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

NASA Astrophysics Data System (ADS)

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

2014-09-01

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

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.

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

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

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.

Bias Correction for the Maximum Likelihood Estimate of Ability. Research Report. ETS RR-05-15

ERIC Educational Resources Information Center

Zhang, Jinming

2005-01-01

Lord's bias function and the weighted likelihood estimation method are effective in reducing the bias of the maximum likelihood estimate of an examinee's ability under the assumption that the true item parameters are known. This paper presents simulation studies to determine the effectiveness of these two methods in reducing the bias when the item…

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.

Algorithms of maximum likelihood data clustering with applications

NASA Astrophysics Data System (ADS)

Giada, Lorenzo; Marsili, Matteo

2002-12-01

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

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.

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.

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

NASA Technical Reports Server (NTRS)

Kelly, D. A.; Fermelia, A.; Lee, G. K. F.

1990-01-01

An adaptive Kalman filter design that utilizes recursive maximum likelihood parameter identification is discussed. At the center of this design is the Kalman filter itself, which has the responsibility for attitude determination. At the same time, the identification algorithm is continually identifying the system parameters. The approach is applicable to nonlinear, as well as linear systems. This adaptive Kalman filter design has much potential for real time implementation, especially considering the fast clock speeds, cache memory and internal RAM available today. The recursive maximum likelihood algorithm is discussed in detail, with special attention directed towards its unique matrix formulation. The procedure for using the algorithm is described along with comments on how this algorithm interacts with the Kalman filter.

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

PubMed

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

1992-08-01

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

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.…

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

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

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

NASA Astrophysics Data System (ADS)

Jiang, Siyuan; Kececioglu, Dimitri

1992-06-01

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

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...

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

PubMed

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

2015-06-01

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

Maximum likelihood estimation 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.

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

PubMed

Bing, Li; Bai, Baoming

2014-01-01

A class of simplified maximum-likelihood receivers designed for continuous phase modulation based multiuser systems is proposed. The presented receiver is built upon a front end employing mismatched filters and a maximum-likelihood detector defined in a low-dimensional signal space. The performance of the proposed receivers is analyzed and compared to some existing receivers. Some schemes are designed to implement the proposed receivers and to reveal the roles of different system parameters. Analysis and numerical results show that the proposed receivers can approach the optimum multiuser receivers with significantly (even exponentially in some cases) reduced complexity and marginal performance degradation.

Maximum likelihood clustering with dependent feature trees

NASA Technical Reports Server (NTRS)

Chittineni, C. B. (Principal Investigator)

1981-01-01

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

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

ERIC Educational Resources Information Center

France, Stephen L.; Batchelder, William H.

2015-01-01

Cultural consensus theory (CCT) is a data aggregation technique with many applications in the social and behavioral sciences. We describe the intuition and theory behind a set of CCT models for continuous type data using maximum likelihood inference methodology. We describe how bias parameters can be incorporated into these models. We introduce…

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

ERIC Educational Resources Information Center

Kelderman, Henk

1992-01-01

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

The Equivalence of Two Methods of Parameter Estimation for the Rasch Model.

ERIC Educational Resources Information Center

Blackwood, Larry G.; Bradley, Edwin L.

1989-01-01

Two methods of estimating parameters in the Rasch model are compared. The equivalence of likelihood estimations from the model of G. J. Mellenbergh and P. Vijn (1981) and from usual unconditional maximum likelihood (UML) estimation is demonstrated. Mellenbergh and Vijn's model is a convenient method of calculating UML estimates. (SLD)

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

NASA Technical Reports Server (NTRS)

1979-01-01

The computer program Linear SCIDNT which evaluates rotorcraft stability and control coefficients from flight or wind tunnel test data is described. It implements the maximum likelihood method to maximize the likelihood function of the parameters based on measured input/output time histories. Linear SCIDNT may be applied to systems modeled by linear constant-coefficient differential equations. This restriction in scope allows the application of several analytical results which simplify the computation and improve its efficiency over the general nonlinear case.

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.

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,…

A Maximum Likelihood Approach to Functional Mapping of Longitudinal Binary Traits

PubMed Central

Wang, Chenguang; Li, Hongying; Wang, Zhong; Wang, Yaqun; Wang, Ningtao; Wang, Zuoheng; Wu, Rongling

2013-01-01

Despite their importance in biology and biomedicine, genetic mapping of binary traits that change over time has not been well explored. In this article, we develop a statistical model for mapping quantitative trait loci (QTLs) that govern longitudinal responses of binary traits. The model is constructed within the maximum likelihood framework by which the association between binary responses is modeled in terms of conditional log odds-ratios. With this parameterization, the maximum likelihood estimates (MLEs) of marginal mean parameters are robust to the misspecification of time dependence. We implement an iterative procedures to obtain the MLEs of QTL genotype-specific parameters that define longitudinal binary responses. The usefulness of the model was validated by analyzing a real example in rice. Simulation studies were performed to investigate the statistical properties of the model, showing that the model has power to identify and map specific QTLs responsible for the temporal pattern of binary traits. PMID:23183762

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.

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

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

ERIC Educational Resources Information Center

Bertoli-Barsotti, Lucio

2005-01-01

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

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.

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.

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

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

PubMed

Chaudhuri, Shomesh E; Merfeld, Daniel M

2013-03-01

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

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…

Statistical Bias in Maximum Likelihood Estimators of Item Parameters.

DTIC Science & Technology

1982-04-01

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

Estimating cellular parameters through optimization procedures: elementary principles and applications.

PubMed

Kimura, Akatsuki; Celani, Antonio; Nagao, Hiromichi; Stasevich, Timothy; Nakamura, Kazuyuki

2015-01-01

Construction of quantitative models is a primary goal of quantitative biology, which aims to understand cellular and organismal phenomena in a quantitative manner. In this article, we introduce optimization procedures to search for parameters in a quantitative model that can reproduce experimental data. The aim of optimization is to minimize the sum of squared errors (SSE) in a prediction or to maximize likelihood. A (local) maximum of likelihood or (local) minimum of the SSE can efficiently be identified using gradient approaches. Addition of a stochastic process enables us to identify the global maximum/minimum without becoming trapped in local maxima/minima. Sampling approaches take advantage of increasing computational power to test numerous sets of parameters in order to determine the optimum set. By combining Bayesian inference with gradient or sampling approaches, we can estimate both the optimum parameters and the form of the likelihood function related to the parameters. Finally, we introduce four examples of research that utilize parameter optimization to obtain biological insights from quantified data: transcriptional regulation, bacterial chemotaxis, morphogenesis, and cell cycle regulation. With practical knowledge of parameter optimization, cell and developmental biologists can develop realistic models that reproduce their observations and thus, obtain mechanistic insights into phenomena of interest.

Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET

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

Gopich, Irina V.

2015-01-21

Photon sequences from single-molecule Förster resonance energy transfer (FRET) experiments can be analyzed using a maximum likelihood method. Parameters of the underlying kinetic model (FRET efficiencies of the states and transition rates between conformational states) are obtained by maximizing the appropriate likelihood function. In addition, the errors (uncertainties) of the extracted parameters can be obtained from the curvature of the likelihood function at the maximum. We study the standard deviations of the parameters of a two-state model obtained from photon sequences with recorded colors and arrival times. The standard deviations can be obtained analytically in a special case when themore » FRET efficiencies of the states are 0 and 1 and in the limiting cases of fast and slow conformational dynamics. These results are compared with the results of numerical simulations. The accuracy and, therefore, the ability to predict model parameters depend on how fast the transition rates are compared to the photon count rate. In the limit of slow transitions, the key parameters that determine the accuracy are the number of transitions between the states and the number of independent photon sequences. In the fast transition limit, the accuracy is determined by the small fraction of photons that are correlated with their neighbors. The relative standard deviation of the relaxation rate has a “chevron” shape as a function of the transition rate in the log-log scale. The location of the minimum of this function dramatically depends on how well the FRET efficiencies of the states are separated.« less

Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET

PubMed Central

Gopich, Irina V.

2015-01-01

Photon sequences from single-molecule Förster resonance energy transfer (FRET) experiments can be analyzed using a maximum likelihood method. Parameters of the underlying kinetic model (FRET efficiencies of the states and transition rates between conformational states) are obtained by maximizing the appropriate likelihood function. In addition, the errors (uncertainties) of the extracted parameters can be obtained from the curvature of the likelihood function at the maximum. We study the standard deviations of the parameters of a two-state model obtained from photon sequences with recorded colors and arrival times. The standard deviations can be obtained analytically in a special case when the FRET efficiencies of the states are 0 and 1 and in the limiting cases of fast and slow conformational dynamics. These results are compared with the results of numerical simulations. The accuracy and, therefore, the ability to predict model parameters depend on how fast the transition rates are compared to the photon count rate. In the limit of slow transitions, the key parameters that determine the accuracy are the number of transitions between the states and the number of independent photon sequences. In the fast transition limit, the accuracy is determined by the small fraction of photons that are correlated with their neighbors. The relative standard deviation of the relaxation rate has a “chevron” shape as a function of the transition rate in the log-log scale. The location of the minimum of this function dramatically depends on how well the FRET efficiencies of the states are separated. PMID:25612692

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.

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

ERIC Educational Resources Information Center

Kelderman, Henk

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

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.

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

PubMed Central

Meyer, Karin

2016-01-01

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

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

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

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.

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.

Development of advanced techniques for rotorcraft state estimation and parameter identification

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

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.

User's manual for MMLE3, a general FORTRAN program for maximum likelihood parameter estimation

NASA Technical Reports Server (NTRS)

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

1980-01-01

A user's manual for the FORTRAN IV computer program MMLE3 is described. It is a maximum likelihood parameter estimation program capable of handling general bilinear dynamic equations of arbitrary order with measurement noise and/or state noise (process noise). The theory and use of the program is described. The basic MMLE3 program is quite general and, therefore, applicable to a wide variety of problems. The basic program can interact with a set of user written problem specific routines to simplify the use of the program on specific systems. A set of user routines for the aircraft stability and control derivative estimation problem is provided with the program.

Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties

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

Stoneking, M.R.; Den Hartog, D.J.

1996-06-01

The fitting of data by {chi}{sup 2}-minimization is valid only when the uncertainties in the data are normally distributed. When analyzing spectroscopic or particle counting data at very low signal level (e.g., a Thomson scattering diagnostic), the uncertainties are distributed with a Poisson distribution. The authors have developed a maximum-likelihood method for fitting data that correctly treats the Poisson statistical character of the uncertainties. This method maximizes the total probability that the observed data are drawn from the assumed fit function using the Poisson probability function to determine the probability for each data point. The algorithm also returns uncertainty estimatesmore » for the fit parameters. They compare this method with a {chi}{sup 2}-minimization routine applied to both simulated and real data. Differences in the returned fits are greater at low signal level (less than {approximately}20 counts per measurement). the maximum-likelihood method is found to be more accurate and robust, returning a narrower distribution of values for the fit parameters with fewer outliers.« less

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

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

NASA Technical Reports Server (NTRS)

Shantaram, S. Pai; Gyekenyesi, John P.

1989-01-01

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

Aircraft parameter estimation

NASA Technical Reports Server (NTRS)

Iliff, Kenneth W.

1987-01-01

The aircraft parameter estimation problem is used to illustrate the utility of parameter estimation, which applies to many engineering and scientific fields. Maximum likelihood estimation has been used to extract stability and control derivatives from flight data for many years. This paper presents some of the basic concepts of aircraft parameter estimation and briefly surveys the literature in the field. The maximum likelihood estimator is discussed, and the basic concepts of minimization and estimation are examined for a simple simulated 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 illustrate the minimization process. Finally, the basic concepts are generalized, and estimation from flight data is discussed. Some of the major conclusions for the simulated example are also developed for the analysis of flight data from the F-14, highly maneuverable aircraft technology (HiMAT), and space shuttle vehicles.

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

USGS Publications Warehouse

Vecchia, A.V.

1985-01-01

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

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.

Variational Bayesian Parameter Estimation Techniques for the General Linear Model

PubMed Central

Starke, Ludger; Ostwald, Dirk

2017-01-01

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

Using the β-binomial distribution to characterize forest health

Treesearch

S.J. Zarnoch; R.L. Anderson; R.M. Sheffield

1995-01-01

The β-binomial distribution is suggested as a model for describing and analyzing the dichotomous data obtained from programs monitoring the health of forests in the United States. Maximum likelihood estimation of the parameters is given as well as asymptotic likelihood ratio tests. The procedure is illustrated with data on dogwood anthracnose infection (caused...

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

EPA Science Inventory

A time series intervention analysis (TSIA) of dendrochronological data to infer the tree growth-climate-disturbance relations and forest disturbance history is described. Maximum likelihood is used to estimate the parameters of a structural time series model with components for ...

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'.

Maximum likelihood: Extracting unbiased information from complex networks

NASA Astrophysics Data System (ADS)

Garlaschelli, Diego; Loffredo, Maria I.

2008-07-01

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

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

PubMed

Scheike, Thomas H; Juul, Anders

2004-04-01

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

The 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.

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.

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)…

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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.

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

PubMed

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

2015-03-01

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

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.

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

PubMed Central

Batchelder, William H.

2014-01-01

Cultural consensus theory (CCT) is a data aggregation technique with many applications in the social and behavioral sciences. We describe the intuition and theory behind a set of CCT models for continuous type data using maximum likelihood inference methodology. We describe how bias parameters can be incorporated into these models. We introduce two extensions to the basic model in order to account for item rating easiness/difficulty. The first extension is a multiplicative model and the second is an additive model. We show how the multiplicative model is related to the Rasch model. We describe several maximum-likelihood estimation procedures for the models and discuss issues of model fit and identifiability. We describe how the CCT models could be used to give alternative consensus-based measures of reliability. We demonstrate the utility of both the basic and extended models on a set of essay rating data and give ideas for future research. PMID:29795812

The Asymptotic Distribution of Ability Estimates: Beyond Dichotomous Items and Unidimensional IRT Models

ERIC Educational Resources Information Center

Sinharay, Sandip

2015-01-01

The maximum likelihood estimate (MLE) of the ability parameter of an item response theory model with known item parameters was proved to be asymptotically normally distributed under a set of regularity conditions for tests involving dichotomous items and a unidimensional ability parameter (Klauer, 1990; Lord, 1983). This article first considers…

Mortality table construction

NASA Astrophysics Data System (ADS)

Sutawanir

2015-12-01

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

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

NASA Technical Reports Server (NTRS)

Pai, Shantaram S.; Gyekenyesi, John P.

1988-01-01

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

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

NASA Astrophysics Data System (ADS)

Hajdziona, Marta; Molski, Andrzej

2011-02-01

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

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.

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

PubMed Central

Chen, Rui; Hyrien, Ollivier

2011-01-01

This article deals with quasi- and pseudo-likelihood estimation in a class of continuous-time multi-type Markov branching processes observed at discrete points in time. “Conventional” and conditional estimation are discussed for both approaches. We compare their properties and identify situations where they lead to asymptotically equivalent estimators. Both approaches possess robustness properties, and coincide with maximum likelihood estimation in some cases. Quasi-likelihood functions involving only linear combinations of the data may be unable to estimate all model parameters. Remedial measures exist, including the resort either to non-linear functions of the data or to conditioning the moments on appropriate sigma-algebras. The method of pseudo-likelihood may also resolve this issue. We investigate the properties of these approaches in three examples: the pure birth process, the linear birth-and-death process, and a two-type process that generalizes the previous two examples. Simulations studies are conducted to evaluate performance in finite samples. PMID:21552356

A Solution to Separation and Multicollinearity in Multiple Logistic Regression

PubMed Central

Shen, Jianzhao; Gao, Sujuan

2010-01-01

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

A Solution to Separation and Multicollinearity in Multiple Logistic Regression.

PubMed

Shen, Jianzhao; Gao, Sujuan

2008-10-01

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

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…

Development of an LSI maximum-likelihood convolutional decoder for advanced forward error correction capability on the NASA 30/20 GHz program

NASA Technical Reports Server (NTRS)

Clark, R. T.; Mccallister, R. D.

1982-01-01

The particular coding option identified as providing the best level of coding gain performance in an LSI-efficient implementation was the optimal constraint length five, rate one-half convolutional code. To determine the specific set of design parameters which optimally matches this decoder to the LSI constraints, a breadboard MCD (maximum-likelihood convolutional decoder) was fabricated and used to generate detailed performance trade-off data. The extensive performance testing data gathered during this design tradeoff study are summarized, and the functional and physical MCD chip characteristics are presented.

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

PubMed Central

Richards, V. M.; Dai, W.

2014-01-01

A MATLAB toolbox for the efficient estimation of the threshold, slope, and lapse rate of the psychometric function is described. The toolbox enables the efficient implementation of the updated maximum-likelihood (UML) procedure. The toolbox uses an object-oriented architecture for organizing the experimental variables and computational algorithms, which provides experimenters with flexibility in experimental design and data management. Descriptions of the UML procedure and the UML Toolbox are provided, followed by toolbox use examples. Finally, guidelines and recommendations of parameter configurations are given. PMID:24671826

F-8C adaptive flight control extensions. [for maximum likelihood estimation

NASA Technical Reports Server (NTRS)

Stein, G.; Hartmann, G. L.

1977-01-01

An adaptive concept which combines gain-scheduled control laws with explicit maximum likelihood estimation (MLE) identification to provide the scheduling values is described. The MLE algorithm was improved by incorporating attitude data, estimating gust statistics for setting filter gains, and improving parameter tracking during changing flight conditions. A lateral MLE algorithm was designed to improve true air speed and angle of attack estimates during lateral maneuvers. Relationships between the pitch axis sensors inherent in the MLE design were examined and used for sensor failure detection. Design details and simulation performance are presented for each of the three areas investigated.

An Extension of the Partial Credit Model with an Application to the Measurement of Change.

ERIC Educational Resources Information Center

Fischer, Gerhard H.; Ponocny, Ivo

1994-01-01

An extension to the partial credit model, the linear partial credit model, is considered under the assumption of a certain linear decomposition of the item x category parameters into basic parameters. A conditional maximum likelihood algorithm for estimating basic parameters is presented and illustrated with simulation and an empirical study. (SLD)

Ramsay-Curve Item Response Theory for the Three-Parameter Logistic Item Response Model

ERIC Educational Resources Information Center

Woods, Carol M.

2008-01-01

In Ramsay-curve item response theory (RC-IRT), the latent variable distribution is estimated simultaneously with the item parameters of a unidimensional item response model using marginal maximum likelihood estimation. This study evaluates RC-IRT for the three-parameter logistic (3PL) model with comparisons to the normal model and to the empirical…

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.

A Note on the Computation of the Second-Order Derivatives of the Elementary Symmetric Functions in the Rasch Model.

ERIC Educational Resources Information Center

Formann, Anton K.

1986-01-01

It is shown that for equal parameters explicit formulas exist, facilitating the application of the Newton-Raphson procedure to estimate the parameters in the Rasch model and related models according to the conditional maximum likelihood principle. (Author/LMO)

The Robustness of LISREL Estimates in Structural Equation Models with Categorical Variables.

ERIC Educational Resources Information Center

Ethington, Corinna A.

1987-01-01

This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical variables. The analysis of mixed matrices produced estimates that closely approximated the model parameters except where dichotomous variables were…

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…

Maximum-likelihood estimation of parameterized wavefronts from multifocal data

PubMed Central

Sakamoto, Julia A.; Barrett, Harrison H.

2012-01-01

A method for determining the pupil phase distribution of an optical system is demonstrated. Coefficients in a wavefront expansion were estimated using likelihood methods, where the data consisted of multiple irradiance patterns near focus. Proof-of-principle results were obtained in both simulation and experiment. Large-aberration wavefronts were handled in the numerical study. Experimentally, we discuss the handling of nuisance parameters. Fisher information matrices, Cramér-Rao bounds, and likelihood surfaces are examined. ML estimates were obtained by simulated annealing to deal with numerous local extrema in the likelihood function. Rapid processing techniques were employed to reduce the computational time. PMID:22772282

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

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.

F-8C adaptive flight control laws

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

Semiparametric Item Response Functions in the Context of Guessing

ERIC Educational Resources Information Center

Falk, Carl F.; Cai, Li

2016-01-01

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood-based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

Genetic and phenotypic parameter estimates for feed intake and other traits in growing beef cattle

USDA-ARS?s Scientific Manuscript database

Genetic parameters for dry matter intake (DMI), residual feed intake (RFI), average daily gain (ADG), mid-period body weight (MBW), gain to feed ratio (G:F) and flight speed (FS) were estimated using 1165 steers from a mixed-breed population using restricted maximum likelihood methodology applied to...

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

PubMed

Hajdziona, Marta; Molski, Andrzej

2011-02-07

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

Mixture class recovery in GMM under varying degrees of class separation: frequentist versus Bayesian estimation.

PubMed

Depaoli, Sarah

2013-06-01

Growth mixture modeling (GMM) represents a technique that is designed to capture change over time for unobserved subgroups (or latent classes) that exhibit qualitatively different patterns of growth. The aim of the current article was to explore the impact of latent class separation (i.e., how similar growth trajectories are across latent classes) on GMM performance. Several estimation conditions were compared: maximum likelihood via the expectation maximization (EM) algorithm and the Bayesian framework implementing diffuse priors, "accurate" informative priors, weakly informative priors, data-driven informative priors, priors reflecting partial-knowledge of parameters, and "inaccurate" (but informative) priors. The main goal was to provide insight about the optimal estimation condition under different degrees of latent class separation for GMM. Results indicated that optimal parameter recovery was obtained though the Bayesian approach using "accurate" informative priors, and partial-knowledge priors showed promise for the recovery of the growth trajectory parameters. Maximum likelihood and the remaining Bayesian estimation conditions yielded poor parameter recovery for the latent class proportions and the growth trajectories. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

Spatial design and strength of spatial signal: Effects on covariance estimation

USGS Publications Warehouse

Irvine, Kathryn M.; Gitelman, Alix I.; Hoeting, Jennifer A.

