocalising species, in which humans act as an acoustic detector array. We use SECR and estimated bearing data from a single-occasion acoustic survey of a gibbon population in northeastern Cambodia to estimate the density of calling groups. The properties of the estimator are assessed using a simulation study, in which a variety of survey designs are also investigated. We then present a new form of the SECR likelihood for multi-occasion data which accounts for the stochastic availability of animals. In the context of gibbon surveys this allows model-based estimation of the proportion of groups that produce territorial vocalisations on a given day, thereby enabling the density of groups, instead of the density of calling groups, to be estimated. We illustrate the performance of this new estimator by simulation. We show that it is possible to estimate density reliably from human acoustic detections of visually cryptic species using SECR methods. For gibbon surveys we also show that incorporating observers' estimates of bearings to detected groups substantially improves estimator performance. Using the new form of the SECR likelihood we demonstrate that estimates of availability, in addition to population density and detection function parameters, can be obtained from multi-occasion data, and that the detection function parameters are not confounded with the availability parameter. This acoustic SECR method provides a means of obtaining reliable density estimates for territorial vocalising species. It is also efficient in terms of data requirements since since it only requires routine survey data. We anticipate that the low-tech field requirements will make this method an attractive option in many situations where populations can be surveyed acoustically by humans.

Modeling abundance effects in distance sampling

USGS Publications Warehouse

Royle, J. Andrew; Dawson, D.K.; Bates, S.

2004-01-01

Distance-sampling methods are commonly used in studies of animal populations to estimate population density. A common objective of such studies is to evaluate the relationship between abundance or density and covariates that describe animal habitat or other environmental influences. However, little attention has been focused on methods of modeling abundance covariate effects in conventional distance-sampling models. In this paper we propose a distance-sampling model that accommodates covariate effects on abundance. The model is based on specification of the distance-sampling likelihood at the level of the sample unit in terms of local abundance (for each sampling unit). This model is augmented with a Poisson regression model for local abundance that is parameterized in terms of available covariates. Maximum-likelihood estimation of detection and density parameters is based on the integrated likelihood, wherein local abundance is removed from the likelihood by integration. We provide an example using avian point-transect data of Ovenbirds (Seiurus aurocapillus) collected using a distance-sampling protocol and two measures of habitat structure (understory cover and basal area of overstory trees). The model yields a sensible description (positive effect of understory cover, negative effect on basal area) of the relationship between habitat and Ovenbird density that can be used to evaluate the effects of habitat management on Ovenbird populations.

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.

Inter-informant agreement and prevalence estimates for mood syndromes: direct interview vs. family history method.

PubMed

Vandeleur, C L; Rothen, S; Lustenberger, Y; Glaus, J; Castelao, E; Preisig, M

2015-01-15

The use of the family history method is recommended in family studies as a type of proxy interview of non-participating relatives. However, using different sources of information can result in bias as direct interviews may provide a higher likelihood of assigning diagnoses than family history reports. The aims of the present study were to: (1) compare diagnoses for threshold and subthreshold mood syndromes from interviews to those relying on information from relatives; (2) test the appropriateness of lowering the diagnostic threshold and combining multiple reports from the family history method to obtain comparable prevalence estimates to the interviews; (3) identify factors that influence the likelihood of agreement and reporting of disorders by informants. Within a family study, 1621 informant-index subject pairs were identified. DSM-5 diagnoses from direct interviews of index subjects were compared to those derived from family history information provided by their first-degree relatives. (1) Inter-informant agreement was acceptable for Mania, but low for all other mood syndromes. (2) Except for Mania and subthreshold depression, the family history method provided significantly lower prevalence estimates. The gap improved for all other syndromes after lowering the threshold of the family history method. (3) Individuals who had a history of depression themselves were more likely to report depression in their relatives. Low proportion of affected individuals for manic syndromes and lack of independence of data. The higher likelihood of reporting disorders by affected informants entails the risk of overestimation of the size of familial aggregation of depression. Copyright © 2014 Elsevier B.V. All rights reserved.

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

Maximum Likelihood as an Operational Tool in Socio-Economic Modeling : As Outlined in a Recent Thesis of D. W. Peterson

DOT National Transportation Integrated Search

1977-02-01

The limitations of currently used estimation procedures in socio-economic modeling have been highlighted in the ongoing work of Senge, in which it is shown where more sophisticated estimation procedures may become necessary. One such advanced method ...

Maximum Marginal Likelihood Estimation of a Monotonic Polynomial Generalized Partial Credit Model with Applications to Multiple Group Analysis.

PubMed

Falk, Carl F; Cai, Li

2016-06-01

We present a semi-parametric approach to estimating item response functions (IRF) useful when the true IRF does not strictly follow commonly used functions. Our approach replaces the linear predictor of the generalized partial credit model with a monotonic polynomial. The model includes the regular generalized partial credit model at the lowest order polynomial. Our approach extends Liang's (A semi-parametric approach to estimate IRFs, Unpublished doctoral dissertation, 2007) method for dichotomous item responses to the case of polytomous data. Furthermore, item parameter estimation is implemented with maximum marginal likelihood using the Bock-Aitkin EM algorithm, thereby facilitating multiple group analyses useful in operational settings. Our approach is demonstrated on both educational and psychological data. We present simulation results comparing our approach to more standard IRF estimation approaches and other non-parametric and semi-parametric alternatives.

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.

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…

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.

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.

Application of parameter estimation to highly unstable aircraft

NASA Technical Reports Server (NTRS)

Maine, R. E.; Murray, J. E.

1986-01-01

This paper discusses the application of parameter estimation to highly unstable aircraft. It includes a discussion of the problems in applying the output error method to such aircraft and demonstrates that the filter error method eliminates these problems. The paper shows that the maximum likelihood estimator with no process noise does not reduce to the output error method when the system is unstable. It also proposes and demonstrates an ad hoc method that is similar in form to the filter error method, but applicable to nonlinear problems. Flight data from the X-29 forward-swept-wing demonstrator is used to illustrate the problems and methods discussed.

Application of parameter estimation to highly unstable aircraft

NASA Technical Reports Server (NTRS)

Maine, R. E.; Murray, J. E.

1986-01-01

The application of parameter estimation to highly unstable aircraft is discussed. Included are a discussion of the problems in applying the output error method to such aircraft and demonstrates that the filter error method eliminates these problems. The paper shows that the maximum likelihood estimator with no process noise does not reduce to the output error method when the system is unstable. It also proposes and demonstrates an ad hoc method that is similar in form to the filter error method, but applicable to nonlinear problems. Flight data from the X-29 forward-swept-wing demonstrator is used to illustrate the problems and methods discussed.

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

Estimation of Two-Parameter Logistic Item Response Curves. Research Report 83-1. Mathematical Sciences Technical Report No. 130.

ERIC Educational Resources Information Center

Tsutakawa, Robert K.

This paper presents a method for estimating certain characteristics of test items which are designed to measure ability, or knowledge, in a particular area. Under the assumption that ability parameters are sampled from a normal distribution, the EM algorithm is used to derive maximum likelihood estimates to item parameters of the two-parameter…

Fitting power-laws in empirical data with estimators that work for all exponents

PubMed Central

Hanel, Rudolf; Corominas-Murtra, Bernat; Liu, Bo; Thurner, Stefan

2017-01-01

Most standard methods based on maximum likelihood (ML) estimates of power-law exponents can only be reliably used to identify exponents smaller than minus one. The argument that power laws are otherwise not normalizable, depends on the underlying sample space the data is drawn from, and is true only for sample spaces that are unbounded from above. Power-laws obtained from bounded sample spaces (as is the case for practically all data related problems) are always free of such limitations and maximum likelihood estimates can be obtained for arbitrary powers without restrictions. Here we first derive the appropriate ML estimator for arbitrary exponents of power-law distributions on bounded discrete sample spaces. We then show that an almost identical estimator also works perfectly for continuous data. We implemented this ML estimator and discuss its performance with previous attempts. We present a general recipe of how to use these estimators and present the associated computer codes. PMID:28245249

Monte Carlo studies of ocean wind vector measurements by SCATT: Objective criteria and maximum likelihood estimates for removal of aliases, and effects of cell size on accuracy of vector winds

NASA Technical Reports Server (NTRS)

Pierson, W. J.

1982-01-01

The scatterometer on the National Oceanic Satellite System (NOSS) is studied by means of Monte Carlo techniques so as to determine the effect of two additional antennas for alias (or ambiguity) removal by means of an objective criteria technique and a normalized maximum likelihood estimator. Cells nominally 10 km by 10 km, 10 km by 50 km, and 50 km by 50 km are simulated for winds of 4, 8, 12 and 24 m/s and incidence angles of 29, 39, 47, and 53.5 deg for 15 deg changes in direction. The normalized maximum likelihood estimate (MLE) is correct a large part of the time, but the objective criterion technique is recommended as a reserve, and more quickly computed, procedure. Both methods for alias removal depend on the differences in the present model function at upwind and downwind. For 10 km by 10 km cells, it is found that the MLE method introduces a correlation between wind speed errors and aspect angle (wind direction) errors that can be as high as 0.8 or 0.9 and that the wind direction errors are unacceptably large, compared to those obtained for the SASS for similar assumptions.

Factors associated with the healing of complex surgical wounds in the breast and abdomen: retrospective cohort study

PubMed Central

Borges, Eline Lima; Pires, José Ferreira; Abreu, Mery Natali Silva; Lima, Vera Lúcia de Araújo; Silva, Patrícia Aparecida Barbosa; Soares, Sônia Maria

2016-01-01

ABSTRACT Objective: to estimate the healing rate of complex surgical wounds and its associated factors. Method: retrospective cohort study from 2003 to 2014 with 160 outpatients of a Brazilian university hospital. Data were obtained through consultation of the medical records. Survival function was estimated using the Kaplan-Meier method and Cox regression model to estimate the likelihood of the occurrence of healing. Results: the complex surgical wound healing rate was 67.8% (95% CI: 60.8-74.9). Factors associated with a higher likelihood of wound healing were segmentectomy/quadrantectomy surgery, consumption of more than 20 grams/day of alcohol, wound extent of less that 17.3 cm2 and the length of existence of the wound prior to outpatient treatment of less than 15 days, while the use of hydrocolloid covering and Marlex mesh were associated with a lower likelihood of healing. Conclusion: the wound healing rate was considered high and was associated with the type of surgical intervention, alcohol consumption, type of covering, extent and length of wound existence. Preventive measures can be implemented during the monitoring of the evolution of the complex surgical wound closure, with possibilities of intervention in the modifiable risk factors. PMID:27737379

An algorithm for computing moments-based flood quantile estimates when historical flood information is available

USGS Publications Warehouse

Cohn, T.A.; Lane, W.L.; Baier, W.G.

1997-01-01

This paper presents the expected moments algorithm (EMA), a simple and efficient method for incorporating historical and paleoflood information into flood frequency studies. EMA can utilize three types of at-site flood information: systematic stream gage record; information about the magnitude of historical floods; and knowledge of the number of years in the historical period when no large flood occurred. EMA employs an iterative procedure to compute method-of-moments parameter estimates. Initial parameter estimates are calculated from systematic stream gage data. These moments are then updated by including the measured historical peaks and the expected moments, given the previously estimated parameters, of the below-threshold floods from the historical period. The updated moments result in new parameter estimates, and the last two steps are repeated until the algorithm converges. Monte Carlo simulations compare EMA, Bulletin 17B's [United States Water Resources Council, 1982] historically weighted moments adjustment, and maximum likelihood estimators when fitting the three parameters of the log-Pearson type III distribution. These simulations demonstrate that EMA is more efficient than the Bulletin 17B method, and that it is nearly as efficient as maximum likelihood estimation (MLE). The experiments also suggest that EMA has two advantages over MLE when dealing with the log-Pearson type III distribution: It appears that EMA estimates always exist and that they are unique, although neither result has been proven. EMA can be used with binomial or interval-censored data and with any distributional family amenable to method-of-moments estimation.

An algorithm for computing moments-based flood quantile estimates when historical flood information is available

NASA Astrophysics Data System (ADS)

Cohn, T. A.; Lane, W. L.; Baier, W. G.

This paper presents the expected moments algorithm (EMA), a simple and efficient method for incorporating historical and paleoflood information into flood frequency studies. EMA can utilize three types of at-site flood information: systematic stream gage record; information about the magnitude of historical floods; and knowledge of the number of years in the historical period when no large flood occurred. EMA employs an iterative procedure to compute method-of-moments parameter estimates. Initial parameter estimates are calculated from systematic stream gage data. These moments are then updated by including the measured historical peaks and the expected moments, given the previously estimated parameters, of the below-threshold floods from the historical period. The updated moments result in new parameter estimates, and the last two steps are repeated until the algorithm converges. Monte Carlo simulations compare EMA, Bulletin 17B's [United States Water Resources Council, 1982] historically weighted moments adjustment, and maximum likelihood estimators when fitting the three parameters of the log-Pearson type III distribution. These simulations demonstrate that EMA is more efficient than the Bulletin 17B method, and that it is nearly as efficient as maximum likelihood estimation (MLE). The experiments also suggest that EMA has two advantages over MLE when dealing with the log-Pearson type III distribution: It appears that EMA estimates always exist and that they are unique, although neither result has been proven. EMA can be used with binomial or interval-censored data and with any distributional family amenable to method-of-moments estimation.

Spatial scan statistics for detection of multiple clusters with arbitrary shapes.

PubMed

Lin, Pei-Sheng; Kung, Yi-Hung; Clayton, Murray

2016-12-01

In applying scan statistics for public health research, it would be valuable to develop a detection method for multiple clusters that accommodates spatial correlation and covariate effects in an integrated model. In this article, we connect the concepts of the likelihood ratio (LR) scan statistic and the quasi-likelihood (QL) scan statistic to provide a series of detection procedures sufficiently flexible to apply to clusters of arbitrary shape. First, we use an independent scan model for detection of clusters and then a variogram tool to examine the existence of spatial correlation and regional variation based on residuals of the independent scan model. When the estimate of regional variation is significantly different from zero, a mixed QL estimating equation is developed to estimate coefficients of geographic clusters and covariates. We use the Benjamini-Hochberg procedure (1995) to find a threshold for p-values to address the multiple testing problem. A quasi-deviance criterion is used to regroup the estimated clusters to find geographic clusters with arbitrary shapes. We conduct simulations to compare the performance of the proposed method with other scan statistics. For illustration, the method is applied to enterovirus data from Taiwan. © 2016, The International Biometric Society.

Likelihood of Tree Topologies with Fossils and Diversification Rate Estimation.

PubMed

Didier, Gilles; Fau, Marine; Laurin, Michel

2017-11-01

Since the diversification process cannot be directly observed at the human scale, it has to be studied from the information available, namely the extant taxa and the fossil record. In this sense, phylogenetic trees including both extant taxa and fossils are the most complete representations of the diversification process that one can get. Such phylogenetic trees can be reconstructed from molecular and morphological data, to some extent. Among the temporal information of such phylogenetic trees, fossil ages are by far the most precisely known (divergence times are inferences calibrated mostly with fossils). We propose here a method to compute the likelihood of a phylogenetic tree with fossils in which the only considered time information is the fossil ages, and apply it to the estimation of the diversification rates from such data. Since it is required in our computation, we provide a method for determining the probability of a tree topology under the standard diversification model. Testing our approach on simulated data shows that the maximum likelihood rate estimates from the phylogenetic tree topology and the fossil dates are almost as accurate as those obtained by taking into account all the data, including the divergence times. Moreover, they are substantially more accurate than the estimates obtained only from the exact divergence times (without taking into account the fossil record). We also provide an empirical example composed of 50 Permo-Carboniferous eupelycosaur (early synapsid) taxa ranging in age from about 315 Ma (Late Carboniferous) to 270 Ma (shortly after the end of the Early Permian). Our analyses suggest a speciation (cladogenesis, or birth) rate of about 0.1 per lineage and per myr, a marginally lower extinction rate, and a considerable hidden paleobiodiversity of early synapsids. [Extinction rate; fossil ages; maximum likelihood estimation; speciation rate.]. © The Author(s) 2017. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Logistic regression for circular data

NASA Astrophysics Data System (ADS)

Al-Daffaie, Kadhem; Khan, Shahjahan

2017-05-01

This paper considers the relationship between a binary response and a circular predictor. It develops the logistic regression model by employing the linear-circular regression approach. The maximum likelihood method is used to estimate the parameters. The Newton-Raphson numerical method is used to find the estimated values of the parameters. A data set from weather records of Toowoomba city is analysed by the proposed methods. Moreover, a simulation study is considered. The R software is used for all computations and simulations.

Free energy reconstruction from steered dynamics without post-processing

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

Athenes, Manuel, E-mail: Manuel.Athenes@cea.f; Condensed Matter and Materials Division, Physics and Life Sciences Directorate, LLNL, Livermore, CA 94551; Marinica, Mihai-Cosmin

2010-09-20

Various methods achieving importance sampling in ensembles of nonequilibrium trajectories enable one to estimate free energy differences and, by maximum-likelihood post-processing, to reconstruct free energy landscapes. Here, based on Bayes theorem, we propose a more direct method in which a posterior likelihood function is used both to construct the steered dynamics and to infer the contribution to equilibrium of all the sampled states. The method is implemented with two steering schedules. First, using non-autonomous steering, we calculate the migration barrier of the vacancy in Fe-{alpha}. Second, using an autonomous scheduling related to metadynamics and equivalent to temperature-accelerated molecular dynamics, wemore » accurately reconstruct the two-dimensional free energy landscape of the 38-atom Lennard-Jones cluster as a function of an orientational bond-order parameter and energy, down to the solid-solid structural transition temperature of the cluster and without maximum-likelihood post-processing.« less

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.

Linkage disequilibrium interval mapping of quantitative trait loci.

PubMed

Boitard, Simon; Abdallah, Jihad; de Rochambeau, Hubert; Cierco-Ayrolles, Christine; Mangin, Brigitte

2006-03-16

For many years gene mapping studies have been performed through linkage analyses based on pedigree data. Recently, linkage disequilibrium methods based on unrelated individuals have been advocated as powerful tools to refine estimates of gene location. Many strategies have been proposed to deal with simply inherited disease traits. However, locating quantitative trait loci is statistically more challenging and considerable research is needed to provide robust and computationally efficient methods. Under a three-locus Wright-Fisher model, we derived approximate expressions for the expected haplotype frequencies in a population. We considered haplotypes comprising one trait locus and two flanking markers. Using these theoretical expressions, we built a likelihood-maximization method, called HAPim, for estimating the location of a quantitative trait locus. For each postulated position, the method only requires information from the two flanking markers. Over a wide range of simulation scenarios it was found to be more accurate than a two-marker composite likelihood method. It also performed as well as identity by descent methods, whilst being valuable in a wider range of populations. Our method makes efficient use of marker information, and can be valuable for fine mapping purposes. Its performance is increased if multiallelic markers are available. Several improvements can be developed to account for more complex evolution scenarios or provide robust confidence intervals for the location estimates.

FPGA Acceleration of the phylogenetic likelihood function for Bayesian MCMC inference methods.

PubMed

Zierke, Stephanie; Bakos, Jason D

2010-04-12

Likelihood (ML)-based phylogenetic inference has become a popular method for estimating the evolutionary relationships among species based on genomic sequence data. This method is used in applications such as RAxML, GARLI, MrBayes, PAML, and PAUP. The Phylogenetic Likelihood Function (PLF) is an important kernel computation for this method. The PLF consists of a loop with no conditional behavior or dependencies between iterations. As such it contains a high potential for exploiting parallelism using micro-architectural techniques. In this paper, we describe a technique for mapping the PLF and supporting logic onto a Field Programmable Gate Array (FPGA)-based co-processor. By leveraging the FPGA's on-chip DSP modules and the high-bandwidth local memory attached to the FPGA, the resultant co-processor can accelerate ML-based methods and outperform state-of-the-art multi-core processors. We use the MrBayes 3 tool as a framework for designing our co-processor. For large datasets, we estimate that our accelerated MrBayes, if run on a current-generation FPGA, achieves a 10x speedup relative to software running on a state-of-the-art server-class microprocessor. The FPGA-based implementation achieves its performance by deeply pipelining the likelihood computations, performing multiple floating-point operations in parallel, and through a natural log approximation that is chosen specifically to leverage a deeply pipelined custom architecture. Heterogeneous computing, which combines general-purpose processors with special-purpose co-processors such as FPGAs and GPUs, is a promising approach for high-performance phylogeny inference as shown by the growing body of literature in this field. FPGAs in particular are well-suited for this task because of their low power consumption as compared to many-core processors and Graphics Processor Units (GPUs).

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.

Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable

ERIC Educational Resources Information Center

du Toit, Stephen H. C.; Cudeck, Robert

2009-01-01

A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution…

Maximum Likelihood Estimation in Meta-Analytic Structural Equation Modeling

ERIC Educational Resources Information Center

Oort, Frans J.; Jak, Suzanne

2016-01-01

Meta-analytic structural equation modeling (MASEM) involves fitting models to a common population correlation matrix that is estimated on the basis of correlation coefficients that are reported by a number of independent studies. MASEM typically consist of two stages. The method that has been found to perform best in terms of statistical…

Period Estimation for Sparsely-sampled Quasi-periodic Light Curves Applied to Miras

NASA Astrophysics Data System (ADS)

He, Shiyuan; Yuan, Wenlong; Huang, Jianhua Z.; Long, James; Macri, Lucas M.

2016-12-01

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

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.

Comparing Different Approaches of Bias Correction for Ability Estimation in IRT Models. Research Report. ETS RR-08-13

ERIC Educational Resources Information Center

Lee, Yi-Hsuan; Zhang, Jinming

2008-01-01

The method of maximum-likelihood is typically applied to item response theory (IRT) models when the ability parameter is estimated while conditioning on the true item parameters. In practice, the item parameters are unknown and need to be estimated first from a calibration sample. Lewis (1985) and Zhang and Lu (2007) proposed the expected response…

Maximum likelihood estimation of linkage disequilibrium in half-sib families.

PubMed

Gomez-Raya, L

2012-05-01

Maximum likelihood methods for the estimation of linkage disequilibrium between biallelic DNA-markers in half-sib families (half-sib method) are developed for single and multifamily situations. Monte Carlo computer simulations were carried out for a variety of scenarios regarding sire genotypes, linkage disequilibrium, recombination fraction, family size, and number of families. A double heterozygote sire was simulated with recombination fraction of 0.00, linkage disequilibrium among dams of δ=0.10, and alleles at both markers segregating at intermediate frequencies for a family size of 500. The average estimates of δ were 0.17, 0.25, and 0.10 for Excoffier and Slatkin (1995), maternal informative haplotypes, and the half-sib method, respectively. A multifamily EM algorithm was tested at intermediate frequencies by computer simulation. The range of the absolute difference between estimated and simulated δ was between 0.000 and 0.008. A cattle half-sib family was genotyped with the Illumina 50K BeadChip. There were 314,730 SNP pairs for which the sire was a homo-heterozygote with average estimates of r2 of 0.115, 0.067, and 0.111 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. There were 208,872 SNP pairs for which the sire was double heterozygote with average estimates of r2 across the genome of 0.100, 0.267, and 0.925 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. Genome analyses for all possible sire genotypes with 829,042 tests showed that ignoring half-sib family structure leads to upward biased estimates of linkage disequilibrium. Published inferences on population structure and evolution of cattle should be revisited after accommodating existing half-sib family structure in the estimation of linkage disequilibrium.

Maximum Likelihood Estimation of Linkage Disequilibrium in Half-Sib Families

PubMed Central

Gomez-Raya, L.

2012-01-01

Maximum likelihood methods for the estimation of linkage disequilibrium between biallelic DNA-markers in half-sib families (half-sib method) are developed for single and multifamily situations. Monte Carlo computer simulations were carried out for a variety of scenarios regarding sire genotypes, linkage disequilibrium, recombination fraction, family size, and number of families. A double heterozygote sire was simulated with recombination fraction of 0.00, linkage disequilibrium among dams of δ = 0.10, and alleles at both markers segregating at intermediate frequencies for a family size of 500. The average estimates of δ were 0.17, 0.25, and 0.10 for Excoffier and Slatkin (1995), maternal informative haplotypes, and the half-sib method, respectively. A multifamily EM algorithm was tested at intermediate frequencies by computer simulation. The range of the absolute difference between estimated and simulated δ was between 0.000 and 0.008. A cattle half-sib family was genotyped with the Illumina 50K BeadChip. There were 314,730 SNP pairs for which the sire was a homo-heterozygote with average estimates of r2 of 0.115, 0.067, and 0.111 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. There were 208,872 SNP pairs for which the sire was double heterozygote with average estimates of r2 across the genome of 0.100, 0.267, and 0.925 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. Genome analyses for all possible sire genotypes with 829,042 tests showed that ignoring half-sib family structure leads to upward biased estimates of linkage disequilibrium. Published inferences on population structure and evolution of cattle should be revisited after accommodating existing half-sib family structure in the estimation of linkage disequilibrium. PMID:22377635

Damage diagnosis algorithm using a sequential change point detection method with an unknown distribution for damage

NASA Astrophysics Data System (ADS)

Noh, Hae Young; Rajagopal, Ram; Kiremidjian, Anne S.