2007-01-01

In a spatial regression context, scientists are often interested in a physical interpretation of components of the parametric covariance function. For example, spatial covariance parameter estimates in ecological settings have been interpreted to describe spatial heterogeneity or “patchiness” in a landscape that cannot be explained by measured covariates. In this article, we investigate the influence of the strength of spatial dependence on maximum likelihood (ML) and restricted maximum likelihood (REML) estimates of covariance parameters in an exponential-with-nugget model, and we also examine these influences under different sampling designs—specifically, lattice designs and more realistic random and cluster designs—at differing intensities of sampling (n=144 and 361). We find that neither ML nor REML estimates perform well when the range parameter and/or the nugget-to-sill ratio is large—ML tends to underestimate the autocorrelation function and REML produces highly variable estimates of the autocorrelation function. The best estimates of both the covariance parameters and the autocorrelation function come under the cluster sampling design and large sample sizes. As a motivating example, we consider a spatial model for stream sulfate concentration.

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.

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

On Obtaining Estimates of the Fraction of Missing Information from Full Information Maximum Likelihood

ERIC Educational Resources Information Center

Savalei, Victoria; Rhemtulla, Mijke

2012-01-01

Fraction of missing information [lambda][subscript j] is a useful measure of the impact of missing data on the quality of estimation of a particular parameter. This measure can be computed for all parameters in the model, and it communicates the relative loss of efficiency in the estimation of a particular parameter due to missing data. It has…

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…

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.

Numerical Experimentation with Maximum Likelihood Identification in Static Distributed Systems

NASA Technical Reports Server (NTRS)

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

1985-01-01

Many important issues in the control of large space structures are intimately related to the fundamental problem of parameter identification. One might also ask how well this identification process can be carried out in the presence of noisy data since no sensor system is perfect. With these considerations in mind the algorithms herein are designed to treat both the case of uncertainties in the modeling and uncertainties in the data. The analytical aspects of maximum likelihood identification are considered in some detail in another paper. The questions relevant to the implementation of these schemes are dealt with, particularly as they apply to models of large space structures. The emphasis is on the influence of the infinite dimensional character of the problem on finite dimensional implementations of the algorithms. Those areas of current and future analysis are highlighted which indicate the interplay between error analysis and possible truncations of the state and parameter spaces.

Maximum Likelihood 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.

Modelling maximum river flow by using Bayesian Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Cheong, R. Y.; Gabda, D.

2017-09-01

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

Optimal and Most Exact Confidence Intervals for Person Parameters in Item Response Theory Models

ERIC Educational Resources Information Center

Doebler, Anna; Doebler, Philipp; Holling, Heinz

2013-01-01

The common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter [theta] is normally distributed. However, this approximation is often inadequate for short and medium test lengths. As a result, the coverage probabilities fall below the given…

Semi-Parametric Item Response Functions in the Context of Guessing. CRESST Report 844

ERIC Educational Resources Information Center

Falk, Carl F.; Cai, Li

2015-01-01

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

Markov Chain Monte Carlo Estimation of Item Parameters for the Generalized Graded Unfolding Model

ERIC Educational Resources Information Center

de la Torre, Jimmy; Stark, Stephen; Chernyshenko, Oleksandr S.

2006-01-01

The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…

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.

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

Restricted maximum likelihood estimation of genetic principal components and smoothed covariance matrices

PubMed Central

Meyer, Karin; Kirkpatrick, Mark

2005-01-01

Principal component analysis is a widely used 'dimension reduction' technique, albeit generally at a phenotypic level. It is shown that we can estimate genetic principal components directly through a simple reparameterisation of the usual linear, mixed model. This is applicable to any analysis fitting multiple, correlated genetic effects, whether effects for individual traits or sets of random regression coefficients to model trajectories. Depending on the magnitude of genetic correlation, a subset of the principal component generally suffices to capture the bulk of genetic variation. Corresponding estimates of genetic covariance matrices are more parsimonious, have reduced rank and are smoothed, with the number of parameters required to model the dispersion structure reduced from k(k + 1)/2 to m(2k - m + 1)/2 for k effects and m principal components. Estimation of these parameters, the largest eigenvalues and pertaining eigenvectors of the genetic covariance matrix, via restricted maximum likelihood using derivatives of the likelihood, is described. It is shown that reduced rank estimation can reduce computational requirements of multivariate analyses substantially. An application to the analysis of eight traits recorded via live ultrasound scanning of beef cattle is given. PMID:15588566

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.

Optimal HRF and smoothing parameters for fMRI time series within an autoregressive modeling framework.

PubMed

Galka, Andreas; Siniatchkin, Michael; Stephani, Ulrich; Groening, Kristina; Wolff, Stephan; Bosch-Bayard, Jorge; Ozaki, Tohru

2010-12-01

The analysis of time series obtained by functional magnetic resonance imaging (fMRI) may be approached by fitting predictive parametric models, such as nearest-neighbor autoregressive models with exogeneous input (NNARX). As a part of the modeling procedure, it is possible to apply instantaneous linear transformations to the data. Spatial smoothing, a common preprocessing step, may be interpreted as such a transformation. The autoregressive parameters may be constrained, such that they provide a response behavior that corresponds to the canonical haemodynamic response function (HRF). We present an algorithm for estimating the parameters of the linear transformations and of the HRF within a rigorous maximum-likelihood framework. Using this approach, an optimal amount of both the spatial smoothing and the HRF can be estimated simultaneously for a given fMRI data set. An example from a motor-task experiment is discussed. It is found that, for this data set, weak, but non-zero, spatial smoothing is optimal. Furthermore, it is demonstrated that activated regions can be estimated within the maximum-likelihood framework.

Rotorcraft Blade Mode Damping Identification from Random Responses Using a Recursive Maximum Likelihood Algorithm

NASA Technical Reports Server (NTRS)

Molusis, J. A.

1982-01-01

An on line technique is presented for the identification of rotor blade modal damping and frequency from rotorcraft random response test data. The identification technique is based upon a recursive maximum likelihood (RML) algorithm, which is demonstrated to have excellent convergence characteristics in the presence of random measurement noise and random excitation. The RML technique requires virtually no user interaction, provides accurate confidence bands on the parameter estimates, and can be used for continuous monitoring of modal damping during wind tunnel or flight testing. Results are presented from simulation random response data which quantify the identified parameter convergence behavior for various levels of random excitation. The data length required for acceptable parameter accuracy is shown to depend upon the amplitude of random response and the modal damping level. Random response amplitudes of 1.25 degrees to .05 degrees are investigated. The RML technique is applied to hingeless rotor test data. The inplane lag regressing mode is identified at different rotor speeds. The identification from the test data is compared with the simulation results and with other available estimates of frequency and damping.

Maximum likelihood orientation estimation of 1-D patterns in Laguerre-Gauss subspaces.

PubMed

Di Claudio, Elio D; Jacovitti, Giovanni; Laurenti, Alberto

2010-05-01

A method for measuring the orientation of linear (1-D) patterns, based on a local expansion with Laguerre-Gauss circular harmonic (LG-CH) functions, is presented. It lies on the property that the polar separable LG-CH functions span the same space as the 2-D Cartesian separable Hermite-Gauss (2-D HG) functions. Exploiting the simple steerability of the LG-CH functions and the peculiar block-linear relationship among the two expansion coefficients sets, maximum likelihood (ML) estimates of orientation and cross section parameters of 1-D patterns are obtained projecting them in a proper subspace of the 2-D HG family. It is shown in this paper that the conditional ML solution, derived by elimination of the cross section parameters, surprisingly yields the same asymptotic accuracy as the ML solution for known cross section parameters. The accuracy of the conditional ML estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials. A thorough proof of the key relationship between the LG-CH and the 2-D HG expansions is also provided.

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.

Maximum likelihood identification and optimal input design for identifying aircraft stability and control derivatives

NASA Technical Reports Server (NTRS)

Stepner, D. E.; Mehra, R. K.

1973-01-01

A new method of extracting aircraft stability and control derivatives from flight test data is developed based on the maximum likelihood cirterion. It is shown that this new method is capable of processing data from both linear and nonlinear models, both with and without process noise and includes output error and equation error methods as special cases. The first application of this method to flight test data is reported for lateral maneuvers of the HL-10 and M2/F3 lifting bodies, including the extraction of stability and control derivatives in the presence of wind gusts. All the problems encountered in this identification study are discussed. Several different methods (including a priori weighting, parameter fixing and constrained parameter values) for dealing with identifiability and uniqueness problems are introduced and the results given. The method for the design of optimal inputs for identifying the parameters of linear dynamic systems is also given. The criterion used for the optimization is the sensitivity of the system output to the unknown parameters. Several simple examples are first given and then the results of an extensive stability and control dervative identification simulation for a C-8 aircraft are detailed.

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.

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

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).

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...

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.

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).

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…

Resolving the Effects of Maternal and Offspring Genotype on Dyadic Outcomes in Genome Wide Complex Trait Analysis (“M-GCTA”)

PubMed Central

Pourcain, Beate St.; Smith, George Davey; York, Timothy P.; Evans, David M.

2014-01-01

Genome wide complex trait analysis (GCTA) is extended to include environmental effects of the maternal genotype on offspring phenotype (“maternal effects”, M-GCTA). The model includes parameters for the direct effects of the offspring genotype, maternal effects and the covariance between direct and maternal effects. Analysis of simulated data, conducted in OpenMx, confirmed that model parameters could be recovered by full information maximum likelihood (FIML) and evaluated the biases that arise in conventional GCTA when indirect genetic effects are ignored. Estimates derived from FIML in OpenMx showed very close agreement to those obtained by restricted maximum likelihood using the published algorithm for GCTA. The method was also applied to illustrative perinatal phenotypes from ∼4,000 mother-offspring pairs from the Avon Longitudinal Study of Parents and Children. The relative merits of extended GCTA in contrast to quantitative genetic approaches based on analyzing the phenotypic covariance structure of kinships are considered. PMID:25060210

Programmer's manual for MMLE3, a general FORTRAN program for maximum likelihood parameter estimation

NASA Technical Reports Server (NTRS)

Maine, R. E.

1981-01-01

The MMLE3 is a maximum likelihood parameter estimation program capable of handling general bilinear dynamic equations of arbitrary order with measurement noise and/or state noise (process noise). The basic MMLE3 program is quite general and, therefore, applicable to a wide variety of problems. The basic program can interact with a set of user written problem specific routines to simplify the use of the program on specific systems. A set of user routines for the aircraft stability and control derivative estimation problem is provided with the program. The implementation of the program on specific computer systems is discussed. The structure of the program is diagrammed, and the function and operation of individual routines is described. Complete listings and reference maps of the routines are included on microfiche as a supplement. Four test cases are discussed; listings of the input cards and program output for the test cases are included on microfiche as a supplement.

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.

Parameter Estimation for Thurstone Choice Models

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

Vojnovic, Milan; Yun, Seyoung

We consider the estimation accuracy of individual strength parameters of a Thurstone choice model when each input observation consists of a choice of one item from a set of two or more items (so called top-1 lists). This model accommodates the well-known choice models such as the Luce choice model for comparison sets of two or more items and the Bradley-Terry model for pair comparisons. We provide a tight characterization of the mean squared error of the maximum likelihood parameter estimator. We also provide similar characterizations for parameter estimators defined by a rank-breaking method, which amounts to deducing one ormore » more pair comparisons from a comparison of two or more items, assuming independence of these pair comparisons, and maximizing a likelihood function derived under these assumptions. We also consider a related binary classification problem where each individual parameter takes value from a set of two possible values and the goal is to correctly classify all items within a prescribed classification error. The results of this paper shed light on how the parameter estimation accuracy depends on given Thurstone choice model and the structure of comparison sets. In particular, we found that for unbiased input comparison sets of a given cardinality, when in expectation each comparison set of given cardinality occurs the same number of times, for a broad class of Thurstone choice models, the mean squared error decreases with the cardinality of comparison sets, but only marginally according to a diminishing returns relation. On the other hand, we found that there exist Thurstone choice models for which the mean squared error of the maximum likelihood parameter estimator can decrease much faster with the cardinality of comparison sets. We report empirical evaluation of some claims and key parameters revealed by theory using both synthetic and real-world input data from some popular sport competitions and online labor platforms.« less

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

Treesearch

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

2005-01-01

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

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

La Russa, D

Purpose: The purpose of this project is to develop a robust method of parameter estimation for a Poisson-based TCP model using Bayesian inference. Methods: Bayesian inference was performed using the PyMC3 probabilistic programming framework written in Python. A Poisson-based TCP regression model that accounts for clonogen proliferation was fit to observed rates of local relapse as a function of equivalent dose in 2 Gy fractions for a population of 623 stage-I non-small-cell lung cancer patients. The Slice Markov Chain Monte Carlo sampling algorithm was used to sample the posterior distributions, and was initiated using the maximum of the posterior distributionsmore » found by optimization. The calculation of TCP with each sample step required integration over the free parameter α, which was performed using an adaptive 24-point Gauss-Legendre quadrature. Convergence was verified via inspection of the trace plot and posterior distribution for each of the fit parameters, as well as with comparisons of the most probable parameter values with their respective maximum likelihood estimates. Results: Posterior distributions for α, the standard deviation of α (σ), the average tumour cell-doubling time (Td), and the repopulation delay time (Tk), were generated assuming α/β = 10 Gy, and a fixed clonogen density of 10{sup 7} cm−{sup 3}. Posterior predictive plots generated from samples from these posterior distributions are in excellent agreement with the observed rates of local relapse used in the Bayesian inference. The most probable values of the model parameters also agree well with maximum likelihood estimates. Conclusion: A robust method of performing Bayesian inference of TCP data using a complex TCP model has been established.« less

Modeling the distribution of extreme share return in Malaysia using Generalized Extreme Value (GEV) distribution

NASA Astrophysics Data System (ADS)

Hasan, Husna; Radi, Noor Fadhilah Ahmad; Kassim, Suraiya

2012-05-01

Extreme share return in Malaysia is studied. The monthly, quarterly, half yearly and yearly maximum returns are fitted to the Generalized Extreme Value (GEV) distribution. The Augmented Dickey Fuller (ADF) and Phillips Perron (PP) tests are performed to test for stationarity, while Mann-Kendall (MK) test is for the presence of monotonic trend. Maximum Likelihood Estimation (MLE) is used to estimate the parameter while L-moments estimate (LMOM) is used to initialize the MLE optimization routine for the stationary model. Likelihood ratio test is performed to determine the best model. Sherman's goodness of fit test is used to assess the quality of convergence of the GEV distribution by these monthly, quarterly, half yearly and yearly maximum. Returns levels are then estimated for prediction and planning purposes. The results show all maximum returns for all selection periods are stationary. The Mann-Kendall test indicates the existence of trend. Thus, we ought to model for non-stationary model too. Model 2, where the location parameter is increasing with time is the best for all selection intervals. Sherman's goodness of fit test shows that monthly, quarterly, half yearly and yearly maximum converge to the GEV distribution. From the results, it seems reasonable to conclude that yearly maximum is better for the convergence to the GEV distribution especially if longer records are available. Return level estimates, which is the return level (in this study return amount) that is expected to be exceeded, an average, once every t time periods starts to appear in the confidence interval of T = 50 for quarterly, half yearly and yearly maximum.

A study of parameter identification

NASA Technical Reports Server (NTRS)

Herget, C. J.; Patterson, R. E., III

1978-01-01

A set of definitions for deterministic parameter identification ability were proposed. Deterministic parameter identificability properties are presented based on four system characteristics: direct parameter recoverability, properties of the system transfer function, properties of output distinguishability, and uniqueness properties of a quadratic cost functional. Stochastic parameter identifiability was defined in terms of the existence of an estimation sequence for the unknown parameters which is consistent in probability. Stochastic parameter identifiability properties are presented based on the following characteristics: convergence properties of the maximum likelihood estimate, properties of the joint probability density functions of the observations, and properties of the information matrix.

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.

Multidimensional stochastic approximation using locally contractive functions

NASA Technical Reports Server (NTRS)

Lawton, W. M.

1975-01-01

A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.

Inverse Ising problem in continuous time: A latent variable approach

NASA Astrophysics Data System (ADS)

Donner, Christian; Opper, Manfred

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

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

NASA Astrophysics Data System (ADS)

Khorram, Soheil; Sameti, Hossein; King, Simon

2015-12-01

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

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.

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

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

Hock, Kiel; Earle, Keith

2016-02-06

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

Exponential Sum-Fitting of Dwell-Time Distributions without Specifying Starting Parameters

PubMed Central

Landowne, David; Yuan, Bin; Magleby, Karl L.

2013-01-01

Fitting dwell-time distributions with sums of exponentials is widely used to characterize histograms of open- and closed-interval durations recorded from single ion channels, as well as for other physical phenomena. However, it can be difficult to identify the contributing exponential components. Here we extend previous methods of exponential sum-fitting to present a maximum-likelihood approach that consistently detects all significant exponentials without the need for user-specified starting parameters. Instead of searching for exponentials, the fitting starts with a very large number of initial exponentials with logarithmically spaced time constants, so that none are missed. Maximum-likelihood fitting then determines the areas of all the initial exponentials keeping the time constants fixed. In an iterative manner, with refitting after each step, the analysis then removes exponentials with negligible area and combines closely spaced adjacent exponentials, until only those exponentials that make significant contributions to the dwell-time distribution remain. There is no limit on the number of significant exponentials and no starting parameters need be specified. We demonstrate fully automated detection for both experimental and simulated data, as well as for classical exponential-sum-fitting problems. PMID:23746510

Elimination of trait blocks from multiple trait mixed model equations with singular (Co)variance parameter matrices

USDA-ARS?s Scientific Manuscript database

Transformations to multiple trait mixed model equations (MME) which are intended to improve computational efficiency in best linear unbiased prediction (BLUP) and restricted maximum likelihood (REML) are described. It is shown that traits that are expected or estimated to have zero residual variance...

Maximum Likelihood and Minimum Distance Applied to Univariate Mixture Distributions.

ERIC Educational Resources Information Center

Wang, Yuh-Yin Wu; Schafer, William D.

This Monte-Carlo study compared modified Newton (NW), expectation-maximization algorithm (EM), and minimum Cramer-von Mises distance (MD), used to estimate parameters of univariate mixtures of two components. Data sets were fixed at size 160 and manipulated by mean separation, variance ratio, component proportion, and non-normality. Results…

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…

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…

Measurement and Structural Model Class Separation in Mixture CFA: ML/EM versus MCMC

ERIC Educational Resources Information Center

Depaoli, Sarah

2012-01-01

Parameter recovery was assessed within mixture confirmatory factor analysis across multiple estimator conditions under different simulated levels of mixture class separation. Mixture class separation was defined in the measurement model (through factor loadings) and the structural model (through factor variances). Maximum likelihood (ML) via the…

Effects of Employing Ridge Regression in Structural Equation Models.

ERIC Educational Resources Information Center

McQuitty, Shaun

1997-01-01

LISREL 8 invokes a ridge option when maximum likelihood or generalized least squares are used to estimate a structural equation model with a nonpositive definite covariance or correlation matrix. Implications of the ridge option for model fit, parameter estimates, and standard errors are explored through two examples. (SLD)

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…

Determinants of Standard Errors of MLEs in Confirmatory Factor Analysis

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Cheng, Ying; Zhang, Wei

2010-01-01

This paper studies changes of standard errors (SE) of the normal-distribution-based maximum likelihood estimates (MLE) for confirmatory factor models as model parameters vary. Using logical analysis, simplified formulas and numerical verification, monotonic relationships between SEs and factor loadings as well as unique variances are found.…

Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies

PubMed Central

Rukhin, Andrew L.

2011-01-01

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

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

PubMed

Rukhin, Andrew L

2011-01-01

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

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1972-01-01

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

Approximated mutual information training for speech recognition using myoelectric signals.

PubMed

Guo, Hua J; Chan, A D C

2006-01-01

A new training algorithm called the approximated maximum mutual information (AMMI) is proposed to improve the accuracy of myoelectric speech recognition using hidden Markov models (HMMs). Previous studies have demonstrated that automatic speech recognition can be performed using myoelectric signals from articulatory muscles of the face. Classification of facial myoelectric signals can be performed using HMMs that are trained using the maximum likelihood (ML) algorithm; however, this algorithm maximizes the likelihood of the observations in the training sequence, which is not directly associated with optimal classification accuracy. The AMMI training algorithm attempts to maximize the mutual information, thereby training the HMMs to optimize their parameters for discrimination. Our results show that AMMI training consistently reduces the error rates compared to these by the ML training, increasing the accuracy by approximately 3% on average.

A Maximum-Likelihood Approach to Force-Field Calibration.