2012-04-01

This paper introduces a damage diagnosis algorithm for civil structures that uses a sequential change point detection method for the cases where the post-damage feature distribution is unknown a priori. This algorithm extracts features from structural vibration data using time-series analysis and then declares damage using the change point detection method. The change point detection method asymptotically minimizes detection delay for a given false alarm rate. The conventional method uses the known pre- and post-damage feature distributions to perform a sequential hypothesis test. In practice, however, the post-damage distribution is unlikely to be known a priori. Therefore, our algorithm estimates and updates this distribution as data are collected using the maximum likelihood and the Bayesian methods. We also applied an approximate method to reduce the computation load and memory requirement associated with the estimation. The algorithm is validated using multiple sets of simulated data and a set of experimental data collected from a four-story steel special moment-resisting frame. Our algorithm was able to estimate the post-damage distribution consistently and resulted in detection delays only a few seconds longer than the delays from the conventional method that assumes we know the post-damage feature distribution. We confirmed that the Bayesian method is particularly efficient in declaring damage with minimal memory requirement, but the maximum likelihood method provides an insightful heuristic approach.

Statistical methods for analysis of radiation effects with tumor and dose location-specific information with application to the WECARE study of asynchronous contralateral breast cancer

PubMed Central

Langholz, Bryan; Thomas, Duncan C.; Stovall, Marilyn; Smith, Susan A.; Boice, John D.; Shore, Roy E.; Bernstein, Leslie; Lynch, Charles F.; Zhang, Xinbo; Bernstein, Jonine L.

2009-01-01

Summary Methods for the analysis of individually matched case-control studies with location-specific radiation dose and tumor location information are described. These include likelihood methods for analyses that just use cases with precise location of tumor information and methods that also include cases with imprecise tumor location information. The theory establishes that each of these likelihood based methods estimates the same radiation rate ratio parameters, within the context of the appropriate model for location and subject level covariate effects. The underlying assumptions are characterized and the potential strengths and limitations of each method are described. The methods are illustrated and compared using the WECARE study of radiation and asynchronous contralateral breast cancer. PMID:18647297

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.

SEPARABLE FACTOR ANALYSIS WITH APPLICATIONS TO MORTALITY DATA

PubMed Central

Fosdick, Bailey K.; Hoff, Peter D.

2014-01-01

Human mortality data sets can be expressed as multiway data arrays, the dimensions of which correspond to categories by which mortality rates are reported, such as age, sex, country and year. Regression models for such data typically assume an independent error distribution or an error model that allows for dependence along at most one or two dimensions of the data array. However, failing to account for other dependencies can lead to inefficient estimates of regression parameters, inaccurate standard errors and poor predictions. An alternative to assuming independent errors is to allow for dependence along each dimension of the array using a separable covariance model. However, the number of parameters in this model increases rapidly with the dimensions of the array and, for many arrays, maximum likelihood estimates of the covariance parameters do not exist. In this paper, we propose a submodel of the separable covariance model that estimates the covariance matrix for each dimension as having factor analytic structure. This model can be viewed as an extension of factor analysis to array-valued data, as it uses a factor model to estimate the covariance along each dimension of the array. We discuss properties of this model as they relate to ordinary factor analysis, describe maximum likelihood and Bayesian estimation methods, and provide a likelihood ratio testing procedure for selecting the factor model ranks. We apply this methodology to the analysis of data from the Human Mortality Database, and show in a cross-validation experiment how it outperforms simpler methods. Additionally, we use this model to impute mortality rates for countries that have no mortality data for several years. Unlike other approaches, our methodology is able to estimate similarities between the mortality rates of countries, time periods and sexes, and use this information to assist with the imputations. PMID:25489353

BAYESIAN LARGE-SCALE MULTIPLE REGRESSION WITH SUMMARY STATISTICS FROM GENOME-WIDE ASSOCIATION STUDIES1

PubMed Central

Zhu, Xiang; Stephens, Matthew

2017-01-01

Bayesian methods for large-scale multiple regression provide attractive approaches to the analysis of genome-wide association studies (GWAS). For example, they can estimate heritability of complex traits, allowing for both polygenic and sparse models; and by incorporating external genomic data into the priors, they can increase power and yield new biological insights. However, these methods require access to individual genotypes and phenotypes, which are often not easily available. Here we provide a framework for performing these analyses without individual-level data. Specifically, we introduce a “Regression with Summary Statistics” (RSS) likelihood, which relates the multiple regression coefficients to univariate regression results that are often easily available. The RSS likelihood requires estimates of correlations among covariates (SNPs), which also can be obtained from public databases. We perform Bayesian multiple regression analysis by combining the RSS likelihood with previously proposed prior distributions, sampling posteriors by Markov chain Monte Carlo. In a wide range of simulations RSS performs similarly to analyses using the individual data, both for estimating heritability and detecting associations. We apply RSS to a GWAS of human height that contains 253,288 individuals typed at 1.06 million SNPs, for which analyses of individual-level data are practically impossible. Estimates of heritability (52%) are consistent with, but more precise, than previous results using subsets of these data. We also identify many previously unreported loci that show evidence for association with height in our analyses. Software is available at https://github.com/stephenslab/rss. PMID:29399241

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;…

Tests for detecting overdispersion in models with measurement error in covariates.

PubMed

Yang, Yingsi; Wong, Man Yu

2015-11-30

Measurement error in covariates can affect the accuracy in count data modeling and analysis. In overdispersion identification, the true mean-variance relationship can be obscured under the influence of measurement error in covariates. In this paper, we propose three tests for detecting overdispersion when covariates are measured with error: a modified score test and two score tests based on the proposed approximate likelihood and quasi-likelihood, respectively. The proposed approximate likelihood is derived under the classical measurement error model, and the resulting approximate maximum likelihood estimator is shown to have superior efficiency. Simulation results also show that the score test based on approximate likelihood outperforms the test based on quasi-likelihood and other alternatives in terms of empirical power. By analyzing a real dataset containing the health-related quality-of-life measurements of a particular group of patients, we demonstrate the importance of the proposed methods by showing that the analyses with and without measurement error correction yield significantly different results. Copyright © 2015 John Wiley & Sons, Ltd.

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.

Patch-based image reconstruction for PET using prior-image derived dictionaries

NASA Astrophysics Data System (ADS)

Tahaei, Marzieh S.; Reader, Andrew J.

2016-09-01

In PET image reconstruction, regularization is often needed to reduce the noise in the resulting images. Patch-based image processing techniques have recently been successfully used for regularization in medical image reconstruction through a penalized likelihood framework. Re-parameterization within reconstruction is another powerful regularization technique in which the object in the scanner is re-parameterized using coefficients for spatially-extensive basis vectors. In this work, a method for extracting patch-based basis vectors from the subject’s MR image is proposed. The coefficients for these basis vectors are then estimated using the conventional MLEM algorithm. Furthermore, using the alternating direction method of multipliers, an algorithm for optimizing the Poisson log-likelihood while imposing sparsity on the parameters is also proposed. This novel method is then utilized to find sparse coefficients for the patch-based basis vectors extracted from the MR image. The results indicate the superiority of the proposed methods to patch-based regularization using the penalized likelihood framework.

Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function

NASA Astrophysics Data System (ADS)

Rizki, S. W.; Mara, M. N.; Sulistianingsih, E.

2017-06-01

This paper elaborates a research of the cancer patients after receiving a treatment in cencored data using Bayesian estimation under Linex Loss function for Survival Model which is assumed as an exponential distribution. By giving Gamma distribution as prior and likelihood function produces a gamma distribution as posterior distribution. The posterior distribution is used to find estimatior {\\hat{λ }}BL by using Linex approximation. After getting {\\hat{λ }}BL, the estimators of hazard function {\\hat{h}}BL and survival function {\\hat{S}}BL can be found. Finally, we compare the result of Maximum Likelihood Estimation (MLE) and Linex approximation to find the best method for this observation by finding smaller MSE. The result shows that MSE of hazard and survival under MLE are 2.91728E-07 and 0.000309004 and by using Bayesian Linex worths 2.8727E-07 and 0.000304131, respectively. It concludes that the Bayesian Linex is better than MLE.

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

Maximum likelihood estimation of signal-to-noise ratio and combiner weight

NASA Technical Reports Server (NTRS)

Kalson, S.; Dolinar, S. J.

1986-01-01

An algorithm for estimating signal to noise ratio and combiner weight parameters for a discrete time series is presented. The algorithm is based upon the joint maximum likelihood estimate of the signal and noise power. The discrete-time series are the sufficient statistics obtained after matched filtering of a biphase modulated signal in additive white Gaussian noise, before maximum likelihood decoding is performed.

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...

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.

Deterministic quantum annealing expectation-maximization algorithm

NASA Astrophysics Data System (ADS)

Miyahara, Hideyuki; Tsumura, Koji; Sughiyama, Yuki

2017-11-01

Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial configurations and fails to find the global optimum. On the other hand, in the field of physics, quantum annealing (QA) was proposed as a novel optimization approach. Motivated by QA, we propose a quantum annealing extension of EM, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm. We also discuss its advantage in terms of the path integral formulation. Furthermore, by employing numerical simulations, we illustrate how DQAEM works in MLE and show that DQAEM moderate the problem of local optima in EM.

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.

A new method of differential structural analysis of gamma-family basic parameters

NASA Technical Reports Server (NTRS)

Melkumian, L. G.; Ter-Antonian, S. V.; Smorodin, Y. A.

1985-01-01

The maximum likelihood method is used for the first time to restore parameters of electron photon cascades registered on X-ray films. The method permits one to carry out a structural analysis of the gamma quanta family darkening spots independent of the gamma quanta overlapping degree, and to obtain maximum admissible accuracies in estimating the energies of the gamma quanta composing a family. The parameter estimation accuracy weakly depends on the value of the parameters themselves and exceeds by an order of the values obtained by integral methods.

Investigating the Impact of Uncertainty about Item Parameters on Ability Estimation

ERIC Educational Resources Information Center

Zhang, Jinming; Xie, Minge; Song, Xiaolan; Lu, Ting

2011-01-01

Asymptotic expansions of the maximum likelihood estimator (MLE) and weighted likelihood estimator (WLE) of an examinee's ability are derived while item parameter estimators are treated as covariates measured with error. The asymptotic formulae present the amount of bias of the ability estimators due to the uncertainty of item parameter estimators.…

Use of inequality constrained least squares estimation in small area estimation

NASA Astrophysics Data System (ADS)

Abeygunawardana, R. A. B.; Wickremasinghe, W. N.

2017-05-01

Traditional surveys provide estimates that are based only on the sample observations collected for the population characteristic of interest. However, these estimates may have unacceptably large variance for certain domains. Small Area Estimation (SAE) deals with determining precise and accurate estimates for population characteristics of interest for such domains. SAE usually uses least squares or maximum likelihood procedures incorporating prior information and current survey data. Many available methods in SAE use constraints in equality form. However there are practical situations where certain inequality restrictions on model parameters are more realistic. It will lead to Inequality Constrained Least Squares (ICLS) estimates if the method used is least squares. In this study ICLS estimation procedure is applied to many proposed small area estimates.

Using DNA fingerprints to infer familial relationships within NHANES III households

PubMed Central

Katki, Hormuzd A.; Sanders, Christopher L.; Graubard, Barry I.; Bergen, Andrew W.

2009-01-01

Developing, targeting, and evaluating genomic strategies for population-based disease prevention require population-based data. In response to this urgent need, genotyping has been conducted within the Third National Health and Nutrition Examination (NHANES III), the nationally-representative household-interview health survey in the U.S. However, before these genetic analyses can occur, family relationships within households must be accurately ascertained. Unfortunately, reported family relationships within NHANES III households based on questionnaire data are incomplete and inconclusive with regards to actual biological relatedness of family members. We inferred family relationships within households using DNA fingerprints (Identifiler®) that contain the DNA loci used by law enforcement agencies for forensic identification of individuals. However, performance of these loci for relationship inference is not well understood. We evaluated two competing statistical methods for relationship inference on pairs of household members: an exact likelihood ratio relying on allele frequencies to an Identical By State (IBS) likelihood ratio that only requires matching alleles. We modified these methods to account for genotyping errors and population substructure. The two methods usually agree on the rankings of the most likely relationships. However, the IBS method underestimates the likelihood ratio by not accounting for the informativeness of matching rare alleles. The likelihood ratio is sensitive to estimates of population substructure, and parent-child relationships are sensitive to the specified genotyping error rate. These loci were unable to distinguish second-degree relationships and cousins from being unrelated. The genetic data is also useful for verifying reported relationships and identifying data quality issues. An important by-product is the first explicitly nationally-representative estimates of allele frequencies at these ubiquitous forensic loci. PMID:20664713

Sequential structural damage diagnosis algorithm using a change point detection method

NASA Astrophysics Data System (ADS)

Noh, H.; Rajagopal, R.; Kiremidjian, A. S.

2013-11-01

This paper introduces a damage diagnosis algorithm for civil structures that uses a sequential change point detection method. The general change point detection method uses the known pre- and post-damage feature distributions to perform a sequential hypothesis test. In practice, however, the post-damage distribution is unlikely to be known a priori, unless we are looking for a known specific type of damage. Therefore, we introduce an additional algorithm that estimates and updates this distribution as data are collected using the maximum likelihood and the Bayesian methods. We also applied an approximate method to reduce the computation load and memory requirement associated with the estimation. The algorithm is validated using a set of experimental data collected from a four-story steel special moment-resisting frame and multiple sets of simulated data. Various features of different dimensions have been explored, and the algorithm was able to identify damage, particularly when it uses multidimensional damage sensitive features and lower false alarm rates, with a known post-damage feature distribution. For unknown feature distribution cases, the post-damage distribution was consistently estimated and the detection delays were only a few time steps longer than the delays from the general method that assumes we know the post-damage feature distribution. We confirmed that the Bayesian method is particularly efficient in declaring damage with minimal memory requirement, but the maximum likelihood method provides an insightful heuristic approach.

A Comparison of Missing-Data Procedures for Arima Time-Series Analysis

ERIC Educational Resources Information Center

Velicer, Wayne F.; Colby, Suzanne M.

2005-01-01

Missing data are a common practical problem for longitudinal designs. Time-series analysis is a longitudinal method that involves a large number of observations on a single unit. Four different missing-data methods (deletion, mean substitution, mean of adjacent observations, and maximum likelihood estimation) were evaluated. Computer-generated…

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 ...

Multilevel Modeling in the Presence of Outliers: A Comparison of Robust Estimation Methods

ERIC Educational Resources Information Center

Finch, Holmes

2017-01-01

Multilevel models (MLMs) have proven themselves to be very useful in social science research, as data from a variety of sources is sampled such that individuals at level-1 are nested within clusters such as schools, hospitals, counseling centers, and business entities at level-2. MLMs using restricted maximum likelihood estimation (REML) provide…

A Simple Method for Estimating Informative Node Age Priors for the Fossil Calibration of Molecular Divergence Time Analyses

PubMed Central

Nowak, Michael D.; Smith, Andrew B.; Simpson, Carl; Zwickl, Derrick J.

2013-01-01

Molecular divergence time analyses often rely on the age of fossil lineages to calibrate node age estimates. Most divergence time analyses are now performed in a Bayesian framework, where fossil calibrations are incorporated as parametric prior probabilities on node ages. It is widely accepted that an ideal parameterization of such node age prior probabilities should be based on a comprehensive analysis of the fossil record of the clade of interest, but there is currently no generally applicable approach for calculating such informative priors. We provide here a simple and easily implemented method that employs fossil data to estimate the likely amount of missing history prior to the oldest fossil occurrence of a clade, which can be used to fit an informative parametric prior probability distribution on a node age. Specifically, our method uses the extant diversity and the stratigraphic distribution of fossil lineages confidently assigned to a clade to fit a branching model of lineage diversification. Conditioning this on a simple model of fossil preservation, we estimate the likely amount of missing history prior to the oldest fossil occurrence of a clade. The likelihood surface of missing history can then be translated into a parametric prior probability distribution on the age of the clade of interest. We show that the method performs well with simulated fossil distribution data, but that the likelihood surface of missing history can at times be too complex for the distribution-fitting algorithm employed by our software tool. An empirical example of the application of our method is performed to estimate echinoid node ages. A simulation-based sensitivity analysis using the echinoid data set shows that node age prior distributions estimated under poor preservation rates are significantly less informative than those estimated under high preservation rates. PMID:23755303

Spurious Latent Class Problem in the Mixed Rasch Model: A Comparison of Three Maximum Likelihood Estimation Methods under Different Ability Distributions

ERIC Educational Resources Information Center

Sen, Sedat

2018-01-01

Recent research has shown that over-extraction of latent classes can be observed in the Bayesian estimation of the mixed Rasch model when the distribution of ability is non-normal. This study examined the effect of non-normal ability distributions on the number of latent classes in the mixed Rasch model when estimated with maximum likelihood…

Selected aspects of prior and likelihood information for a Bayesian classifier in a road safety analysis.

PubMed

Nowakowska, Marzena

2017-04-01

The development of the Bayesian logistic regression model classifying the road accident severity is discussed. The already exploited informative priors (method of moments, maximum likelihood estimation, and two-stage Bayesian updating), along with the original idea of a Boot prior proposal, are investigated when no expert opinion has been available. In addition, two possible approaches to updating the priors, in the form of unbalanced and balanced training data sets, are presented. The obtained logistic Bayesian models are assessed on the basis of a deviance information criterion (DIC), highest probability density (HPD) intervals, and coefficients of variation estimated for the model parameters. The verification of the model accuracy has been based on sensitivity, specificity and the harmonic mean of sensitivity and specificity, all calculated from a test data set. The models obtained from the balanced training data set have a better classification quality than the ones obtained from the unbalanced training data set. The two-stage Bayesian updating prior model and the Boot prior model, both identified with the use of the balanced training data set, outperform the non-informative, method of moments, and maximum likelihood estimation prior models. It is important to note that one should be careful when interpreting the parameters since different priors can lead to different models. Copyright © 2017 Elsevier Ltd. All rights reserved.

Matching mammographic regions in mediolateral oblique and cranio caudal views: a probabilistic approach

NASA Astrophysics Data System (ADS)

Samulski, Maurice; Karssemeijer, Nico

2008-03-01

Most of the current CAD systems detect suspicious mass regions independently in single views. In this paper we present a method to match corresponding regions in mediolateral oblique (MLO) and craniocaudal (CC) mammographic views of the breast. For every possible combination of mass regions in the MLO view and CC view, a number of features are computed, such as the difference in distance of a region to the nipple, a texture similarity measure, the gray scale correlation and the likelihood of malignancy of both regions computed by single-view analysis. In previous research, Linear Discriminant Analysis was used to discriminate between correct and incorrect links. In this paper we investigate if the performance can be improved by employing a statistical method in which four classes are distinguished. These four classes are defined by the combinations of view (MLO/CC) and pathology (TP/FP) labels. We use distance-weighted k-Nearest Neighbor density estimation to estimate the likelihood of a region combination. Next, a correspondence score is calculated as the likelihood that the region combination is a TP-TP link. The method was tested on 412 cases with a malignant lesion visible in at least one of the views. In 82.4% of the cases a correct link could be established between the TP detections in both views. In future work, we will use the framework presented here to develop a context dependent region matching scheme, which takes the number and likelihood of possible alternatives into account. It is expected that more accurate determination of matching probabilities will lead to improved CAD performance.

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.

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.

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.

Comparison of smoothing methods for the development of a smoothed seismicity model for Alaska and the implications for seismic hazard

NASA Astrophysics Data System (ADS)

Moschetti, M. P.; Mueller, C. S.; Boyd, O. S.; Petersen, M. D.

2013-12-01

In anticipation of the update of the Alaska seismic hazard maps (ASHMs) by the U. S. Geological Survey, we report progress on the comparison of smoothed seismicity models developed using fixed and adaptive smoothing algorithms, and investigate the sensitivity of seismic hazard to the models. While fault-based sources, such as those for great earthquakes in the Alaska-Aleutian subduction zone and for the ~10 shallow crustal faults within Alaska, dominate the seismic hazard estimates for locations near to the sources, smoothed seismicity rates make important contributions to seismic hazard away from fault-based sources and where knowledge of recurrence and magnitude is not sufficient for use in hazard studies. Recent developments in adaptive smoothing methods and statistical tests for evaluating and comparing rate models prompt us to investigate the appropriateness of adaptive smoothing for the ASHMs. We develop smoothed seismicity models for Alaska using fixed and adaptive smoothing methods and compare the resulting models by calculating and evaluating the joint likelihood test. We use the earthquake catalog, and associated completeness levels, developed for the 2007 ASHM to produce fixed-bandwidth-smoothed models with smoothing distances varying from 10 to 100 km and adaptively smoothed models. Adaptive smoothing follows the method of Helmstetter et al. and defines a unique smoothing distance for each earthquake epicenter from the distance to the nth nearest neighbor. The consequence of the adaptive smoothing methods is to reduce smoothing distances, causing locally increased seismicity rates, where seismicity rates are high and to increase smoothing distances where seismicity is sparse. We follow guidance from previous studies to optimize the neighbor number (n-value) by comparing model likelihood values, which estimate the likelihood that the observed earthquake epicenters from the recent catalog are derived from the smoothed rate models. We compare likelihood values from all rate models to rank the smoothing methods. We find that adaptively smoothed seismicity models yield better likelihood values than the fixed smoothing models. Holding all other (source and ground motion) models constant, we calculate seismic hazard curves for all points across Alaska on a 0.1 degree grid, using the adaptively smoothed and fixed smoothed seismicity models separately. Because adaptively smoothed models concentrate seismicity near the earthquake epicenters where seismicity rates are high, the corresponding hazard values are higher, locally, but reduced with distance from observed seismicity, relative to the hazard from fixed-bandwidth models. We suggest that adaptively smoothed seismicity models be considered for implementation in the update to the ASHMs because of their improved likelihood estimates relative to fixed smoothing methods; however, concomitant increases in seismic hazard will cause significant changes in regions of high seismicity, such as near the subduction zone, northeast of Kotzebue, and along the NNE trending zone of seismicity in the Alaskan interior.

Comparison of smoothing methods for the development of a smoothed seismicity model for Alaska and the implications for seismic hazard

USGS Publications Warehouse

Moschetti, Morgan P.; Mueller, Charles S.; Boyd, Oliver S.; Petersen, Mark D.

2014-01-01

In anticipation of the update of the Alaska seismic hazard maps (ASHMs) by the U. S. Geological Survey, we report progress on the comparison of smoothed seismicity models developed using fixed and adaptive smoothing algorithms, and investigate the sensitivity of seismic hazard to the models. While fault-based sources, such as those for great earthquakes in the Alaska-Aleutian subduction zone and for the ~10 shallow crustal faults within Alaska, dominate the seismic hazard estimates for locations near to the sources, smoothed seismicity rates make important contributions to seismic hazard away from fault-based sources and where knowledge of recurrence and magnitude is not sufficient for use in hazard studies. Recent developments in adaptive smoothing methods and statistical tests for evaluating and comparing rate models prompt us to investigate the appropriateness of adaptive smoothing for the ASHMs. We develop smoothed seismicity models for Alaska using fixed and adaptive smoothing methods and compare the resulting models by calculating and evaluating the joint likelihood test. We use the earthquake catalog, and associated completeness levels, developed for the 2007 ASHM to produce fixed-bandwidth-smoothed models with smoothing distances varying from 10 to 100 km and adaptively smoothed models. Adaptive smoothing follows the method of Helmstetter et al. and defines a unique smoothing distance for each earthquake epicenter from the distance to the nth nearest neighbor. The consequence of the adaptive smoothing methods is to reduce smoothing distances, causing locally increased seismicity rates, where seismicity rates are high and to increase smoothing distances where seismicity is sparse. We follow guidance from previous studies to optimize the neighbor number (n-value) by comparing model likelihood values, which estimate the likelihood that the observed earthquake epicenters from the recent catalog are derived from the smoothed rate models. We compare likelihood values from all rate models to rank the smoothing methods. We find that adaptively smoothed seismicity models yield better likelihood values than the fixed smoothing models. Holding all other (source and ground motion) models constant, we calculate seismic hazard curves for all points across Alaska on a 0.1 degree grid, using the adaptively smoothed and fixed smoothed seismicity models separately. Because adaptively smoothed models concentrate seismicity near the earthquake epicenters where seismicity rates are high, the corresponding hazard values are higher, locally, but reduced with distance from observed seismicity, relative to the hazard from fixed-bandwidth models. We suggest that adaptively smoothed seismicity models be considered for implementation in the update to the ASHMs because of their improved likelihood estimates relative to fixed smoothing methods; however, concomitant increases in seismic hazard will cause significant changes in regions of high seismicity, such as near the subduction zone, northeast of Kotzebue, and along the NNE trending zone of seismicity in the Alaskan interior.

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

Stochastic capture zone analysis of an arsenic-contaminated well using the generalized likelihood uncertainty estimator (GLUE) methodology

NASA Astrophysics Data System (ADS)

Morse, Brad S.; Pohll, Greg; Huntington, Justin; Rodriguez Castillo, Ramiro

2003-06-01

In 1992, Mexican researchers discovered concentrations of arsenic in excess of World Heath Organization (WHO) standards in several municipal wells in the Zimapan Valley of Mexico. This study describes a method to delineate a capture zone for one of the most highly contaminated wells to aid in future well siting. A stochastic approach was used to model the capture zone because of the high level of uncertainty in several input parameters. Two stochastic techniques were performed and compared: "standard" Monte Carlo analysis and the generalized likelihood uncertainty estimator (GLUE) methodology. The GLUE procedure differs from standard Monte Carlo analysis in that it incorporates a goodness of fit (termed a likelihood measure) in evaluating the model. This allows for more information (in this case, head data) to be used in the uncertainty analysis, resulting in smaller prediction uncertainty. Two likelihood measures are tested in this study to determine which are in better agreement with the observed heads. While the standard Monte Carlo approach does not aid in parameter estimation, the GLUE methodology indicates best fit models when hydraulic conductivity is approximately 10-6.5 m/s, with vertically isotropic conditions and large quantities of interbasin flow entering the basin. Probabilistic isochrones (capture zone boundaries) are then presented, and as predicted, the GLUE-derived capture zones are significantly smaller in area than those from the standard Monte Carlo approach.