PubMed

Zaborowski, Bartłomiej; Jagieła, Dawid; Czaplewski, Cezary; Hałabis, Anna; Lewandowska, Agnieszka; Żmudzińska, Wioletta; Ołdziej, Stanisław; Karczyńska, Agnieszka; Omieczynski, Christian; Wirecki, Tomasz; Liwo, Adam

2015-09-28

A new approach to the calibration of the force fields is proposed, in which the force-field parameters are obtained by maximum-likelihood fitting of the calculated conformational ensembles to the experimental ensembles of training system(s). The maximum-likelihood function is composed of logarithms of the Boltzmann probabilities of the experimental conformations, calculated with the current energy function. Because the theoretical distribution is given in the form of the simulated conformations only, the contributions from all of the simulated conformations, with Gaussian weights in the distances from a given experimental conformation, are added to give the contribution to the target function from this conformation. In contrast to earlier methods for force-field calibration, the approach does not suffer from the arbitrariness of dividing the decoy set into native-like and non-native structures; however, if such a division is made instead of using Gaussian weights, application of the maximum-likelihood method results in the well-known energy-gap maximization. The computational procedure consists of cycles of decoy generation and maximum-likelihood-function optimization, which are iterated until convergence is reached. The method was tested with Gaussian distributions and then applied to the physics-based coarse-grained UNRES force field for proteins. The NMR structures of the tryptophan cage, a small α-helical protein, determined at three temperatures (T = 280, 305, and 313 K) by Hałabis et al. ( J. Phys. Chem. B 2012 , 116 , 6898 - 6907 ), were used. Multiplexed replica-exchange molecular dynamics was used to generate the decoys. The iterative procedure exhibited steady convergence. Three variants of optimization were tried: optimization of the energy-term weights alone and use of the experimental ensemble of the folded protein only at T = 280 K (run 1); optimization of the energy-term weights and use of experimental ensembles at all three temperatures (run 2); and optimization of the energy-term weights and the coefficients of the torsional and multibody energy terms and use of experimental ensembles at all three temperatures (run 3). The force fields were subsequently tested with a set of 14 α-helical and two α + β proteins. Optimization run 1 resulted in better agreement with the experimental ensemble at T = 280 K compared with optimization run 2 and in comparable performance on the test set but poorer agreement of the calculated folding temperature with the experimental folding temperature. Optimization run 3 resulted in the best fit of the calculated ensembles to the experimental ones for the tryptophan cage but in much poorer performance on the training set, suggesting that use of a small α-helical protein for extensive force-field calibration resulted in overfitting of the data for this protein at the expense of transferability. The optimized force field resulting from run 2 was found to fold 13 of the 14 tested α-helical proteins and one small α + β protein with the correct topologies; the average structures of 10 of them were predicted with accuracies of about 5 Å C(α) root-mean-square deviation or better. Test simulations with an additional set of 12 α-helical proteins demonstrated that this force field performed better on α-helical proteins than the previous parametrizations of UNRES. The proposed approach is applicable to any problem of maximum-likelihood parameter estimation when the contributions to the maximum-likelihood function cannot be evaluated at the experimental points and the dimension of the configurational space is too high to construct histograms of the experimental distributions.

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

Estimating Function Approaches for Spatial Point Processes

NASA Astrophysics Data System (ADS)

Deng, Chong

Spatial point pattern data consist of locations of events that are often of interest in biological and ecological studies. Such data are commonly viewed as a realization from a stochastic process called spatial point process. To fit a parametric spatial point process model to such data, likelihood-based methods have been widely studied. However, while maximum likelihood estimation is often too computationally intensive for Cox and cluster processes, pairwise likelihood methods such as composite likelihood, Palm likelihood usually suffer from the loss of information due to the ignorance of correlation among pairs. For many types of correlated data other than spatial point processes, when likelihood-based approaches are not desirable, estimating functions have been widely used for model fitting. In this dissertation, we explore the estimating function approaches for fitting spatial point process models. These approaches, which are based on the asymptotic optimal estimating function theories, can be used to incorporate the correlation among data and yield more efficient estimators. We conducted a series of studies to demonstrate that these estmating function approaches are good alternatives to balance the trade-off between computation complexity and estimating efficiency. First, we propose a new estimating procedure that improves the efficiency of pairwise composite likelihood method in estimating clustering parameters. Our approach combines estimating functions derived from pairwise composite likeli-hood estimation and estimating functions that account for correlations among the pairwise contributions. Our method can be used to fit a variety of parametric spatial point process models and can yield more efficient estimators for the clustering parameters than pairwise composite likelihood estimation. We demonstrate its efficacy through a simulation study and an application to the longleaf pine data. Second, we further explore the quasi-likelihood approach on fitting second-order intensity function of spatial point processes. However, the original second-order quasi-likelihood is barely feasible due to the intense computation and high memory requirement needed to solve a large linear system. Motivated by the existence of geometric regular patterns in the stationary point processes, we find a lower dimension representation of the optimal weight function and propose a reduced second-order quasi-likelihood approach. Through a simulation study, we show that the proposed method not only demonstrates superior performance in fitting the clustering parameter but also merits in the relaxation of the constraint of the tuning parameter, H. Third, we studied the quasi-likelihood type estimating funciton that is optimal in a certain class of first-order estimating functions for estimating the regression parameter in spatial point process models. Then, by using a novel spectral representation, we construct an implementation that is computationally much more efficient and can be applied to more general setup than the original quasi-likelihood method.

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.

An application of the Krylov-FSP-SSA method to parameter fitting with maximum likelihood

NASA Astrophysics Data System (ADS)

Dinh, Khanh N.; Sidje, Roger B.

2017-12-01

Monte Carlo methods such as the stochastic simulation algorithm (SSA) have traditionally been employed in gene regulation problems. However, there has been increasing interest to directly obtain the probability distribution of the molecules involved by solving the chemical master equation (CME). This requires addressing the curse of dimensionality that is inherent in most gene regulation problems. The finite state projection (FSP) seeks to address the challenge and there have been variants that further reduce the size of the projection or that accelerate the resulting matrix exponential. The Krylov-FSP-SSA variant has proved numerically efficient by combining, on one hand, the SSA to adaptively drive the FSP, and on the other hand, adaptive Krylov techniques to evaluate the matrix exponential. Here we apply this Krylov-FSP-SSA to a mutual inhibitory gene network synthetically engineered in Saccharomyces cerevisiae, in which bimodality arises. We show numerically that the approach can efficiently approximate the transient probability distribution, and this has important implications for parameter fitting, where the CME has to be solved for many different parameter sets. The fitting scheme amounts to an optimization problem of finding the parameter set so that the transient probability distributions fit the observations with maximum likelihood. We compare five optimization schemes for this difficult problem, thereby providing further insights into this approach of parameter estimation that is often applied to models in systems biology where there is a need to calibrate free parameters. Work supported by NSF grant DMS-1320849.

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…

Fitting ARMA Time Series by Structural Equation Models.

ERIC Educational Resources Information Center

van Buuren, Stef

1997-01-01

This paper outlines how the stationary ARMA (p,q) model (G. Box and G. Jenkins, 1976) can be specified as a structural equation model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitting structural equation models. The method is applied to three problem types. (SLD)

Group Comparisons in the Presence of Missing Data Using Latent Variable Modeling Techniques

ERIC Educational Resources Information Center

Raykov, Tenko; Marcoulides, George A.

2010-01-01

A latent variable modeling approach for examining population similarities and differences in observed variable relationship and mean indexes in incomplete data sets is discussed. The method is based on the full information maximum likelihood procedure of model fitting and parameter estimation. The procedure can be employed to test group identities…

A Test-Length Correction to the Estimation of Extreme Proficiency Levels

ERIC Educational Resources Information Center

Magis, David; Beland, Sebastien; Raiche, Gilles

2011-01-01

In this study, the estimation of extremely large or extremely small proficiency levels, given the item parameters of a logistic item response model, is investigated. On one hand, the estimation of proficiency levels by maximum likelihood (ML), despite being asymptotically unbiased, may yield infinite estimates. On the other hand, with an…

Logistic Achievement Test Scaling and Equating with Fixed versus Estimated Lower Asymptotes.

ERIC Educational Resources Information Center

Phillips, S. E.

This study compared the lower asymptotes estimated by the maximum likelihood procedures of the LOGIST computer program with those obtained via application of the Norton methodology. The study also compared the equating results from the three-parameter logistic model with those obtained from the equipercentile, Rasch, and conditional…

Estimation in SEM: A Concrete Example

ERIC Educational Resources Information Center

Ferron, John M.; Hess, Melinda R.

2007-01-01

A concrete example is used to illustrate maximum likelihood estimation of a structural equation model with two unknown parameters. The fitting function is found for the example, as are the vector of first-order partial derivatives, the matrix of second-order partial derivatives, and the estimates obtained from each iteration of the Newton-Raphson…

The Robustness of LISREL Estimates in Structural Equation Models with Categorical Variables.

ERIC Educational Resources Information Center

Ethington, Corinna A.

This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical manifest variables. Two types of correlation matrices were analyzed; one containing Pearson product-moment correlations and one containing tetrachoric,…

Maximum likelihood decoding of Reed Solomon Codes

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

Sudan, M.

We present a randomized algorithm which takes as input n distinct points ((x{sub i}, y{sub i})){sup n}{sub i=1} from F x F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in at least t places (i.e., y{sub i} = f (x{sub i}) for at least t values of i), provided t = {Omega}({radical}nd). The running time is bounded by a polynomial in n. This immediately provides a maximum likelihoodmore » decoding algorithm for Reed Solomon Codes, which works in a setting with a larger number of errors than any previously known algorithm. To the best of our knowledge, this is the first efficient (i.e., polynomial time bounded) algorithm which provides some maximum likelihood decoding for any efficient (i.e., constant or even polynomial rate) code.« less

Box-Cox transformation for QTL mapping.

PubMed

Yang, Runqing; Yi, Nengjun; Xu, Shizhong

2006-01-01

The maximum likelihood method of QTL mapping assumes that the phenotypic values of a quantitative trait follow a normal distribution. If the assumption is violated, some forms of transformation should be taken to make the assumption approximately true. The Box-Cox transformation is a general transformation method which can be applied to many different types of data. The flexibility of the Box-Cox transformation is due to a variable, called transformation factor, appearing in the Box-Cox formula. We developed a maximum likelihood method that treats the transformation factor as an unknown parameter, which is estimated from the data simultaneously along with the QTL parameters. The method makes an objective choice of data transformation and thus can be applied to QTL analysis for many different types of data. Simulation studies show that (1) Box-Cox transformation can substantially increase the power of QTL detection; (2) Box-Cox transformation can replace some specialized transformation methods that are commonly used in QTL mapping; and (3) applying the Box-Cox transformation to data already normally distributed does not harm the result.

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.

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

PubMed

Galili, Tal; Meilijson, Isaac

2016-01-02

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

Image classification at low light levels

NASA Astrophysics Data System (ADS)

Wernick, Miles N.; Morris, G. Michael

1986-12-01

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

The effect of high leverage points on the logistic ridge regression estimator having multicollinearity

NASA Astrophysics Data System (ADS)

Ariffin, Syaiba Balqish; Midi, Habshah

2014-06-01

This article is concerned with the performance of logistic ridge regression estimation technique in the presence of multicollinearity and high leverage points. In logistic regression, multicollinearity exists among predictors and in the information matrix. The maximum likelihood estimator suffers a huge setback in the presence of multicollinearity which cause regression estimates to have unduly large standard errors. To remedy this problem, a logistic ridge regression estimator is put forward. It is evident that the logistic ridge regression estimator outperforms the maximum likelihood approach for handling multicollinearity. The effect of high leverage points are then investigated on the performance of the logistic ridge regression estimator through real data set and simulation study. The findings signify that logistic ridge regression estimator fails to provide better parameter estimates in the presence of both high leverage points and multicollinearity.

A real-time signal combining system for Ka-band feed arrays using maximum-likelihood weight estimates

NASA Technical Reports Server (NTRS)

Vilnrotter, V. A.; Rodemich, E. R.

1990-01-01

A real-time digital signal combining system for use with Ka-band feed arrays is proposed. The combining system attempts to compensate for signal-to-noise ratio (SNR) loss resulting from antenna deformations induced by gravitational and atmospheric effects. The combining weights are obtained directly from the observed samples by using a sliding-window implementation of a vector maximum-likelihood parameter estimator. It is shown that with averaging times of about 0.1 second, combining loss for a seven-element array can be limited to about 0.1 dB in a realistic operational environment. This result suggests that the real-time combining system proposed here is capable of recovering virtually all of the signal power captured by the feed array, even in the presence of severe wind gusts and similar disturbances.

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.

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

PubMed

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

2016-01-01

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

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

PubMed Central

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

2016-01-01

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

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

PubMed

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

2017-05-01

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

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.

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

PubMed

Koziol, James A; Jia, Zhenyu

2009-06-01

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

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.

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 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…

Monte Carlo Method for Determining Earthquake Recurrence Parameters from Short Paleoseismic Catalogs: Example Calculations for California

USGS Publications Warehouse

Parsons, Tom

2008-01-01

Paleoearthquake observations often lack enough events at a given site to directly define a probability density function (PDF) for earthquake recurrence. Sites with fewer than 10-15 intervals do not provide enough information to reliably determine the shape of the PDF using standard maximum-likelihood techniques [e.g., Ellsworth et al., 1999]. In this paper I present a method that attempts to fit wide ranges of distribution parameters to short paleoseismic series. From repeated Monte Carlo draws, it becomes possible to quantitatively estimate most likely recurrence PDF parameters, and a ranked distribution of parameters is returned that can be used to assess uncertainties in hazard calculations. In tests on short synthetic earthquake series, the method gives results that cluster around the mean of the input distribution, whereas maximum likelihood methods return the sample means [e.g., NIST/SEMATECH, 2006]. For short series (fewer than 10 intervals), sample means tend to reflect the median of an asymmetric recurrence distribution, possibly leading to an overestimate of the hazard should they be used in probability calculations. Therefore a Monte Carlo approach may be useful for assessing recurrence from limited paleoearthquake records. Further, the degree of functional dependence among parameters like mean recurrence interval and coefficient of variation can be established. The method is described for use with time-independent and time-dependent PDF?s, and results from 19 paleoseismic sequences on strike-slip faults throughout the state of California are given.

Monte Carlo method for determining earthquake recurrence parameters from short paleoseismic catalogs: Example calculations for California

USGS Publications Warehouse

Parsons, T.

2008-01-01

Paleoearthquake observations often lack enough events at a given site to directly define a probability density function (PDF) for earthquake recurrence. Sites with fewer than 10-15 intervals do not provide enough information to reliably determine the shape of the PDF using standard maximum-likelihood techniques (e.g., Ellsworth et al., 1999). In this paper I present a method that attempts to fit wide ranges of distribution parameters to short paleoseismic series. From repeated Monte Carlo draws, it becomes possible to quantitatively estimate most likely recurrence PDF parameters, and a ranked distribution of parameters is returned that can be used to assess uncertainties in hazard calculations. In tests on short synthetic earthquake series, the method gives results that cluster around the mean of the input distribution, whereas maximum likelihood methods return the sample means (e.g., NIST/SEMATECH, 2006). For short series (fewer than 10 intervals), sample means tend to reflect the median of an asymmetric recurrence distribution, possibly leading to an overestimate of the hazard should they be used in probability calculations. Therefore a Monte Carlo approach may be useful for assessing recurrence from limited paleoearthquake records. Further, the degree of functional dependence among parameters like mean recurrence interval and coefficient of variation can be established. The method is described for use with time-independent and time-dependent PDFs, and results from 19 paleoseismic sequences on strike-slip faults throughout the state of California are given.

CALIBRATION OF SEMI-ANALYTIC MODELS OF GALAXY FORMATION USING PARTICLE SWARM OPTIMIZATION

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

Ruiz, Andrés N.; Domínguez, Mariano J.; Yaryura, Yamila

2015-03-10

We present a fast and accurate method to select an optimal set of parameters in semi-analytic models of galaxy formation and evolution (SAMs). Our approach compares the results of a model against a set of observables applying a stochastic technique called Particle Swarm Optimization (PSO), a self-learning algorithm for localizing regions of maximum likelihood in multidimensional spaces that outperforms traditional sampling methods in terms of computational cost. We apply the PSO technique to the SAG semi-analytic model combined with merger trees extracted from a standard Lambda Cold Dark Matter N-body simulation. The calibration is performed using a combination of observedmore » galaxy properties as constraints, including the local stellar mass function and the black hole to bulge mass relation. We test the ability of the PSO algorithm to find the best set of free parameters of the model by comparing the results with those obtained using a MCMC exploration. Both methods find the same maximum likelihood region, however, the PSO method requires one order of magnitude fewer evaluations. This new approach allows a fast estimation of the best-fitting parameter set in multidimensional spaces, providing a practical tool to test the consequences of including other astrophysical processes in SAMs.« less

Training in cortical control of neuroprosthetic devices improves signal extraction from small neuronal ensembles.

PubMed

Helms Tillery, S I; Taylor, D M; Schwartz, A B

2003-01-01

We have recently developed a closed-loop environment in which we can test the ability of primates to control the motion of a virtual device using ensembles of simultaneously recorded neurons /29/. Here we use a maximum likelihood method to assess the information about task performance contained in the neuronal ensemble. We trained two animals to control the motion of a computer cursor in three dimensions. Initially the animals controlled cursor motion using arm movements, but eventually they learned to drive the cursor directly from cortical activity. Using a population vector (PV) based upon the relation between cortical activity and arm motion, the animals were able to control the cursor directly from the brain in a closed-loop environment, but with difficulty. We added a supervised learning method that modified the parameters of the PV according to task performance (adaptive PV), and found that animals were able to exert much finer control over the cursor motion from brain signals. Here we describe a maximum likelihood method (ML) to assess the information about target contained in neuronal ensemble activity. Using this method, we compared the information about target contained in the ensemble during arm control, during brain control early in the adaptive PV, and during brain control after the adaptive PV had settled and the animal could drive the cursor reliably and with fine gradations. During the arm-control task, the ML was able to determine the target of the movement in as few as 10% of the trials, and as many as 75% of the trials, with an average of 65%. This average dropped when the animals used a population vector to control motion of the cursor. On average we could determine the target in around 35% of the trials. This low percentage was also reflected in poor control of the cursor, so that the animal was unable to reach the target in a large percentage of trials. Supervised adjustment of the population vector parameters produced new weighting coefficients and directional tuning parameters for many neurons. This produced a much better performance of the brain-controlled cursor motion. It was also reflected in the maximum likelihood measure of cell activity, producing the correct target based only on neuronal activity in over 80% of the trials on average. The changes in maximum likelihood estimates of target location based on ensemble firing show that an animal's ability to regulate the motion of a cortically controlled device is not crucially dependent on the experimenter's ability to estimate intention from neuronal activity.

Comparison of stability and control parameters for a light, single-engine, high-winged aircraft using different flight test and parameter estimation techniques

NASA Technical Reports Server (NTRS)

Suit, W. T.; Cannaday, R. L.

1979-01-01

The longitudinal and lateral stability and control parameters for a high wing, general aviation, airplane are examined. Estimations using flight data obtained at various flight conditions within the normal range of the aircraft are presented. The estimations techniques, an output error technique (maximum likelihood) and an equation error technique (linear regression), are presented. The longitudinal static parameters are estimated from climbing, descending, and quasi steady state flight data. The lateral excitations involve a combination of rudder and ailerons. The sensitivity of the aircraft modes of motion to variations in the parameter estimates are discussed.

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.

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…

The recursive maximum likelihood proportion estimator: User's guide and test results

NASA Technical Reports Server (NTRS)

Vanrooy, D. L.

1976-01-01

Implementation of the recursive maximum likelihood proportion estimator is described. A user's guide to programs as they currently exist on the IBM 360/67 at LARS, Purdue is included, and test results on LANDSAT data are described. On Hill County data, the algorithm yields results comparable to the standard maximum likelihood proportion estimator.

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

PubMed

McCoy, Airlie J

2002-10-01

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

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

USGS Publications Warehouse

Hefley, Trevor J.; Hooten, Mevin B.

2015-01-01

It is important to identify conditions for which maximum likelihood estimates are unlikely to be identifiable from presence-only data. In data sets where the maximum likelihood estimates do not exist, penalized likelihood and Bayesian methods will produce coefficient estimates, but these are sensitive to the choice of estimation procedure and prior or penalty term. When sample size is small or it is thought that habitat preferences are strong, we propose a suite of estimation procedures researchers can consider using.

A hyperbolastic type-I diffusion process: Parameter estimation by means of the firefly algorithm.

PubMed

Barrera, Antonio; Román-Román, Patricia; Torres-Ruiz, Francisco

2018-01-01

A stochastic diffusion process, whose mean function is a hyperbolastic curve of type I, is presented. The main characteristics of the process are studied and the problem of maximum likelihood estimation for the parameters of the process is considered. To this end, the firefly metaheuristic optimization algorithm is applied after bounding the parametric space by a stagewise procedure. Some examples based on simulated sample paths and real data illustrate this development. Copyright © 2017 Elsevier B.V. All rights reserved.

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

Spatial Prediction and Optimized Sampling Design for Sodium Concentration in Groundwater

PubMed Central

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

2016-01-01

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

MIXOR: a computer program for mixed-effects ordinal regression analysis.

PubMed

Hedeker, D; Gibbons, R D

1996-03-01

MIXOR provides maximum marginal likelihood estimates for mixed-effects ordinal probit, logistic, and complementary log-log regression models. These models can be used for analysis of dichotomous and ordinal outcomes from either a clustered or longitudinal design. For clustered data, the mixed-effects model assumes that data within clusters are dependent. The degree of dependency is jointly estimated with the usual model parameters, thus adjusting for dependence resulting from clustering of the data. Similarly, for longitudinal data, the mixed-effects approach can allow for individual-varying intercepts and slopes across time, and can estimate the degree to which these time-related effects vary in the population of individuals. MIXOR uses marginal maximum likelihood estimation, utilizing a Fisher-scoring solution. For the scoring solution, the Cholesky factor of the random-effects variance-covariance matrix is estimated, along with the effects of model covariates. Examples illustrating usage and features of MIXOR are provided.