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.

Generalized Likelihood Uncertainty Estimation (GLUE) methodology for optimization of extraction in natural products.

PubMed

Maulidiani; Rudiyanto; Abas, Faridah; Ismail, Intan Safinar; Lajis, Nordin H

2018-06-01

Optimization process is an important aspect in the natural product extractions. Herein, an alternative approach is proposed for the optimization in extraction, namely, the Generalized Likelihood Uncertainty Estimation (GLUE). The approach combines the Latin hypercube sampling, the feasible range of independent variables, the Monte Carlo simulation, and the threshold criteria of response variables. The GLUE method is tested in three different techniques including the ultrasound, the microwave, and the supercritical CO 2 assisted extractions utilizing the data from previously published reports. The study found that this method can: provide more information on the combined effects of the independent variables on the response variables in the dotty plots; deal with unlimited number of independent and response variables; consider combined multiple threshold criteria, which is subjective depending on the target of the investigation for response variables; and provide a range of values with their distribution for the optimization. Copyright © 2018 Elsevier Ltd. All rights reserved.

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

Likelihood Ratios for Glaucoma Diagnosis Using Spectral Domain Optical Coherence Tomography

PubMed Central

Lisboa, Renato; Mansouri, Kaweh; Zangwill, Linda M.; Weinreb, Robert N.; Medeiros, Felipe A.

2014-01-01

Purpose To present a methodology for calculating likelihood ratios for glaucoma diagnosis for continuous retinal nerve fiber layer (RNFL) thickness measurements from spectral domain optical coherence tomography (spectral-domain OCT). Design Observational cohort study. Methods 262 eyes of 187 patients with glaucoma and 190 eyes of 100 control subjects were included in the study. Subjects were recruited from the Diagnostic Innovations Glaucoma Study. Eyes with preperimetric and perimetric glaucomatous damage were included in the glaucoma group. The control group was composed of healthy eyes with normal visual fields from subjects recruited from the general population. All eyes underwent RNFL imaging with Spectralis spectral-domain OCT. Likelihood ratios for glaucoma diagnosis were estimated for specific global RNFL thickness measurements using a methodology based on estimating the tangents to the Receiver Operating Characteristic (ROC) curve. Results Likelihood ratios could be determined for continuous values of average RNFL thickness. Average RNFL thickness values lower than 86μm were associated with positive LRs, i.e., LRs greater than 1; whereas RNFL thickness values higher than 86μm were associated with negative LRs, i.e., LRs smaller than 1. A modified Fagan nomogram was provided to assist calculation of post-test probability of disease from the calculated likelihood ratios and pretest probability of disease. Conclusion The methodology allowed calculation of likelihood ratios for specific RNFL thickness values. By avoiding arbitrary categorization of test results, it potentially allows for an improved integration of test results into diagnostic clinical decision-making. PMID:23972303

A comprehensive assessment of collision likelihood in Geosynchronous Earth Orbit

NASA Astrophysics Data System (ADS)

Oltrogge, D. L.; Alfano, S.; Law, C.; Cacioni, A.; Kelso, T. S.

2018-06-01

Knowing the likelihood of collision for satellites operating in Geosynchronous Earth Orbit (GEO) is of extreme importance and interest to the global community and the operators of GEO spacecraft. Yet for all of its importance, a comprehensive assessment of GEO collision likelihood is difficult to do and has never been done. In this paper, we employ six independent and diverse assessment methods to estimate GEO collision likelihood. Taken in aggregate, this comprehensive assessment offer new insights into GEO collision likelihood that are within a factor of 3.5 of each other. These results are then compared to four collision and seven encounter rate estimates previously published. Collectively, these new findings indicate that collision likelihood in GEO is as much as four orders of magnitude higher than previously published by other researchers. Results indicate that a collision is likely to occur every 4 years for one satellite out of the entire GEO active satellite population against a 1 cm RSO catalogue, and every 50 years against a 20 cm RSO catalogue. Further, previous assertions that collision relative velocities are low (i.e., <1 km/s) in GEO are disproven, with some GEO relative velocities as high as 4 km/s identified. These new findings indicate that unless operators successfully mitigate this collision risk, the GEO orbital arc is and will remain at high risk of collision, with the potential for serious follow-on collision threats from post-collision debris when a substantial GEO collision occurs.

On the Relationships between Jeffreys Modal and Weighted Likelihood Estimation of Ability under Logistic IRT Models

ERIC Educational Resources Information Center

Magis, David; Raiche, Gilles

2012-01-01

This paper focuses on two estimators of ability with logistic item response theory models: the Bayesian modal (BM) estimator and the weighted likelihood (WL) estimator. For the BM estimator, Jeffreys' prior distribution is considered, and the corresponding estimator is referred to as the Jeffreys modal (JM) estimator. It is established that under…

Modelling of extreme rainfall events in Peninsular Malaysia based on annual maximum and partial duration series

NASA Astrophysics Data System (ADS)

Zin, Wan Zawiah Wan; Shinyie, Wendy Ling; Jemain, Abdul Aziz

2015-02-01

In this study, two series of data for extreme rainfall events are generated based on Annual Maximum and Partial Duration Methods, derived from 102 rain-gauge stations in Peninsular from 1982-2012. To determine the optimal threshold for each station, several requirements must be satisfied and Adapted Hill estimator is employed for this purpose. A semi-parametric bootstrap is then used to estimate the mean square error (MSE) of the estimator at each threshold and the optimal threshold is selected based on the smallest MSE. The mean annual frequency is also checked to ensure that it lies in the range of one to five and the resulting data is also de-clustered to ensure independence. The two data series are then fitted to Generalized Extreme Value and Generalized Pareto distributions for annual maximum and partial duration series, respectively. The parameter estimation methods used are the Maximum Likelihood and the L-moment methods. Two goodness of fit tests are then used to evaluate the best-fitted distribution. The results showed that the Partial Duration series with Generalized Pareto distribution and Maximum Likelihood parameter estimation provides the best representation for extreme rainfall events in Peninsular Malaysia for majority of the stations studied. Based on these findings, several return values are also derived and spatial mapping are constructed to identify the distribution characteristic of extreme rainfall in Peninsular Malaysia.

An EM-based semi-parametric mixture model approach to the regression analysis of competing-risks data.

PubMed

Ng, S K; McLachlan, G J

2003-04-15

We consider a mixture model approach to the regression analysis of competing-risks data. Attention is focused on inference concerning the effects of factors on both the probability of occurrence and the hazard rate conditional on each of the failure types. These two quantities are specified in the mixture model using the logistic model and the proportional hazards model, respectively. We propose a semi-parametric mixture method to estimate the logistic and regression coefficients jointly, whereby the component-baseline hazard functions are completely unspecified. Estimation is based on maximum likelihood on the basis of the full likelihood, implemented via an expectation-conditional maximization (ECM) algorithm. Simulation studies are performed to compare the performance of the proposed semi-parametric method with a fully parametric mixture approach. The results show that when the component-baseline hazard is monotonic increasing, the semi-parametric and fully parametric mixture approaches are comparable for mildly and moderately censored samples. When the component-baseline hazard is not monotonic increasing, the semi-parametric method consistently provides less biased estimates than a fully parametric approach and is comparable in efficiency in the estimation of the parameters for all levels of censoring. The methods are illustrated using a real data set of prostate cancer patients treated with different dosages of the drug diethylstilbestrol. Copyright 2003 John Wiley & Sons, Ltd.

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…

Improving Depth, Energy and Timing Estimation in PET Detectors with Deconvolution and Maximum Likelihood Pulse Shape Discrimination

PubMed Central

Berg, Eric; Roncali, Emilie; Hutchcroft, Will; Qi, Jinyi; Cherry, Simon R.

2016-01-01

In a scintillation detector, the light generated in the scintillator by a gamma interaction is converted to photoelectrons by a photodetector and produces a time-dependent waveform, the shape of which depends on the scintillator properties and the photodetector response. Several depth-of-interaction (DOI) encoding strategies have been developed that manipulate the scintillator’s temporal response along the crystal length and therefore require pulse shape discrimination techniques to differentiate waveform shapes. In this work, we demonstrate how maximum likelihood (ML) estimation methods can be applied to pulse shape discrimination to better estimate deposited energy, DOI and interaction time (for time-of-flight (TOF) PET) of a gamma ray in a scintillation detector. We developed likelihood models based on either the estimated detection times of individual photoelectrons or the number of photoelectrons in discrete time bins, and applied to two phosphor-coated crystals (LFS and LYSO) used in a previously developed TOF-DOI detector concept. Compared with conventional analytical methods, ML pulse shape discrimination improved DOI encoding by 27% for both crystals. Using the ML DOI estimate, we were able to counter depth-dependent changes in light collection inherent to long scintillator crystals and recover the energy resolution measured with fixed depth irradiation (~11.5% for both crystals). Lastly, we demonstrated how the Richardson-Lucy algorithm, an iterative, ML-based deconvolution technique, can be applied to the digitized waveforms to deconvolve the photodetector’s single photoelectron response and produce waveforms with a faster rising edge. After deconvolution and applying DOI and time-walk corrections, we demonstrated a 13% improvement in coincidence timing resolution (from 290 to 254 ps) with the LFS crystal and an 8% improvement (323 to 297 ps) with the LYSO crystal. PMID:27295658

Improving Depth, Energy and Timing Estimation in PET Detectors with Deconvolution and Maximum Likelihood Pulse Shape Discrimination.

PubMed

Berg, Eric; Roncali, Emilie; Hutchcroft, Will; Qi, Jinyi; Cherry, Simon R

2016-11-01

In a scintillation detector, the light generated in the scintillator by a gamma interaction is converted to photoelectrons by a photodetector and produces a time-dependent waveform, the shape of which depends on the scintillator properties and the photodetector response. Several depth-of-interaction (DOI) encoding strategies have been developed that manipulate the scintillator's temporal response along the crystal length and therefore require pulse shape discrimination techniques to differentiate waveform shapes. In this work, we demonstrate how maximum likelihood (ML) estimation methods can be applied to pulse shape discrimination to better estimate deposited energy, DOI and interaction time (for time-of-flight (TOF) PET) of a gamma ray in a scintillation detector. We developed likelihood models based on either the estimated detection times of individual photoelectrons or the number of photoelectrons in discrete time bins, and applied to two phosphor-coated crystals (LFS and LYSO) used in a previously developed TOF-DOI detector concept. Compared with conventional analytical methods, ML pulse shape discrimination improved DOI encoding by 27% for both crystals. Using the ML DOI estimate, we were able to counter depth-dependent changes in light collection inherent to long scintillator crystals and recover the energy resolution measured with fixed depth irradiation (~11.5% for both crystals). Lastly, we demonstrated how the Richardson-Lucy algorithm, an iterative, ML-based deconvolution technique, can be applied to the digitized waveforms to deconvolve the photodetector's single photoelectron response and produce waveforms with a faster rising edge. After deconvolution and applying DOI and time-walk corrections, we demonstrated a 13% improvement in coincidence timing resolution (from 290 to 254 ps) with the LFS crystal and an 8% improvement (323 to 297 ps) with the LYSO crystal.

Likelihood ratio meta-analysis: New motivation and approach for an old method.

PubMed

Dormuth, Colin R; Filion, Kristian B; Platt, Robert W

2016-03-01

A 95% confidence interval (CI) in an updated meta-analysis may not have the expected 95% coverage. If a meta-analysis is simply updated with additional data, then the resulting 95% CI will be wrong because it will not have accounted for the fact that the earlier meta-analysis failed or succeeded to exclude the null. This situation can be avoided by using the likelihood ratio (LR) as a measure of evidence that does not depend on type-1 error. We show how an LR-based approach, first advanced by Goodman, can be used in a meta-analysis to pool data from separate studies to quantitatively assess where the total evidence points. The method works by estimating the log-likelihood ratio (LogLR) function from each study. Those functions are then summed to obtain a combined function, which is then used to retrieve the total effect estimate, and a corresponding 'intrinsic' confidence interval. Using as illustrations the CAPRIE trial of clopidogrel versus aspirin in the prevention of ischemic events, and our own meta-analysis of higher potency statins and the risk of acute kidney injury, we show that the LR-based method yields the same point estimate as the traditional analysis, but with an intrinsic confidence interval that is appropriately wider than the traditional 95% CI. The LR-based method can be used to conduct both fixed effect and random effects meta-analyses, it can be applied to old and new meta-analyses alike, and results can be presented in a format that is familiar to a meta-analytic audience. Copyright © 2016 Elsevier Inc. All rights reserved.

DECONV-TOOL: An IDL based deconvolution software package

NASA Technical Reports Server (NTRS)

Varosi, F.; Landsman, W. B.

1992-01-01

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

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.

Predicting the evolution of complex networks via similarity dynamics

NASA Astrophysics Data System (ADS)

Wu, Tao; Chen, Leiting; Zhong, Linfeng; Xian, Xingping

2017-01-01

Almost all real-world networks are subject to constant evolution, and plenty of them have been investigated empirically to uncover the underlying evolution mechanism. However, the evolution prediction of dynamic networks still remains a challenging problem. The crux of this matter is to estimate the future network links of dynamic networks. This paper studies the evolution prediction of dynamic networks with link prediction paradigm. To estimate the likelihood of the existence of links more accurate, an effective and robust similarity index is presented by exploiting network structure adaptively. Moreover, most of the existing link prediction methods do not make a clear distinction between future links and missing links. In order to predict the future links, the networks are regarded as dynamic systems in this paper, and a similarity updating method, spatial-temporal position drift model, is developed to simulate the evolutionary dynamics of node similarity. Then the updated similarities are used as input information for the future links' likelihood estimation. Extensive experiments on real-world networks suggest that the proposed similarity index performs better than baseline methods and the position drift model performs well for evolution prediction in real-world evolving networks.

Standardized likelihood ratio test for comparing several log-normal means and confidence interval for the common mean.

PubMed

Krishnamoorthy, K; Oral, Evrim

2017-12-01

Standardized likelihood ratio test (SLRT) for testing the equality of means of several log-normal distributions is proposed. The properties of the SLRT and an available modified likelihood ratio test (MLRT) and a generalized variable (GV) test are evaluated by Monte Carlo simulation and compared. Evaluation studies indicate that the SLRT is accurate even for small samples, whereas the MLRT could be quite liberal for some parameter values, and the GV test is in general conservative and less powerful than the SLRT. Furthermore, a closed-form approximate confidence interval for the common mean of several log-normal distributions is developed using the method of variance estimate recovery, and compared with the generalized confidence interval with respect to coverage probabilities and precision. Simulation studies indicate that the proposed confidence interval is accurate and better than the generalized confidence interval in terms of coverage probabilities. The methods are illustrated using two examples.

The Performance of ML, GLS, and WLS Estimation in Structural Equation Modeling under Conditions of Misspecification and Nonnormality.

ERIC Educational Resources Information Center

Olsson, Ulf Henning; Foss, Tron; Troye, Sigurd V.; Howell, Roy D.

2000-01-01

Used simulation to demonstrate how the choice of estimation method affects indexes of fit and parameter bias for different sample sizes when nested models vary in terms of specification error and the data demonstrate different levels of kurtosis. Discusses results for maximum likelihood (ML), generalized least squares (GLS), and weighted least…

Joint reconstruction of activity and attenuation in Time-of-Flight PET: A Quantitative Analysis.

PubMed

Rezaei, Ahmadreza; Deroose, Christophe M; Vahle, Thomas; Boada, Fernando; Nuyts, Johan

2018-03-01

Joint activity and attenuation reconstruction methods from time of flight (TOF) positron emission tomography (PET) data provide an effective solution to attenuation correction when no (or incomplete/inaccurate) information on the attenuation is available. One of the main barriers limiting their use in clinical practice is the lack of validation of these methods on a relatively large patient database. In this contribution, we aim at validating the activity reconstructions of the maximum likelihood activity reconstruction and attenuation registration (MLRR) algorithm on a whole-body patient data set. Furthermore, a partial validation (since the scale problem of the algorithm is avoided for now) of the maximum likelihood activity and attenuation reconstruction (MLAA) algorithm is also provided. We present a quantitative comparison of the joint reconstructions to the current clinical gold-standard maximum likelihood expectation maximization (MLEM) reconstruction with CT-based attenuation correction. Methods: The whole-body TOF-PET emission data of each patient data set is processed as a whole to reconstruct an activity volume covering all the acquired bed positions, which helps to reduce the problem of a scale per bed position in MLAA to a global scale for the entire activity volume. Three reconstruction algorithms are used: MLEM, MLRR and MLAA. A maximum likelihood (ML) scaling of the single scatter simulation (SSS) estimate to the emission data is used for scatter correction. The reconstruction results are then analyzed in different regions of interest. Results: The joint reconstructions of the whole-body patient data set provide better quantification in case of PET and CT misalignments caused by patient and organ motion. Our quantitative analysis shows a difference of -4.2% (±2.3%) and -7.5% (±4.6%) between the joint reconstructions of MLRR and MLAA compared to MLEM, averaged over all regions of interest, respectively. Conclusion: Joint activity and attenuation estimation methods provide a useful means to estimate the tracer distribution in cases where CT-based attenuation images are subject to misalignments or are not available. With an accurate estimate of the scatter contribution in the emission measurements, the joint TOF-PET reconstructions are within clinical acceptable accuracy. Copyright © 2018 by the Society of Nuclear Medicine and Molecular Imaging, Inc.

Identification of multiple leaks in pipeline: Linearized model, maximum likelihood, and super-resolution localization

NASA Astrophysics Data System (ADS)

Wang, Xun; Ghidaoui, Mohamed S.

2018-07-01

This paper considers the problem of identifying multiple leaks in a water-filled pipeline based on inverse transient wave theory. The analytical solution to this problem involves nonlinear interaction terms between the various leaks. This paper shows analytically and numerically that these nonlinear terms are of the order of the leak sizes to the power two and; thus, negligible. As a result of this simplification, a maximum likelihood (ML) scheme that identifies leak locations and leak sizes separately is formulated and tested. It is found that the ML estimation scheme is highly efficient and robust with respect to noise. In addition, the ML method is a super-resolution leak localization scheme because its resolvable leak distance (approximately 0.15λmin , where λmin is the minimum wavelength) is below the Nyquist-Shannon sampling theorem limit (0.5λmin). Moreover, the Cramér-Rao lower bound (CRLB) is derived and used to show the efficiency of the ML scheme estimates. The variance of the ML estimator approximates the CRLB proving that the ML scheme belongs to class of best unbiased estimator of leak localization methods.

MIXED MODEL AND ESTIMATING EQUATION APPROACHES FOR ZERO INFLATION IN CLUSTERED BINARY RESPONSE DATA WITH APPLICATION TO A DATING VIOLENCE STUDY1

PubMed Central

Fulton, Kara A.; Liu, Danping; Haynie, Denise L.; Albert, Paul S.

2016-01-01

The NEXT Generation Health study investigates the dating violence of adolescents using a survey questionnaire. Each student is asked to affirm or deny multiple instances of violence in his/her dating relationship. There is, however, evidence suggesting that students not in a relationship responded to the survey, resulting in excessive zeros in the responses. This paper proposes likelihood-based and estimating equation approaches to analyze the zero-inflated clustered binary response data. We adopt a mixed model method to account for the cluster effect, and the model parameters are estimated using a maximum-likelihood (ML) approach that requires a Gaussian–Hermite quadrature (GHQ) approximation for implementation. Since an incorrect assumption on the random effects distribution may bias the results, we construct generalized estimating equations (GEE) that do not require the correct specification of within-cluster correlation. In a series of simulation studies, we examine the performance of ML and GEE methods in terms of their bias, efficiency and robustness. We illustrate the importance of properly accounting for this zero inflation by reanalyzing the NEXT data where this issue has previously been ignored. PMID:26937263

Imputation of a true endpoint from a surrogate: application to a cluster randomized controlled trial with partial information on the true endpoint.

PubMed

Nixon, Richard M; Duffy, Stephen W; Fender, Guy R K

2003-09-24

The Anglia Menorrhagia Education Study (AMES) is a randomized controlled trial testing the effectiveness of an education package applied to general practices. Binary data are available from two sources; general practitioner reported referrals to hospital, and referrals to hospital determined by independent audit of the general practices. The former may be regarded as a surrogate for the latter, which is regarded as the true endpoint. Data are only available for the true end point on a sub set of the practices, but there are surrogate data for almost all of the audited practices and for most of the remaining practices. The aim of this paper was to estimate the treatment effect using data from every practice in the study. Where the true endpoint was not available, it was estimated by three approaches, a regression method, multiple imputation and a full likelihood model. Including the surrogate data in the analysis yielded an estimate of the treatment effect which was more precise than an estimate gained from using the true end point data alone. The full likelihood method provides a new imputation tool at the disposal of trials with surrogate data.

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

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

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

2016-12-01

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

Semiparametric Time-to-Event Modeling in the Presence of a Latent Progression Event

PubMed Central

Rice, John D.; Tsodikov, Alex

2017-01-01

Summary In cancer research, interest frequently centers on factors influencing a latent event that must precede a terminal event. In practice it is often impossible to observe the latent event precisely, making inference about this process difficult. To address this problem, we propose a joint model for the unobserved time to the latent and terminal events, with the two events linked by the baseline hazard. Covariates enter the model parametrically as linear combinations that multiply, respectively, the hazard for the latent event and the hazard for the terminal event conditional on the latent one. We derive the partial likelihood estimators for this problem assuming the latent event is observed, and propose a profile likelihood–based method for estimation when the latent event is unobserved. The baseline hazard in this case is estimated nonparametrically using the EM algorithm, which allows for closed-form Breslow-type estimators at each iteration, bringing improved computational efficiency and stability compared with maximizing the marginal likelihood directly. We present simulation studies to illustrate the finite-sample properties of the method; its use in practice is demonstrated in the analysis of a prostate cancer data set. PMID:27556886

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

Generating Multiple Imputations for Matrix Sampling Data Analyzed with Item Response Models.

ERIC Educational Resources Information Center

Thomas, Neal; Gan, Nianci

1997-01-01

Describes and assesses missing data methods currently used to analyze data from matrix sampling designs implemented by the National Assessment of Educational Progress. Several improved methods are developed, and these models are evaluated using an EM algorithm to obtain maximum likelihood estimates followed by multiple imputation of complete data…

Effects of Missing Data Methods in Structural Equation Modeling with Nonnormal Longitudinal Data

ERIC Educational Resources Information Center

Shin, Tacksoo; Davison, Mark L.; Long, Jeffrey D.

2009-01-01

The purpose of this study is to investigate the effects of missing data techniques in longitudinal studies under diverse conditions. A Monte Carlo simulation examined the performance of 3 missing data methods in latent growth modeling: listwise deletion (LD), maximum likelihood estimation using the expectation and maximization algorithm with a…

Abstract: Inference and Interval Estimation for Indirect Effects With Latent Variable Models.

PubMed

Falk, Carl F; Biesanz, Jeremy C

2011-11-30

Models specifying indirect effects (or mediation) and structural equation modeling are both popular in the social sciences. Yet relatively little research has compared methods that test for indirect effects among latent variables and provided precise estimates of the effectiveness of different methods. This simulation study provides an extensive comparison of methods for constructing confidence intervals and for making inferences about indirect effects with latent variables. We compared the percentile (PC) bootstrap, bias-corrected (BC) bootstrap, bias-corrected accelerated (BC a ) bootstrap, likelihood-based confidence intervals (Neale & Miller, 1997), partial posterior predictive (Biesanz, Falk, and Savalei, 2010), and joint significance tests based on Wald tests or likelihood ratio tests. All models included three reflective latent variables representing the independent, dependent, and mediating variables. The design included the following fully crossed conditions: (a) sample size: 100, 200, and 500; (b) number of indicators per latent variable: 3 versus 5; (c) reliability per set of indicators: .7 versus .9; (d) and 16 different path combinations for the indirect effect (α = 0, .14, .39, or .59; and β = 0, .14, .39, or .59). Simulations were performed using a WestGrid cluster of 1680 3.06GHz Intel Xeon processors running R and OpenMx. Results based on 1,000 replications per cell and 2,000 resamples per bootstrap method indicated that the BC and BC a bootstrap methods have inflated Type I error rates. Likelihood-based confidence intervals and the PC bootstrap emerged as methods that adequately control Type I error and have good coverage rates.

Identification of dynamic systems, theory and formulation

NASA Technical Reports Server (NTRS)

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

1985-01-01

The problem of estimating parameters of dynamic systems is addressed in order to present the theoretical basis of system identification and parameter estimation in a manner that is complete and rigorous, yet understandable with minimal prerequisites. Maximum likelihood and related estimators are highlighted. The approach used requires familiarity with calculus, linear algebra, and probability, but does not require knowledge of stochastic processes or functional analysis. The treatment emphasizes unification of the various areas in estimation in dynamic systems is treated as a direct outgrowth of the static system theory. Topics covered include basic concepts and definitions; numerical optimization methods; probability; statistical estimators; estimation in static systems; stochastic processes; state estimation in dynamic systems; output error, filter error, and equation error methods of parameter estimation in dynamic systems, and the accuracy of the estimates.

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

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

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Likelihood-based gene annotations for gap filling and quality assessment in genome-scale metabolic models

DOE PAGES

Benedict, Matthew N.; Mundy, Michael B.; Henry, Christopher S.; ...

2014-10-16

Genome-scale metabolic models provide a powerful means to harness information from genomes to deepen biological insights. With exponentially increasing sequencing capacity, there is an enormous need for automated reconstruction techniques that can provide more accurate models in a short time frame. Current methods for automated metabolic network reconstruction rely on gene and reaction annotations to build draft metabolic networks and algorithms to fill gaps in these networks. However, automated reconstruction is hampered by database inconsistencies, incorrect annotations, and gap filling largely without considering genomic information. Here we develop an approach for applying genomic information to predict alternative functions for genesmore » and estimate their likelihoods from sequence homology. We show that computed likelihood values were significantly higher for annotations found in manually curated metabolic networks than those that were not. We then apply these alternative functional predictions to estimate reaction likelihoods, which are used in a new gap filling approach called likelihood-based gap filling to predict more genomically consistent solutions. To validate the likelihood-based gap filling approach, we applied it to models where essential pathways were removed, finding that likelihood-based gap filling identified more biologically relevant solutions than parsimony-based gap filling approaches. We also demonstrate that models gap filled using likelihood-based gap filling provide greater coverage and genomic consistency with metabolic gene functions compared to parsimony-based approaches. Interestingly, despite these findings, we found that likelihoods did not significantly affect consistency of gap filled models with Biolog and knockout lethality data. This indicates that the phenotype data alone cannot necessarily be used to discriminate between alternative solutions for gap filling and therefore, that the use of other information is necessary to obtain a more accurate network. All described workflows are implemented as part of the DOE Systems Biology Knowledgebase (KBase) and are publicly available via API or command-line web interface.« less

Likelihood-Based Gene Annotations for Gap Filling and Quality Assessment in Genome-Scale Metabolic Models

PubMed Central

Benedict, Matthew N.; Mundy, Michael B.; Henry, Christopher S.; Chia, Nicholas; Price, Nathan D.

2014-01-01

Genome-scale metabolic models provide a powerful means to harness information from genomes to deepen biological insights. With exponentially increasing sequencing capacity, there is an enormous need for automated reconstruction techniques that can provide more accurate models in a short time frame. Current methods for automated metabolic network reconstruction rely on gene and reaction annotations to build draft metabolic networks and algorithms to fill gaps in these networks. However, automated reconstruction is hampered by database inconsistencies, incorrect annotations, and gap filling largely without considering genomic information. Here we develop an approach for applying genomic information to predict alternative functions for genes and estimate their likelihoods from sequence homology. We show that computed likelihood values were significantly higher for annotations found in manually curated metabolic networks than those that were not. We then apply these alternative functional predictions to estimate reaction likelihoods, which are used in a new gap filling approach called likelihood-based gap filling to predict more genomically consistent solutions. To validate the likelihood-based gap filling approach, we applied it to models where essential pathways were removed, finding that likelihood-based gap filling identified more biologically relevant solutions than parsimony-based gap filling approaches. We also demonstrate that models gap filled using likelihood-based gap filling provide greater coverage and genomic consistency with metabolic gene functions compared to parsimony-based approaches. Interestingly, despite these findings, we found that likelihoods did not significantly affect consistency of gap filled models with Biolog and knockout lethality data. This indicates that the phenotype data alone cannot necessarily be used to discriminate between alternative solutions for gap filling and therefore, that the use of other information is necessary to obtain a more accurate network. All described workflows are implemented as part of the DOE Systems Biology Knowledgebase (KBase) and are publicly available via API or command-line web interface. PMID:25329157

Using latent class analysis to model prescription medications in the measurement of falling among a community elderly population

PubMed Central

2013-01-01

Background Falls among the elderly are a major public health concern. Therefore, the possibility of a modeling technique which could better estimate fall probability is both timely and needed. Using biomedical, pharmacological and demographic variables as predictors, latent class analysis (LCA) is demonstrated as a tool for the prediction of falls among community dwelling elderly. Methods Using a retrospective data-set a two-step LCA modeling approach was employed. First, we looked for the optimal number of latent classes for the seven medical indicators, along with the patients’ prescription medication and three covariates (age, gender, and number of medications). Second, the appropriate latent class structure, with the covariates, were modeled on the distal outcome (fall/no fall). The default estimator was maximum likelihood with robust standard errors. The Pearson chi-square, likelihood ratio chi-square, BIC, Lo-Mendell-Rubin Adjusted Likelihood Ratio test and the bootstrap likelihood ratio test were used for model comparisons. Results A review of the model fit indices with covariates shows that a six-class solution was preferred. The predictive probability for latent classes ranged from 84% to 97%. Entropy, a measure of classification accuracy, was good at 90%. Specific prescription medications were found to strongly influence group membership. Conclusions In conclusion the LCA method was effective at finding relevant subgroups within a heterogenous at-risk population for falling. This study demonstrated that LCA offers researchers a valuable tool to model medical data. PMID:23705639

Two-part models with stochastic processes for modelling longitudinal semicontinuous data: Computationally efficient inference and modelling the overall marginal mean.

PubMed

Yiu, Sean; Tom, Brian Dm

2017-01-01

Several researchers have described two-part models with patient-specific stochastic processes for analysing longitudinal semicontinuous data. In theory, such models can offer greater flexibility than the standard two-part model with patient-specific random effects. However, in practice, the high dimensional integrations involved in the marginal likelihood (i.e. integrated over the stochastic processes) significantly complicates model fitting. Thus, non-standard computationally intensive procedures based on simulating the marginal likelihood have so far only been proposed. In this paper, we describe an efficient method of implementation by demonstrating how the high dimensional integrations involved in the marginal likelihood can be computed efficiently. Specifically, by using a property of the multivariate normal distribution and the standard marginal cumulative distribution function identity, we transform the marginal likelihood so that the high dimensional integrations are contained in the cumulative distribution function of a multivariate normal distribution, which can then be efficiently evaluated. Hence, maximum likelihood estimation can be used to obtain parameter estimates and asymptotic standard errors (from the observed information matrix) of model parameters. We describe our proposed efficient implementation procedure for the standard two-part model parameterisation and when it is of interest to directly model the overall marginal mean. The methodology is applied on a psoriatic arthritis data set concerning functional disability.

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.

Normal Theory Two-Stage ML Estimator When Data Are Missing at the Item Level

PubMed Central

Savalei, Victoria; Rhemtulla, Mijke

2017-01-01

In many modeling contexts, the variables in the model are linear composites of the raw items measured for each participant; for instance, regression and path analysis models rely on scale scores, and structural equation models often use parcels as indicators of latent constructs. Currently, no analytic estimation method exists to appropriately handle missing data at the item level. Item-level multiple imputation (MI), however, can handle such missing data straightforwardly. In this article, we develop an analytic approach for dealing with item-level missing data—that is, one that obtains a unique set of parameter estimates directly from the incomplete data set and does not require imputations. The proposed approach is a variant of the two-stage maximum likelihood (TSML) methodology, and it is the analytic equivalent of item-level MI. We compare the new TSML approach to three existing alternatives for handling item-level missing data: scale-level full information maximum likelihood, available-case maximum likelihood, and item-level MI. We find that the TSML approach is the best analytic approach, and its performance is similar to item-level MI. We recommend its implementation in popular software and its further study. PMID:29276371

Normal Theory Two-Stage ML Estimator When Data Are Missing at the Item Level.

PubMed

Savalei, Victoria; Rhemtulla, Mijke

2017-08-01

In many modeling contexts, the variables in the model are linear composites of the raw items measured for each participant; for instance, regression and path analysis models rely on scale scores, and structural equation models often use parcels as indicators of latent constructs. Currently, no analytic estimation method exists to appropriately handle missing data at the item level. Item-level multiple imputation (MI), however, can handle such missing data straightforwardly. In this article, we develop an analytic approach for dealing with item-level missing data-that is, one that obtains a unique set of parameter estimates directly from the incomplete data set and does not require imputations. The proposed approach is a variant of the two-stage maximum likelihood (TSML) methodology, and it is the analytic equivalent of item-level MI. We compare the new TSML approach to three existing alternatives for handling item-level missing data: scale-level full information maximum likelihood, available-case maximum likelihood, and item-level MI. We find that the TSML approach is the best analytic approach, and its performance is similar to item-level MI. We recommend its implementation in popular software and its further study.

Modeling and E-M estimation of haplotype-specific relative risks from genotype data for a case-control study of unrelated individuals.

PubMed

Stram, Daniel O; Leigh Pearce, Celeste; Bretsky, Phillip; Freedman, Matthew; Hirschhorn, Joel N; Altshuler, David; Kolonel, Laurence N; Henderson, Brian E; Thomas, Duncan C

2003-01-01

The US National Cancer Institute has recently sponsored the formation of a Cohort Consortium (http://2002.cancer.gov/scpgenes.htm) to facilitate the pooling of data on very large numbers of people, concerning the effects of genes and environment on cancer incidence. One likely goal of these efforts will be generate a large population-based case-control series for which a number of candidate genes will be investigated using SNP haplotype as well as genotype analysis. The goal of this paper is to outline the issues involved in choosing a method of estimating haplotype-specific risk estimates for such data that is technically appropriate and yet attractive to epidemiologists who are already comfortable with odds ratios and logistic regression. Our interest is to develop and evaluate extensions of methods, based on haplotype imputation, that have been recently described (Schaid et al., Am J Hum Genet, 2002, and Zaykin et al., Hum Hered, 2002) as providing score tests of the null hypothesis of no effect of SNP haplotypes upon risk, which may be used for more complex tasks, such as providing confidence intervals, and tests of equivalence of haplotype-specific risks in two or more separate populations. In order to do so we (1) develop a cohort approach towards odds ratio analysis by expanding the E-M algorithm to provide maximum likelihood estimates of haplotype-specific odds ratios as well as genotype frequencies; (2) show how to correct the cohort approach, to give essentially unbiased estimates for population-based or nested case-control studies by incorporating the probability of selection as a case or control into the likelihood, based on a simplified model of case and control selection, and (3) finally, in an example data set (CYP17 and breast cancer, from the Multiethnic Cohort Study) we compare likelihood-based confidence interval estimates from the two methods with each other, and with the use of the single-imputation approach of Zaykin et al. applied under both null and alternative hypotheses. We conclude that so long as haplotypes are well predicted by SNP genotypes (we use the Rh2 criteria of Stram et al. [1]) the differences between the three methods are very small and in particular that the single imputation method may be expected to work extremely well. Copyright 2003 S. Karger AG, Basel

Estimation of channel parameters and background irradiance for free-space optical link.

PubMed

Khatoon, Afsana; Cowley, William G; Letzepis, Nick; Giggenbach, Dirk

2013-05-10

Free-space optical communication can experience severe fading due to optical scintillation in long-range links. Channel estimation is also corrupted by background and electrical noise. Accurate estimation of channel parameters and scintillation index (SI) depends on perfect removal of background irradiance. In this paper, we propose three different methods, the minimum-value (MV), mean-power (MP), and maximum-likelihood (ML) based methods, to remove the background irradiance from channel samples. The MV and MP methods do not require knowledge of the scintillation distribution. While the ML-based method assumes gamma-gamma scintillation, it can be easily modified to accommodate other distributions. Each estimator's performance is compared using simulation data as well as experimental measurements. The estimators' performance are evaluated from low- to high-SI areas using simulation data as well as experimental trials. The MV and MP methods have much lower complexity than the ML-based method. However, the ML-based method shows better SI and background-irradiance estimation performance.

Estimating overall exposure effects for the clustered and censored outcome using random effect Tobit regression models.

PubMed

Wang, Wei; Griswold, Michael E

2016-11-30

The random effect Tobit model is a regression model that accommodates both left- and/or right-censoring and within-cluster dependence of the outcome variable. Regression coefficients of random effect Tobit models have conditional interpretations on a constructed latent dependent variable and do not provide inference of overall exposure effects on the original outcome scale. Marginalized random effects model (MREM) permits likelihood-based estimation of marginal mean parameters for the clustered data. For random effect Tobit models, we extend the MREM to marginalize over both the random effects and the normal space and boundary components of the censored response to estimate overall exposure effects at population level. We also extend the 'Average Predicted Value' method to estimate the model-predicted marginal means for each person under different exposure status in a designated reference group by integrating over the random effects and then use the calculated difference to assess the overall exposure effect. The maximum likelihood estimation is proposed utilizing a quasi-Newton optimization algorithm with Gauss-Hermite quadrature to approximate the integration of the random effects. We use these methods to carefully analyze two real datasets. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Efficient Bayesian experimental design for contaminant source identification

NASA Astrophysics Data System (ADS)

Zhang, Jiangjiang; Zeng, Lingzao; Chen, Cheng; Chen, Dingjiang; Wu, Laosheng

2015-01-01

In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameters identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from concentration measurements in identifying unknown parameters. In this approach, the sampling locations that give the maximum expected relative entropy are selected as the optimal design. After the sampling locations are determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport equation. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. It is shown that the methods can be used to assist in both single sampling location and monitoring network design for contaminant source identifications in groundwater.

On the validity of cosmological Fisher matrix forecasts

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

Wolz, Laura; Kilbinger, Martin; Weller, Jochen

2012-09-01

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

A 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.

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

NASA Technical Reports Server (NTRS)

Murphy, Patrick Charles

1985-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

Profile-likelihood Confidence Intervals in Item Response Theory Models.

PubMed

Chalmers, R Philip; Pek, Jolynn; Liu, Yang

2017-01-01

Confidence intervals (CIs) are fundamental inferential devices which quantify the sampling variability of parameter estimates. In item response theory, CIs have been primarily obtained from large-sample Wald-type approaches based on standard error estimates, derived from the observed or expected information matrix, after parameters have been estimated via maximum likelihood. An alternative approach to constructing CIs is to quantify sampling variability directly from the likelihood function with a technique known as profile-likelihood confidence intervals (PL CIs). In this article, we introduce PL CIs for item response theory models, compare PL CIs to classical large-sample Wald-type CIs, and demonstrate important distinctions among these CIs. CIs are then constructed for parameters directly estimated in the specified model and for transformed parameters which are often obtained post-estimation. Monte Carlo simulation results suggest that PL CIs perform consistently better than Wald-type CIs for both non-transformed and transformed parameters.

Hyperspectral image reconstruction for x-ray fluorescence tomography

DOE PAGES

Gürsoy, Doǧa; Biçer, Tekin; Lanzirotti, Antonio; ...

2015-01-01

A penalized maximum-likelihood estimation is proposed to perform hyperspectral (spatio-spectral) image reconstruction for X-ray fluorescence tomography. The approach minimizes a Poisson-based negative log-likelihood of the observed photon counts, and uses a penalty term that has the effect of encouraging local continuity of model parameter estimates in both spatial and spectral dimensions simultaneously. The performance of the reconstruction method is demonstrated with experimental data acquired from a seed of arabidopsis thaliana collected at the 13-ID-E microprobe beamline at the Advanced Photon Source. The resulting element distribution estimates with the proposed approach show significantly better reconstruction quality than the conventional analytical inversionmore » approaches, and allows for a high data compression factor which can reduce data acquisition times remarkably. In particular, this technique provides the capability to tomographically reconstruct full energy dispersive spectra without compromising reconstruction artifacts that impact the interpretation of results.« less

Alternative Methods for Handling Attrition

PubMed Central

Foster, E. Michael; Fang, Grace Y.

2009-01-01

Using data from the evaluation of the Fast Track intervention, this article illustrates three methods for handling attrition. Multiple imputation and ignorable maximum likelihood estimation produce estimates that are similar to those based on listwise-deleted data. A panel selection model that allows for selective dropout reveals that highly aggressive boys accumulate in the treatment group over time and produces a larger estimate of treatment effect. In contrast, this model produces a smaller treatment effect for girls. The article's conclusion discusses the strengths and weaknesses of the alternative approaches and outlines ways in which researchers might improve their handling of attrition. PMID:15358906

Quantum State Tomography via Linear Regression Estimation

PubMed Central

Qi, Bo; Hou, Zhibo; Li, Li; Dong, Daoyi; Xiang, Guoyong; Guo, Guangcan

2013-01-01

A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography. PMID:24336519

A Study of Algorithms for Covariance Structure Analysis with Specific Comparisons Using Factor Analysis.

ERIC Educational Resources Information Center

Lee, S. Y.; Jennrich, R. I.

1979-01-01

A variety of algorithms for analyzing covariance structures are considered. Additionally, two methods of estimation, maximum likelihood, and weighted least squares are considered. Comparisons are made between these algorithms and factor analysis. (Author/JKS)

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.

[Differences between experts and novices in estimations of cue predictive power in crime].

PubMed

García-Retamero, Rocío; Dhami, Mandeep K

2009-08-01

In this study, we compared experts' and novices' estimates of the power of several cues to predict residential burglary. Participants were experienced police officers and burglars, and graduates with no experience in this domain. They all estimated the weight of each cue in predicting the likelihood of a property being burgled. In addition, they ranked the cues according to how useful they would be in predicting the likelihood of burglary. Results showed that the two expert groups differed substantially in their cue weights and rankings, and the police officers were actually more similar to novices in this regard. Beyond this, the two expert groups were more consistent in their responses than novices, that is, they showed less variability in their estimates when using different response method and were more consistent with other participants from their own group. Our results extend the literature on expert-novice differences, and have implications for criminal justice policy and decision making.

The logistic model for predicting the non-gonoactive Aedes aegypti females.

PubMed

Reyes-Villanueva, Filiberto; Rodríguez-Pérez, Mario A

2004-01-01

To estimate, using logistic regression, the likelihood of occurrence of a non-gonoactive Aedes aegypti female, previously fed human blood, with relation to body size and collection method. This study was conducted in Monterrey, Mexico, between 1994 and 1996. Ten samplings of 60 mosquitoes of Ae. aegypti females were carried out in three dengue endemic areas: six of biting females, two of emerging mosquitoes, and two of indoor resting females. Gravid females, as well as those with blood in the gut were removed. Mosquitoes were taken to the laboratory and engorged on human blood. After 48 hours, ovaries were dissected to register whether they were gonoactive or non-gonoactive. Wing-length in mm was an indicator for body size. The logistic regression model was used to assess the likelihood of non-gonoactivity, as a binary variable, in relation to wing-length and collection method. Of the 600 females, 164 (27%) remained non-gonoactive, with a wing-length range of 1.9-3.2 mm, almost equal to that of all females (1.8-3.3 mm). The logistic regression model showed a significant likelihood of a female remaining non-gonoactive (Y=1). The collection method did not influence the binary response, but there was an inverse relationship between non-gonoactivity and wing-length. Dengue vector populations from Monterrey, Mexico display a wide-range body size. Logistic regression was a useful tool to estimate the likelihood for an engorged female to remain non-gonoactive. The necessity for a second blood meal is present in any female, but small mosquitoes are more likely to bite again within a 2-day interval, in order to attain egg maturation. The English version of this paper is available too at: http://www.insp.mx/salud/index.html.

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…

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

PubMed

Rad, Kamiar Rahnama; Paninski, Liam

2010-01-01

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

Bayesian forecasting and uncertainty quantifying of stream flows using Metropolis-Hastings Markov Chain Monte Carlo algorithm

NASA Astrophysics Data System (ADS)

Wang, Hongrui; Wang, Cheng; Wang, Ying; Gao, Xiong; Yu, Chen

2017-06-01

This paper presents a Bayesian approach using Metropolis-Hastings Markov Chain Monte Carlo algorithm and applies this method for daily river flow rate forecast and uncertainty quantification for Zhujiachuan River using data collected from Qiaotoubao Gage Station and other 13 gage stations in Zhujiachuan watershed in China. The proposed method is also compared with the conventional maximum likelihood estimation (MLE) for parameter estimation and quantification of associated uncertainties. While the Bayesian method performs similarly in estimating the mean value of daily flow rate, it performs over the conventional MLE method on uncertainty quantification, providing relatively narrower reliable interval than the MLE confidence interval and thus more precise estimation by using the related information from regional gage stations. The Bayesian MCMC method might be more favorable in the uncertainty analysis and risk management.

Building unbiased estimators from non-gaussian likelihoods with application to shear estimation

DOE PAGES

Madhavacheril, Mathew S.; McDonald, Patrick; Sehgal, Neelima; ...

2015-01-15

We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we expand the likelihood. We apply this formalism to rederive the optimal quadratic estimator and show how the replacement of the second derivative matrix with the Fisher matrix is a generic way of creating an unbiased estimator (assuming choice of the fiducial model is independent of data). Next we apply the approach to estimation of shear lensing, closely following the workmore » of Bernstein and Armstrong (2014). Our first order estimator reduces to their estimator in the limit of zero shear, but it also naturally allows for the case of non-constant shear and the easy calculation of correlation functions or power spectra using standard methods. Both our first-order estimator and Bernstein and Armstrong’s estimator exhibit a bias which is quadratic in true shear. Our third-order estimator is, at least in the realm of the toy problem of Bernstein and Armstrong, unbiased to 0.1% in relative shear errors Δg/g for shears up to |g| = 0.2.« less

Building unbiased estimators from non-Gaussian likelihoods with application to shear estimation

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

Madhavacheril, Mathew S.; Sehgal, Neelima; McDonald, Patrick

2015-01-01

We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we expand the likelihood. We apply this formalism to rederive the optimal quadratic estimator and show how the replacement of the second derivative matrix with the Fisher matrix is a generic way of creating an unbiased estimator (assuming choice of the fiducial model is independent of data). Next we apply the approach to estimation of shear lensing, closely following the workmore » of Bernstein and Armstrong (2014). Our first order estimator reduces to their estimator in the limit of zero shear, but it also naturally allows for the case of non-constant shear and the easy calculation of correlation functions or power spectra using standard methods. Both our first-order estimator and Bernstein and Armstrong's estimator exhibit a bias which is quadratic in true shear. Our third-order estimator is, at least in the realm of the toy problem of Bernstein and Armstrong, unbiased to 0.1% in relative shear errors Δg/g for shears up to |g|=0.2.« less

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.

Adaptively Reevaluated Bayesian Localization (ARBL). A Novel Technique for Radiological Source Localization

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

Miller, Erin A.; Robinson, Sean M.; Anderson, Kevin K.

2015-01-19

Here we present a novel technique for the localization of radiological sources in urban or rural environments from an aerial platform. The technique is based on a Bayesian approach to localization, in which measured count rates in a time series are compared with predicted count rates from a series of pre-calculated test sources to define likelihood. Furthermore, this technique is expanded by using a localized treatment with a limited field of view (FOV), coupled with a likelihood ratio reevaluation, allowing for real-time computation on commodity hardware for arbitrarily complex detector models and terrain. In particular, detectors with inherent asymmetry ofmore » response (such as those employing internal collimation or self-shielding for enhanced directional awareness) are leveraged by this approach to provide improved localization. Our results from the localization technique are shown for simulated flight data using monolithic as well as directionally-aware detector models, and the capability of the methodology to locate radioisotopes is estimated for several test cases. This localization technique is shown to facilitate urban search by allowing quick and adaptive estimates of source location, in many cases from a single flyover near a source. In particular, this method represents a significant advancement from earlier methods like full-field Bayesian likelihood, which is not generally fast enough to allow for broad-field search in real time, and highest-net-counts estimation, which has a localization error that depends strongly on flight path and cannot generally operate without exhaustive search« less

Fast automated analysis of strong gravitational lenses with convolutional neural networks.

PubMed

Hezaveh, Yashar D; Levasseur, Laurence Perreault; Marshall, Philip J

2017-08-30

Quantifying image distortions caused by strong gravitational lensing-the formation of multiple images of distant sources due to the deflection of their light by the gravity of intervening structures-and estimating the corresponding matter distribution of these structures (the 'gravitational lens') has primarily been performed using maximum likelihood modelling of observations. This procedure is typically time- and resource-consuming, requiring sophisticated lensing codes, several data preparation steps, and finding the maximum likelihood model parameters in a computationally expensive process with downhill optimizers. Accurate analysis of a single gravitational lens can take up to a few weeks and requires expert knowledge of the physical processes and methods involved. Tens of thousands of new lenses are expected to be discovered with the upcoming generation of ground and space surveys. Here we report the use of deep convolutional neural networks to estimate lensing parameters in an extremely fast and automated way, circumventing the difficulties that are faced by maximum likelihood methods. We also show that the removal of lens light can be made fast and automated using independent component analysis of multi-filter imaging data. Our networks can recover the parameters of the 'singular isothermal ellipsoid' density profile, which is commonly used to model strong lensing systems, with an accuracy comparable to the uncertainties of sophisticated models but about ten million times faster: 100 systems in approximately one second on a single graphics processing unit. These networks can provide a way for non-experts to obtain estimates of lensing parameters for large samples of data.

A decision directed detector for the phase incoherent Gaussian channel

NASA Technical Reports Server (NTRS)

Kazakos, D.