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.

Maximum likelihood estimation for semiparametric transformation models with interval-censored data

PubMed Central

Mao, Lu; Lin, D. Y.

2016-01-01

Abstract Interval censoring arises frequently in clinical, epidemiological, financial and sociological studies, where the event or failure of interest is known only to occur within an interval induced by periodic monitoring. We formulate the effects of potentially time-dependent covariates on the interval-censored failure time through a broad class of semiparametric transformation models that encompasses proportional hazards and proportional odds models. We consider nonparametric maximum likelihood estimation for this class of models with an arbitrary number of monitoring times for each subject. We devise an EM-type algorithm that converges stably, even in the presence of time-dependent covariates, and show that the estimators for the regression parameters are consistent, asymptotically normal, and asymptotically efficient with an easily estimated covariance matrix. Finally, we demonstrate the performance of our procedures through simulation studies and application to an HIV/AIDS study conducted in Thailand. PMID:27279656

Optimization of a Nucleic Acids united-RESidue 2-Point model (NARES-2P) with a maximum-likelihood approach

NASA Astrophysics Data System (ADS)

He, Yi; Liwo, Adam; Scheraga, Harold A.

2015-12-01

Coarse-grained models are useful tools to investigate the structural and thermodynamic properties of biomolecules. They are obtained by merging several atoms into one interaction site. Such simplified models try to capture as much as possible information of the original biomolecular system in all-atom representation but the resulting parameters of these coarse-grained force fields still need further optimization. In this paper, a force field optimization method, which is based on maximum-likelihood fitting of the simulated to the experimental conformational ensembles and least-squares fitting of the simulated to the experimental heat-capacity curves, is applied to optimize the Nucleic Acid united-RESidue 2-point (NARES-2P) model for coarse-grained simulations of nucleic acids recently developed in our laboratory. The optimized NARES-2P force field reproduces the structural and thermodynamic data of small DNA molecules much better than the original force field.

A Bayesian-Based Novel Methodology to Generate Reliable Site Response Mapping Sensitive to Data Uncertainties

NASA Astrophysics Data System (ADS)

Chakraborty, A.; Goto, H.

2017-12-01

The 2011 off the Pacific coast of Tohoku earthquake caused severe damage in many areas further inside the mainland because of site-amplification. Furukawa district in Miyagi Prefecture, Japan recorded significant spatial differences in ground motion even at sub-kilometer scales. The site responses in the damage zone far exceeded the levels in the hazard maps. A reason why the mismatch occurred is that mapping follow only the mean value at the measurement locations with no regard to the data uncertainties and thus are not always reliable. Our research objective is to develop a methodology to incorporate data uncertainties in mapping and propose a reliable map. The methodology is based on a hierarchical Bayesian modeling of normally-distributed site responses in space where the mean (μ), site-specific variance (σ2) and between-sites variance(s2) parameters are treated as unknowns with a prior distribution. The observation data is artificially created site responses with varying means and variances for 150 seismic events across 50 locations in one-dimensional space. Spatially auto-correlated random effects were added to the mean (μ) using a conditionally autoregressive (CAR) prior. The inferences on the unknown parameters are done using Markov Chain Monte Carlo methods from the posterior distribution. The goal is to find reliable estimates of μ sensitive to uncertainties. During initial trials, we observed that the tau (=1/s2) parameter of CAR prior controls the μ estimation. Using a constraint, s = 1/(k×σ), five spatial models with varying k-values were created. We define reliability to be measured by the model likelihood and propose the maximum likelihood model to be highly reliable. The model with maximum likelihood was selected using a 5-fold cross-validation technique. The results show that the maximum likelihood model (μ*) follows the site-specific mean at low uncertainties and converges to the model-mean at higher uncertainties (Fig.1). This result is highly significant as it successfully incorporates the effect of data uncertainties in mapping. This novel approach can be applied to any research field using mapping techniques. The methodology is now being applied to real records from a very dense seismic network in Furukawa district, Miyagi Prefecture, Japan to generate a reliable map of the site responses.

R programming for parameters estimation of geographically weighted ordinal logistic regression (GWOLR) model based on Newton Raphson

NASA Astrophysics Data System (ADS)

Zuhdi, Shaifudin; Saputro, Dewi Retno Sari

2017-03-01

GWOLR model used for represent relationship between dependent variable has categories and scale of category is ordinal with independent variable influenced the geographical location of the observation site. Parameters estimation of GWOLR model use maximum likelihood provide system of nonlinear equations and hard to be found the result in analytic resolution. By finishing it, it means determine the maximum completion, this thing associated with optimizing problem. The completion nonlinear system of equations optimize use numerical approximation, which one is Newton Raphson method. The purpose of this research is to make iteration algorithm Newton Raphson and program using R software to estimate GWOLR model. Based on the research obtained that program in R can be used to estimate the parameters of GWOLR model by forming a syntax program with command "while".

Upper bounds on sequential decoding performance parameters

NASA Technical Reports Server (NTRS)

Jelinek, F.

1974-01-01

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

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.

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

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.

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.

Parameter Estimation in Epidemiology: from Simple to Complex Dynamics

NASA Astrophysics Data System (ADS)

Aguiar, Maíra; Ballesteros, Sebastién; Boto, João Pedro; Kooi, Bob W.; Mateus, Luís; Stollenwerk, Nico

2011-09-01

We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models like multi-strain dynamics to describe the virus-host interaction in dengue fever, even most recently developed parameter estimation techniques, like maximum likelihood iterated filtering, come to their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.

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

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

Kane, V.E.

1982-01-01

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

A Two-Stage Approach to Missing Data: Theory and Application to Auxiliary Variables

ERIC Educational Resources Information Center

Savalei, Victoria; Bentler, Peter M.

2009-01-01

A well-known ad-hoc approach to conducting structural equation modeling with missing data is to obtain a saturated maximum likelihood (ML) estimate of the population covariance matrix and then to use this estimate in the complete data ML fitting function to obtain parameter estimates. This 2-stage (TS) approach is appealing because it minimizes a…

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…

A New Lifetime Distribution with Bathtube and Unimodal Hazard Function

NASA Astrophysics Data System (ADS)

Barriga, Gladys D. C.; Louzada-Neto, Francisco; Cancho, Vicente G.

2008-11-01

In this paper we propose a new lifetime distribution which accommodate bathtub-shaped, unimodal, increasing and decreasing hazard function. Some special particular cases are derived, including the standard Weibull distribution. Maximum likelihood estimation is considered for estimate the tree parameters present in the model. The methodology is illustrated in a real data set on industrial devices on a lite test.

Sources of variation in Landsat autocorrelation

NASA Technical Reports Server (NTRS)

Craig, R. G.; Labovitz, M. L.

1980-01-01

Analysis of sixty-four scan lines representing diverse conditions across satellites, channels, scanners, locations and cloud cover confirms that Landsat data are autocorrelated and consistently follow an Arima (1,0,1) pattern. The AR parameter varies significantly with location and the MA coefficient with cloud cover. Maximum likelihood classification functions are considerably in error unless this autocorrelation is compensated for in sampling.

Factor Analysis with EM Algorithm Never Gives Improper Solutions when Sample Covariance and Initial Parameter Matrices Are Proper

ERIC Educational Resources Information Center

Adachi, Kohei

2013-01-01

Rubin and Thayer ("Psychometrika," 47:69-76, 1982) proposed the EM algorithm for exploratory and confirmatory maximum likelihood factor analysis. In this paper, we prove the following fact: the EM algorithm always gives a proper solution with positive unique variances and factor correlations with absolute values that do not exceed one,…

State-Space Modeling of Dynamic Psychological Processes via the Kalman Smoother Algorithm: Rationale, Finite Sample Properties, and Applications

ERIC Educational Resources Information Center

Song, Hairong; Ferrer, Emilio

2009-01-01

This article presents a state-space modeling (SSM) technique for fitting process factor analysis models directly to raw data. The Kalman smoother via the expectation-maximization algorithm to obtain maximum likelihood parameter estimates is used. To examine the finite sample properties of the estimates in SSM when common factors are involved, a…

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 maximum likelihood map of chromosome 1.

PubMed Central

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

1979-01-01

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

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

ERIC Educational Resources Information Center

Mahmud, Jumailiyah; Sutikno, Muzayanah; Naga, Dali S.

2016-01-01

The aim of this study is to determine variance difference between maximum likelihood and expected A posteriori estimation methods viewed from number of test items of aptitude test. The variance presents an accuracy generated by both maximum likelihood and Bayes estimation methods. The test consists of three subtests, each with 40 multiple-choice…

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

Treesearch

Changren Weng; Thomas L. Kubisiak; C. Dana Nelson; James P. Geaghan; Michael Stine

1999-01-01

Single marker regression and single marker maximum likelihood estimation were tied to detect quantitative trait loci (QTLs) controlling the early height growth of longleaf pine and slash pine using a ((longleaf pine x slash pine) x slash pine) BC, population consisting of 83 progeny. Maximum likelihood estimation was found to be more power than regression and could...

Addressing Data Analysis Challenges in Gravitational Wave Searches Using the Particle Swarm Optimization Algorithm

NASA Astrophysics Data System (ADS)

Weerathunga, Thilina Shihan

2017-08-01

Gravitational waves are a fundamental prediction of Einstein's General Theory of Relativity. The first experimental proof of their existence was provided by the Nobel Prize winning discovery by Taylor and Hulse of orbital decay in a binary pulsar system. The first detection of gravitational waves incident on earth from an astrophysical source was announced in 2016 by the LIGO Scientific Collaboration, launching the new era of gravitational wave (GW) astronomy. The signal detected was from the merger of two black holes, which is an example of sources called Compact Binary Coalescences (CBCs). Data analysis strategies used in the search for CBC signals are derivatives of the Maximum-Likelihood (ML) method. The ML method applied to data from a network of geographically distributed GW detectors--called fully coherent network analysis--is currently the best approach for estimating source location and GW polarization waveforms. However, in the case of CBCs, especially for lower mass systems (O(1M solar masses)) such as double neutron star binaries, fully coherent network analysis is computationally expensive. The ML method requires locating the global maximum of the likelihood function over a nine dimensional parameter space, where the computation of the likelihood at each point requires correlations involving O(104) to O(106) samples between the data and the corresponding candidate signal waveform template. Approximations, such as semi-coherent coincidence searches, are currently used to circumvent the computational barrier but incur a concomitant loss in sensitivity. We explored the effectiveness of Particle Swarm Optimization (PSO), a well-known algorithm in the field of swarm intelligence, in addressing the fully coherent network analysis problem. As an example, we used a four-detector network consisting of the two LIGO detectors at Hanford and Livingston, Virgo and Kagra, all having initial LIGO noise power spectral densities, and show that PSO can locate the global maximum with less than 240,000 likelihood evaluations for a component mass range of 1.0 to 10.0 solar masses at a realistic coherent network signal to noise ratio of 9.0. Our results show that PSO can successfully deliver a fully-coherent all-sky search with < (1/10 ) the number of likelihood evaluations needed for a grid-based search. Used as a follow-up step, the savings in the number of likelihood evaluations may also reduce latency in obtaining ML estimates of source parameters in semi-coherent searches.

Maximum likelihood estimation for periodic autoregressive moving average models

USGS Publications Warehouse

Vecchia, A.V.

1985-01-01

A useful class of models for seasonal time series that cannot be filtered or standardized to achieve second-order stationarity is that of periodic autoregressive moving average (PARMA) models, which are extensions of ARMA models that allow periodic (seasonal) parameters. An approximation to the exact likelihood for Gaussian PARMA processes is developed, and a straightforward algorithm for its maximization is presented. The algorithm is tested on several periodic ARMA(1, 1) models through simulation studies and is compared to moment estimation via the seasonal Yule-Walker equations. Applicability of the technique is demonstrated through an analysis of a seasonal stream-flow series from the Rio Caroni River in Venezuela.

Evaluation of several schemes for classification of remotely sensed data: Their parameters and performance. [Foster County, North Dakota; Grant County, Kansas; Iroquois County, Illinois, Tippecanoe County, Indiana; and Pottawattamie and Shelby Counties, Iowa

NASA Technical Reports Server (NTRS)

Scholz, D.; Fuhs, N.; Hixson, M.; Akiyama, T. (Principal Investigator)

1979-01-01

The author has identified the following significant results. Data sets for corn, soybeans, winter wheat, and spring wheat were used to evaluate the following schemes for crop identification: (1) per point Gaussian maximum classifier; (2) per point sum of normal densities classifiers; (3) per point linear classifier; (4) per point Gaussian maximum likelihood decision tree classifiers; and (5) texture sensitive per field Gaussian maximum likelihood classifier. Test site location and classifier both had significant effects on classification accuracy of small grains; classifiers did not differ significantly in overall accuracy, with the majority of the difference among classifiers being attributed to training method rather than to the classification algorithm applied. The complexity of use and computer costs for the classifiers varied significantly. A linear classification rule which assigns each pixel to the class whose mean is closest in Euclidean distance was the easiest for the analyst and cost the least per classification.

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.

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 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.

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.

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.

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.

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

PubMed

Lohse, Konrad; Frantz, Laurent A F

2014-04-01

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

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

PubMed Central

Lohse, Konrad; Frantz, Laurent A. F.

2014-01-01

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

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

NASA Technical Reports Server (NTRS)

Hoffbeck, Joseph P.; Landgrebe, David A.

1994-01-01

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

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.

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

PubMed

Lin, Feng-Chang; Zhu, Jun

2012-01-01

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

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

PubMed Central

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

2015-01-01

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

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.

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).

M-dwarf exoplanet surface density distribution. A log-normal fit from 0.07 to 400 AU

NASA Astrophysics Data System (ADS)

Meyer, Michael R.; Amara, Adam; Reggiani, Maddalena; Quanz, Sascha P.

2018-04-01

Aims: We fit a log-normal function to the M-dwarf orbital surface density distribution of gas giant planets, over the mass range 1-10 times that of Jupiter, from 0.07 to 400 AU. Methods: We used a Markov chain Monte Carlo approach to explore the likelihoods of various parameter values consistent with point estimates of the data given our assumed functional form. Results: This fit is consistent with radial velocity, microlensing, and direct-imaging observations, is well-motivated from theoretical and phenomenological points of view, and predicts results of future surveys. We present probability distributions for each parameter and a maximum likelihood estimate solution. Conclusions: We suggest that this function makes more physical sense than other widely used functions, and we explore the implications of our results on the design of future exoplanet surveys.

Testing the causality of Hawkes processes with time reversal

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Maximum likelihood estimation for predicting the probability of obtaining variable shortleaf pine regeneration densities

Treesearch

Thomas B. Lynch; Jean Nkouka; Michael M. Huebschmann; James M. Guldin

2003-01-01

A logistic equation is the basis for a model that predicts the probability of obtaining regeneration at specified densities. The density of regeneration (trees/ha) for which an estimate of probability is desired can be specified by means of independent variables in the model. When estimating parameters, the dependent variable is set to 1 if the regeneration density (...

On an Extension of the Rasch Model to the Case of Polychotomously Scored Items.

ERIC Educational Resources Information Center

Vogt, Dorothee K.

The Rasch model for the probability of a person's response to an item is extended to the case where this response depends on a set of scoring or category weights, in addition to person and item parameters. The maximum likelihood approach introduced by Wright for the dichotomous case is applicable here also, and it is shown to yield a unique…

Pseudo-coherent demodulation for mobile satellite systems

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Simon, Marvin K.

1993-01-01

This paper proposes three so-called pseudo-coherent demodulation schemes for use in land mobile satellite channels. The schemes are derived based on maximum likelihood (ML) estimation and detection of an N-symbol observation of the received signal. Simulation results for all three demodulators are presented to allow comparison with the performance of differential PSK (DPSK) and ideal coherent demodulation for various system parameter sets of practical interest.

F-8C adaptive control law refinement and software development

NASA Technical Reports Server (NTRS)

Hartmann, G. L.; Stein, G.

1981-01-01

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

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.

Missing data methods for dealing with missing items in quality of life questionnaires. A comparison by simulation of personal mean score, full information maximum likelihood, multiple imputation, and hot deck techniques applied to the SF-36 in the French 2003 decennial health survey.

PubMed

Peyre, Hugo; Leplège, Alain; Coste, Joël

2011-03-01

Missing items are common in quality of life (QoL) questionnaires and present a challenge for research in this field. It remains unclear which of the various methods proposed to deal with missing data performs best in this context. We compared personal mean score, full information maximum likelihood, multiple imputation, and hot deck techniques using various realistic simulation scenarios of item missingness in QoL questionnaires constructed within the framework of classical test theory. Samples of 300 and 1,000 subjects were randomly drawn from the 2003 INSEE Decennial Health Survey (of 23,018 subjects representative of the French population and having completed the SF-36) and various patterns of missing data were generated according to three different item non-response rates (3, 6, and 9%) and three types of missing data (Little and Rubin's "missing completely at random," "missing at random," and "missing not at random"). The missing data methods were evaluated in terms of accuracy and precision for the analysis of one descriptive and one association parameter for three different scales of the SF-36. For all item non-response rates and types of missing data, multiple imputation and full information maximum likelihood appeared superior to the personal mean score and especially to hot deck in terms of accuracy and precision; however, the use of personal mean score was associated with insignificant bias (relative bias <2%) in all studied situations. Whereas multiple imputation and full information maximum likelihood are confirmed as reference methods, the personal mean score appears nonetheless appropriate for dealing with items missing from completed SF-36 questionnaires in most situations of routine use. These results can reasonably be extended to other questionnaires constructed according to classical test theory.

Speech processing using conditional observable maximum likelihood continuity mapping

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

Hogden, John; Nix, David

A computer implemented method enables the recognition of speech and speech characteristics. Parameters are initialized of first probability density functions that map between the symbols in the vocabulary of one or more sequences of speech codes that represent speech sounds and a continuity map. Parameters are also initialized of second probability density functions that map between the elements in the vocabulary of one or more desired sequences of speech transcription symbols and the continuity map. The parameters of the probability density functions are then trained to maximize the probabilities of the desired sequences of speech-transcription symbols. A new sequence ofmore » speech codes is then input to the continuity map having the trained first and second probability function parameters. A smooth path is identified on the continuity map that has the maximum probability for the new sequence of speech codes. The probability of each speech transcription symbol for each input speech code can then be output.« less

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 Detection Of Noncoherent CPM

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Simon, Marvin K.

1993-01-01

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

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

DTIC Science & Technology

1990-11-01

Technical Report 1373 November 1990 Cramer-Rao Bound, MUSIC , And Maximum Likelihood Effects of Temporal Phase o Difference C. V. TranI OTIC Approved... MUSIC , and Maximum Likelihood (ML) asymptotic variances corresponding to the two-source direction-of-arrival estimation where sources were modeled as...1pI = 1.00, SNR = 20 dB ..................................... 27 2. MUSIC for two equipowered signals impinging on a 5-element ULA (a) IpI = 0.50, SNR

The use of copulas to practical estimation of multivariate stochastic differential equation mixed effects models

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

Rupšys, P.

A system of stochastic differential equations (SDE) with mixed-effects parameters and multivariate normal copula density function were used to develop tree height model for Scots pine trees in Lithuania. A two-step maximum likelihood parameter estimation method is used and computational guidelines are given. After fitting the conditional probability density functions to outside bark diameter at breast height, and total tree height, a bivariate normal copula distribution model was constructed. Predictions from the mixed-effects parameters SDE tree height model calculated during this research were compared to the regression tree height equations. The results are implemented in the symbolic computational language MAPLE.

A novel description of FDG excretion in the renal system: application to metformin-treated models

NASA Astrophysics Data System (ADS)

Garbarino, S.; Caviglia, G.; Sambuceti, G.; Benvenuto, F.; Piana, M.

2014-05-01

This paper introduces a novel compartmental model describing the excretion of 18F-fluoro-deoxyglucose (FDG) in the renal system and a numerical method based on the maximum likelihood for its reduction. This approach accounts for variations in FDG concentration due to water re-absorption in renal tubules and the increase of the bladder’s volume during the FDG excretion process. From the computational viewpoint, the reconstruction of the tracer kinetic parameters is obtained by solving the maximum likelihood problem iteratively, using a non-stationary, steepest descent approach that explicitly accounts for the Poisson nature of nuclear medicine data. The reliability of the method is validated against two sets of synthetic data realized according to realistic conditions. Finally we applied this model to describe FDG excretion in the case of animal models treated with metformin. In particular we show that our approach allows the quantitative estimation of the reduction of FDG de-phosphorylation induced by metformin.

Application and performance of an ML-EM algorithm in NEXT

NASA Astrophysics Data System (ADS)

Simón, A.; Lerche, C.; Monrabal, F.; Gómez-Cadenas, J. J.; Álvarez, V.; Azevedo, C. D. R.; Benlloch-Rodríguez, J. M.; Borges, F. I. G. M.; Botas, A.; Cárcel, S.; Carrión, J. V.; Cebrián, S.; Conde, C. A. N.; Díaz, J.; Diesburg, M.; Escada, J.; Esteve, R.; Felkai, R.; Fernandes, L. M. P.; Ferrario, P.; Ferreira, A. L.; Freitas, E. D. C.; Goldschmidt, A.; González-Díaz, D.; Gutiérrez, R. M.; Hauptman, J.; Henriques, C. A. O.; Hernandez, A. I.; Hernando Morata, J. A.; Herrero, V.; Jones, B. J. P.; Labarga, L.; Laing, A.; Lebrun, P.; Liubarsky, I.; López-March, N.; Losada, M.; Martín-Albo, J.; Martínez-Lema, G.; Martínez, A.; McDonald, A. D.; Monteiro, C. M. B.; Mora, F. J.; Moutinho, L. M.; Muñoz Vidal, J.; Musti, M.; Nebot-Guinot, M.; Novella, P.; Nygren, D. R.; Palmeiro, B.; Para, A.; Pérez, J.; Querol, M.; Renner, J.; Ripoll, L.; Rodríguez, J.; Rogers, L.; Santos, F. P.; dos Santos, J. M. F.; Sofka, C.; Sorel, M.; Stiegler, T.; Toledo, J. F.; Torrent, J.; Tsamalaidze, Z.; Veloso, J. F. C. A.; Webb, R.; White, J. T.; Yahlali, N.

2017-08-01

The goal of the NEXT experiment is the observation of neutrinoless double beta decay in 136Xe using a gaseous xenon TPC with electroluminescent amplification and specialized photodetector arrays for calorimetry and tracking. The NEXT Collaboration is exploring a number of reconstruction algorithms to exploit the full potential of the detector. This paper describes one of them: the Maximum Likelihood Expectation Maximization (ML-EM) method, a generic iterative algorithm to find maximum-likelihood estimates of parameters that has been applied to solve many different types of complex inverse problems. In particular, we discuss a bi-dimensional version of the method in which the photosensor signals integrated over time are used to reconstruct a transverse projection of the event. First results show that, when applied to detector simulation data, the algorithm achieves nearly optimal energy resolution (better than 0.5% FWHM at the Q value of 136Xe) for events distributed over the full active volume of the TPC.

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.

A comparison of minimum distance and maximum likelihood techniques for proportion estimation

NASA Technical Reports Server (NTRS)

Woodward, W. A.; Schucany, W. R.; Lindsey, H.; Gray, H. L.

1982-01-01

The estimation of mixing proportions P sub 1, P sub 2,...P sub m in the mixture density f(x) = the sum of the series P sub i F sub i(X) with i = 1 to M is often encountered in agricultural remote sensing problems in which case the p sub i's usually represent crop proportions. In these remote sensing applications, component densities f sub i(x) have typically been assumed to be normally distributed, and parameter estimation has been accomplished using maximum likelihood (ML) techniques. Minimum distance (MD) estimation is examined as an alternative to ML where, in this investigation, both procedures are based upon normal components. Results indicate that ML techniques are superior to MD when component distributions actually are normal, while MD estimation provides better estimates than ML under symmetric departures from normality. When component distributions are not symmetric, however, it is seen that neither of these normal based techniques provides satisfactory results.

Maximum likelihood techniques applied to quasi-elastic light scattering

NASA Technical Reports Server (NTRS)

Edwards, Robert V.

1992-01-01

There is a necessity of having an automatic procedure for reliable estimation of the quality of the measurement of particle size from QELS (Quasi-Elastic Light Scattering). Getting the measurement itself, before any error estimates can be made, is a problem because it is obtained by a very indirect measurement of a signal derived from the motion of particles in the system and requires the solution of an inverse problem. The eigenvalue structure of the transform that generates the signal is such that an arbitrarily small amount of noise can obliterate parts of any practical inversion spectrum. This project uses the Maximum Likelihood Estimation (MLE) as a framework to generate a theory and a functioning set of software to oversee the measurement process and extract the particle size information, while at the same time providing error estimates for those measurements. The theory involved verifying a correct form of the covariance matrix for the noise on the measurement and then estimating particle size parameters using a modified histogram approach.

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.

US Transuranium and Uranium Registries case study on accidental exposure to uranium hexafluoride.

PubMed

Avtandilashvili, Maia; Puncher, Matthew; McComish, Stacey L; Tolmachev, Sergei Y

2015-03-01

The United States Transuranium and Uranium Registries' (USTUR) whole-body donor (Case 1031) was exposed to an acute inhalation of uranium hexafluoride (UF6) produced from an explosion at a uranium processing plant 65 years prior to his death. The USTUR measurements of tissue samples collected at the autopsy indicated long-term retention of inhaled slightly enriched uranium material (0.85% (235)U) in the deep lungs and thoracic lymph nodes. In the present study, the authors combined the tissue measurement results with historical bioassay data, and analysed them with International Commission on Radiological Protection (ICRP) respiratory tract models and the ICRP Publication 69 systemic model for uranium using maximum likelihood and Bayesian statistical methods. The purpose of the analysis was to estimate intakes and model parameter values that best describe the data, and evaluate their effect on dose assessment. The maximum likelihood analysis, which used the ICRP Publication 66 human respiratory tract model, resulted in a point estimate of 79 mg of uranium for the occupational intake composed of 86% soluble, type F material and 14% insoluble, type S material. For the Bayesian approach, the authors applied the Markov Chain Monte Carlo method, but this time used the revised human respiratory tract model, which is currently being used by ICRP to calculate new dose coefficients for workers. The Bayesian analysis estimated that the mean uranium intake was 160 mg, and calculated the case-specific lung dissolution parameters with their associated uncertainties. The parameters were consistent with the inhaled uranium material being predominantly soluble with a small but significant insoluble component. The 95% posterior range of the rapid dissolution fraction (the fraction of deposited material that is absorbed to blood rapidly) was 0.12 to 0.91 with a median of 0.37. The remaining fraction was absorbed slowly, with a 95% range of 0.000 22 d(-1) to 0.000 36 d(-1) and a median of 0.000 31 d(-1). The effective dose per unit intake calculated using the dissolution parameters derived from the maximum likelihood and the Bayesian analyses was higher than the current ICRP dose coefficient for type F uranium by a factor of 2 or 7, respectively; the higher value of the latter was due to use of the revised respiratory tract model. The dissolution parameter values obtained here may be more appropriate to use for radiation protection purposes when individuals are exposed to a UF6 mixture that contains an insoluble uranium component.

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

PubMed

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

2017-03-01

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

Efficient Bayesian experimental design for contaminant source identification

NASA Astrophysics Data System (ADS)

Zhang, J.; Zeng, L.

2013-12-01

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

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

ERIC Educational Resources Information Center

Wothke, Werner; Burket, George; Chen, Li-Sue; Gao, Furong; Shu, Lianghua; Chia, Mike

2011-01-01

It has been known for some time that item response theory (IRT) models may exhibit a likelihood function of a respondent's ability which may have multiple modes, flat modes, or both. These conditions, often associated with guessing of multiple-choice (MC) questions, can introduce uncertainty and bias to ability estimation by maximum likelihood…

Model-Based Clustering and Data Transformations for Gene Expression Data

DTIC Science & Technology

2001-04-30

transformation parameters, e.g. Andrews, Gnanadesikan , and Warner (1973). Aitchison tests: Aitchison (1986) tested three aspects of the data for...N in the Box-Cox transformation in Equation (5) is estimated by maximum likelihood using the observa- tions (Andrews, Gnanadesikan , and Warner 1973...Compositional Data. Chapman and Hall. Andrews, D. F., R. Gnanadesikan , and J. L. Warner (1973). Methods for assessing multivari- ate normality. In P. R

An Analysis of Factor Extraction Strategies: A Comparison of the Relative Strengths of Principal Axis, Ordinary Least Squares, and Maximum Likelihood in Research Contexts That Include Both Categorical and Continuous Variables

ERIC Educational Resources Information Center

Coughlin, Kevin B.

2013-01-01

This study is intended to provide researchers with empirically derived guidelines for conducting factor analytic studies in research contexts that include dichotomous and continuous levels of measurement. This study is based on the hypotheses that ordinary least squares (OLS) factor analysis will yield more accurate parameter estimates than…

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.

Maximum mutual information estimation of a simplified hidden MRF for offline handwritten Chinese character recognition

NASA Astrophysics Data System (ADS)

Xiong, Yan; Reichenbach, Stephen E.

1999-01-01

Understanding of hand-written Chinese characters is at such a primitive stage that models include some assumptions about hand-written Chinese characters that are simply false. So Maximum Likelihood Estimation (MLE) may not be an optimal method for hand-written Chinese characters recognition. This concern motivates the research effort to consider alternative criteria. Maximum Mutual Information Estimation (MMIE) is an alternative method for parameter estimation that does not derive its rationale from presumed model correctness, but instead examines the pattern-modeling problem in automatic recognition system from an information- theoretic point of view. The objective of MMIE is to find a set of parameters in such that the resultant model allows the system to derive from the observed data as much information as possible about the class. We consider MMIE for recognition of hand-written Chinese characters using on a simplified hidden Markov Random Field. MMIE provides improved performance improvement over MLE in this application.

Maximum likelihood estimation of protein kinetic parameters under weak assumptions from unfolding force spectroscopy experiments

NASA Astrophysics Data System (ADS)

Aioanei, Daniel; Samorì, Bruno; Brucale, Marco

2009-12-01

Single molecule force spectroscopy (SMFS) is extensively used to characterize the mechanical unfolding behavior of individual protein domains under applied force by pulling chimeric polyproteins consisting of identical tandem repeats. Constant velocity unfolding SMFS data can be employed to reconstruct the protein unfolding energy landscape and kinetics. The methods applied so far require the specification of a single stretching force increase function, either theoretically derived or experimentally inferred, which must then be assumed to accurately describe the entirety of the experimental data. The very existence of a suitable optimal force model, even in the context of a single experimental data set, is still questioned. Herein, we propose a maximum likelihood (ML) framework for the estimation of protein kinetic parameters which can accommodate all the established theoretical force increase models. Our framework does not presuppose the existence of a single force characteristic function. Rather, it can be used with a heterogeneous set of functions, each describing the protein behavior in the stretching time range leading to one rupture event. We propose a simple way of constructing such a set of functions via piecewise linear approximation of the SMFS force vs time data and we prove the suitability of the approach both with synthetic data and experimentally. Additionally, when the spontaneous unfolding rate is the only unknown parameter, we find a correction factor that eliminates the bias of the ML estimator while also reducing its variance. Finally, we investigate which of several time-constrained experiment designs leads to better estimators.

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

PubMed

Wynant, Willy; Abrahamowicz, Michal

2016-11-01

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

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.

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

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…

Modeling annual extreme temperature using generalized extreme value distribution: A case study in Malaysia

NASA Astrophysics Data System (ADS)

Hasan, Husna; Salam, Norfatin; Kassim, Suraiya

2013-04-01

Extreme temperature of several stations in Malaysia is modeled by fitting the annual maximum to the Generalized Extreme Value (GEV) distribution. The Augmented Dickey Fuller (ADF) and Phillips Perron (PP) tests are used to detect stochastic trends among the stations. The Mann-Kendall (MK) test suggests a non-stationary model. Three models are considered for stations with trend and the Likelihood Ratio test is used to determine the best-fitting model. The results show that Subang and Bayan Lepas stations favour a model which is linear for the location parameters while Kota Kinabalu and Sibu stations are suitable with a model in the logarithm of the scale parameters. The return level is the level of events (maximum temperature) which is expected to be exceeded once, on average, in a given number of years, is obtained.

Formulation and implementation of a practical algorithm for parameter estimation with process and measurement noise

NASA Technical Reports Server (NTRS)

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

1980-01-01

A new formulation is proposed for the problem of parameter estimation of dynamic systems with both process and measurement noise. The formulation gives estimates that are maximum likelihood asymptotically in time. The means used to overcome the difficulties encountered by previous formulations are discussed. It is then shown how the proposed formulation can be efficiently implemented in a computer program. A computer program using the proposed formulation is available in a form suitable for routine application. Examples with simulated and real data are given to illustrate that the program works well.

Local neighborhood transition probability estimation and its use in contextual classification

NASA Technical Reports Server (NTRS)

Chittineni, C. B.

1979-01-01

The problem of incorporating spatial or contextual information into classifications is considered. A simple model that describes the spatial dependencies between the neighboring pixels with a single parameter, Theta, is presented. Expressions are derived for updating the posteriori probabilities of the states of nature of the pattern under consideration using information from the neighboring patterns, both for spatially uniform context and for Markov dependencies in terms of Theta. Techniques for obtaining the optimal value of the parameter Theta as a maximum likelihood estimate from the local neighborhood of the pattern under consideration are developed.

Volume effects of late term normal tissue toxicity in prostate cancer radiotherapy

NASA Astrophysics Data System (ADS)

Bonta, Dacian Viorel

Modeling of volume effects for treatment toxicity is paramount for optimization of radiation therapy. This thesis proposes a new model for calculating volume effects in gastro-intestinal and genito-urinary normal tissue complication probability (NTCP) following radiation therapy for prostate carcinoma. The radiobiological and the pathological basis for this model and its relationship to other models are detailed. A review of the radiobiological experiments and published clinical data identified salient features and specific properties a biologically adequate model has to conform to. The new model was fit to a set of actual clinical data. In order to verify the goodness of fit, two established NTCP models and a non-NTCP measure for complication risk were fitted to the same clinical data. The method of fit for the model parameters was maximum likelihood estimation. Within the framework of the maximum likelihood approach I estimated the parameter uncertainties for each complication prediction model. The quality-of-fit was determined using the Aikaike Information Criterion. Based on the model that provided the best fit, I identified the volume effects for both types of toxicities. Computer-based bootstrap resampling of the original dataset was used to estimate the bias and variance for the fitted parameter values. Computer simulation was also used to estimate the population size that generates a specific uncertainty level (3%) in the value of predicted complication probability. The same method was used to estimate the size of the patient population needed for accurate choice of the model underlying the NTCP. The results indicate that, depending on the number of parameters of a specific NTCP model, 100 (for two parameter models) and 500 patients (for three parameter models) are needed for accurate parameter fit. Correlation of complication occurrence in patients was also investigated. The results suggest that complication outcomes are correlated in a patient, although the correlation coefficient is rather small.

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

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

NASA Astrophysics Data System (ADS)

Abe, Sumiyoshi

2014-11-01

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

Effects of control inputs on the estimation of stability and control parameters of a light airplane

NASA Technical Reports Server (NTRS)

Cannaday, R. L.; Suit, W. T.

1977-01-01

The maximum likelihood parameter estimation technique was used to determine the values of stability and control derivatives from flight test data for a low-wing, single-engine, light airplane. Several input forms were used during the tests to investigate the consistency of parameter estimates as it relates to inputs. These consistencies were compared by using the ensemble variance and estimated Cramer-Rao lower bound. In addition, the relationship between inputs and parameter correlations was investigated. Results from the stabilator inputs are inconclusive but the sequence of rudder input followed by aileron input or aileron followed by rudder gave more consistent estimates than did rudder or ailerons individually. Also, square-wave inputs appeared to provide slightly improved consistency in the parameter estimates when compared to sine-wave inputs.

Effects of wing modification on an aircraft's aerodynamic parameters as determined from flight data

NASA Technical Reports Server (NTRS)

Hess, R. A.

1986-01-01

A study of the effects of four wing-leading-edge modifications on a general aviation aircraft's stability and control parameters is presented. Flight data from the basic aircraft configuration and configurations with wing modifications are analyzed to determine each wing geometry's stability and control parameters. The parameter estimates and aerodynamic model forms are obtained using the stepwise regression and maximum likelihood techniques. The resulting parameter estimates and aerodynamic models are verified using vortex-lattice theory and by analysis of each model's ability to predict aircraft behavior. Comparisons of the stability and control derivative estimates from the basic wing and the four leading-edge modifications are accomplished so that the effects of each modification on aircraft stability and control derivatives can be determined.

Anatomy of the ATLAS diboson anomaly

NASA Astrophysics Data System (ADS)

Allanach, B. C.; Gripaios, Ben; Sutherland, Dave

2015-09-01

We perform a general analysis of new physics interpretations of the recent ATLAS diboson excesses over standard model expectations in LHC Run I collisions. First, we estimate a likelihood function in terms of the truth signal in the W W , W Z , and Z Z channels, finding that the maximum has zero events in the W Z channel, though the likelihood is sufficiently flat to allow other scenarios. Second, we survey the possible effective field theories containing the standard model plus a new resonance that could explain the data, identifying two possibilities, viz. a vector that is either a left- or right-handed S U (2 ) triplet. Finally, we compare these models with other experimental data and determine the parameter regions in which they provide a consistent explanation.

Optimum detection of tones transmitted by a spacecraft

NASA Technical Reports Server (NTRS)

Simon, M. K.; Shihabi, M. M.; Moon, T.

1995-01-01

The performance of a scheme proposed for automated routine monitoring of deep-space missions is presented. The scheme uses four different tones (sinusoids) transmitted from the spacecraft (S/C) to a ground station with the positive identification of each of them used to indicate different states of the S/C. Performance is measured in terms of detection probability versus false alarm probability with detection signal-to-noise ratio as a parameter. The cases where the phase of the received tone is unknown and where both the phase and frequency of the received tone are unknown are treated separately. The decision rules proposed for detecting the tones are formulated from average-likelihood ratio and maximum-likelihood ratio tests, the former resulting in optimum receiver structures.

Population genetics of polymorphism and divergence for diploid selection models with arbitrary dominance.

PubMed

Williamson, Scott; Fledel-Alon, Adi; Bustamante, Carlos D

2004-09-01

We develop a Poisson random-field model of polymorphism and divergence that allows arbitrary dominance relations in a diploid context. This model provides a maximum-likelihood framework for estimating both selection and dominance parameters of new mutations using information on the frequency spectrum of sequence polymorphisms. This is the first DNA sequence-based estimator of the dominance parameter. Our model also leads to a likelihood-ratio test for distinguishing nongenic from genic selection; simulations indicate that this test is quite powerful when a large number of segregating sites are available. We also use simulations to explore the bias in selection parameter estimates caused by unacknowledged dominance relations. When inference is based on the frequency spectrum of polymorphisms, genic selection estimates of the selection parameter can be very strongly biased even for minor deviations from the genic selection model. Surprisingly, however, when inference is based on polymorphism and divergence (McDonald-Kreitman) data, genic selection estimates of the selection parameter are nearly unbiased, even for completely dominant or recessive mutations. Further, we find that weak overdominant selection can increase, rather than decrease, the substitution rate relative to levels of polymorphism. This nonintuitive result has major implications for the interpretation of several popular tests of neutrality.

PSYCHOACOUSTICS: a comprehensive MATLAB toolbox for auditory testing.

PubMed

Soranzo, Alessandro; Grassi, Massimo

2014-01-01

PSYCHOACOUSTICS is a new MATLAB toolbox which implements three classic adaptive procedures for auditory threshold estimation. The first includes those of the Staircase family (method of limits, simple up-down and transformed up-down); the second is the Parameter Estimation by Sequential Testing (PEST); and the third is the Maximum Likelihood Procedure (MLP). The toolbox comes with more than twenty built-in experiments each provided with the recommended (default) parameters. However, if desired, these parameters can be modified through an intuitive and user friendly graphical interface and stored for future use (no programming skills are required). Finally, PSYCHOACOUSTICS is very flexible as it comes with several signal generators and can be easily extended for any experiment.

Model-based estimation for dynamic cardiac studies using ECT.

PubMed

Chiao, P C; Rogers, W L; Clinthorne, N H; Fessler, J A; Hero, A O

1994-01-01

The authors develop a strategy for joint estimation of physiological parameters and myocardial boundaries using ECT (emission computed tomography). They construct an observation model to relate parameters of interest to the projection data and to account for limited ECT system resolution and measurement noise. The authors then use a maximum likelihood (ML) estimator to jointly estimate all the parameters directly from the projection data without reconstruction of intermediate images. They also simulate myocardial perfusion studies based on a simplified heart model to evaluate the performance of the model-based joint ML estimator and compare this performance to the Cramer-Rao lower bound. Finally, the authors discuss model assumptions and potential uses of the joint estimation strategy.

Estimation of the sea surface's two-scale backscatter parameters

NASA Technical Reports Server (NTRS)

Wentz, F. J.

1978-01-01

The relationship between the sea-surface normalized radar cross section and the friction velocity vector is determined using a parametric two-scale scattering model. The model parameters are found from a nonlinear maximum likelihood estimation. The estimation is based on aircraft scatterometer measurements and the sea-surface anemometer measurements collected during the JONSWAP '75 experiment. The estimates of the ten model parameters converge to realistic values that are in good agreement with the available oceanographic data. The rms discrepancy between the model and the cross section measurements is 0.7 db, which is the rms sum of a 0.3 db average measurement error and a 0.6 db modeling error.

PSYCHOACOUSTICS: a comprehensive MATLAB toolbox for auditory testing

PubMed Central

Soranzo, Alessandro; Grassi, Massimo

2014-01-01

PSYCHOACOUSTICS is a new MATLAB toolbox which implements three classic adaptive procedures for auditory threshold estimation. The first includes those of the Staircase family (method of limits, simple up-down and transformed up-down); the second is the Parameter Estimation by Sequential Testing (PEST); and the third is the Maximum Likelihood Procedure (MLP). The toolbox comes with more than twenty built-in experiments each provided with the recommended (default) parameters. However, if desired, these parameters can be modified through an intuitive and user friendly graphical interface and stored for future use (no programming skills are required). Finally, PSYCHOACOUSTICS is very flexible as it comes with several signal generators and can be easily extended for any experiment. PMID:25101013

Estimation of stochastic volatility by using Ornstein-Uhlenbeck type models

NASA Astrophysics Data System (ADS)

Mariani, Maria C.; Bhuiyan, Md Al Masum; Tweneboah, Osei K.