1975-01-01

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

Practical Implementation of Multiple Model Adaptive Estimation Using Neyman-Pearson Based Hypothesis Testing and Spectral Estimation Tools

DTIC Science & Technology

1996-09-01

Generalized Likelihood Ratio (GLR) and voting techniques. The third class consisted of multiple hypothesis filter detectors, specifically the MMAE. The...vector version, versus a tensor if we use the matrix version of the power spectral density estimate. Using this notation, we will derive an...as MATLAB , have an intrinsic sample covariance computation available, which makes this method quite easy to implement. In practice, the mean for the

A Maximum-Likelihood Method to Correct for Allelic Dropout in Microsatellite Data with No Replicate Genotypes

PubMed Central

Wang, Chaolong; Schroeder, Kari B.; Rosenberg, Noah A.

2012-01-01

Allelic dropout is a commonly observed source of missing data in microsatellite genotypes, in which one or both allelic copies at a locus fail to be amplified by the polymerase chain reaction. Especially for samples with poor DNA quality, this problem causes a downward bias in estimates of observed heterozygosity and an upward bias in estimates of inbreeding, owing to mistaken classifications of heterozygotes as homozygotes when one of the two copies drops out. One general approach for avoiding allelic dropout involves repeated genotyping of homozygous loci to minimize the effects of experimental error. Existing computational alternatives often require replicate genotyping as well. These approaches, however, are costly and are suitable only when enough DNA is available for repeated genotyping. In this study, we propose a maximum-likelihood approach together with an expectation-maximization algorithm to jointly estimate allelic dropout rates and allele frequencies when only one set of nonreplicated genotypes is available. Our method considers estimates of allelic dropout caused by both sample-specific factors and locus-specific factors, and it allows for deviation from Hardy–Weinberg equilibrium owing to inbreeding. Using the estimated parameters, we correct the bias in the estimation of observed heterozygosity through the use of multiple imputations of alleles in cases where dropout might have occurred. With simulated data, we show that our method can (1) effectively reproduce patterns of missing data and heterozygosity observed in real data; (2) correctly estimate model parameters, including sample-specific dropout rates, locus-specific dropout rates, and the inbreeding coefficient; and (3) successfully correct the downward bias in estimating the observed heterozygosity. We find that our method is fairly robust to violations of model assumptions caused by population structure and by genotyping errors from sources other than allelic dropout. Because the data sets imputed under our model can be investigated in additional subsequent analyses, our method will be useful for preparing data for applications in diverse contexts in population genetics and molecular ecology. PMID:22851645

Robust Multipoint Water-Fat Separation Using Fat Likelihood Analysis

PubMed Central

Yu, Huanzhou; Reeder, Scott B.; Shimakawa, Ann; McKenzie, Charles A.; Brittain, Jean H.

2016-01-01

Fat suppression is an essential part of routine MRI scanning. Multiecho chemical-shift based water-fat separation methods estimate and correct for Bo field inhomogeneity. However, they must contend with the intrinsic challenge of water-fat ambiguity that can result in water-fat swapping. This problem arises because the signals from two chemical species, when both are modeled as a single discrete spectral peak, may appear indistinguishable in the presence of Bo off-resonance. In conventional methods, the water-fat ambiguity is typically removed by enforcing field map smoothness using region growing based algorithms. In reality, the fat spectrum has multiple spectral peaks. Using this spectral complexity, we introduce a novel concept that identifies water and fat for multiecho acquisitions by exploiting the spectral differences between water and fat. A fat likelihood map is produced to indicate if a pixel is likely to be water-dominant or fat-dominant by comparing the fitting residuals of two different signal models. The fat likelihood analysis and field map smoothness provide complementary information, and we designed an algorithm (Fat Likelihood Analysis for Multiecho Signals) to exploit both mechanisms. It is demonstrated in a wide variety of data that the Fat Likelihood Analysis for Multiecho Signals algorithm offers highly robust water-fat separation for 6-echo acquisitions, particularly in some previously challenging applications. PMID:21842498

Exploiting Non-sequence Data in Dynamic Model Learning

DTIC Science & Technology

2013-10-01

For our experiments here and in Section 3.5, we implement the proposed algorithms in MATLAB and use the maximum directed spanning tree solver...embarrassingly parallelizable, whereas PM’s maximum directed spanning tree procedure is harder to parallelize. In this experiment, our MATLAB ...some estimation problems, this approach is able to give unique and consistent estimates while the maximum- likelihood method gets entangled in

When Can Categorical Variables Be Treated as Continuous? A Comparison of Robust Continuous and Categorical SEM Estimation Methods under Suboptimal Conditions

ERIC Educational Resources Information Center

Rhemtulla, Mijke; Brosseau-Liard, Patricia E.; Savalei, Victoria

2012-01-01

A simulation study compared the performance of robust normal theory maximum likelihood (ML) and robust categorical least squares (cat-LS) methodology for estimating confirmatory factor analysis models with ordinal variables. Data were generated from 2 models with 2-7 categories, 4 sample sizes, 2 latent distributions, and 5 patterns of category…

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…

Radar modulation classification using time-frequency representation and nonlinear regression

NASA Astrophysics Data System (ADS)

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

1999-09-01

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

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

NASA Astrophysics Data System (ADS)

Voss, Sebastian; Zimmermann, Beate; Zimmermann, Alexander

2016-09-01

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

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…

Parameter Estimation and Model Selection for Indoor Environments Based on Sparse Observations

NASA Astrophysics Data System (ADS)

Dehbi, Y.; Loch-Dehbi, S.; Plümer, L.

2017-09-01

This paper presents a novel method for the parameter estimation and model selection for the reconstruction of indoor environments based on sparse observations. While most approaches for the reconstruction of indoor models rely on dense observations, we predict scenes of the interior with high accuracy in the absence of indoor measurements. We use a model-based top-down approach and incorporate strong but profound prior knowledge. The latter includes probability density functions for model parameters and sparse observations such as room areas and the building footprint. The floorplan model is characterized by linear and bi-linear relations with discrete and continuous parameters. We focus on the stochastic estimation of model parameters based on a topological model derived by combinatorial reasoning in a first step. A Gauss-Markov model is applied for estimation and simulation of the model parameters. Symmetries are represented and exploited during the estimation process. Background knowledge as well as observations are incorporated in a maximum likelihood estimation and model selection is performed with AIC/BIC. The likelihood is also used for the detection and correction of potential errors in the topological model. Estimation results are presented and discussed.

Methods and Tools for Evaluating Uncertainty in Ecological Models: A Survey

EPA Science Inventory

Poster presented at the Ecological Society of America Meeting. Ecologists are familiar with a variety of uncertainty techniques, particularly in the intersection of maximum likelihood parameter estimation and Monte Carlo analysis techniques, as well as a recent increase in Baye...

Inter-Rater Reliability of Provider Interpretations of Irritable Bowel Syndrome Food and Symptom Journals

PubMed Central

Chung, Chia-Fang; Xu, Kaiyuan; Dong, Yi; Schenk, Jeanette M.; Cain, Kevin; Munson, Sean; Heitkemper, Margaret M.

2017-01-01

There are currently no standardized methods for identifying trigger food(s) from irritable bowel syndrome (IBS) food and symptom journals. The primary aim of this study was to assess the inter-rater reliability of providers’ interpretations of IBS journals. A second aim was to describe whether these interpretations varied for each patient. Eight providers reviewed 17 IBS journals and rated how likely key food groups (fermentable oligo-di-monosaccharides and polyols, high-calorie, gluten, caffeine, high-fiber) were to trigger IBS symptoms for each patient. Agreement of trigger food ratings was calculated using Krippendorff’s α-reliability estimate. Providers were also asked to write down recommendations they would give to each patient. Estimates of agreement of trigger food likelihood ratings were poor (average α = 0.07). Most providers gave similar trigger food likelihood ratings for over half the food groups. Four providers gave the exact same written recommendation(s) (range 3–7) to over half the patients. Inter-rater reliability of provider interpretations of IBS food and symptom journals was poor. Providers favored certain trigger food likelihood ratings and written recommendations. This supports the need for a more standardized method for interpreting these journals and/or more rigorous techniques to accurately identify personalized IBS food triggers. PMID:29113044

A method for modeling bias in a person's estimates of likelihoods of events

NASA Technical Reports Server (NTRS)

Nygren, Thomas E.; Morera, Osvaldo

1988-01-01

It is of practical importance in decision situations involving risk to train individuals to transform uncertainties into subjective probability estimates that are both accurate and unbiased. We have found that in decision situations involving risk, people often introduce subjective bias in their estimation of the likelihoods of events depending on whether the possible outcomes are perceived as being good or bad. Until now, however, the successful measurement of individual differences in the magnitude of such biases has not been attempted. In this paper we illustrate a modification of a procedure originally outlined by Davidson, Suppes, and Siegel (3) to allow for a quantitatively-based methodology for simultaneously estimating an individual's subjective utility and subjective probability functions. The procedure is now an interactive computer-based algorithm, DSS, that allows for the measurement of biases in probability estimation by obtaining independent measures of two subjective probability functions (S+ and S-) for winning (i.e., good outcomes) and for losing (i.e., bad outcomes) respectively for each individual, and for different experimental conditions within individuals. The algorithm and some recent empirical data are described.

The influence of SO4 and NO3 to the acidity (pH) of rainwater using minimum variance quadratic unbiased estimation (MIVQUE) and maximum likelihood methods

NASA Astrophysics Data System (ADS)

Dilla, Shintia Ulfa; Andriyana, Yudhie; Sudartianto

2017-03-01

Acid rain causes many bad effects in life. It is formed by two strong acids, sulfuric acid (H2SO4) and nitric acid (HNO3), where sulfuric acid is derived from SO2 and nitric acid from NOx {x=1,2}. The purpose of the research is to find out the influence of So4 and NO3 levels contained in the rain to the acidity (pH) of rainwater. The data are incomplete panel data with two-way error component model. The panel data is a collection of some of the observations that observed from time to time. It is said incomplete if each individual has a different amount of observation. The model used in this research is in the form of random effects model (REM). Minimum variance quadratic unbiased estimation (MIVQUE) is used to estimate the variance error components, while maximum likelihood estimation is used to estimate the parameters. As a result, we obtain the following model: Ŷ* = 0.41276446 - 0.00107302X1 + 0.00215470X2.

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…

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…

Effectiveness of phylogenomic data and coalescent species-tree methods for resolving difficult nodes in the phylogeny of advanced snakes (Serpentes: Caenophidia).

PubMed

Pyron, R Alexander; Hendry, Catriona R; Chou, Vincent M; Lemmon, Emily M; Lemmon, Alan R; Burbrink, Frank T

2014-12-01

Next-generation genomic sequencing promises to quickly and cheaply resolve remaining contentious nodes in the Tree of Life, and facilitates species-tree estimation while taking into account stochastic genealogical discordance among loci. Recent methods for estimating species trees bypass full likelihood-based estimates of the multi-species coalescent, and approximate the true species-tree using simpler summary metrics. These methods converge on the true species-tree with sufficient genomic sampling, even in the anomaly zone. However, no studies have yet evaluated their efficacy on a large-scale phylogenomic dataset, and compared them to previous concatenation strategies. Here, we generate such a dataset for Caenophidian snakes, a group with >2500 species that contains several rapid radiations that were poorly resolved with fewer loci. We generate sequence data for 333 single-copy nuclear loci with ∼100% coverage (∼0% missing data) for 31 major lineages. We estimate phylogenies using neighbor joining, maximum parsimony, maximum likelihood, and three summary species-tree approaches (NJst, STAR, and MP-EST). All methods yield similar resolution and support for most nodes. However, not all methods support monophyly of Caenophidia, with Acrochordidae placed as the sister taxon to Pythonidae in some analyses. Thus, phylogenomic species-tree estimation may occasionally disagree with well-supported relationships from concatenated analyses of small numbers of nuclear or mitochondrial genes, a consideration for future studies. In contrast for at least two diverse, rapid radiations (Lamprophiidae and Colubridae), phylogenomic data and species-tree inference do little to improve resolution and support. Thus, certain nodes may lack strong signal, and larger datasets and more sophisticated analyses may still fail to resolve them. Copyright © 2014 Elsevier Inc. All rights reserved.

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.

Gaussian copula as a likelihood function for environmental models

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Experimental Design for Parameter Estimation of Gene Regulatory Networks

PubMed Central

Timmer, Jens

2012-01-01

Systems biology aims for building quantitative models to address unresolved issues in molecular biology. In order to describe the behavior of biological cells adequately, gene regulatory networks (GRNs) are intensively investigated. As the validity of models built for GRNs depends crucially on the kinetic rates, various methods have been developed to estimate these parameters from experimental data. For this purpose, it is favorable to choose the experimental conditions yielding maximal information. However, existing experimental design principles often rely on unfulfilled mathematical assumptions or become computationally demanding with growing model complexity. To solve this problem, we combined advanced methods for parameter and uncertainty estimation with experimental design considerations. As a showcase, we optimized three simulated GRNs in one of the challenges from the Dialogue for Reverse Engineering Assessment and Methods (DREAM). This article presents our approach, which was awarded the best performing procedure at the DREAM6 Estimation of Model Parameters challenge. For fast and reliable parameter estimation, local deterministic optimization of the likelihood was applied. We analyzed identifiability and precision of the estimates by calculating the profile likelihood. Furthermore, the profiles provided a way to uncover a selection of most informative experiments, from which the optimal one was chosen using additional criteria at every step of the design process. In conclusion, we provide a strategy for optimal experimental design and show its successful application on three highly nonlinear dynamic models. Although presented in the context of the GRNs to be inferred for the DREAM6 challenge, the approach is generic and applicable to most types of quantitative models in systems biology and other disciplines. PMID:22815723

Mining pharmacovigilance data using Bayesian logistic regression with James-Stein type shrinkage estimation.

PubMed

An, Lihua; Fung, Karen Y; Krewski, Daniel

2010-09-01

Spontaneous adverse event reporting systems are widely used to identify adverse reactions to drugs following their introduction into the marketplace. In this article, a James-Stein type shrinkage estimation strategy was developed in a Bayesian logistic regression model to analyze pharmacovigilance data. This method is effective in detecting signals as it combines information and borrows strength across medically related adverse events. Computer simulation demonstrated that the shrinkage estimator is uniformly better than the maximum likelihood estimator in terms of mean squared error. This method was used to investigate the possible association of a series of diabetic drugs and the risk of cardiovascular events using data from the Canada Vigilance Online Database.

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.

Methodology and method and apparatus for signaling with capacity optimized constellations

NASA Technical Reports Server (NTRS)

Barsoum, Maged F. (Inventor); Jones, Christopher R. (Inventor)

2011-01-01

Communication systems having transmitter, includes a coder configured to receive user bits and output encoded bits at an expanded output encoded bit rate, a mapper configured to map encoded bits to symbols in a symbol constellation, a modulator configured to generate a signal for transmission via the communication channel using symbols generated by the mapper. In addition, the receiver includes a demodulator configured to demodulate the received signal via the communication channel, a demapper configured to estimate likelihoods from the demodulated signal, a decoder that is configured to estimate decoded bits from the likelihoods generated by the demapper. Furthermore, the symbol constellation is a capacity optimized geometrically spaced symbol constellation that provides a given capacity at a reduced signal-to-noise ratio compared to a signal constellation that maximizes d.sub.min.

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

NASA Astrophysics Data System (ADS)

Voss, Sebastian; Zimmermann, Beate; Zimmermann, Alexander

2016-04-01

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

Detecting the sampling rate through observations

NASA Astrophysics Data System (ADS)

Shoji, Isao

2018-09-01

This paper proposes a method to detect the sampling rate of discrete time series of diffusion processes. Using the maximum likelihood estimates of the parameters of a diffusion process, we establish a criterion based on the Kullback-Leibler divergence and thereby estimate the sampling rate. Simulation studies are conducted to check whether the method can detect the sampling rates from data and their results show a good performance in the detection. In addition, the method is applied to a financial time series sampled on daily basis and shows the detected sampling rate is different from the conventional rates.

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.

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.

Bayesian Estimation of Reliability Burr Type XII Under Al-Bayyatis’ Suggest Loss Function with Numerical Solution

NASA Astrophysics Data System (ADS)

Mohammed, Amal A.; Abraheem, Sudad K.; Fezaa Al-Obedy, Nadia J.

2018-05-01

In this paper is considered with Burr type XII distribution. The maximum likelihood, Bayes methods of estimation are used for estimating the unknown scale parameter (α). Al-Bayyatis’ loss function and suggest loss function are used to find the reliability with the least loss. So the reliability function is expanded in terms of a set of power function. For this performance, the Matlab (ver.9) is used in computations and some examples are given.

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).

Multiple robustness in factorized likelihood models.

PubMed

Molina, J; Rotnitzky, A; Sued, M; Robins, J M

2017-09-01

We consider inference under a nonparametric or semiparametric model with likelihood that factorizes as the product of two or more variation-independent factors. We are interested in a finite-dimensional parameter that depends on only one of the likelihood factors and whose estimation requires the auxiliary estimation of one or several nuisance functions. We investigate general structures conducive to the construction of so-called multiply robust estimating functions, whose computation requires postulating several dimension-reducing models but which have mean zero at the true parameter value provided one of these models is correct.

Fundamentals of health risk assessment. Use, derivation, validity and limitations of safety indices.

PubMed

Putzrath, R M; Wilson, J D

1999-04-01

We investigated the way results of human health risk assessments are used, and the theory used to describe those methods, sometimes called the "NAS paradigm." Contrary to a key tenet of that theory, current methods have strictly limited utility. The characterizations now considered standard, Safety Indices such as "Acceptable Daily Intake," "Reference Dose," and so on, usefully inform only decisions that require a choice between two policy alternatives (e.g., approve a food additive or not), decided solely on the basis of a finding of safety. Risk is characterized as the quotient of one of these Safety Indices divided by an estimate of exposure: a quotient greater than one implies that the situation may be considered safe. Such decisions are very widespread, both in the U.S. federal government and elsewhere. No current method is universal; different policies lead to different practices, for example, in California's "Proposition 65," where statutory provisions specify some practices. Further, an important kind of human health risk assessment is not recognized by this theory: this kind characterizes risk as likelihood of harm, given estimates of exposure consequent to various decision choices. Likelihood estimates are necessary whenever decision makers have many possible decision choices and must weigh more than two societal values, such as in EPA's implementation of "conventional air pollutants." These estimates can not be derived using current methods; different methods are needed. Our analysis suggests changes needed in both the theory and practice of human health risk assessment, and how what is done is depicted.

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.

A Joint Model for Longitudinal Measurements and Survival Data in the Presence of Multiple Failure Types

PubMed Central

Elashoff, Robert M.; Li, Gang; Li, Ning

2009-01-01

Summary In this article we study a joint model for longitudinal measurements and competing risks survival data. Our joint model provides a flexible approach to handle possible nonignorable missing data in the longitudinal measurements due to dropout. It is also an extension of previous joint models with a single failure type, offering a possible way to model informatively censored events as a competing risk. Our model consists of a linear mixed effects submodel for the longitudinal outcome and a proportional cause-specific hazards frailty submodel (Prentice et al., 1978, Biometrics 34, 541-554) for the competing risks survival data, linked together by some latent random effects. We propose to obtain the maximum likelihood estimates of the parameters by an expectation maximization (EM) algorithm and estimate their standard errors using a profile likelihood method. The developed method works well in our simulation studies and is applied to a clinical trial for the scleroderma lung disease. PMID:18162112

Determining the linkage of disease-resistance genes to molecular markers: the LOD-SCORE method revisited with regard to necessary sample sizes.

PubMed

Hühn, M

1995-05-01

Some approaches to molecular marker-assisted linkage detection for a dominant disease-resistance trait based on a segregating F2 population are discussed. Analysis of two-point linkage is carried out by the traditional measure of maximum lod score. It depends on (1) the maximum-likelihood estimate of the recombination fraction between the marker and the disease-resistance gene locus, (2) the observed absolute frequencies, and (3) the unknown number of tested individuals. If one replaces the absolute frequencies by expressions depending on the unknown sample size and the maximum-likelihood estimate of recombination value, the conventional rule for significant linkage (maximum lod score exceeds a given linkage threshold) can be resolved for the sample size. For each sub-population used for linkage analysis [susceptible (= recessive) individuals, resistant (= dominant) individuals, complete F2] this approach gives a lower bound for the necessary number of individuals required for the detection of significant two-point linkage by the lod-score method.

Comparing the performance of geostatistical models with additional information from covariates for sewage plume characterization.

PubMed

Del Monego, Maurici; Ribeiro, Paulo Justiniano; Ramos, Patrícia

2015-04-01

In this work, kriging with covariates is used to model and map the spatial distribution of salinity measurements gathered by an autonomous underwater vehicle in a sea outfall monitoring campaign aiming to distinguish the effluent plume from the receiving waters and characterize its spatial variability in the vicinity of the discharge. Four different geostatistical linear models for salinity were assumed, where the distance to diffuser, the west-east positioning, and the south-north positioning were used as covariates. Sample variograms were fitted by the Matèrn models using weighted least squares and maximum likelihood estimation methods as a way to detect eventual discrepancies. Typically, the maximum likelihood method estimated very low ranges which have limited the kriging process. So, at least for these data sets, weighted least squares showed to be the most appropriate estimation method for variogram fitting. The kriged maps show clearly the spatial variation of salinity, and it is possible to identify the effluent plume in the area studied. The results obtained show some guidelines for sewage monitoring if a geostatistical analysis of the data is in mind. It is important to treat properly the existence of anomalous values and to adopt a sampling strategy that includes transects parallel and perpendicular to the effluent dispersion.

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.

Processing of Antenna-Array Signals on the Basis of the Interference Model Including a Rank-Deficient Correlation Matrix

NASA Astrophysics Data System (ADS)

Rodionov, A. A.; Turchin, V. I.

2017-06-01

We propose a new method of signal processing in antenna arrays, which is called the Maximum-Likelihood Signal Classification. The proposed method is based on the model in which interference includes a component with a rank-deficient correlation matrix. Using numerical simulation, we show that the proposed method allows one to ensure variance of the estimated arrival angle of the plane wave, which is close to the Cramer-Rao lower boundary and more efficient than the best-known MUSIC method. It is also shown that the proposed technique can be efficiently used for estimating the time dependence of the useful signal.

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.

Estimation and classification by sigmoids based on mutual information

NASA Technical Reports Server (NTRS)

Baram, Yoram

1994-01-01

An estimate of the probability density function of a random vector is obtained by maximizing the mutual information between the input and the output of a feedforward network of sigmoidal units with respect to the input weights. Classification problems can be solved by selecting the class associated with the maximal estimated density. Newton's s method, applied to an estimated density, yields a recursive maximum likelihood estimator, consisting of a single internal layer of sigmoids, for a random variable or a random sequence. Applications to the diamond classification and to the prediction of a sun-spot process are demonstrated.

Bayesian forecasting and uncertainty quantifying of stream flows using Metropolis–Hastings Markov Chain Monte Carlo algorithm

DOE PAGES

Wang, Hongrui; Wang, Cheng; Wang, Ying; ...

2017-04-05

This paper presents a Bayesian approach using Metropolis-Hastings Markov Chain Monte Carlo algorithm and applies this method for daily river flow rate forecast and uncertainty quantification for Zhujiachuan River using data collected from Qiaotoubao Gage Station and other 13 gage stations in Zhujiachuan watershed in China. The proposed method is also compared with the conventional maximum likelihood estimation (MLE) for parameter estimation and quantification of associated uncertainties. While the Bayesian method performs similarly in estimating the mean value of daily flow rate, it performs over the conventional MLE method on uncertainty quantification, providing relatively narrower reliable interval than the MLEmore » confidence interval and thus more precise estimation by using the related information from regional gage stations. As a result, the Bayesian MCMC method might be more favorable in the uncertainty analysis and risk management.« less

A Novel Method for Block Size Forensics Based on Morphological Operations

NASA Astrophysics Data System (ADS)

Luo, Weiqi; Huang, Jiwu; Qiu, Guoping

Passive forensics analysis aims to find out how multimedia data is acquired and processed without relying on pre-embedded or pre-registered information. Since most existing compression schemes for digital images are based on block processing, one of the fundamental steps for subsequent forensics analysis is to detect the presence of block artifacts and estimate the block size for a given image. In this paper, we propose a novel method for blind block size estimation. A 2×2 cross-differential filter is first applied to detect all possible block artifact boundaries, morphological operations are then used to remove the boundary effects caused by the edges of the actual image contents, and finally maximum-likelihood estimation (MLE) is employed to estimate the block size. The experimental results evaluated on over 1300 nature images show the effectiveness of our proposed method. Compared with existing gradient-based detection method, our method achieves over 39% accuracy improvement on average.

Estimating Tree Height-Diameter Models with the Bayesian Method

PubMed Central

Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the “best” model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2. PMID:24711733

Estimating tree height-diameter models with the Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the "best" model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.

Expectation Maximization Algorithm for Box-Cox Transformation Cure Rate Model and Assessment of Model Misspecification Under Weibull Lifetimes.

PubMed

Pal, Suvra; Balakrishnan, Narayanaswamy

2018-05-01

In this paper, we develop likelihood inference based on the expectation maximization algorithm for the Box-Cox transformation cure rate model assuming the lifetimes to follow a Weibull distribution. A simulation study is carried out to demonstrate the performance of the proposed estimation method. Through Monte Carlo simulations, we also study the effect of model misspecification on the estimate of cure rate. Finally, we analyze a well-known data on melanoma with the model and the inferential method developed here.

Estimating ambiguity preferences and perceptions in multiple prior models: Evidence from the field.

PubMed

Dimmock, Stephen G; Kouwenberg, Roy; Mitchell, Olivia S; Peijnenburg, Kim

2015-12-01

We develop a tractable method to estimate multiple prior models of decision-making under ambiguity. In a representative sample of the U.S. population, we measure ambiguity attitudes in the gain and loss domains. We find that ambiguity aversion is common for uncertain events of moderate to high likelihood involving gains, but ambiguity seeking prevails for low likelihoods and for losses. We show that choices made under ambiguity in the gain domain are best explained by the α-MaxMin model, with one parameter measuring ambiguity aversion (ambiguity preferences) and a second parameter quantifying the perceived degree of ambiguity (perceptions about ambiguity). The ambiguity aversion parameter α is constant and prior probability sets are asymmetric for low and high likelihood events. The data reject several other models, such as MaxMin and MaxMax, as well as symmetric probability intervals. Ambiguity aversion and the perceived degree of ambiguity are both higher for men and for the college-educated. Ambiguity aversion (but not perceived ambiguity) is also positively related to risk aversion. In the loss domain, we find evidence of reflection, implying that ambiguity aversion for gains tends to reverse into ambiguity seeking for losses. Our model's estimates for preferences and perceptions about ambiguity can be used to analyze the economic and financial implications of such preferences.

Stochastic differential equation (SDE) model of opening gold share price of bursa saham malaysia

NASA Astrophysics Data System (ADS)

Hussin, F. N.; Rahman, H. A.; Bahar, A.

2017-09-01

Black and Scholes option pricing model is one of the most recognized stochastic differential equation model in mathematical finance. Two parameter estimation methods have been utilized for the Geometric Brownian model (GBM); historical and discrete method. The historical method is a statistical method which uses the property of independence and normality logarithmic return, giving out the simplest parameter estimation. Meanwhile, discrete method considers the function of density of transition from the process of diffusion normal log which has been derived from maximum likelihood method. These two methods are used to find the parameter estimates samples of Malaysians Gold Share Price data such as: Financial Times and Stock Exchange (FTSE) Bursa Malaysia Emas, and Financial Times and Stock Exchange (FTSE) Bursa Malaysia Emas Shariah. Modelling of gold share price is essential since fluctuation of gold affects worldwide economy nowadays, including Malaysia. It is found that discrete method gives the best parameter estimates than historical method due to the smallest Root Mean Square Error (RMSE) value.

Moment and maximum likelihood estimators for Weibull distributions under length- and area-biased sampling

Treesearch

Jeffrey H. Gove

2003-01-01

Many of the most popular sampling schemes used in forestry are probability proportional to size methods. These methods are also referred to as size biased because sampling is actually from a weighted form of the underlying population distribution. Length- and area-biased sampling are special cases of size-biased sampling where the probability weighting comes from a...

Postmodeling Sensitivity Analysis to Detect the Effect of Missing Data Mechanisms

ERIC Educational Resources Information Center

Jamshidian, Mortaza; Mata, Matthew

2008-01-01

Incomplete or missing data is a common problem in almost all areas of empirical research. It is well known that simple and ad hoc methods such as complete case analysis or mean imputation can lead to biased and/or inefficient estimates. The method of maximum likelihood works well; however, when the missing data mechanism is not one of missing…

An Analysis of Methods Used To Reduce Nonresponse Bias in Survey Research.

ERIC Educational Resources Information Center

Johnson, Victoria A.

The effectiveness of five methods used to estimate the population parameters of a variable of interest from a random sample in the presence of non-response to mail surveys was tested in conditions that vary the return rate and the relationship of the variable of interest to the likelihood of response. Data from 125,092 adult Alabama residents in…

Parameter Estimation of a Spiking Silicon Neuron

PubMed Central

Russell, Alexander; Mazurek, Kevin; Mihalaş, Stefan; Niebur, Ernst; Etienne-Cummings, Ralph

2012-01-01

Spiking neuron models are used in a multitude of tasks ranging from understanding neural behavior at its most basic level to neuroprosthetics. Parameter estimation of a single neuron model, such that the model’s output matches that of a biological neuron is an extremely important task. Hand tuning of parameters to obtain such behaviors is a difficult and time consuming process. This is further complicated when the neuron is instantiated in silicon (an attractive medium in which to implement these models) as fabrication imperfections make the task of parameter configuration more complex. In this paper we show two methods to automate the configuration of a silicon (hardware) neuron’s parameters. First, we show how a Maximum Likelihood method can be applied to a leaky integrate and fire silicon neuron with spike induced currents to fit the neuron’s output to desired spike times. We then show how a distance based method which approximates the negative log likelihood of the lognormal distribution can also be used to tune the neuron’s parameters. We conclude that the distance based method is better suited for parameter configuration of silicon neurons due to its superior optimization speed. PMID:23852978

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).

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

Jennings, E.; Madigan, M.

Given the complexity of modern cosmological parameter inference where we arefaced with non-Gaussian data and noise, correlated systematics and multi-probecorrelated data sets, the Approximate Bayesian Computation (ABC) method is apromising alternative to traditional Markov Chain Monte Carlo approaches in thecase where the Likelihood is intractable or unknown. The ABC method is called"Likelihood free" as it avoids explicit evaluation of the Likelihood by using aforward model simulation of the data which can include systematics. Weintroduce astroABC, an open source ABC Sequential Monte Carlo (SMC) sampler forparameter estimation. A key challenge in astrophysics is the efficient use oflarge multi-probe datasets to constrainmore » high dimensional, possibly correlatedparameter spaces. With this in mind astroABC allows for massive parallelizationusing MPI, a framework that handles spawning of jobs across multiple nodes. Akey new feature of astroABC is the ability to create MPI groups with differentcommunicators, one for the sampler and several others for the forward modelsimulation, which speeds up sampling time considerably. For smaller jobs thePython multiprocessing option is also available. Other key features include: aSequential Monte Carlo sampler, a method for iteratively adapting tolerancelevels, local covariance estimate using scikit-learn's KDTree, modules forspecifying optimal covariance matrix for a component-wise or multivariatenormal perturbation kernel, output and restart files are backed up everyiteration, user defined metric and simulation methods, a module for specifyingheterogeneous parameter priors including non-standard prior PDFs, a module forspecifying a constant, linear, log or exponential tolerance level,well-documented examples and sample scripts. This code is hosted online athttps://github.com/EliseJ/astroABC« less

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.

A hybrid model for combining case-control and cohort studies in systematic reviews of diagnostic tests

PubMed Central

Chen, Yong; Liu, Yulun; Ning, Jing; Cormier, Janice; Chu, Haitao

2014-01-01

Systematic reviews of diagnostic tests often involve a mixture of case-control and cohort studies. The standard methods for evaluating diagnostic accuracy only focus on sensitivity and specificity and ignore the information on disease prevalence contained in cohort studies. Consequently, such methods cannot provide estimates of measures related to disease prevalence, such as population averaged or overall positive and negative predictive values, which reflect the clinical utility of a diagnostic test. In this paper, we propose a hybrid approach that jointly models the disease prevalence along with the diagnostic test sensitivity and specificity in cohort studies, and the sensitivity and specificity in case-control studies. In order to overcome the potential computational difficulties in the standard full likelihood inference of the proposed hybrid model, we propose an alternative inference procedure based on the composite likelihood. Such composite likelihood based inference does not suffer computational problems and maintains high relative efficiency. In addition, it is more robust to model mis-specifications compared to the standard full likelihood inference. We apply our approach to a review of the performance of contemporary diagnostic imaging modalities for detecting metastases in patients with melanoma. PMID:25897179

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Hybrid pairwise likelihood analysis of animal behavior experiments.

PubMed

Cattelan, Manuela; Varin, Cristiano

2013-12-01

The study of the determinants of fights between animals is an important issue in understanding animal behavior. For this purpose, tournament experiments among a set of animals are often used by zoologists. The results of these tournament experiments are naturally analyzed by paired comparison models. Proper statistical analysis of these models is complicated by the presence of dependence between the outcomes of fights because the same animal is involved in different contests. This paper discusses two different model specifications to account for between-fights dependence. Models are fitted through the hybrid pairwise likelihood method that iterates between optimal estimating equations for the regression parameters and pairwise likelihood inference for the association parameters. This approach requires the specification of means and covariances only. For this reason, the method can be applied also when the computation of the joint distribution is difficult or inconvenient. The proposed methodology is investigated by simulation studies and applied to real data about adult male Cape Dwarf Chameleons. © 2013, The International Biometric Society.

Efficient simulation and likelihood methods for non-neutral multi-allele models.

PubMed

Joyce, Paul; Genz, Alan; Buzbas, Erkan Ozge

2012-06-01

Throughout the 1980s, Simon Tavaré made numerous significant contributions to population genetics theory. As genetic data, in particular DNA sequence, became more readily available, a need to connect population-genetic models to data became the central issue. The seminal work of Griffiths and Tavaré (1994a , 1994b , 1994c) was among the first to develop a likelihood method to estimate the population-genetic parameters using full DNA sequences. Now, we are in the genomics era where methods need to scale-up to handle massive data sets, and Tavaré has led the way to new approaches. However, performing statistical inference under non-neutral models has proved elusive. In tribute to Simon Tavaré, we present an article in spirit of his work that provides a computationally tractable method for simulating and analyzing data under a class of non-neutral population-genetic models. Computational methods for approximating likelihood functions and generating samples under a class of allele-frequency based non-neutral parent-independent mutation models were proposed by Donnelly, Nordborg, and Joyce (DNJ) (Donnelly et al., 2001). DNJ (2001) simulated samples of allele frequencies from non-neutral models using neutral models as auxiliary distribution in a rejection algorithm. However, patterns of allele frequencies produced by neutral models are dissimilar to patterns of allele frequencies produced by non-neutral models, making the rejection method inefficient. For example, in some cases the methods in DNJ (2001) require 10(9) rejections before a sample from the non-neutral model is accepted. Our method simulates samples directly from the distribution of non-neutral models, making simulation methods a practical tool to study the behavior of the likelihood and to perform inference on the strength of selection.

Nonparametric modeling of longitudinal covariance structure in functional mapping of quantitative trait loci.

PubMed

Yap, John Stephen; Fan, Jianqing; Wu, Rongling

2009-12-01

Estimation of the covariance structure of longitudinal processes is a fundamental prerequisite for the practical deployment of functional mapping designed to study the genetic regulation and network of quantitative variation in dynamic complex traits. We present a nonparametric approach for estimating the covariance structure of a quantitative trait measured repeatedly at a series of time points. Specifically, we adopt Huang et al.'s (2006, Biometrika 93, 85-98) approach of invoking the modified Cholesky decomposition and converting the problem into modeling a sequence of regressions of responses. A regularized covariance estimator is obtained using a normal penalized likelihood with an L(2) penalty. This approach, embedded within a mixture likelihood framework, leads to enhanced accuracy, precision, and flexibility of functional mapping while preserving its biological relevance. Simulation studies are performed to reveal the statistical properties and advantages of the proposed method. A real example from a mouse genome project is analyzed to illustrate the utilization of the methodology. The new method will provide a useful tool for genome-wide scanning for the existence and distribution of quantitative trait loci underlying a dynamic trait important to agriculture, biology, and health sciences.

Fast automated analysis of strong gravitational lenses with convolutional neural networks

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

Hezaveh, Yashar D.; Levasseur, Laurence Perreault; Marshall, Philip J.

Quantifying image distortions caused by strong gravitational lensing—the formation of multiple images of distant sources due to the deflection of their light by the gravity of intervening structures—and estimating the corresponding matter distribution of these structures (the ‘gravitational lens’) has primarily been performed using maximum likelihood modelling of observations. Our procedure is typically time- and resource-consuming, requiring sophisticated lensing codes, several data preparation steps, and finding the maximum likelihood model parameters in a computationally expensive process with downhill optimizers. Accurate analysis of a single gravitational lens can take up to a few weeks and requires expert knowledge of the physicalmore » processes and methods involved. Tens of thousands of new lenses are expected to be discovered with the upcoming generation of ground and space surveys. We report the use of deep convolutional neural networks to estimate lensing parameters in an extremely fast and automated way, circumventing the difficulties that are faced by maximum likelihood methods. We also show that the removal of lens light can be made fast and automated using independent component analysis of multi-filter imaging data. Our networks can recover the parameters of the ‘singular isothermal ellipsoid’ density profile, which is commonly used to model strong lensing systems, with an accuracy comparable to the uncertainties of sophisticated models but about ten million times faster: 100 systems in approximately one second on a single graphics processing unit. These networks can provide a way for non-experts to obtain estimates of lensing parameters for large samples of data.« less

Fast automated analysis of strong gravitational lenses with convolutional neural networks

DOE PAGES

Hezaveh, Yashar D.; Levasseur, Laurence Perreault; Marshall, Philip J.

2017-08-30

Quantifying image distortions caused by strong gravitational lensing—the formation of multiple images of distant sources due to the deflection of their light by the gravity of intervening structures—and estimating the corresponding matter distribution of these structures (the ‘gravitational lens’) has primarily been performed using maximum likelihood modelling of observations. Our procedure is typically time- and resource-consuming, requiring sophisticated lensing codes, several data preparation steps, and finding the maximum likelihood model parameters in a computationally expensive process with downhill optimizers. Accurate analysis of a single gravitational lens can take up to a few weeks and requires expert knowledge of the physicalmore » processes and methods involved. Tens of thousands of new lenses are expected to be discovered with the upcoming generation of ground and space surveys. We report the use of deep convolutional neural networks to estimate lensing parameters in an extremely fast and automated way, circumventing the difficulties that are faced by maximum likelihood methods. We also show that the removal of lens light can be made fast and automated using independent component analysis of multi-filter imaging data. Our networks can recover the parameters of the ‘singular isothermal ellipsoid’ density profile, which is commonly used to model strong lensing systems, with an accuracy comparable to the uncertainties of sophisticated models but about ten million times faster: 100 systems in approximately one second on a single graphics processing unit. These networks can provide a way for non-experts to obtain estimates of lensing parameters for large samples of data.« less

Fast automated analysis of strong gravitational lenses with convolutional neural networks

NASA Astrophysics Data System (ADS)

Hezaveh, Yashar D.; Levasseur, Laurence Perreault; Marshall, Philip J.

2017-08-01

Quantifying image distortions caused by strong gravitational lensing—the formation of multiple images of distant sources due to the deflection of their light by the gravity of intervening structures—and estimating the corresponding matter distribution of these structures (the ‘gravitational lens’) has primarily been performed using maximum likelihood modelling of observations. This procedure is typically time- and resource-consuming, requiring sophisticated lensing codes, several data preparation steps, and finding the maximum likelihood model parameters in a computationally expensive process with downhill optimizers. Accurate analysis of a single gravitational lens can take up to a few weeks and requires expert knowledge of the physical processes and methods involved. Tens of thousands of new lenses are expected to be discovered with the upcoming generation of ground and space surveys. Here we report the use of deep convolutional neural networks to estimate lensing parameters in an extremely fast and automated way, circumventing the difficulties that are faced by maximum likelihood methods. We also show that the removal of lens light can be made fast and automated using independent component analysis of multi-filter imaging data. Our networks can recover the parameters of the ‘singular isothermal ellipsoid’ density profile, which is commonly used to model strong lensing systems, with an accuracy comparable to the uncertainties of sophisticated models but about ten million times faster: 100 systems in approximately one second on a single graphics processing unit. These networks can provide a way for non-experts to obtain estimates of lensing parameters for large samples of data.

Explaining the effect of event valence on unrealistic optimism.

PubMed

Gold, Ron S; Brown, Mark G

2009-05-01

People typically exhibit 'unrealistic optimism' (UO): they believe they have a lower chance of experiencing negative events and a higher chance of experiencing positive events than does the average person. UO has been found to be greater for negative than positive events. This 'valence effect' has been explained in terms of motivational processes. An alternative explanation is provided by the 'numerosity model', which views the valence effect simply as a by-product of a tendency for likelihood estimates pertaining to the average member of a group to increase with the size of the group. Predictions made by the numerosity model were tested in two studies. In each, UO for a single event was assessed. In Study 1 (n = 115 students), valence was manipulated by framing the event either negatively or positively, and participants estimated their own likelihood and that of the average student at their university. In Study 2 (n = 139 students), valence was again manipulated and participants again estimated their own likelihood; additionally, group size was manipulated by having participants estimate the likelihood of the average student in a small, medium-sized, or large group. In each study, the valence effect was found, but was due to an effect on estimates of own likelihood, not the average person's likelihood. In Study 2, valence did not interact with group size. The findings contradict the numerosity model, but are in accord with the motivational explanation. Implications for health education are discussed.

Cox Regression Models with Functional Covariates for Survival Data.

PubMed

Gellar, Jonathan E; Colantuoni, Elizabeth; Needham, Dale M; Crainiceanu, Ciprian M

2015-06-01

We extend the Cox proportional hazards model to cases when the exposure is a densely sampled functional process, measured at baseline. The fundamental idea is to combine penalized signal regression with methods developed for mixed effects proportional hazards models. The model is fit by maximizing the penalized partial likelihood, with smoothing parameters estimated by a likelihood-based criterion such as AIC or EPIC. The model may be extended to allow for multiple functional predictors, time varying coefficients, and missing or unequally-spaced data. Methods were inspired by and applied to a study of the association between time to death after hospital discharge and daily measures of disease severity collected in the intensive care unit, among survivors of acute respiratory distress syndrome.

[Implication of inverse-probability weighting method in the evaluation of diagnostic test with verification bias].

PubMed

Kang, Leni; Zhang, Shaokai; Zhao, Fanghui; Qiao, Youlin

2014-03-01

To evaluate and adjust the verification bias existed in the screening or diagnostic tests. Inverse-probability weighting method was used to adjust the sensitivity and specificity of the diagnostic tests, with an example of cervical cancer screening used to introduce the Compare Tests package in R software which could be implemented. Sensitivity and specificity calculated from the traditional method and maximum likelihood estimation method were compared to the results from Inverse-probability weighting method in the random-sampled example. The true sensitivity and specificity of the HPV self-sampling test were 83.53% (95%CI:74.23-89.93)and 85.86% (95%CI: 84.23-87.36). In the analysis of data with randomly missing verification by gold standard, the sensitivity and specificity calculated by traditional method were 90.48% (95%CI:80.74-95.56)and 71.96% (95%CI:68.71-75.00), respectively. The adjusted sensitivity and specificity under the use of Inverse-probability weighting method were 82.25% (95% CI:63.11-92.62) and 85.80% (95% CI: 85.09-86.47), respectively, whereas they were 80.13% (95%CI:66.81-93.46)and 85.80% (95%CI: 84.20-87.41) under the maximum likelihood estimation method. The inverse-probability weighting method could effectively adjust the sensitivity and specificity of a diagnostic test when verification bias existed, especially when complex sampling appeared.

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

Quantifying rainfall-derived inflow and infiltration in sanitary sewer systems based on conductivity monitoring

NASA Astrophysics Data System (ADS)

Zhang, Mingkai; Liu, Yanchen; Cheng, Xun; Zhu, David Z.; Shi, Hanchang; Yuan, Zhiguo

2018-03-01

Quantifying rainfall-derived inflow and infiltration (RDII) in a sanitary sewer is difficult when RDII and overflow occur simultaneously. This study proposes a novel conductivity-based method for estimating RDII. The method separately decomposes rainfall-derived inflow (RDI) and rainfall-induced infiltration (RII) on the basis of conductivity data. Fast Fourier transform was adopted to analyze variations in the flow and water quality during dry weather. Nonlinear curve fitting based on the least squares algorithm was used to optimize parameters in the proposed RDII model. The method was successfully applied to real-life case studies, in which inflow and infiltration were successfully estimated for three typical rainfall events with total rainfall volumes of 6.25 mm (light), 28.15 mm (medium), and 178 mm (heavy). Uncertainties of model parameters were estimated using the generalized likelihood uncertainty estimation (GLUE) method and were found to be acceptable. Compared with traditional flow-based methods, the proposed approach exhibits distinct advantages in estimating RDII and overflow, particularly when the two processes happen simultaneously.

Parameter estimation of an ARMA model for river flow forecasting using goal programming

NASA Astrophysics Data System (ADS)

Mohammadi, Kourosh; Eslami, H. R.; Kahawita, Rene

2006-11-01

SummaryRiver flow forecasting constitutes one of the most important applications in hydrology. Several methods have been developed for this purpose and one of the most famous techniques is the Auto regressive moving average (ARMA) model. In the research reported here, the goal was to minimize the error for a specific season of the year as well as for the complete series. Goal programming (GP) was used to estimate the ARMA model parameters. Shaloo Bridge station on the Karun River with 68 years of observed stream flow data was selected to evaluate the performance of the proposed method. The results when compared with the usual method of maximum likelihood estimation were favorable with respect to the new proposed algorithm.

astroABC : An Approximate Bayesian Computation Sequential Monte Carlo sampler for cosmological parameter estimation

NASA Astrophysics Data System (ADS)

Jennings, E.; Madigan, M.

2017-04-01

Given the complexity of modern cosmological parameter inference where we are faced with non-Gaussian data and noise, correlated systematics and multi-probe correlated datasets,the Approximate Bayesian Computation (ABC) method is a promising alternative to traditional Markov Chain Monte Carlo approaches in the case where the Likelihood is intractable or unknown. The ABC method is called "Likelihood free" as it avoids explicit evaluation of the Likelihood by using a forward model simulation of the data which can include systematics. We introduce astroABC, an open source ABC Sequential Monte Carlo (SMC) sampler for parameter estimation. A key challenge in astrophysics is the efficient use of large multi-probe datasets to constrain high dimensional, possibly correlated parameter spaces. With this in mind astroABC allows for massive parallelization using MPI, a framework that handles spawning of processes across multiple nodes. A key new feature of astroABC is the ability to create MPI groups with different communicators, one for the sampler and several others for the forward model simulation, which speeds up sampling time considerably. For smaller jobs the Python multiprocessing option is also available. Other key features of this new sampler include: a Sequential Monte Carlo sampler; a method for iteratively adapting tolerance levels; local covariance estimate using scikit-learn's KDTree; modules for specifying optimal covariance matrix for a component-wise or multivariate normal perturbation kernel and a weighted covariance metric; restart files output frequently so an interrupted sampling run can be resumed at any iteration; output and restart files are backed up at every iteration; user defined distance metric and simulation methods; a module for specifying heterogeneous parameter priors including non-standard prior PDFs; a module for specifying a constant, linear, log or exponential tolerance level; well-documented examples and sample scripts. This code is hosted online at https://github.com/EliseJ/astroABC.

Parameter estimation in astronomy through application of the likelihood ratio. [satellite data analysis techniques

NASA Technical Reports Server (NTRS)

Cash, W.

1979-01-01

Many problems in the experimental estimation of parameters for models can be solved through use of the likelihood ratio test. Applications of the likelihood ratio, with particular attention to photon counting experiments, are discussed. The procedures presented solve a greater range of problems than those currently in use, yet are no more difficult to apply. The procedures are proved analytically, and examples from current problems in astronomy are discussed.

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

NASA Technical Reports Server (NTRS)

Lai, Jonathan Y.

1994-01-01

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

Optimal designs based on the maximum quasi-likelihood estimator

PubMed Central

Shen, Gang; Hyun, Seung Won; Wong, Weng Kee

2016-01-01

We use optimal design theory and construct locally optimal designs based on the maximum quasi-likelihood estimator (MqLE), which is derived under less stringent conditions than those required for the MLE method. We show that the proposed locally optimal designs are asymptotically as efficient as those based on the MLE when the error distribution is from an exponential family, and they perform just as well or better than optimal designs based on any other asymptotically linear unbiased estimators such as the least square estimator (LSE). In addition, we show current algorithms for finding optimal designs can be directly used to find optimal designs based on the MqLE. As an illustrative application, we construct a variety of locally optimal designs based on the MqLE for the 4-parameter logistic (4PL) model and study their robustness properties to misspecifications in the model using asymptotic relative efficiency. The results suggest that optimal designs based on the MqLE can be easily generated and they are quite robust to mis-specification in the probability distribution of the responses. PMID:28163359

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.

Smooth centile curves for skew and kurtotic data modelled using the Box-Cox power exponential distribution.

PubMed

Rigby, Robert A; Stasinopoulos, D Mikis

2004-10-15

The Box-Cox power exponential (BCPE) distribution, developed in this paper, provides a model for a dependent variable Y exhibiting both skewness and kurtosis (leptokurtosis or platykurtosis). The distribution is defined by a power transformation Y(nu) having a shifted and scaled (truncated) standard power exponential distribution with parameter tau. The distribution has four parameters and is denoted BCPE (mu,sigma,nu,tau). The parameters, mu, sigma, nu and tau, may be interpreted as relating to location (median), scale (approximate coefficient of variation), skewness (transformation to symmetry) and kurtosis (power exponential parameter), respectively. Smooth centile curves are obtained by modelling each of the four parameters of the distribution as a smooth non-parametric function of an explanatory variable. A Fisher scoring algorithm is used to fit the non-parametric model by maximizing a penalized likelihood. The first and expected second and cross derivatives of the likelihood, with respect to mu, sigma, nu and tau, required for the algorithm, are provided. The centiles of the BCPE distribution are easy to calculate, so it is highly suited to centile estimation. This application of the BCPE distribution to smooth centile estimation provides a generalization of the LMS method of the centile estimation to data exhibiting kurtosis (as well as skewness) different from that of a normal distribution and is named here the LMSP method of centile estimation. The LMSP method of centile estimation is applied to modelling the body mass index of Dutch males against age. 2004 John Wiley & Sons, Ltd.