2018-02-01

In this study, we develop a technique for estimating the stochastic volatility (SV) of a financial time series by using Ornstein-Uhlenbeck type models. Using the daily closing prices from developed and emergent stock markets, we conclude that the incorporation of stochastic volatility into the time varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. Furthermore, our estimation algorithm is feasible with large data sets and have good convergence properties.

Modelling the cancer growth process by Stochastic Differential Equations with the effect of Chondroitin Sulfate (CS) as anticancer therapeutics

NASA Astrophysics Data System (ADS)

Syahidatul Ayuni Mazlan, Mazma; Rosli, Norhayati; Jauhari Arief Ichwan, Solachuddin; Suhaity Azmi, Nina

2017-09-01

A stochastic model is introduced to describe the growth of cancer affected by anti-cancer therapeutics of Chondroitin Sulfate (CS). The parameters values of the stochastic model are estimated via maximum likelihood function. The numerical method of Euler-Maruyama will be employed to solve the model numerically. The efficiency of the stochastic model is measured by comparing the simulated result with the experimental data.

A high powered radar interference mitigation technique for communications signal recovery with fpga implementation

DTIC Science & Technology

2017-03-01

2016.7485263.] 14. SUBJECT TERMS parameter estimation; matched- filter detection; QPSK; radar; interference; LSE, cyber, electronic warfare 15. NUMBER OF...signal is routed through a maximum-likelihood detector (MLD), which is a bank of four filters matched to the four symbols of the QPSK constellation... filters matched for each of the QPSK symbols is used to demodulate the signal after cancellation. The matched filters are defined as the complex

Maximum likelihood estimation of the parameters of a bivariate Gaussian-Weibull distribution from machine stress-rated data

Treesearch

Steve P. Verrill; David E. Kretschmann; James W. Evans

2016-01-01

Two important wood properties are stiffness (modulus of elasticity, MOE) and bending strength (modulus of rupture, MOR). In the past, MOE has often been modeled as a Gaussian and MOR as a lognormal or a two- or threeparameter Weibull. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior of MOE and MOR for the purposes of wood...

Closed-loop carrier phase synchronization techniques motivated by likelihood functions

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Trajectory Dispersed Vehicle Process for Space Launch System

NASA Technical Reports Server (NTRS)

Statham, Tamara; Thompson, Seth

2017-01-01

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

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.

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.

Low-complexity approximations to maximum likelihood MPSK modulation classification

NASA Technical Reports Server (NTRS)

Hamkins, Jon

2004-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2011-06-01

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

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.

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.

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.

Maximum likelihood decoding analysis of accumulate-repeat-accumulate codes

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

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

NASA Technical Reports Server (NTRS)

Thadani, S. G.

1977-01-01

The Maximum Likelihood Estimation of Signature Transformation (MLEST) algorithm is used to obtain maximum likelihood estimates (MLE) of affine transformation. The algorithm has been evaluated for three sets of data: simulated (training and recognition segment pairs), consecutive-day (data gathered from Landsat images), and geographical-extension (large-area crop inventory experiment) data sets. For each set, MLEST signature extension runs were made to determine MLE values and the affine-transformed training segment signatures were used to classify the recognition segments. The classification results were used to estimate wheat proportions at 0 and 1% threshold values.

Maximum-likelihood block detection of noncoherent continuous phase modulation

NASA Technical Reports Server (NTRS)

Simon, Marvin K.; Divsalar, Dariush

1993-01-01

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

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…

Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors

USGS Publications Warehouse

Langbein, John O.

2017-01-01

Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1/fα">1/fα1/fα with frequency, f. With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013. doi:10.1007/s00190-012-0605-0) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.

Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors

NASA Astrophysics Data System (ADS)

Langbein, John

2017-08-01

Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1/f^{α } with frequency, f. With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013. doi: 10.1007/s00190-012-0605-0) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.

Parameter recovery, bias and standard errors in the linear ballistic accumulator model.

PubMed

Visser, Ingmar; Poessé, Rens

2017-05-01

The linear ballistic accumulator (LBA) model (Brown & Heathcote, , Cogn. Psychol., 57, 153) is increasingly popular in modelling response times from experimental data. An R package, glba, has been developed to fit the LBA model using maximum likelihood estimation which is validated by means of a parameter recovery study. At sufficient sample sizes parameter recovery is good, whereas at smaller sample sizes there can be large bias in parameters. In a second simulation study, two methods for computing parameter standard errors are compared. The Hessian-based method is found to be adequate and is (much) faster than the alternative bootstrap method. The use of parameter standard errors in model selection and inference is illustrated in an example using data from an implicit learning experiment (Visser et al., , Mem. Cogn., 35, 1502). It is shown that typical implicit learning effects are captured by different parameters of the LBA model. © 2017 The British Psychological Society.

Stochastic models for atomic clocks

NASA Technical Reports Server (NTRS)

Barnes, J. A.; Jones, R. H.; Tryon, P. V.; Allan, D. W.

1983-01-01

For the atomic clocks used in the National Bureau of Standards Time Scales, an adequate model is the superposition of white FM, random walk FM, and linear frequency drift for times longer than about one minute. The model was tested on several clocks using maximum likelihood techniques for parameter estimation and the residuals were acceptably random. Conventional diagnostics indicate that additional model elements contribute no significant improvement to the model even at the expense of the added model complexity.

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

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

Theoretical Analysis of Penalized Maximum-Likelihood Patlak Parametric Image Reconstruction in Dynamic PET for Lesion Detection.

PubMed

Yang, Li; Wang, Guobao; Qi, Jinyi

2016-04-01

Detecting cancerous lesions is a major clinical application of emission tomography. In a previous work, we studied penalized maximum-likelihood (PML) image reconstruction for lesion detection in static PET. Here we extend our theoretical analysis of static PET reconstruction to dynamic PET. We study both the conventional indirect reconstruction and direct reconstruction for Patlak parametric image estimation. In indirect reconstruction, Patlak parametric images are generated by first reconstructing a sequence of dynamic PET images, and then performing Patlak analysis on the time activity curves (TACs) pixel-by-pixel. In direct reconstruction, Patlak parametric images are estimated directly from raw sinogram data by incorporating the Patlak model into the image reconstruction procedure. PML reconstruction is used in both the indirect and direct reconstruction methods. We use a channelized Hotelling observer (CHO) to assess lesion detectability in Patlak parametric images. Simplified expressions for evaluating the lesion detectability have been derived and applied to the selection of the regularization parameter value to maximize detection performance. The proposed method is validated using computer-based Monte Carlo simulations. Good agreements between the theoretical predictions and the Monte Carlo results are observed. Both theoretical predictions and Monte Carlo simulation results show the benefit of the indirect and direct methods under optimized regularization parameters in dynamic PET reconstruction for lesion detection, when compared with the conventional static PET reconstruction.

X-31 aerodynamic characteristics determined from flight data

NASA Technical Reports Server (NTRS)

Kokolios, Alex

1993-01-01

The lateral aerodynamic characteristics of the X-31 were determined at angles of attack ranging from 20 to 45 deg. Estimates of the lateral stability and control parameters were obtained by applying two parameter estimation techniques, linear regression, and the extended Kalman filter to flight test data. An attempt to apply maximum likelihood to extract parameters from the flight data was also made but failed for the reasons presented. An overview of the System Identification process is given. The overview includes a listing of the more important properties of all three estimation techniques that were applied to the data. A comparison is given of results obtained from flight test data and wind tunnel data for four important lateral parameters. Finally, future research to be conducted in this area is discussed.

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.

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

Multilevel modeling of single-case data: A comparison of maximum likelihood and Bayesian estimation.

PubMed

Moeyaert, Mariola; Rindskopf, David; Onghena, Patrick; Van den Noortgate, Wim

2017-12-01

The focus of this article is to describe Bayesian estimation, including construction of prior distributions, and to compare parameter recovery under the Bayesian framework (using weakly informative priors) and the maximum likelihood (ML) framework in the context of multilevel modeling of single-case experimental data. Bayesian estimation results were found similar to ML estimation results in terms of the treatment effect estimates, regardless of the functional form and degree of information included in the prior specification in the Bayesian framework. In terms of the variance component estimates, both the ML and Bayesian estimation procedures result in biased and less precise variance estimates when the number of participants is small (i.e., 3). By increasing the number of participants to 5 or 7, the relative bias is close to 5% and more precise estimates are obtained for all approaches, except for the inverse-Wishart prior using the identity matrix. When a more informative prior was added, more precise estimates for the fixed effects and random effects were obtained, even when only 3 participants were included. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Rating Movies and Rating the Raters Who Rate Them

PubMed Central

Zhou, Hua; Lange, Kenneth

2010-01-01

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

Rating Movies and Rating the Raters Who Rate Them.

PubMed

Zhou, Hua; Lange, Kenneth

2009-11-01

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

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.

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.

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.

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

MEGA5: Molecular Evolutionary Genetics Analysis Using Maximum Likelihood, Evolutionary Distance, and Maximum Parsimony Methods

PubMed Central

Tamura, Koichiro; Peterson, Daniel; Peterson, Nicholas; Stecher, Glen; Nei, Masatoshi; Kumar, Sudhir

2011-01-01

Comparative analysis of molecular sequence data is essential for reconstructing the evolutionary histories of species and inferring the nature and extent of selective forces shaping the evolution of genes and species. Here, we announce the release of Molecular Evolutionary Genetics Analysis version 5 (MEGA5), which is a user-friendly software for mining online databases, building sequence alignments and phylogenetic trees, and using methods of evolutionary bioinformatics in basic biology, biomedicine, and evolution. The newest addition in MEGA5 is a collection of maximum likelihood (ML) analyses for inferring evolutionary trees, selecting best-fit substitution models (nucleotide or amino acid), inferring ancestral states and sequences (along with probabilities), and estimating evolutionary rates site-by-site. In computer simulation analyses, ML tree inference algorithms in MEGA5 compared favorably with other software packages in terms of computational efficiency and the accuracy of the estimates of phylogenetic trees, substitution parameters, and rate variation among sites. The MEGA user interface has now been enhanced to be activity driven to make it easier for the use of both beginners and experienced scientists. This version of MEGA is intended for the Windows platform, and it has been configured for effective use on Mac OS X and Linux desktops. It is available free of charge from http://www.megasoftware.net. PMID:21546353

Distribution of rain height over subtropical region: Durban, South Africa for satellite communication systems

NASA Astrophysics Data System (ADS)

Olurotimi, E. O.; Sokoya, O.; Ojo, J. S.; Owolawi, P. A.

2018-03-01

Rain height is one of the significant parameters for prediction of rain attenuation for Earth-space telecommunication links, especially those operating at frequencies above 10 GHz. This study examines Three-parameter Dagum distribution of the rain height over Durban, South Africa. 5-year data were used to study the monthly, seasonal, and annual variations using the parameters estimated by the maximum likelihood of the distribution. The performance estimation of the distribution was determined using the statistical goodness of fit. Three-parameter Dagum distribution shows an appropriate distribution for the modeling of rain height over Durban with the Root Mean Square Error of 0.26. Also, the shape and scale parameters for the distribution show a wide variation. The probability exceedance of time for 0.01% indicates the high probability of rain attenuation at higher frequencies.

Photon Counting Data Analysis: Application of the Maximum Likelihood and Related Methods for the Determination of Lifetimes in Mixtures of Rose Bengal and Rhodamine B

DOE PAGES

Santra, Kalyan; Smith, Emily A.; Petrich, Jacob W.; ...

2016-12-12

It is often convenient to know the minimum amount of data needed in order to obtain a result of desired accuracy and precision. It is a necessity in the case of subdiffraction-limited microscopies, such as stimulated emission depletion (STED) microscopy, owing to the limited sample volumes and the extreme sensitivity of the samples to photobleaching and photodamage. We present a detailed comparison of probability-based techniques (the maximum likelihood method and methods based on the binomial and the Poisson distributions) with residual minimization-based techniques for retrieving the fluorescence decay parameters for various two-fluorophore mixtures, as a function of the total numbermore » of photon counts, in time-correlated, single-photon counting experiments. The probability-based techniques proved to be the most robust (insensitive to initial values) in retrieving the target parameters and, in fact, performed equivalently to 2-3 significant figures. This is to be expected, as we demonstrate that the three methods are fundamentally related. Furthermore, methods based on the Poisson and binomial distributions have the desirable feature of providing a bin-by-bin analysis of a single fluorescence decay trace, which thus permits statistics to be acquired using only the one trace for not only the mean and median values of the fluorescence decay parameters but also for the associated standard deviations. Lastly, these probability-based methods lend themselves well to the analysis of the sparse data sets that are encountered in subdiffraction-limited microscopies.« less

Inference of R 0 and Transmission Heterogeneity from the Size Distribution of Stuttering Chains

PubMed Central

Blumberg, Seth; Lloyd-Smith, James O.

2013-01-01

For many infectious disease processes such as emerging zoonoses and vaccine-preventable diseases, and infections occur as self-limited stuttering transmission chains. A mechanistic understanding of transmission is essential for characterizing the risk of emerging diseases and monitoring spatio-temporal dynamics. Thus methods for inferring and the degree of heterogeneity in transmission from stuttering chain data have important applications in disease surveillance and management. Previous researchers have used chain size distributions to infer , but estimation of the degree of individual-level variation in infectiousness (as quantified by the dispersion parameter, ) has typically required contact tracing data. Utilizing branching process theory along with a negative binomial offspring distribution, we demonstrate how maximum likelihood estimation can be applied to chain size data to infer both and the dispersion parameter that characterizes heterogeneity. While the maximum likelihood value for is a simple function of the average chain size, the associated confidence intervals are dependent on the inferred degree of transmission heterogeneity. As demonstrated for monkeypox data from the Democratic Republic of Congo, this impacts when a statistically significant change in is detectable. In addition, by allowing for superspreading events, inference of shifts the threshold above which a transmission chain should be considered anomalously large for a given value of (thus reducing the probability of false alarms about pathogen adaptation). Our analysis of monkeypox also clarifies the various ways that imperfect observation can impact inference of transmission parameters, and highlights the need to quantitatively evaluate whether observation is likely to significantly bias results. PMID:23658504

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

ERIC Educational Resources Information Center

Ramsay, J. O.

1980-01-01

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

ATAC Autocuer Modeling Analysis.

DTIC Science & Technology

1981-01-01

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

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

PubMed

Campos-Filho, N; Franco, E L

1989-02-01

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

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

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

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

2016-10-18

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

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.

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

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

NASA Astrophysics Data System (ADS)

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

2013-08-01

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

An empirical Bayes approach for the Poisson life distribution.

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1973-01-01

A smooth empirical Bayes estimator is derived for the intensity parameter (hazard rate) in the Poisson distribution as used in life testing. The reliability function is also estimated either by using the empirical Bayes estimate of the parameter, or by obtaining the expectation of the reliability function. The behavior of the empirical Bayes procedure is studied through Monte Carlo simulation in which estimates of mean-squared errors of the empirical Bayes estimators are compared with those of conventional estimators such as minimum variance unbiased or maximum likelihood. Results indicate a significant reduction in mean-squared error of the empirical Bayes estimators over the conventional variety.

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.

Model-based estimation for dynamic cardiac studies using ECT

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

Chiao, P.C.; Rogers, W.L.; Clinthorne, N.H.

1994-06-01

In this paper, the authors develop a strategy for joint estimation of physiological parameters and myocardial boundaries using ECT (Emission Computed Tomography). The authors construct an observation model to relate parameters of interest to the projection data and to account for limited ECT system resolution and measurement noise. The authors then use a maximum likelihood (ML) estimator to jointly estimate all the parameters directly from the projection data without reconstruction of intermediate images. The authors also simulate myocardial perfusion studies based on a simplified heart model to evaluate the performance of the model-based joint ML estimator and compare this performancemore » to the Cramer-Rao lower bound. Finally, model assumptions and potential uses of the joint estimation strategy are discussed.« less

Efficient estimation of Pareto model: Some modified percentile estimators.

PubMed

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

2018-01-01

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

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

NASA Technical Reports Server (NTRS)

Mccallister, R. D.; Crawford, J. J.

1981-01-01

It is pointed out that the NASA 30/20 GHz program will place in geosynchronous orbit a technically advanced communication satellite which can process time-division multiple access (TDMA) information bursts with a data throughput in excess of 4 GBPS. To guarantee acceptable data quality during periods of signal attenuation it will be necessary to provide a significant forward error correction (FEC) capability. Convolutional decoding (utilizing the maximum-likelihood techniques) was identified as the most attractive FEC strategy. Design trade-offs regarding a maximum-likelihood convolutional decoder (MCD) in a single-chip CMOS implementation are discussed.

PAMLX: a graphical user interface for PAML.

PubMed

Xu, Bo; Yang, Ziheng

2013-12-01

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

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.

Maximum Likelihood Estimation of Nonlinear Structural Equation Models.

ERIC Educational Resources Information Center

Lee, Sik-Yum; Zhu, Hong-Tu

2002-01-01

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

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

ERIC Educational Resources Information Center

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

2003-01-01

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

Maximum likelihood phase-retrieval algorithm: applications.

PubMed

Nahrstedt, D A; Southwell, W H

1984-12-01

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

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

PubMed

Wu, Yufeng

2012-03-01

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

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

PubMed

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

2018-04-19

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

On Muthen's Maximum Likelihood for Two-Level Covariance Structure Models

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Hayashi, Kentaro

2005-01-01

Data in social and behavioral sciences are often hierarchically organized. Special statistical procedures that take into account the dependence of such observations have been developed. Among procedures for 2-level covariance structure analysis, Muthen's maximum likelihood (MUML) has the advantage of easier computation and faster convergence. When…

Maximum Likelihood Estimation of Nonlinear Structural Equation Models with Ignorable Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum; Song, Xin-Yuan; Lee, John C. K.

2003-01-01

The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models…

Mixture Rasch Models with Joint Maximum Likelihood Estimation

ERIC Educational Resources Information Center

Willse, John T.

2011-01-01

This research provides a demonstration of the utility of mixture Rasch models. Specifically, a model capable of estimating a mixture partial credit model using joint maximum likelihood is presented. Like the partial credit model, the mixture partial credit model has the beneficial feature of being appropriate for analysis of assessment data…

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

EPA Science Inventory

Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood e...

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

ERIC Educational Resources Information Center

Mayberry, Paul W.

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

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

ERIC Educational Resources Information Center

Baldwin, Beatrice

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

The Mediation Formula: A Guide to the Assessment of Causal Pathways in Nonlinear Models

DTIC Science & Technology

2011-10-27

through (25), (26) and (27), rather than going through (23) ( van der Laan and Rubin, 2006). 29 values, though disparities in parameters may not...graphs. Epidemiology 22 378–381. Petersen, M., Sinisi, S. and van der Laan, M. (2006). Estimation of direct causal effects. Epidemiology 17 276–284...and J. Halpern, eds.). College Publications, UK, 415–444. van der Laan, M. J. and Rubin, D. (2006). Targeted maximum likelihood learning. The

Estimation in a discrete tail rate family of recapture sampling models

NASA Technical Reports Server (NTRS)

Gupta, Rajan; Lee, Larry D.

1990-01-01

In the context of recapture sampling design for debugging experiments the problem of estimating the error or hitting rate of the faults remaining in a system is considered. Moment estimators are derived for a family of models in which the rate parameters are assumed proportional to the tail probabilities of a discrete distribution on the positive integers. The estimators are shown to be asymptotically normal and fully efficient. Their fixed sample properties are compared, through simulation, with those of the conditional maximum likelihood estimators.

Simulation and study of small numbers of random events

NASA Technical Reports Server (NTRS)

Shelton, R. D.

1986-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1983-01-01

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

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.

Lateral stability and control derivatives extracted from five early flights of the space shuttle Columbia

NASA Technical Reports Server (NTRS)

Schiess, J. R.

1986-01-01

Flight data taken from the first five flights (STS-2, 3, 4, 5 and 9) of the Space Transportation System Shuttle Columbia during entry are analyzed to determine the Shuttle lateral aerodynamic characteristics. Maximum likelihood estimation is applied to data derived from accelerometer and rate gyro measurements and trajectory, meteorological and control surface data to estimate lateral-directional stability and control derivatives. The estimated parameters are compared across the five flights and to preflight predicted values.

Semiparametric Estimation of the Impacts of Longitudinal Interventions on Adolescent Obesity using Targeted Maximum-Likelihood: Accessible Estimation with the ltmle Package

PubMed Central

Decker, Anna L.; Hubbard, Alan; Crespi, Catherine M.; Seto, Edmund Y.W.; Wang, May C.

2015-01-01

While child and adolescent obesity is a serious public health concern, few studies have utilized parameters based on the causal inference literature to examine the potential impacts of early intervention. The purpose of this analysis was to estimate the causal effects of early interventions to improve physical activity and diet during adolescence on body mass index (BMI), a measure of adiposity, using improved techniques. The most widespread statistical method in studies of child and adolescent obesity is multi-variable regression, with the parameter of interest being the coefficient on the variable of interest. This approach does not appropriately adjust for time-dependent confounding, and the modeling assumptions may not always be met. An alternative parameter to estimate is one motivated by the causal inference literature, which can be interpreted as the mean change in the outcome under interventions to set the exposure of interest. The underlying data-generating distribution, upon which the estimator is based, can be estimated via a parametric or semi-parametric approach. Using data from the National Heart, Lung, and Blood Institute Growth and Health Study, a 10-year prospective cohort study of adolescent girls, we estimated the longitudinal impact of physical activity and diet interventions on 10-year BMI z-scores via a parameter motivated by the causal inference literature, using both parametric and semi-parametric estimation approaches. The parameters of interest were estimated with a recently released R package, ltmle, for estimating means based upon general longitudinal treatment regimes. We found that early, sustained intervention on total calories had a greater impact than a physical activity intervention or non-sustained interventions. Multivariable linear regression yielded inflated effect estimates compared to estimates based on targeted maximum-likelihood estimation and data-adaptive super learning. Our analysis demonstrates that sophisticated, optimal semiparametric estimation of longitudinal treatment-specific means via ltmle provides an incredibly powerful, yet easy-to-use tool, removing impediments for putting theory into practice. PMID:26046009

SPOTting model parameters using a ready-made Python package

NASA Astrophysics Data System (ADS)

Houska, Tobias; Kraft, Philipp; Breuer, Lutz

2015-04-01

The selection and parameterization of reliable process descriptions in ecological modelling is driven by several uncertainties. The procedure is highly dependent on various criteria, like the used algorithm, the likelihood function selected and the definition of the prior parameter distributions. A wide variety of tools have been developed in the past decades to optimize parameters. Some of the tools are closed source. Due to this, the choice for a specific parameter estimation method is sometimes more dependent on its availability than the performance. A toolbox with a large set of methods can support users in deciding about the most suitable method. Further, it enables to test and compare different methods. We developed the SPOT (Statistical Parameter Optimization Tool), an open source python package containing a comprehensive set of modules, to analyze and optimize parameters of (environmental) models. SPOT comes along with a selected set of algorithms for parameter optimization and uncertainty analyses (Monte Carlo, MC; Latin Hypercube Sampling, LHS; Maximum Likelihood, MLE; Markov Chain Monte Carlo, MCMC; Scuffled Complex Evolution, SCE-UA; Differential Evolution Markov Chain, DE-MCZ), together with several likelihood functions (Bias, (log-) Nash-Sutcliff model efficiency, Correlation Coefficient, Coefficient of Determination, Covariance, (Decomposed-, Relative-, Root-) Mean Squared Error, Mean Absolute Error, Agreement Index) and prior distributions (Binomial, Chi-Square, Dirichlet, Exponential, Laplace, (log-, multivariate-) Normal, Pareto, Poisson, Cauchy, Uniform, Weibull) to sample from. The model-independent structure makes it suitable to analyze a wide range of applications. We apply all algorithms of the SPOT package in three different case studies. Firstly, we investigate the response of the Rosenbrock function, where the MLE algorithm shows its strengths. Secondly, we study the Griewank function, which has a challenging response surface for optimization methods. Here we see simple algorithms like the MCMC struggling to find the global optimum of the function, while algorithms like SCE-UA and DE-MCZ show their strengths. Thirdly, we apply an uncertainty analysis of a one-dimensional physically based hydrological model build with the Catchment Modelling Framework (CMF). The model is driven by meteorological and groundwater data from a Free Air Carbon Enrichment (FACE) experiment in Linden (Hesse, Germany). Simulation results are evaluated with measured soil moisture data. We search for optimal parameter sets of the van Genuchten-Mualem function and find different equally optimal solutions with some of the algorithms. The case studies reveal that the implemented SPOT methods work sufficiently well. They further show the benefit of having one tool at hand that includes a number of parameter search methods, likelihood functions and a priori parameter distributions within one platform independent package.

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.

Maximum-likelihood soft-decision decoding of block codes using the A* algorithm

NASA Technical Reports Server (NTRS)

Ekroot, L.; Dolinar, S.

1994-01-01

The A* algorithm finds the path in a finite depth binary tree that optimizes a function. Here, it is applied to maximum-likelihood soft-decision decoding of block codes where the function optimized over the codewords is the likelihood function of the received sequence given each codeword. The algorithm considers codewords one bit at a time, making use of the most reliable received symbols first and pursuing only the partially expanded codewords that might be maximally likely. A version of the A* algorithm for maximum-likelihood decoding of block codes has been implemented for block codes up to 64 bits in length. The efficiency of this algorithm makes simulations of codes up to length 64 feasible. This article details the implementation currently in use, compares the decoding complexity with that of exhaustive search and Viterbi decoding algorithms, and presents performance curves obtained with this implementation of the A* algorithm for several codes.

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

NASA Astrophysics Data System (ADS)

Rutkowska, Agnieszka; Kohnová, Silvia; Banasik, Kazimierz

2018-04-01

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

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

ERIC Educational Resources Information Center

Klein, Andreas G.; Muthen, Bengt O.

2007-01-01

In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly…

Maximum Likelihood Analysis of Nonlinear Structural Equation Models with Dichotomous Variables

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lee, Sik-Yum

2005-01-01

In this article, a maximum likelihood approach is developed to analyze structural equation models with dichotomous variables that are common in behavioral, psychological and social research. To assess nonlinear causal effects among the latent variables, the structural equation in the model is defined by a nonlinear function. The basic idea of the…

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

DTIC Science & Technology

1990-12-31

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

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

ERIC Educational Resources Information Center

Savalei, Victoria

2010-01-01

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

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

ERIC Educational Resources Information Center

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

2006-01-01

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

Bias and Efficiency in Structural Equation Modeling: Maximum Likelihood versus Robust Methods

ERIC Educational Resources Information Center

Zhong, Xiaoling; Yuan, Ke-Hai

2011-01-01

In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…

Five Methods for Estimating Angoff Cut Scores with IRT

ERIC Educational Resources Information Center

Wyse, Adam E.

2017-01-01

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

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

ERIC Educational Resources Information Center

Cai, Li

2010-01-01

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

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

Treesearch

John Hogland; Nedret Billor; Nathaniel Anderson

2013-01-01

Discriminant analysis, referred to as maximum likelihood classification within popular remote sensing software packages, is a common supervised technique used by analysts. Polytomous logistic regression (PLR), also referred to as multinomial logistic regression, is an alternative classification approach that is less restrictive, more flexible, and easy to interpret. To...

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

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.

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.

New robust statistical procedures for the polytomous logistic regression models.

PubMed

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

2018-05-17

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

Markov modulated Poisson process models incorporating covariates for rainfall intensity.

PubMed

Thayakaran, R; Ramesh, N I

2013-01-01

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

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

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

Kane, V.E.

1979-10-01

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

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.

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

PubMed

Lepage, Kyle Q; MacDonald, Christopher J

2015-06-01

A recent report estimates that the number of simultaneously recorded neurons is growing exponentially. A commonly employed statistical paradigm using discrete-time point process models of neural activity involves the computation of a maximum-likelihood estimate. The time to computate this estimate, per neuron, is proportional to the number of bins in a finely spaced discretization of time. By using continuous-time models of neural activity and the optimally efficient Gaussian quadrature, memory requirements and computation times are dramatically decreased in the commonly encountered situation where the number of parameters p is much less than the number of time-bins n. In this regime, with q equal to the quadrature order, memory requirements are decreased from O(np) to O(qp), and the number of floating-point operations are decreased from O(np(2)) to O(qp(2)). Accuracy of the proposed estimates is assessed based upon physiological consideration, error bounds, and mathematical results describing the relation between numerical integration error and numerical error affecting both parameter estimates and the observed Fisher information. A check is provided which is used to adapt the order of numerical integration. The procedure is verified in simulation and for hippocampal recordings. It is found that in 95 % of hippocampal recordings a q of 60 yields numerical error negligible with respect to parameter estimate standard error. Statistical inference using the proposed methodology is a fast and convenient alternative to statistical inference performed using a discrete-time point process model of neural activity. It enables the employment of the statistical methodology available with discrete-time inference, but is faster, uses less memory, and avoids any error due to discretization.

Parameter expansion for estimation of reduced rank covariance matrices (Open Access publication)

PubMed Central

Meyer, Karin

2008-01-01

Parameter expanded and standard expectation maximisation algorithms are described for reduced rank estimation of covariance matrices by restricted maximum likelihood, fitting the leading principal components only. Convergence behaviour of these algorithms is examined for several examples and contrasted to that of the average information algorithm, and implications for practical analyses are discussed. It is shown that expectation maximisation type algorithms are readily adapted to reduced rank estimation and converge reliably. However, as is well known for the full rank case, the convergence is linear and thus slow. Hence, these algorithms are most useful in combination with the quadratically convergent average information algorithm, in particular in the initial stages of an iterative solution scheme. PMID:18096112

Flight data processing with the F-8 adaptive algorithm

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

In search of best fitted composite model to the ALAE data set with transformed Gamma and inversed transformed Gamma families

NASA Astrophysics Data System (ADS)

Maghsoudi, Mastoureh; Bakar, Shaiful Anuar Abu

2017-05-01

In this paper, a recent novel approach is applied to estimate the threshold parameter of a composite model. Several composite models from Transformed Gamma and Inverse Transformed Gamma families are constructed based on this approach and their parameters are estimated by the maximum likelihood method. These composite models are fitted to allocated loss adjustment expenses (ALAE). In comparison to all composite models studied, the composite Weibull-Inverse Transformed Gamma model is proved to be a competitor candidate as it best fit the loss data. The final part considers the backtesting method to verify the validation of VaR and CTE risk measures.

Parameter Estimation for a Model of Space-Time Rainfall

NASA Astrophysics Data System (ADS)

Smith, James A.; Karr, Alan F.

1985-08-01

In this paper, parameter estimation procedures, based on data from a network of rainfall gages, are developed for a class of space-time rainfall models. The models, which are designed to represent the spatial distribution of daily rainfall, have three components, one that governs the temporal occurrence of storms, a second that distributes rain cells spatially for a given storm, and a third that determines the rainfall pattern within a rain cell. Maximum likelihood and method of moments procedures are developed. We illustrate that limitations on model structure are imposed by restricting data sources to rain gage networks. The estimation procedures are applied to a 240-mi2 (621 km2) catchment in the Potomac River basin.

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

PubMed

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

2012-09-01

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

Dynamically heterogenous partitions and phylogenetic inference: an evaluation of analytical strategies with cytochrome b and ND6 gene sequences in cranes.

PubMed

Krajewski, C; Fain, M G; Buckley, L; King, D G

1999-11-01

ki ctes over whether molecular sequence data should be partitioned for phylogenetic analysis often confound two types of heterogeneity among partitions. We distinguish historical heterogeneity (i.e., different partitions have different evolutionary relationships) from dynamic heterogeneity (i.e., different partitions show different patterns of sequence evolution) and explore the impact of the latter on phylogenetic accuracy and precision with a two-gene, mitochondrial data set for cranes. The well-established phylogeny of cranes allows us to contrast tree-based estimates of relevant parameter values with estimates based on pairwise comparisons and to ascertain the effects of incorporating different amounts of process information into phylogenetic estimates. We show that codon positions in the cytochrome b and NADH dehydrogenase subunit 6 genes are dynamically heterogenous under both Poisson and invariable-sites + gamma-rates versions of the F84 model and that heterogeneity includes variation in base composition and transition bias as well as substitution rate. Estimates of transition-bias and relative-rate parameters from pairwise sequence comparisons were comparable to those obtained as tree-based maximum likelihood estimates. Neither rate-category nor mixed-model partitioning strategies resulted in a loss of phylogenetic precision relative to unpartitioned analyses. We suggest that weighted-average distances provide a computationally feasible alternative to direct maximum likelihood estimates of phylogeny for mixed-model analyses of large, dynamically heterogenous data sets. Copyright 1999 Academic Press.

Reconstruction of far-field tsunami amplitude distributions from earthquake sources

USGS Publications Warehouse

Geist, Eric L.; Parsons, Thomas E.

2016-01-01

The probability distribution of far-field tsunami amplitudes is explained in relation to the distribution of seismic moment at subduction zones. Tsunami amplitude distributions at tide gauge stations follow a similar functional form, well described by a tapered Pareto distribution that is parameterized by a power-law exponent and a corner amplitude. Distribution parameters are first established for eight tide gauge stations in the Pacific, using maximum likelihood estimation. A procedure is then developed to reconstruct the tsunami amplitude distribution that consists of four steps: (1) define the distribution of seismic moment at subduction zones; (2) establish a source-station scaling relation from regression analysis; (3) transform the seismic moment distribution to a tsunami amplitude distribution for each subduction zone; and (4) mix the transformed distribution for all subduction zones to an aggregate tsunami amplitude distribution specific to the tide gauge station. The tsunami amplitude distribution is adequately reconstructed for four tide gauge stations using globally constant seismic moment distribution parameters established in previous studies. In comparisons to empirical tsunami amplitude distributions from maximum likelihood estimation, the reconstructed distributions consistently exhibit higher corner amplitude values, implying that in most cases, the empirical catalogs are too short to include the largest amplitudes. Because the reconstructed distribution is based on a catalog of earthquakes that is much larger than the tsunami catalog, it is less susceptible to the effects of record-breaking events and more indicative of the actual distribution of tsunami amplitudes.

Learning maximum entropy models from finite-size data sets: A fast data-driven algorithm allows sampling from the posterior distribution.

PubMed

Ferrari, Ulisse

2016-08-01

Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case of large but finite datasets. We first show how the steepest descent dynamics is not optimal as it is slowed down by the inhomogeneous curvature of the model parameters' space. We then provide a way for rectifying this space which relies only on dataset properties and does not require large computational efforts. We conclude by solving the long-time limit of the parameters' dynamics including the randomness generated by the systematic use of Gibbs sampling. In this stochastic framework, rather than converging to a fixed point, the dynamics reaches a stationary distribution, which for the rectified dynamics reproduces the posterior distribution of the parameters. We sum up all these insights in a "rectified" data-driven algorithm that is fast and by sampling from the parameters' posterior avoids both under- and overfitting along all the directions of the parameters' space. Through the learning of pairwise Ising models from the recording of a large population of retina neurons, we show how our algorithm outperforms the steepest descent method.

Maximum Likelihood Analysis of a Two-Level Nonlinear Structural Equation Model with Fixed Covariates

ERIC Educational Resources Information Center

Lee, Sik-Yum; Song, Xin-Yuan

2005-01-01

In this article, a maximum likelihood (ML) approach for analyzing a rather general two-level structural equation model is developed for hierarchically structured data that are very common in educational and/or behavioral research. The proposed two-level model can accommodate nonlinear causal relations among latent variables as well as effects…

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

PubMed

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

2015-02-01

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

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

ERIC Educational Resources Information Center

Han, Kyung T.; Guo, Fanmin

2014-01-01

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

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…

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…

Maximum Likelihood Compton Polarimetry with the Compton Spectrometer and Imager

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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.

Single particle maximum likelihood reconstruction from superresolution microscopy images

PubMed Central

Verdier, Timothée; Gunzenhauser, Julia; Manley, Suliana; Castelnovo, Martin

2017-01-01

Point localization superresolution microscopy enables fluorescently tagged molecules to be imaged beyond the optical diffraction limit, reaching single molecule localization precisions down to a few nanometers. For small objects whose sizes are few times this precision, localization uncertainty prevents the straightforward extraction of a structural model from the reconstructed images. We demonstrate in the present work that this limitation can be overcome at the single particle level, requiring no particle averaging, by using a maximum likelihood reconstruction (MLR) method perfectly suited to the stochastic nature of such superresolution imaging. We validate this method by extracting structural information from both simulated and experimental PALM data of immature virus-like particles of the Human Immunodeficiency Virus (HIV-1). MLR allows us to measure the radii of individual viruses with precision of a few nanometers and confirms the incomplete closure of the viral protein lattice. The quantitative results of our analysis are consistent with previous cryoelectron microscopy characterizations. Our study establishes the framework for a method that can be broadly applied to PALM data to determine the structural parameters for an existing structural model, and is particularly well suited to heterogeneous features due to its single particle implementation. PMID:28253349

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.

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.

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.

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

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

A random walk rule for phase I clinical trials.

PubMed

Durham, S D; Flournoy, N; Rosenberger, W F

1997-06-01

We describe a family of random walk rules for the sequential allocation of dose levels to patients in a dose-response study, or phase I clinical trial. Patients are sequentially assigned the next higher, same, or next lower dose level according to some probability distribution, which may be determined by ethical considerations as well as the patient's response. It is shown that one can choose these probabilities in order to center dose level assignments unimodally around any target quantile of interest. Estimation of the quantile is discussed; the maximum likelihood estimator and its variance are derived under a two-parameter logistic distribution, and the maximum likelihood estimator is compared with other nonparametric estimators. Random walk rules have clear advantages: they are simple to implement, and finite and asymptotic distribution theory is completely worked out. For a specific random walk rule, we compute finite and asymptotic properties and give examples of its use in planning studies. Having the finite distribution theory available and tractable obviates the need for elaborate simulation studies to analyze the properties of the design. The small sample properties of our rule, as determined by exact theory, compare favorably to those of the continual reassessment method, determined by simulation.

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

NASA Technical Reports Server (NTRS)

Pierson, Willard J., Jr.

1989-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2011-09-01

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

Aerodynamic parameter estimation via Fourier modulating function techniques

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1995-01-01

Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.

Estimating Arrhenius parameters using temperature programmed molecular dynamics.

PubMed

Imandi, Venkataramana; Chatterjee, Abhijit

2016-07-21

Kinetic rates at different temperatures and the associated Arrhenius parameters, whenever Arrhenius law is obeyed, are efficiently estimated by applying maximum likelihood analysis to waiting times collected using the temperature programmed molecular dynamics method. When transitions involving many activated pathways are available in the dataset, their rates may be calculated using the same collection of waiting times. Arrhenius behaviour is ascertained by comparing rates at the sampled temperatures with ones from the Arrhenius expression. Three prototype systems with corrugated energy landscapes, namely, solvated alanine dipeptide, diffusion at the metal-solvent interphase, and lithium diffusion in silicon, are studied to highlight various aspects of the method. The method becomes particularly appealing when the Arrhenius parameters can be used to find rates at low temperatures where transitions are rare. Systematic coarse-graining of states can further extend the time scales accessible to the method. Good estimates for the rate parameters are obtained with 500-1000 waiting times.

Maximum profile likelihood estimation of differential equation parameters through model based smoothing state estimates.

PubMed

Campbell, D A; Chkrebtii, O

2013-12-01

Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories. Crown Copyright © 2013. Published by Elsevier Inc. All rights reserved.

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

NASA Technical Reports Server (NTRS)

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

1976-01-01

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

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

ERIC Educational Resources Information Center

Khattab, Ali-Maher; And Others

1982-01-01

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

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.

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

Identification of internal properties of fibers and micro-swimmers

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

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.

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.

Study of radar pulse compression for high resolution satellite altimetry

NASA Technical Reports Server (NTRS)

Dooley, R. P.; Nathanson, F. E.; Brooks, L. W.

1974-01-01

Pulse compression techniques are studied which are applicable to a satellite altimeter having a topographic resolution of + 10 cm. A systematic design procedure is used to determine the system parameters. The performance of an optimum, maximum likelihood processor is analysed, which provides the basis for modifying the standard split-gate tracker to achieve improved performance. Bandwidth considerations lead to the recommendation of a full deramp STRETCH pulse compression technique followed by an analog filter bank to separate range returns. The implementation of the recommended technique is examined.

A computer program for estimation from incomplete multinomial data

NASA Technical Reports Server (NTRS)

Credeur, K. R.

1978-01-01

Coding is given for maximum likelihood and Bayesian estimation of the vector p of multinomial cell probabilities from incomplete data. Also included is coding to calculate and approximate elements of the posterior mean and covariance matrices. The program is written in FORTRAN 4 language for the Control Data CYBER 170 series digital computer system with network operating system (NOS) 1.1. The program requires approximately 44000 octal locations of core storage. A typical case requires from 72 seconds to 92 seconds on CYBER 175 depending on the value of the prior parameter.

Maximum Likelihood Compton Polarimetry with the Compton Spectrometer and Imager

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

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

2017-10-20

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

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.

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

Petiteau, Antoine; Shang Yu; Babak, Stanislav

Coalescing massive black hole binaries are the strongest and probably the most important gravitational wave sources in the LISA band. The spin and orbital precessions bring complexity in the waveform and make the likelihood surface richer in structure as compared to the nonspinning case. We introduce an extended multimodal genetic algorithm which utilizes the properties of the signal and the detector response function to analyze the data from the third round of mock LISA data challenge (MLDC3.2). The performance of this method is comparable, if not better, to already existing algorithms. We have found all five sources present in MLDC3.2more » and recovered the coalescence time, chirp mass, mass ratio, and sky location with reasonable accuracy. As for the orbital angular momentum and two spins of the black holes, we have found a large number of widely separated modes in the parameter space with similar maximum likelihood values.« less

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

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

PubMed

Stringham, H M; Boehnke, M

2001-07-01

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

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

ERIC Educational Resources Information Center

Paek, Insu; Wilson, Mark

2011-01-01

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

Multisite EPR oximetry from multiple quadrature harmonics.

PubMed

Ahmad, R; Som, S; Johnson, D H; Zweier, J L; Kuppusamy, P; Potter, L C

2012-01-01

Multisite continuous wave (CW) electron paramagnetic resonance (EPR) oximetry using multiple quadrature field modulation harmonics is presented. First, a recently developed digital receiver is used to extract multiple harmonics of field modulated projection data. Second, a forward model is presented that relates the projection data to unknown parameters, including linewidth at each site. Third, a maximum likelihood estimator of unknown parameters is reported using an iterative algorithm capable of jointly processing multiple quadrature harmonics. The data modeling and processing are applicable for parametric lineshapes under nonsaturating conditions. Joint processing of multiple harmonics leads to 2-3-fold acceleration of EPR data acquisition. For demonstration in two spatial dimensions, both simulations and phantom studies on an L-band system are reported. Copyright © 2011 Elsevier Inc. All rights reserved.