Pre-test probability of obstructive coronary stenosis in patients undergoing coronary CT angiography: Comparative performance of the modified diamond-Forrester algorithm versus methods incorporating cardiovascular risk factors.

PubMed

Ferreira, António Miguel; Marques, Hugo; Tralhão, António; Santos, Miguel Borges; Santos, Ana Rita; Cardoso, Gonçalo; Dores, Hélder; Carvalho, Maria Salomé; Madeira, Sérgio; Machado, Francisco Pereira; Cardim, Nuno; de Araújo Gonçalves, Pedro

2016-11-01

Current guidelines recommend the use of the Modified Diamond-Forrester (MDF) method to assess the pre-test likelihood of obstructive coronary artery disease (CAD). We aimed to compare the performance of the MDF method with two contemporary algorithms derived from multicenter trials that additionally incorporate cardiovascular risk factors: the calculator-based 'CAD Consortium 2' method, and the integer-based CONFIRM score. We assessed 1069 consecutive patients without known CAD undergoing coronary CT angiography (CCTA) for stable chest pain. Obstructive CAD was defined as the presence of coronary stenosis ≥50% on 64-slice dual-source CT. The three methods were assessed for calibration, discrimination, net reclassification, and changes in proposed downstream testing based upon calculated pre-test likelihoods. The observed prevalence of obstructive CAD was 13.8% (n=147). Overestimations of the likelihood of obstructive CAD were 140.1%, 9.8%, and 18.8%, respectively, for the MDF, CAD Consortium 2 and CONFIRM methods. The CAD Consortium 2 showed greater discriminative power than the MDF method, with a C-statistic of 0.73 vs. 0.70 (p<0.001), while the CONFIRM score did not (C-statistic 0.71, p=0.492). Reclassification of pre-test likelihood using the 'CAD Consortium 2' or CONFIRM scores resulted in a net reclassification improvement of 0.19 and 0.18, respectively, which would change the diagnostic strategy in approximately half of the patients. Newer risk factor-encompassing models allow for a more precise estimation of pre-test probabilities of obstructive CAD than the guideline-recommended MDF method. Adoption of these scores may improve disease prediction and change the diagnostic pathway in a significant proportion of patients. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Efficient parameter estimation in longitudinal data analysis using a hybrid GEE method.

PubMed

Leung, Denis H Y; Wang, You-Gan; Zhu, Min

2009-07-01

The method of generalized estimating equations (GEEs) provides consistent estimates of the regression parameters in a marginal regression model for longitudinal data, even when the working correlation model is misspecified (Liang and Zeger, 1986). However, the efficiency of a GEE estimate can be seriously affected by the choice of the working correlation model. This study addresses this problem by proposing a hybrid method that combines multiple GEEs based on different working correlation models, using the empirical likelihood method (Qin and Lawless, 1994). Analyses show that this hybrid method is more efficient than a GEE using a misspecified working correlation model. Furthermore, if one of the working correlation structures correctly models the within-subject correlations, then this hybrid method provides the most efficient parameter estimates. In simulations, the hybrid method's finite-sample performance is superior to a GEE under any of the commonly used working correlation models and is almost fully efficient in all scenarios studied. The hybrid method is illustrated using data from a longitudinal study of the respiratory infection rates in 275 Indonesian children.

Object recognition and localization from 3D point clouds by maximum-likelihood estimation

NASA Astrophysics Data System (ADS)

Dantanarayana, Harshana G.; Huntley, Jonathan M.

2017-08-01

We present an algorithm based on maximum-likelihood analysis for the automated recognition of objects, and estimation of their pose, from 3D point clouds. Surfaces segmented from depth images are used as the features, unlike `interest point'-based algorithms which normally discard such data. Compared to the 6D Hough transform, it has negligible memory requirements, and is computationally efficient compared to iterative closest point algorithms. The same method is applicable to both the initial recognition/pose estimation problem as well as subsequent pose refinement through appropriate choice of the dispersion of the probability density functions. This single unified approach therefore avoids the usual requirement for different algorithms for these two tasks. In addition to the theoretical description, a simple 2 degrees of freedom (d.f.) example is given, followed by a full 6 d.f. analysis of 3D point cloud data from a cluttered scene acquired by a projected fringe-based scanner, which demonstrated an RMS alignment error as low as 0.3 mm.

Expectation maximization-based likelihood inference for flexible cure rate models with Weibull lifetimes.

PubMed

Balakrishnan, Narayanaswamy; Pal, Suvra

2016-08-01

Recently, a flexible cure rate survival model has been developed by assuming the number of competing causes of the event of interest to follow the Conway-Maxwell-Poisson distribution. This model includes some of the well-known cure rate models discussed in the literature as special cases. Data obtained from cancer clinical trials are often right censored and expectation maximization algorithm can be used in this case to efficiently estimate the model parameters based on right censored data. In this paper, we consider the competing cause scenario and assuming the time-to-event to follow the Weibull distribution, we derive the necessary steps of the expectation maximization algorithm for estimating the parameters of different cure rate survival models. The standard errors of the maximum likelihood estimates are obtained by inverting the observed information matrix. The method of inference developed here is examined by means of an extensive Monte Carlo simulation study. Finally, we illustrate the proposed methodology with a real data on cancer recurrence. © The Author(s) 2013.

A simple, remote, video based breathing monitor.

PubMed

Regev, Nir; Wulich, Dov

2017-07-01

Breathing monitors have become the all-important cornerstone of a wide variety of commercial and personal safety applications, ranging from elderly care to baby monitoring. Many such monitors exist in the market, some, with vital signs monitoring capabilities, but none remote. This paper presents a simple, yet efficient, real time method of extracting the subject's breathing sinus rhythm. Points of interest are detected on the subject's body, and the corresponding optical flow is estimated and tracked using the well known Lucas-Kanade algorithm on a frame by frame basis. A generalized likelihood ratio test is then utilized on each of the many interest points to detect which is moving in harmonic fashion. Finally, a spectral estimation algorithm based on Pisarenko harmonic decomposition tracks the harmonic frequency in real time, and a fusion maximum likelihood algorithm optimally estimates the breathing rate using all points considered. The results show a maximal error of 1 BPM between the true breathing rate and the algorithm's calculated rate, based on experiments on two babies and three adults.

Conditional estimation using prior information in 2-stage group sequential designs assuming asymptotic normality when the trial terminated early.

PubMed

Shimura, Masashi; Maruo, Kazushi; Gosho, Masahiko

2018-04-23

Two-stage designs are widely used to determine whether a clinical trial should be terminated early. In such trials, a maximum likelihood estimate is often adopted to describe the difference in efficacy between the experimental and reference treatments; however, this method is known to display conditional bias. To reduce such bias, a conditional mean-adjusted estimator (CMAE) has been proposed, although the remaining bias may be nonnegligible when a trial is stopped for efficacy at the interim analysis. We propose a new estimator for adjusting the conditional bias of the treatment effect by extending the idea of the CMAE. This estimator is calculated by weighting the maximum likelihood estimate obtained at the interim analysis and the effect size prespecified when calculating the sample size. We evaluate the performance of the proposed estimator through analytical and simulation studies in various settings in which a trial is stopped for efficacy or futility at the interim analysis. We find that the conditional bias of the proposed estimator is smaller than that of the CMAE when the information time at the interim analysis is small. In addition, the mean-squared error of the proposed estimator is also smaller than that of the CMAE. In conclusion, we recommend the use of the proposed estimator for trials that are terminated early for efficacy or futility. Copyright © 2018 John Wiley & Sons, Ltd.

Cosmological parameters from a re-analysis of the WMAP 7 year low-resolution maps

NASA Astrophysics Data System (ADS)

Finelli, F.; De Rosa, A.; Gruppuso, A.; Paoletti, D.

2013-06-01

Cosmological parameters from Wilkinson Microwave Anisotropy Probe (WMAP) 7 year data are re-analysed by substituting a pixel-based likelihood estimator to the one delivered publicly by the WMAP team. Our pixel-based estimator handles exactly intensity and polarization in a joint manner, allowing us to use low-resolution maps and noise covariance matrices in T, Q, U at the same resolution, which in this work is 3.6°. We describe the features and the performances of the code implementing our pixel-based likelihood estimator. We perform a battery of tests on the application of our pixel-based likelihood routine to WMAP publicly available low-resolution foreground-cleaned products, in combination with the WMAP high-ℓ likelihood, reporting the differences on cosmological parameters evaluated by the full WMAP likelihood public package. The differences are not only due to the treatment of polarization, but also to the marginalization over monopole and dipole uncertainties present in the WMAP pixel likelihood code for temperature. The credible central value for the cosmological parameters change below the 1σ level with respect to the evaluation by the full WMAP 7 year likelihood code, with the largest difference in a shift to smaller values of the scalar spectral index nS.

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.

Development of advanced acreage estimation methods

NASA Technical Reports Server (NTRS)

Guseman, L. F., Jr. (Principal Investigator)

1980-01-01

The use of the AMOEBA clustering/classification algorithm was investigated as a basis for both a color display generation technique and maximum likelihood proportion estimation procedure. An approach to analyzing large data reduction systems was formulated and an exploratory empirical study of spatial correlation in LANDSAT data was also carried out. Topics addressed include: (1) development of multiimage color images; (2) spectral spatial classification algorithm development; (3) spatial correlation studies; and (4) evaluation of data systems.

NLSCIDNT user's guide maximum likehood parameter identification computer program with nonlinear rotorcraft model

NASA Technical Reports Server (NTRS)

1979-01-01

A nonlinear, maximum likelihood, parameter identification computer program (NLSCIDNT) is described which evaluates rotorcraft stability and control coefficients from flight test data. The optimal estimates of the parameters (stability and control coefficients) are determined (identified) by minimizing the negative log likelihood cost function. The minimization technique is the Levenberg-Marquardt method, which behaves like the steepest descent method when it is far from the minimum and behaves like the modified Newton-Raphson method when it is nearer the minimum. Twenty-one states and 40 measurement variables are modeled, and any subset may be selected. States which are not integrated may be fixed at an input value, or time history data may be substituted for the state in the equations of motion. Any aerodynamic coefficient may be expressed as a nonlinear polynomial function of selected 'expansion variables'.

Information loss in approximately bayesian data assimilation: a comparison of generative and discriminative approaches to estimating agricultural yield

USDA-ARS?s Scientific Manuscript database

Data assimilation and regression are two commonly used methods for predicting agricultural yield from remote sensing observations. Data assimilation is a generative approach because it requires explicit approximations of the Bayesian prior and likelihood to compute the probability density function...

Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions.

ERIC Educational Resources Information Center

Holland, Paul W.; Thayer, Dorothy T.

2000-01-01

Applied the theory of exponential families of distributions to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. Considers efficient computation of the maximum likelihood estimates of the parameters using Newton's Method and computationally efficient…

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.

Allowing for Correlations between Correlations in Random-Effects Meta-Analysis of Correlation Matrices

ERIC Educational Resources Information Center

Prevost, A. Toby; Mason, Dan; Griffin, Simon; Kinmonth, Ann-Louise; Sutton, Stephen; Spiegelhalter, David

2007-01-01

Practical meta-analysis of correlation matrices generally ignores covariances (and hence correlations) between correlation estimates. The authors consider various methods for allowing for covariances, including generalized least squares, maximum marginal likelihood, and Bayesian approaches, illustrated using a 6-dimensional response in a series of…

Local Influence and Robust Procedures for Mediation Analysis

ERIC Educational Resources Information Center

Zu, Jiyun; Yuan, Ke-Hai

2010-01-01

Existing studies of mediation models have been limited to normal-theory maximum likelihood (ML). Because real data in the social and behavioral sciences are seldom normally distributed and often contain outliers, classical methods generally lead to inefficient or biased parameter estimates. Consequently, the conclusions from a mediation analysis…

Maximum likelihood estimation in calibrating a stereo camera setup.

PubMed

Muijtjens, A M; Roos, J M; Arts, T; Hasman, A

1999-02-01

Motion and deformation of the cardiac wall may be measured by following the positions of implanted radiopaque markers in three dimensions, using two x-ray cameras simultaneously. Regularly, calibration of the position measurement system is obtained by registration of the images of a calibration object, containing 10-20 radiopaque markers at known positions. Unfortunately, an accidental change of the position of a camera after calibration requires complete recalibration. Alternatively, redundant information in the measured image positions of stereo pairs can be used for calibration. Thus, a separate calibration procedure can be avoided. In the current study a model is developed that describes the geometry of the camera setup by five dimensionless parameters. Maximum Likelihood (ML) estimates of these parameters were obtained in an error analysis. It is shown that the ML estimates can be found by application of a nonlinear least squares procedure. Compared to the standard unweighted least squares procedure, the ML method resulted in more accurate estimates without noticeable bias. The accuracy of the ML method was investigated in relation to the object aperture. The reconstruction problem appeared well conditioned as long as the object aperture is larger than 0.1 rad. The angle between the two viewing directions appeared to be the parameter that was most likely to cause major inaccuracies in the reconstruction of the 3-D positions of the markers. Hence, attempts to improve the robustness of the method should primarily focus on reduction of the error in this parameter.

An evaluation of inferential procedures for adaptive clinical trial designs with pre-specified rules for modifying the sample size.

PubMed

Levin, Gregory P; Emerson, Sarah C; Emerson, Scott S

2014-09-01

Many papers have introduced adaptive clinical trial methods that allow modifications to the sample size based on interim estimates of treatment effect. There has been extensive commentary on type I error control and efficiency considerations, but little research on estimation after an adaptive hypothesis test. We evaluate the reliability and precision of different inferential procedures in the presence of an adaptive design with pre-specified rules for modifying the sampling plan. We extend group sequential orderings of the outcome space based on the stage at stopping, likelihood ratio statistic, and sample mean to the adaptive setting in order to compute median-unbiased point estimates, exact confidence intervals, and P-values uniformly distributed under the null hypothesis. The likelihood ratio ordering is found to average shorter confidence intervals and produce higher probabilities of P-values below important thresholds than alternative approaches. The bias adjusted mean demonstrates the lowest mean squared error among candidate point estimates. A conditional error-based approach in the literature has the benefit of being the only method that accommodates unplanned adaptations. We compare the performance of this and other methods in order to quantify the cost of failing to plan ahead in settings where adaptations could realistically be pre-specified at the design stage. We find the cost to be meaningful for all designs and treatment effects considered, and to be substantial for designs frequently proposed in the literature. © 2014, The International Biometric Society.

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

PubMed

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

2011-01-01

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

Robust Likelihoods for Inflationary Gravitational Waves from Maps of Cosmic Microwave Background Polarization

NASA Technical Reports Server (NTRS)

Switzer, Eric Ryan; Watts, Duncan J.

2016-01-01

The B-mode polarization of the cosmic microwave background provides a unique window into tensor perturbations from inflationary gravitational waves. Survey effects complicate the estimation and description of the power spectrum on the largest angular scales. The pixel-space likelihood yields parameter distributions without the power spectrum as an intermediate step, but it does not have the large suite of tests available to power spectral methods. Searches for primordial B-modes must rigorously reject and rule out contamination. Many forms of contamination vary or are uncorrelated across epochs, frequencies, surveys, or other data treatment subsets. The cross power and the power spectrum of the difference of subset maps provide approaches to reject and isolate excess variance. We develop an analogous joint pixel-space likelihood. Contamination not modeled in the likelihood produces parameter-dependent bias and complicates the interpretation of the difference map. We describe a null test that consistently weights the difference map. Excess variance should either be explicitly modeled in the covariance or be removed through reprocessing the data.

Comparison of estimators of standard deviation for hydrologic time series

USGS Publications Warehouse

Tasker, Gary D.; Gilroy, Edward J.

1982-01-01

Unbiasing factors as a function of serial correlation, ρ, and sample size, n for the sample standard deviation of a lag one autoregressive model were generated by random number simulation. Monte Carlo experiments were used to compare the performance of several alternative methods for estimating the standard deviation σ of a lag one autoregressive model in terms of bias, root mean square error, probability of underestimation, and expected opportunity design loss. Three methods provided estimates of σ which were much less biased but had greater mean square errors than the usual estimate of σ: s = (1/(n - 1) ∑ (xi −x¯)2)½. The three methods may be briefly characterized as (1) a method using a maximum likelihood estimate of the unbiasing factor, (2) a method using an empirical Bayes estimate of the unbiasing factor, and (3) a robust nonparametric estimate of σ suggested by Quenouille. Because s tends to underestimate σ, its use as an estimate of a model parameter results in a tendency to underdesign. If underdesign losses are considered more serious than overdesign losses, then the choice of one of the less biased methods may be wise.

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(')

Low-complexity DOA estimation from short data snapshots for ULA systems using the annihilating filter technique

NASA Astrophysics Data System (ADS)

Bellili, Faouzi; Amor, Souheib Ben; Affes, Sofiène; Ghrayeb, Ali

2017-12-01

This paper addresses the problem of DOA estimation using uniform linear array (ULA) antenna configurations. We propose a new low-cost method of multiple DOA estimation from very short data snapshots. The new estimator is based on the annihilating filter (AF) technique. It is non-data-aided (NDA) and does not impinge therefore on the whole throughput of the system. The noise components are assumed temporally and spatially white across the receiving antenna elements. The transmitted signals are also temporally and spatially white across the transmitting sources. The new method is compared in performance to the Cramér-Rao lower bound (CRLB), the root-MUSIC algorithm, the deterministic maximum likelihood estimator and another Bayesian method developed precisely for the single snapshot case. Simulations show that the new estimator performs well over a wide SNR range. Prominently, the main advantage of the new AF-based method is that it succeeds in accurately estimating the DOAs from short data snapshots and even from a single snapshot outperforming by far the state-of-the-art techniques both in DOA estimation accuracy and computational cost.

Inference for the effect of treatment on survival probability in randomized trials with noncompliance and administrative censoring.

PubMed

Nie, Hui; Cheng, Jing; Small, Dylan S

2011-12-01

In many clinical studies with a survival outcome, administrative censoring occurs when follow-up ends at a prespecified date and many subjects are still alive. An additional complication in some trials is that there is noncompliance with the assigned treatment. For this setting, we study the estimation of the causal effect of treatment on survival probability up to a given time point among those subjects who would comply with the assignment to both treatment and control. We first discuss the standard instrumental variable (IV) method for survival outcomes and parametric maximum likelihood methods, and then develop an efficient plug-in nonparametric empirical maximum likelihood estimation (PNEMLE) approach. The PNEMLE method does not make any assumptions on outcome distributions, and makes use of the mixture structure in the data to gain efficiency over the standard IV method. Theoretical results of the PNEMLE are derived and the method is illustrated by an analysis of data from a breast cancer screening trial. From our limited mortality analysis with administrative censoring times 10 years into the follow-up, we find a significant benefit of screening is present after 4 years (at the 5% level) and this persists at 10 years follow-up. © 2011, The International Biometric Society.

Using effort information with change-in-ratio data for population estimation

USGS Publications Warehouse

Udevitz, Mark S.; Pollock, Kenneth H.

1995-01-01

Most change-in-ratio (CIR) methods for estimating fish and wildlife population sizes have been based only on assumptions about how encounter probabilities vary among population subclasses. When information on sampling effort is available, it is also possible to derive CIR estimators based on assumptions about how encounter probabilities vary over time. This paper presents a generalization of previous CIR models that allows explicit consideration of a range of assumptions about the variation of encounter probabilities among subclasses and over time. Explicit estimators are derived under this model for specific sets of assumptions about the encounter probabilities. Numerical methods are presented for obtaining estimators under the full range of possible assumptions. Likelihood ratio tests for these assumptions are described. Emphasis is on obtaining estimators based on assumptions about variation of encounter probabilities over time.

Bayesian estimation of the transmissivity spatial structure from pumping test data

NASA Astrophysics Data System (ADS)

Demir, Mehmet Taner; Copty, Nadim K.; Trinchero, Paolo; Sanchez-Vila, Xavier

2017-06-01

Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests.

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.

Use of Multiple Imputation Method to Improve Estimation of Missing Baseline Serum Creatinine in Acute Kidney Injury Research

PubMed Central

Peterson, Josh F.; Eden, Svetlana K.; Moons, Karel G.; Ikizler, T. Alp; Matheny, Michael E.

2013-01-01

Summary Background and objectives Baseline creatinine (BCr) is frequently missing in AKI studies. Common surrogate estimates can misclassify AKI and adversely affect the study of related outcomes. This study examined whether multiple imputation improved accuracy of estimating missing BCr beyond current recommendations to apply assumed estimated GFR (eGFR) of 75 ml/min per 1.73 m2 (eGFR 75). Design, setting, participants, & measurements From 41,114 unique adult admissions (13,003 with and 28,111 without BCr data) at Vanderbilt University Hospital between 2006 and 2008, a propensity score model was developed to predict likelihood of missing BCr. Propensity scoring identified 6502 patients with highest likelihood of missing BCr among 13,003 patients with known BCr to simulate a “missing” data scenario while preserving actual reference BCr. Within this cohort (n=6502), the ability of various multiple-imputation approaches to estimate BCr and classify AKI were compared with that of eGFR 75. Results All multiple-imputation methods except the basic one more closely approximated actual BCr than did eGFR 75. Total AKI misclassification was lower with multiple imputation (full multiple imputation + serum creatinine) (9.0%) than with eGFR 75 (12.3%; P<0.001). Improvements in misclassification were greater in patients with impaired kidney function (full multiple imputation + serum creatinine) (15.3%) versus eGFR 75 (40.5%; P<0.001). Multiple imputation improved specificity and positive predictive value for detecting AKI at the expense of modestly decreasing sensitivity relative to eGFR 75. Conclusions Multiple imputation can improve accuracy in estimating missing BCr and reduce misclassification of AKI beyond currently proposed methods. PMID:23037980

Examining the types and payments of the disabilities of the insurants in the National Farmers' Health Insurance program in Taiwan.

PubMed

Wang, Jiun-Hao; Chang, Hung-Hao

2010-10-26

In contrast to the considerable body of literature concerning the disabilities of the general population, little information exists pertaining to the disabilities of the farm population. Focusing on the disability issue to the insurants in the Farmers' Health Insurance (FHI) program in Taiwan, this paper examines the associations among socio-demographic characteristics, insured factors, and the introduction of the national health insurance program, as well as the types and payments of disabilities among the insurants. A unique dataset containing 1,594,439 insurants in 2008 was used in this research. A logistic regression model was estimated for the likelihood of received disability payments. By focusing on the recipients, a disability payment and a disability type equation were estimated using the ordinary least squares method and a multinomial logistic model, respectively, to investigate the effects of the exogenous factors on their received payments and the likelihood of having different types of disabilities. Age and different job categories are significantly associated with the likelihood of receiving disability payments. Compared to those under age 45, the likelihood is higher among recipients aged 85 and above (the odds ratio is 8.04). Compared to hired workers, the odds ratios for self-employed and spouses of farm operators who were not members of farmers' associations are 0.97 and 0.85, respectively. In addition, older insurants are more likely to have eye problems; few differences in disability types are related to insured job categories. Results indicate that older farmers are more likely to receive disability payments, but the likelihood is not much different among insurants of various job categories. Among all of the selected types of disability, a highest likelihood is found for eye disability. In addition, the introduction of the national health insurance program decreases the likelihood of receiving disability payments. The experience in Taiwan can be valuable for other countries that are in an initial stage to implement a universal health insurance program.

Relationship between two indicators of coronary risk estimated by the Framingham Risk Score and the number of metabolic syndrome components in Japanese male manufacturing workers.

PubMed

Kawada, Tomoyuki; Otsuka, Toshiaki; Inagaki, Hirofumi; Wakayama, Yoko; Li, Qing; Katsumata, Masao

2009-10-01

The Framingham Risk Score (FRS) has frequently been used in the United States to predict the 10-year risk of coronary heart disease (CHD). Components of the metabolic syndrome and several lifestyle factors have also been evaluated to estimate the risk of CHD. To determine the relationship between the FRS and components of metabolic syndrome as coronary risk indicators, the authors conducted a cross-sectional study of 2,619 Japanese male workers, ranging in age from 40 to 64 years, at a single workplace. Although the estimation by the FRS and metabolic syndrome involved some different factors, significant association of the risk estimated by the 2 methods was observed. When logistic regression analysis was conducted with adjustment for several lifestyle factors, the FRS and serum insulin were found to be significantly associated with the risk of likelihood of metabolic syndrome. The odds ratios and 95% confidence intervals of FRS by per standard deviation increment and serum insulin by increasing 1 microIU/mL for the prediction of metabolic syndrome were 2.50 (2.17-2.88) and 1.24 (1.20-1.27), respectively. A preventive effect of abstaining from drinking every day and eating breakfast almost daily against the likelihood of metabolic syndrome was also observed. In conclusion, the FRS and insulin were found to be significantly associated with the risk of likelihood of metabolic syndrome, even after controlling for weight change.

A three domain covariance framework for EEG/MEG data.

PubMed

Roś, Beata P; Bijma, Fetsje; de Gunst, Mathisca C M; de Munck, Jan C

2015-10-01

In this paper we introduce a covariance framework for the analysis of single subject EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. Our covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, like in combined EEG-fMRI experiments in which the correlation between EEG and fMRI signals is investigated. We use a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. We apply our method to real EEG and MEG data sets. Copyright © 2015 Elsevier Inc. All rights reserved.

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.

A Dirichlet-Multinomial Bayes Classifier for Disease Diagnosis with Microbial Compositions.

PubMed

Gao, Xiang; Lin, Huaiying; Dong, Qunfeng

2017-01-01

Dysbiosis of microbial communities is associated with various human diseases, raising the possibility of using microbial compositions as biomarkers for disease diagnosis. We have developed a Bayes classifier by modeling microbial compositions with Dirichlet-multinomial distributions, which are widely used to model multicategorical count data with extra variation. The parameters of the Dirichlet-multinomial distributions are estimated from training microbiome data sets based on maximum likelihood. The posterior probability of a microbiome sample belonging to a disease or healthy category is calculated based on Bayes' theorem, using the likelihood values computed from the estimated Dirichlet-multinomial distribution, as well as a prior probability estimated from the training microbiome data set or previously published information on disease prevalence. When tested on real-world microbiome data sets, our method, called DMBC (for Dirichlet-multinomial Bayes classifier), shows better classification accuracy than the only existing Bayesian microbiome classifier based on a Dirichlet-multinomial mixture model and the popular random forest method. The advantage of DMBC is its built-in automatic feature selection, capable of identifying a subset of microbial taxa with the best classification accuracy between different classes of samples based on cross-validation. This unique ability enables DMBC to maintain and even improve its accuracy at modeling species-level taxa. The R package for DMBC is freely available at https://github.com/qunfengdong/DMBC. IMPORTANCE By incorporating prior information on disease prevalence, Bayes classifiers have the potential to estimate disease probability better than other common machine-learning methods. Thus, it is important to develop Bayes classifiers specifically tailored for microbiome data. Our method shows higher classification accuracy than the only existing Bayesian classifier and the popular random forest method, and thus provides an alternative option for using microbial compositions for disease diagnosis.

Work Status and Return to the Workforce after Coronary Artery Bypass Grafting and/or Heart Valve Surgery: A One-Year-Follow Up Study.

PubMed

Fonager, Kirsten; Lundbye-Christensen, Søren; Andreasen, Jan Jesper; Futtrup, Mikkel; Christensen, Anette Luther; Ahmad, Khalil; Nørgaard, Martin Agge

2014-01-01

Background. Several characteristics appear to be important for estimating the likelihood of reentering the workforce after surgery. The aim of the present study was to describe work status in a two-year time period around the time of cardiac surgery and estimate the probability of returning to the workforce. Methods. We included 681 patients undergoing coronary artery bypass grafting and/or heart valve procedures from 2003 to 2007 in the North Denmark Region. We linked hospital data to data in the DREAM database which holds information of everyone receiving social benefits. Results. At the time of surgery 17.3% were allocated disability pension and 2.3% were allocated a permanent part-time benefit. Being unemployed one year before surgery reduced the likelihood of return to the workforce (RR = 0.74 (0.60-0.92)) whereas unemployment at the time of surgery had no impact on return to the workforce (RR = 0.96 (0.78-1.18)). Sickness absence before surgery reduced the likelihood of return to the workforce. Conclusion. This study found the work status before surgery to be associated with the likelihood of return to the workforce within one year after surgery. Before surgery one-fifth of the population either was allocated disability pension or received a permanent part-time benefit.

Work Status and Return to the Workforce after Coronary Artery Bypass Grafting and/or Heart Valve Surgery: A One-Year-Follow Up Study

PubMed Central

Fonager, Kirsten; Lundbye-Christensen, Søren; Andreasen, Jan Jesper; Futtrup, Mikkel; Christensen, Anette Luther; Ahmad, Khalil; Nørgaard, Martin Agge

2014-01-01

Background. Several characteristics appear to be important for estimating the likelihood of reentering the workforce after surgery. The aim of the present study was to describe work status in a two-year time period around the time of cardiac surgery and estimate the probability of returning to the workforce. Methods. We included 681 patients undergoing coronary artery bypass grafting and/or heart valve procedures from 2003 to 2007 in the North Denmark Region. We linked hospital data to data in the DREAM database which holds information of everyone receiving social benefits. Results. At the time of surgery 17.3% were allocated disability pension and 2.3% were allocated a permanent part-time benefit. Being unemployed one year before surgery reduced the likelihood of return to the workforce (RR = 0.74 (0.60–0.92)) whereas unemployment at the time of surgery had no impact on return to the workforce (RR = 0.96 (0.78–1.18)). Sickness absence before surgery reduced the likelihood of return to the workforce. Conclusion. This study found the work status before surgery to be associated with the likelihood of return to the workforce within one year after surgery. Before surgery one-fifth of the population either was allocated disability pension or received a permanent part-time benefit. PMID:25024848

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)

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

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

A spatially explicit capture-recapture estimator for single-catch traps.

PubMed

Distiller, Greg; Borchers, David L

2015-11-01

Single-catch traps are frequently used in live-trapping studies of small mammals. Thus far, a likelihood for single-catch traps has proven elusive and usually the likelihood for multicatch traps is used for spatially explicit capture-recapture (SECR) analyses of such data. Previous work found the multicatch likelihood to provide a robust estimator of average density. We build on a recently developed continuous-time model for SECR to derive a likelihood for single-catch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multicatch estimator for various scenarios with nonconstant density surfaces. While the multicatch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height of the detection function. By contrast, the single-catch estimators of density, distribution, and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constant over the survey region, then the multicatch estimator performs well with single-catch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the single-catch estimator when trap saturation is above about 60%. The estimator's performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a single-catch likelihood with unknown capture times remains intractable for now, researchers using single-catch traps should aim to incorporate timing devices with their traps.

A Modified Cramer-von Mises and Anderson-Darling Test for the Weibull Distribution with Unknown Location and Scale Parameters.

DTIC Science & Technology

1981-12-01

preventing the generation of 16 6 negative location estimators. Because of the invariant pro- perty of the EDF statistics, this transformation will...likelihood. If the parameter estimation method developed by Harter and Moore is used, care must be taken to prevent the location estimators from being...vs A 2 Critical Values, Level-.Ol, n-30 128 , 0 6N m m • w - APPENDIX E Computer Prgrams 129 Program to Calculate the Cramer-von Mises Critical Values

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.

Maintained Individual Data Distributed Likelihood Estimation (MIDDLE)

PubMed Central

Boker, Steven M.; Brick, Timothy R.; Pritikin, Joshua N.; Wang, Yang; von Oertzen, Timo; Brown, Donald; Lach, John; Estabrook, Ryne; Hunter, Michael D.; Maes, Hermine H.; Neale, Michael C.

2015-01-01

Maintained Individual Data Distributed Likelihood Estimation (MIDDLE) is a novel paradigm for research in the behavioral, social, and health sciences. The MIDDLE approach is based on the seemingly-impossible idea that data can be privately maintained by participants and never revealed to researchers, while still enabling statistical models to be fit and scientific hypotheses tested. MIDDLE rests on the assumption that participant data should belong to, be controlled by, and remain in the possession of the participants themselves. Distributed likelihood estimation refers to fitting statistical models by sending an objective function and vector of parameters to each participants’ personal device (e.g., smartphone, tablet, computer), where the likelihood of that individual’s data is calculated locally. Only the likelihood value is returned to the central optimizer. The optimizer aggregates likelihood values from responding participants and chooses new vectors of parameters until the model converges. A MIDDLE study provides significantly greater privacy for participants, automatic management of opt-in and opt-out consent, lower cost for the researcher and funding institute, and faster determination of results. Furthermore, if a participant opts into several studies simultaneously and opts into data sharing, these studies automatically have access to individual-level longitudinal data linked across all studies. PMID:26717128

Generalized weighted likelihood density estimators with application to finite mixture of exponential family distributions

PubMed Central

Zhan, Tingting; Chevoneva, Inna; Iglewicz, Boris

2010-01-01

The family of weighted likelihood estimators largely overlaps with minimum divergence estimators. They are robust to data contaminations compared to MLE. We define the class of generalized weighted likelihood estimators (GWLE), provide its influence function and discuss the efficiency requirements. We introduce a new truncated cubic-inverse weight, which is both first and second order efficient and more robust than previously reported weights. We also discuss new ways of selecting the smoothing bandwidth and weighted starting values for the iterative algorithm. The advantage of the truncated cubic-inverse weight is illustrated in a simulation study of three-components normal mixtures model with large overlaps and heavy contaminations. A real data example is also provided. PMID:20835375

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.

Diallel analysis for sex-linked and maternal effects.

PubMed

Zhu, J; Weir, B S

1996-01-01

Genetic models including sex-linked and maternal effects as well as autosomal gene effects are described. Monte Carlo simulations were conducted to compare efficiencies of estimation by minimum norm quadratic unbiased estimation (MINQUE) and restricted maximum likelihood (REML) methods. MINQUE(1), which has 1 for all prior values, has a similar efficiency to MINQUE(θ), which requires prior estimates of parameter values. MINQUE(1) has the advantage over REML of unbiased estimation and convenient computation. An adjusted unbiased prediction (AUP) method is developed for predicting random genetic effects. AUP is desirable for its easy computation and unbiasedness of both mean and variance of predictors. The jackknife procedure is appropriate for estimating the sampling variances of estimated variances (or covariances) and of predicted genetic effects. A t-test based on jackknife variances is applicable for detecting significance of variation. Worked examples from mice and silkworm data are given in order to demonstrate variance and covariance estimation and genetic effect prediction.

Applications of non-standard maximum likelihood techniques in energy and resource economics

NASA Astrophysics Data System (ADS)

Moeltner, Klaus

Two important types of non-standard maximum likelihood techniques, Simulated Maximum Likelihood (SML) and Pseudo-Maximum Likelihood (PML), have only recently found consideration in the applied economic literature. The objective of this thesis is to demonstrate how these methods can be successfully employed in the analysis of energy and resource models. Chapter I focuses on SML. It constitutes the first application of this technique in the field of energy economics. The framework is as follows: Surveys on the cost of power outages to commercial and industrial customers usually capture multiple observations on the dependent variable for a given firm. The resulting pooled data set is censored and exhibits cross-sectional heterogeneity. We propose a model that addresses these issues by allowing regression coefficients to vary randomly across respondents and by using the Geweke-Hajivassiliou-Keane simulator and Halton sequences to estimate high-order cumulative distribution terms. This adjustment requires the use of SML in the estimation process. Our framework allows for a more comprehensive analysis of outage costs than existing models, which rely on the assumptions of parameter constancy and cross-sectional homogeneity. Our results strongly reject both of these restrictions. The central topic of the second Chapter is the use of PML, a robust estimation technique, in count data analysis of visitor demand for a system of recreation sites. PML has been popular with researchers in this context, since it guards against many types of mis-specification errors. We demonstrate, however, that estimation results will generally be biased even if derived through PML if the recreation model is based on aggregate, or zonal data. To countervail this problem, we propose a zonal model of recreation that captures some of the underlying heterogeneity of individual visitors by incorporating distributional information on per-capita income into the aggregate demand function. This adjustment eliminates the unrealistic constraint of constant income across zonal residents, and thus reduces the risk of aggregation bias in estimated macro-parameters. The corrected aggregate specification reinstates the applicability of PML. It also increases model efficiency, and allows-for the generation of welfare estimates for population subgroups.

Branching-ratio approximation for the self-exciting Hawkes process

NASA Astrophysics Data System (ADS)

Hardiman, Stephen J.; Bouchaud, Jean-Philippe

2014-12-01

We introduce a model-independent approximation for the branching ratio of Hawkes self-exciting point processes. Our estimator requires knowing only the mean and variance of the event count in a sufficiently large time window, statistics that are readily obtained from empirical data. The method we propose greatly simplifies the estimation of the Hawkes branching ratio, recently proposed as a proxy for market endogeneity and formerly estimated using numerical likelihood maximization. We employ our method to support recent theoretical and experimental results indicating that the best fitting Hawkes model to describe S&P futures price changes is in fact critical (now and in the recent past) in light of the long memory of financial market activity.

Assessing Interval Estimation Methods for Hill Model ...

EPA Pesticide Factsheets

The Hill model of concentration-response is ubiquitous in toxicology, perhaps because its parameters directly relate to biologically significant metrics of toxicity such as efficacy and potency. Point estimates of these parameters obtained through least squares regression or maximum likelihood are commonly used in high-throughput risk assessment, but such estimates typically fail to include reliable information concerning confidence in (or precision of) the estimates. To address this issue, we examined methods for assessing uncertainty in Hill model parameter estimates derived from concentration-response data. In particular, using a sample of ToxCast concentration-response data sets, we applied four methods for obtaining interval estimates that are based on asymptotic theory, bootstrapping (two varieties), and Bayesian parameter estimation, and then compared the results. These interval estimation methods generally did not agree, so we devised a simulation study to assess their relative performance. We generated simulated data by constructing four statistical error models capable of producing concentration-response data sets comparable to those observed in ToxCast. We then applied the four interval estimation methods to the simulated data and compared the actual coverage of the interval estimates to the nominal coverage (e.g., 95%) in order to quantify performance of each of the methods in a variety of cases (i.e., different values of the true Hill model paramet

New estimates of the CMB angular power spectra from the WMAP 5 year low-resolution data

NASA Astrophysics Data System (ADS)

Gruppuso, A.; de Rosa, A.; Cabella, P.; Paci, F.; Finelli, F.; Natoli, P.; de Gasperis, G.; Mandolesi, N.

2009-11-01

A quadratic maximum likelihood (QML) estimator is applied to the Wilkinson Microwave Anisotropy Probe (WMAP) 5 year low-resolution maps to compute the cosmic microwave background angular power spectra (APS) at large scales for both temperature and polarization. Estimates and error bars for the six APS are provided up to l = 32 and compared, when possible, to those obtained by the WMAP team, without finding any inconsistency. The conditional likelihood slices are also computed for the Cl of all the six power spectra from l = 2 to 10 through a pixel-based likelihood code. Both the codes treat the covariance for (T, Q, U) in a single matrix without employing any approximation. The inputs of both the codes (foreground-reduced maps, related covariances and masks) are provided by the WMAP team. The peaks of the likelihood slices are always consistent with the QML estimates within the error bars; however, an excellent agreement occurs when the QML estimates are used as a fiducial power spectrum instead of the best-fitting theoretical power spectrum. By the full computation of the conditional likelihood on the estimated spectra, the value of the temperature quadrupole CTTl=2 is found to be less than 2σ away from the WMAP 5 year Λ cold dark matter best-fitting value. The BB spectrum is found to be well consistent with zero, and upper limits on the B modes are provided. The parity odd signals TB and EB are found to be consistent with zero.

An Adaptive Kalman Filter using a Simple Residual Tuning Method

NASA Technical Reports Server (NTRS)

Harman, Richard R.

1999-01-01

One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.

Quantifying uncertainties in streamflow predictions through signature based inference of hydrological model parameters

NASA Astrophysics Data System (ADS)

Fenicia, Fabrizio; Reichert, Peter; Kavetski, Dmitri; Albert, Calro

2016-04-01

The calibration of hydrological models based on signatures (e.g. Flow Duration Curves - FDCs) is often advocated as an alternative to model calibration based on the full time series of system responses (e.g. hydrographs). Signature based calibration is motivated by various arguments. From a conceptual perspective, calibration on signatures is a way to filter out errors that are difficult to represent when calibrating on the full time series. Such errors may for example occur when observed and simulated hydrographs are shifted, either on the "time" axis (i.e. left or right), or on the "streamflow" axis (i.e. above or below). These shifts may be due to errors in the precipitation input (time or amount), and if not properly accounted in the likelihood function, may cause biased parameter estimates (e.g. estimated model parameters that do not reproduce the recession characteristics of a hydrograph). From a practical perspective, signature based calibration is seen as a possible solution for making predictions in ungauged basins. Where streamflow data are not available, it may in fact be possible to reliably estimate streamflow signatures. Previous research has for example shown how FDCs can be reliably estimated at ungauged locations based on climatic and physiographic influence factors. Typically, the goal of signature based calibration is not the prediction of the signatures themselves, but the prediction of the system responses. Ideally, the prediction of system responses should be accompanied by a reliable quantification of the associated uncertainties. Previous approaches for signature based calibration, however, do not allow reliable estimates of streamflow predictive distributions. Here, we illustrate how the Bayesian approach can be employed to obtain reliable streamflow predictive distributions based on signatures. A case study is presented, where a hydrological model is calibrated on FDCs and additional signatures. We propose an approach where the likelihood function for the signatures is derived from the likelihood for streamflow (rather than using an "ad-hoc" likelihood for the signatures as done in previous approaches). This likelihood is not easily tractable analytically and we therefore cannot apply "simple" MCMC methods. This numerical problem is solved using Approximate Bayesian Computation (ABC). Our result indicate that the proposed approach is suitable for producing reliable streamflow predictive distributions based on calibration to signature data. Moreover, our results provide indications on which signatures are more appropriate to represent the information content of the hydrograph.

Quality of antenatal care service provision in health facilities across sub–Saharan Africa: Evidence from nationally representative health facility assessments

PubMed Central

Kanyangarara, Mufaro; Munos, Melinda K; Walker, Neff

2017-01-01

Background Utilization of antenatal care (ANC) services has increased over the past two decades. Continued gains in maternal and newborn health will require an understanding of both access and quality of ANC services. We linked health facility and household survey data to examine the quality of service provision for five ANC interventions across health facilities in sub–Saharan Africa. Methods Using data from 20 nationally representative health facility assessments – the Service Provision Assessment (SPA) and the Service Availability and Readiness Assessment (SARA), we estimated facility level readiness to deliver five ANC interventions: tetanus toxoid vaccine for pregnant women, intermittent preventive treatment for malaria in pregnancy (IPTp), syphilis detection and treatment in pregnancy, iron supplementation and hypertensive disease case management. Facility level indicators were stratified by health facility type, managing authority and location, then linked to estimates of ANC utilization in that stratum from the corresponding Demographic and Health Surveys (DHS) to generate population level estimates of the ‘likelihood of appropriate care’. Finally, the association between estimates of the ‘likelihood of appropriate care’ from the linking approach and estimates of coverage levels from the DHS were assessed. Findings A total of 10 534 health facilities were surveyed in the 20 health facility assessments, of which 8742 reported offering ANC services and were included in the analysis. Health facility readiness to deliver IPTp, iron supplementation, and tetanus toxoid vaccination was higher (median: 84.1%, 84.9% and 82.8% respectively) than readiness to deliver hypertensive disease case management and syphilis detection and treatment (median: 23.0% and 19.9% respectively). Coverage of at least 4 ANC visits ranged from 24.8% to 75.8%. Estimates of the likelihood of appropriate care derived from linking health facility and household survey data showed marked gaps for all interventions, particularly hypertensive disease case management and syphilis detection and treatment. There was fairly good concordance between our estimates of high likelihood of appropriate care and DHS estimates of coverage for iron supplementation, IPTp, and tetanus toxoid vaccination. Conclusion Linking household surveys to health facility assessments revealed marked gaps in population–level coverage of quality ANC interventions and underscored the need for a double–pronged approach to increase ANC utilization and improve the quality of ANC services. PMID:29163936

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.

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

USGS Publications Warehouse

Donato, David I.

2012-01-01

This report presents the mathematical expressions and the computational techniques required to compute maximum-likelihood estimates for the parameters of the National Descriptive Model of Mercury in Fish (NDMMF), a statistical model used to predict the concentration of methylmercury in fish tissue. The expressions and techniques reported here were prepared to support the development of custom software capable of computing NDMMF parameter estimates more quickly and using less computer memory than is currently possible with available general-purpose statistical software. Computation of maximum-likelihood estimates for the NDMMF by numerical solution of a system of simultaneous equations through repeated Newton-Raphson iterations is described. This report explains the derivation of the mathematical expressions required for computational parameter estimation in sufficient detail to facilitate future derivations for any revised versions of the NDMMF that may be developed.

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)

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

Regularity of a renewal process estimated from binary data.

PubMed

Rice, John D; Strawderman, Robert L; Johnson, Brent A

2017-10-09

Assessment of the regularity of a sequence of events over time is important for clinical decision-making as well as informing public health policy. Our motivating example involves determining the effect of an intervention on the regularity of HIV self-testing behavior among high-risk individuals when exact self-testing times are not recorded. Assuming that these unobserved testing times follow a renewal process, the goals of this work are to develop suitable methods for estimating its distributional parameters when only the presence or absence of at least one event per subject in each of several observation windows is recorded. We propose two approaches to estimation and inference: a likelihood-based discrete survival model using only time to first event; and a potentially more efficient quasi-likelihood approach based on the forward recurrence time distribution using all available data. Regularity is quantified and estimated by the coefficient of variation (CV) of the interevent time distribution. Focusing on the gamma renewal process, where the shape parameter of the corresponding interevent time distribution has a monotone relationship with its CV, we conduct simulation studies to evaluate the performance of the proposed methods. We then apply them to our motivating example, concluding that the use of text message reminders significantly improves the regularity of self-testing, but not its frequency. A discussion on interesting directions for further research is provided. © 2017, The International Biometric Society.

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

PubMed

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

2014-12-01

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

A Single Camera Motion Capture System for Human-Computer Interaction

NASA Astrophysics Data System (ADS)

Okada, Ryuzo; Stenger, Björn

This paper presents a method for markerless human motion capture using a single camera. It uses tree-based filtering to efficiently propagate a probability distribution over poses of a 3D body model. The pose vectors and associated shapes are arranged in a tree, which is constructed by hierarchical pairwise clustering, in order to efficiently evaluate the likelihood in each frame. Anew likelihood function based on silhouette matching is proposed that improves the pose estimation of thinner body parts, i. e. the limbs. The dynamic model takes self-occlusion into account by increasing the variance of occluded body-parts, thus allowing for recovery when the body part reappears. We present two applications of our method that work in real-time on a Cell Broadband Engine™: a computer game and a virtual clothing application.

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

PubMed

Engemann, Denis A; Gramfort, Alexandre

2015-03-01

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

Estimating ambiguity preferences and perceptions in multiple prior models: Evidence from the field

PubMed Central

Dimmock, Stephen G.; Kouwenberg, Roy; Mitchell, Olivia S.; Peijnenburg, Kim

2016-01-01

We develop a tractable method to estimate multiple prior models of decision-making under ambiguity. In a representative sample of the U.S. population, we measure ambiguity attitudes in the gain and loss domains. We find that ambiguity aversion is common for uncertain events of moderate to high likelihood involving gains, but ambiguity seeking prevails for low likelihoods and for losses. We show that choices made under ambiguity in the gain domain are best explained by the α-MaxMin model, with one parameter measuring ambiguity aversion (ambiguity preferences) and a second parameter quantifying the perceived degree of ambiguity (perceptions about ambiguity). The ambiguity aversion parameter α is constant and prior probability sets are asymmetric for low and high likelihood events. The data reject several other models, such as MaxMin and MaxMax, as well as symmetric probability intervals. Ambiguity aversion and the perceived degree of ambiguity are both higher for men and for the college-educated. Ambiguity aversion (but not perceived ambiguity) is also positively related to risk aversion. In the loss domain, we find evidence of reflection, implying that ambiguity aversion for gains tends to reverse into ambiguity seeking for losses. Our model’s estimates for preferences and perceptions about ambiguity can be used to analyze the economic and financial implications of such preferences. PMID:26924890

Competing risk models in reliability systems, a weibull distribution model with bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, Ismed; Satria Gondokaryono, Yudi

2016-02-01

In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components. Another problem in reliability theory is one of estimating the parameters of the assumed failure models. The estimation may be based on data collected over censored or uncensored life tests. In many reliability problems, the failure data are simply quantitatively inadequate, especially in engineering design and maintenance system. The Bayesian analyses are more beneficial than the classical one in such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in the form of an apriori distribution with life test data to make inferences of the parameter of interest. In this paper, we have investigated the application of the Bayesian estimation analyses to competing risk systems. The cases are limited to the models with independent causes of failure by using the Weibull distribution as our model. A simulation is conducted for this distribution with the objectives of verifying the models and the estimators and investigating the performance of the estimators for varying sample size. The simulation data are analyzed by using Bayesian and the maximum likelihood analyses. The simulation results show that the change of the true of parameter relatively to another will change the value of standard deviation in an opposite direction. For a perfect information on the prior distribution, the estimation methods of the Bayesian analyses are better than those of the maximum likelihood. The sensitivity analyses show some amount of sensitivity over the shifts of the prior locations. They also show the robustness of the Bayesian analysis within the range between the true value and the maximum likelihood estimated value lines.

Estimation of selection intensity under overdominance by Bayesian methods.

PubMed

Buzbas, Erkan Ozge; Joyce, Paul; Abdo, Zaid

2009-01-01

A balanced pattern in the allele frequencies of polymorphic loci is a potential sign of selection, particularly of overdominance. Although this type of selection is of some interest in population genetics, there exists no likelihood based approaches specifically tailored to make inference on selection intensity. To fill this gap, we present Bayesian methods to estimate selection intensity under k-allele models with overdominance. Our model allows for an arbitrary number of loci and alleles within a locus. The neutral and selected variability within each locus are modeled with corresponding k-allele models. To estimate the posterior distribution of the mean selection intensity in a multilocus region, a hierarchical setup between loci is used. The methods are demonstrated with data at the Human Leukocyte Antigen loci from world-wide populations.

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