Estimating Phenomenological Parameters in Multi-Assets Markets

NASA Astrophysics Data System (ADS)

Raffaelli, Giacomo; Marsili, Matteo

Financial correlations exhibit a non-trivial dynamic behavior. This is reproduced by a simple phenomenological model of a multi-asset financial market, which takes into account the impact of portfolio investment on price dynamics. This captures the fact that correlations determine the optimal portfolio but are affected by investment based on it. Such a feedback on correlations gives rise to an instability when the volume of investment exceeds a critical value. Close to the critical point the model exhibits dynamical correlations very similar to those observed in real markets. We discuss how the model's parameter can be estimated in real market data with a maximum likelihood principle. This confirms the main conclusion that real markets operate close to a dynamically unstable point.

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

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

NASA Astrophysics Data System (ADS)

Abu-Zinadah, Hanaa H.

2017-08-01

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

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.

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.

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

PubMed

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

2012-02-01

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

Bayesian image reconstruction for improving detection performance of muon tomography.

PubMed

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

2009-05-01

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

Robust inference in the negative binomial regression model with an application to falls data.

PubMed

Aeberhard, William H; Cantoni, Eva; Heritier, Stephane

2014-12-01

A popular way to model overdispersed count data, such as the number of falls reported during intervention studies, is by means of the negative binomial (NB) distribution. Classical estimating methods are well-known to be sensitive to model misspecifications, taking the form of patients falling much more than expected in such intervention studies where the NB regression model is used. We extend in this article two approaches for building robust M-estimators of the regression parameters in the class of generalized linear models to the NB distribution. The first approach achieves robustness in the response by applying a bounded function on the Pearson residuals arising in the maximum likelihood estimating equations, while the second approach achieves robustness by bounding the unscaled deviance components. For both approaches, we explore different choices for the bounding functions. Through a unified notation, we show how close these approaches may actually be as long as the bounding functions are chosen and tuned appropriately, and provide the asymptotic distributions of the resulting estimators. Moreover, we introduce a robust weighted maximum likelihood estimator for the overdispersion parameter, specific to the NB distribution. Simulations under various settings show that redescending bounding functions yield estimates with smaller biases under contamination while keeping high efficiency at the assumed model, and this for both approaches. We present an application to a recent randomized controlled trial measuring the effectiveness of an exercise program at reducing the number of falls among people suffering from Parkinsons disease to illustrate the diagnostic use of such robust procedures and their need for reliable inference. © 2014, The International Biometric Society.

Analyzing small data sets using Bayesian estimation: the case of posttraumatic stress symptoms following mechanical ventilation in burn survivors

PubMed Central

van de Schoot, Rens; Broere, Joris J.; Perryck, Koen H.; Zondervan-Zwijnenburg, Mariëlle; van Loey, Nancy E.

2015-01-01

Background The analysis of small data sets in longitudinal studies can lead to power issues and often suffers from biased parameter values. These issues can be solved by using Bayesian estimation in conjunction with informative prior distributions. By means of a simulation study and an empirical example concerning posttraumatic stress symptoms (PTSS) following mechanical ventilation in burn survivors, we demonstrate the advantages and potential pitfalls of using Bayesian estimation. Methods First, we show how to specify prior distributions and by means of a sensitivity analysis we demonstrate how to check the exact influence of the prior (mis-) specification. Thereafter, we show by means of a simulation the situations in which the Bayesian approach outperforms the default, maximum likelihood and approach. Finally, we re-analyze empirical data on burn survivors which provided preliminary evidence of an aversive influence of a period of mechanical ventilation on the course of PTSS following burns. Results Not suprisingly, maximum likelihood estimation showed insufficient coverage as well as power with very small samples. Only when Bayesian analysis, in conjunction with informative priors, was used power increased to acceptable levels. As expected, we showed that the smaller the sample size the more the results rely on the prior specification. Conclusion We show that two issues often encountered during analysis of small samples, power and biased parameters, can be solved by including prior information into Bayesian analysis. We argue that the use of informative priors should always be reported together with a sensitivity analysis. PMID:25765534

Analyzing small data sets using Bayesian estimation: the case of posttraumatic stress symptoms following mechanical ventilation in burn survivors.

PubMed

van de Schoot, Rens; Broere, Joris J; Perryck, Koen H; Zondervan-Zwijnenburg, Mariëlle; van Loey, Nancy E

2015-01-01

Background : The analysis of small data sets in longitudinal studies can lead to power issues and often suffers from biased parameter values. These issues can be solved by using Bayesian estimation in conjunction with informative prior distributions. By means of a simulation study and an empirical example concerning posttraumatic stress symptoms (PTSS) following mechanical ventilation in burn survivors, we demonstrate the advantages and potential pitfalls of using Bayesian estimation. Methods : First, we show how to specify prior distributions and by means of a sensitivity analysis we demonstrate how to check the exact influence of the prior (mis-) specification. Thereafter, we show by means of a simulation the situations in which the Bayesian approach outperforms the default, maximum likelihood and approach. Finally, we re-analyze empirical data on burn survivors which provided preliminary evidence of an aversive influence of a period of mechanical ventilation on the course of PTSS following burns. Results : Not suprisingly, maximum likelihood estimation showed insufficient coverage as well as power with very small samples. Only when Bayesian analysis, in conjunction with informative priors, was used power increased to acceptable levels. As expected, we showed that the smaller the sample size the more the results rely on the prior specification. Conclusion : We show that two issues often encountered during analysis of small samples, power and biased parameters, can be solved by including prior information into Bayesian analysis. We argue that the use of informative priors should always be reported together with a sensitivity analysis.

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

PubMed

Lacerda, Miguel; Seoighe, Cathal

2014-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

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.

Linear functional minimization for inverse modeling

DOE PAGES

Barajas-Solano, David A.; Wohlberg, Brendt Egon; Vesselinov, Velimir Valentinov; ...

2015-06-01

In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulicmore » head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.« less

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

NASA Technical Reports Server (NTRS)

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

1981-01-01

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

Computational Software to Fit Seismic Data Using Epidemic-Type Aftershock Sequence Models and Modeling Performance Comparisons

NASA Astrophysics Data System (ADS)

Chu, A.

2016-12-01

Modern earthquake catalogs are often analyzed using spatial-temporal point process models such as the epidemic-type aftershock sequence (ETAS) models of Ogata (1998). My work implements three of the homogeneous ETAS models described in Ogata (1998). With a model's log-likelihood function, my software finds the Maximum-Likelihood Estimates (MLEs) of the model's parameters to estimate the homogeneous background rate and the temporal and spatial parameters that govern triggering effects. EM-algorithm is employed for its advantages of stability and robustness (Veen and Schoenberg, 2008). My work also presents comparisons among the three models in robustness, convergence speed, and implementations from theory to computing practice. Up-to-date regional seismic data of seismic active areas such as Southern California and Japan are used to demonstrate the comparisons. Data analysis has been done using computer languages Java and R. Java has the advantages of being strong-typed and easiness of controlling memory resources, while R has the advantages of having numerous available functions in statistical computing. Comparisons are also made between the two programming languages in convergence and stability, computational speed, and easiness of implementation. Issues that may affect convergence such as spatial shapes are discussed.

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

ERIC Educational Resources Information Center

Beauducel, Andre; Herzberg, Philipp Yorck

2006-01-01

This simulation study compared maximum likelihood (ML) estimation with weighted least squares means and variance adjusted (WLSMV) estimation. The study was based on confirmatory factor analyses with 1, 2, 4, and 8 factors, based on 250, 500, 750, and 1,000 cases, and on 5, 10, 20, and 40 variables with 2, 3, 4, 5, and 6 categories. There was no…

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

PubMed

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

2013-12-15

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

Fast registration and reconstruction of aliased low-resolution frames by use of a modified maximum-likelihood approach.

PubMed

Alam, M S; Bognar, J G; Cain, S; Yasuda, B J

1998-03-10

During the process of microscanning a controlled vibrating mirror typically is used to produce subpixel shifts in a sequence of forward-looking infrared (FLIR) images. If the FLIR is mounted on a moving platform, such as an aircraft, uncontrolled random vibrations associated with the platform can be used to generate the shifts. Iterative techniques such as the expectation-maximization (EM) approach by means of the maximum-likelihood algorithm can be used to generate high-resolution images from multiple randomly shifted aliased frames. In the maximum-likelihood approach the data are considered to be Poisson random variables and an EM algorithm is developed that iteratively estimates an unaliased image that is compensated for known imager-system blur while it simultaneously estimates the translational shifts. Although this algorithm yields high-resolution images from a sequence of randomly shifted frames, it requires significant computation time and cannot be implemented for real-time applications that use the currently available high-performance processors. The new image shifts are iteratively calculated by evaluation of a cost function that compares the shifted and interlaced data frames with the corresponding values in the algorithm's latest estimate of the high-resolution image. We present a registration algorithm that estimates the shifts in one step. The shift parameters provided by the new algorithm are accurate enough to eliminate the need for iterative recalculation of translational shifts. Using this shift information, we apply a simplified version of the EM algorithm to estimate a high-resolution image from a given sequence of video frames. The proposed modified EM algorithm has been found to reduce significantly the computational burden when compared with the original EM algorithm, thus making it more attractive for practical implementation. Both simulation and experimental results are presented to verify the effectiveness of the proposed technique.

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

PubMed Central

Huang, Chiung-Yu; Qin, Jing

2013-01-01

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

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

PubMed Central

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

2016-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

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

PubMed

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

2010-03-01

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

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.

Bayesian Monte Carlo and Maximum Likelihood Approach for ...

EPA Pesticide Factsheets

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Halo-independent determination of the unmodulated WIMP signal in DAMA: the isotropic case

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

Gondolo, Paolo; Scopel, Stefano, E-mail: paolo.gondolo@utah.edu, E-mail: scopel@sogang.ac.kr

2017-09-01

We present a halo-independent determination of the unmodulated signal corresponding to the DAMA modulation if interpreted as due to dark matter weakly interacting massive particles (WIMPs). First we show how a modulated signal gives information on the WIMP velocity distribution function in the Galactic rest frame from which the unmodulated signal descends. Then we describe a mathematically-sound profile likelihood analysis in which the likelihood is profiled over a continuum of nuisance parameters (namely, the WIMP velocity distribution). As a first application of the method, which is very general and valid for any class of velocity distributions, we restrict the analysismore » to velocity distributions that are isotropic in the Galactic frame. In this way we obtain halo-independent maximum-likelihood estimates and confidence intervals for the DAMA unmodulated signal. We find that the estimated unmodulated signal is in line with expectations for a WIMP-induced modulation and is compatible with the DAMA background+signal rate. Specifically, for the isotropic case we find that the modulated amplitude ranges between a few percent and about 25% of the unmodulated amplitude, depending on the WIMP mass.« less

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

PubMed

Koyama, Shinsuke

2015-07-01

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

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

PubMed

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

2017-04-01

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

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

Blaut, Arkadiusz; Babak, Stanislav; Krolak, Andrzej

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

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

NASA Technical Reports Server (NTRS)

Van Buren, Dave

1986-01-01

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

ARMA models for earthquake ground motions. Seismic safety margins research program

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

Chang, M. K.; Kwiatkowski, J. W.; Nau, R. F.

1981-02-01

Four major California earthquake records were analyzed by use of a class of discrete linear time-domain processes commonly referred to as ARMA (Autoregressive/Moving-Average) models. It was possible to analyze these different earthquakes, identify the order of the appropriate ARMA model(s), estimate parameters, and test the residuals generated by these models. It was also possible to show the connections, similarities, and differences between the traditional continuous models (with parameter estimates based on spectral analyses) and the discrete models with parameters estimated by various maximum-likelihood techniques applied to digitized acceleration data in the time domain. The methodology proposed is suitable for simulatingmore » earthquake ground motions in the time domain, and appears to be easily adapted to serve as inputs for nonlinear discrete time models of structural motions. 60 references, 19 figures, 9 tables.« less

XENON100 exclusion limit without considering Leff as a nuisance parameter

NASA Astrophysics Data System (ADS)

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

2012-07-01

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

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

NASA Technical Reports Server (NTRS)

Chittineni, C. B.

1979-01-01

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

Bayesian structural equation modeling in sport and exercise psychology.

PubMed

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

2015-08-01

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

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

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

Beer, M.

1980-12-01

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

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

PubMed Central

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

2014-01-01

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

Predicting critical transitions in dynamical systems from time series using nonstationary probability density modeling.

PubMed

Kwasniok, Frank

2013-11-01

A time series analysis method for predicting the probability density of a dynamical system is proposed. A nonstationary parametric model of the probability density is estimated from data within a maximum likelihood framework and then extrapolated to forecast the future probability density and explore the system for critical transitions or tipping points. A full systematic account of parameter uncertainty is taken. The technique is generic, independent of the underlying dynamics of the system. The method is verified on simulated data and then applied to prediction of Arctic sea-ice extent.

The minimum distance approach to classification

NASA Technical Reports Server (NTRS)

Wacker, A. G.; Landgrebe, D. A.

1971-01-01

The work to advance the state-of-the-art of miminum distance classification is reportd. This is accomplished through a combination of theoretical and comprehensive experimental investigations based on multispectral scanner data. A survey of the literature for suitable distance measures was conducted and the results of this survey are presented. It is shown that minimum distance classification, using density estimators and Kullback-Leibler numbers as the distance measure, is equivalent to a form of maximum likelihood sample classification. It is also shown that for the parametric case, minimum distance classification is equivalent to nearest neighbor classification in the parameter space.

Maximum-Likelihood Parameter Estimation of a Generalized Gumbel Distribution

DTIC Science & Technology

1989-03-24

Calculate the roots of g(.) and ht .) IERR = 0 CALL R0UTG( XROOT ,YROUT,IEHRJ IF (LERR.NE.0) GOTO 900 Calculate the value of b TEMP1 = OLOG( YROOT) - PSI(YRGOT...TEMP2 = XBAR - XROOT OVAL = TEMP2 / TEMP1 RLAM = XROOT - DSHIF1 ELSE C Scale 8VAL to match HOOTH routine IF (XC(NCL).GT.70.D0) THEN ALPHA - XC NCL...ICNT) 10 CONTINUE RETURN END c C *ROOTG( XROOT ,YROOT,IERR) C 31 Aug 88 C *Res. Dir., C E Hall, Jr. SUBROUTINE ROOTG( XRDOT , ROOT ,IERRJ IMPLICIT DOUBLE

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.

Driving style recognition method using braking characteristics based on hidden Markov model

PubMed Central

Wu, Chaozhong; Lyu, Nengchao; Huang, Zhen

2017-01-01

Since the advantage of hidden Markov model in dealing with time series data and for the sake of identifying driving style, three driving style (aggressive, moderate and mild) are modeled reasonably through hidden Markov model based on driver braking characteristics to achieve efficient driving style. Firstly, braking impulse and the maximum braking unit area of vacuum booster within a certain time are collected from braking operation, and then general braking and emergency braking characteristics are extracted to code the braking characteristics. Secondly, the braking behavior observation sequence is used to describe the initial parameters of hidden Markov model, and the generation of the hidden Markov model for differentiating and an observation sequence which is trained and judged by the driving style is introduced. Thirdly, the maximum likelihood logarithm could be implied from the observable parameters. The recognition accuracy of algorithm is verified through experiments and two common pattern recognition algorithms. The results showed that the driving style discrimination based on hidden Markov model algorithm could realize effective discriminant of driving style. PMID:28837580

Radar cross section models for limited aspect angle windows

NASA Astrophysics Data System (ADS)

Robinson, Mark C.

1992-12-01

This thesis presents a method for building Radar Cross Section (RCS) models of aircraft based on static data taken from limited aspect angle windows. These models statistically characterize static RCS. This is done to show that a limited number of samples can be used to effectively characterize static aircraft RCS. The optimum models are determined by performing both a Kolmogorov and a Chi-Square goodness-of-fit test comparing the static RCS data with a variety of probability density functions (pdf) that are known to be effective at approximating the static RCS of aircraft. The optimum parameter estimator is also determined by the goodness of-fit tests if there is a difference in pdf parameters obtained by the Maximum Likelihood Estimator (MLE) and the Method of Moments (MoM) estimators.

Assessment of Characteristic Function Modulus of Vibroacoustic Signal Given a Limit State Parameter of Diagnosed Equipment

NASA Astrophysics Data System (ADS)

Kostyukov, V. N.; Naumenko, A. P.; Kudryavtseva, I. S.

2018-01-01

Improvement of distinguishing criteria, determining defects of machinery and mechanisms, by vibroacoustic signals is a recent problem for technical diagnostics. The work objective is assessment of instantaneous values by methods of statistical decision making theory and risk of regulatory values of characteristic function modulus. The modulus of the characteristic function is determined given a fixed parameter of the characteristic function. It is possible to determine the limits of the modulus, which correspond to different machine’s condition. The data of the modulus values are used as diagnostic features in the vibration diagnostics and monitoring systems. Using such static decision-making methods as: minimum number of wrong decisions, maximum likelihood, minimax, Neumann-Pearson characteristic function modulus limits are determined, separating conditions of a diagnosed object.

An economic model of friendship and enmity for measuring social balance in networks

NASA Astrophysics Data System (ADS)

Lee, Kyu-Min; Shin, Euncheol; You, Seungil

2017-12-01

We propose a dynamic economic model of networks where agents can be friends or enemies with one another. This is a decentralized relationship model in that agents decide whether to change their relationships so as to minimize their imbalanced triads. In this model, there is a single parameter, which we call social temperature, that captures the degree to which agents care about social balance in their relationships. We show that the global structure of relationship configuration converges to a unique stationary distribution. Using this stationary distribution, we characterize the maximum likelihood estimator of the social temperature parameter. Since the estimator is computationally challenging to calculate from real social network datasets, we provide a simple simulation algorithm and verify its performance with real social network datasets.

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.

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

USGS Publications Warehouse

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

2015-01-01

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

Estimating Cosmic-Ray Spectral Parameters from Simulated Detector Responses with Detector Design Implications

NASA Technical Reports Server (NTRS)

Howell, L. W.

2001-01-01

A simple power law model consisting of a single spectral index (alpha-1) is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at knee energy (E(sub k)) to a steeper spectral index alpha-2 > alpha-1 above E(sub k). The maximum likelihood procedure is developed for estimating these three spectral parameters of the broken power law energy spectrum from simulated detector responses. These estimates and their surrounding statistical uncertainty are being used to derive the requirements in energy resolution, calorimeter size, and energy response of a proposed sampling calorimeter for the Advanced Cosmic-ray Composition Experiment for the Space Station (ACCESS). This study thereby permits instrument developers to make important trade studies in design parameters as a function of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose rigorous practical limits to the design envelope.

Estimating Arrhenius parameters using temperature programmed molecular dynamics

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

Imandi, Venkataramana; Chatterjee, Abhijit, E-mail: abhijit@che.iitb.ac.in

2016-07-21

Kinetic rates at different temperatures and the associated Arrhenius parameters, whenever Arrhenius law is obeyed, are efficiently estimated by applying maximum likelihood analysis to waiting times collected using the temperature programmed molecular dynamics method. When transitions involving many activated pathways are available in the dataset, their rates may be calculated using the same collection of waiting times. Arrhenius behaviour is ascertained by comparing rates at the sampled temperatures with ones from the Arrhenius expression. Three prototype systems with corrugated energy landscapes, namely, solvated alanine dipeptide, diffusion at the metal-solvent interphase, and lithium diffusion in silicon, are studied to highlight variousmore » aspects of the method. The method becomes particularly appealing when the Arrhenius parameters can be used to find rates at low temperatures where transitions are rare. Systematic coarse-graining of states can further extend the time scales accessible to the method. Good estimates for the rate parameters are obtained with 500-1000 waiting times.« less

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Development and system identification of a light unmanned aircraft for flying qualities research

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

Peters, M.E.; Andrisani, D. II

This paper describes the design, construction, flight testing and system identification of a light weight remotely piloted aircraft and its use in studying flying qualities in the longitudinal axis. The short period approximation to the longitudinal dynamics of the aircraft was used. Parameters in this model were determined a priori using various empirical estimators. These parameters were then estimated from flight data using a maximum likelihood parameter identification method. A comparison of the parameter values revealed that the stability derivatives obtained from the empirical estimators were reasonably close to the flight test results. However, the control derivatives determined by themore » empirical estimators were too large by a factor of two. The aircraft was also flown to determine how the longitudinal flying qualities of light weight remotely piloted aircraft compared to full size manned aircraft. It was shown that light weight remotely piloted aircraft require much faster short period dynamics to achieve level I flying qualities in an up-and-away flight task.« less

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.

Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models

PubMed Central

Schwab, Joshua; Gruber, Susan; Blaser, Nello; Schomaker, Michael; van der Laan, Mark

2015-01-01

This paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates, and a possibly time-dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention-specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because the true shape of this function is rarely known, the marginal structural model is used as a working model. The causal quantity of interest is defined as the projection of the true function onto this working model. Iterated conditional expectation double robust estimators for marginal structural model parameters were previously proposed by Robins (2000, 2002) and Bang and Robins (2005). Here we build on this work and present a pooled TMLE for the parameters of marginal structural working models. We compare this pooled estimator to a stratified TMLE (Schnitzer et al. 2014) that is based on estimating the intervention-specific mean separately for each intervention of interest. The performance of the pooled TMLE is compared to the performance of the stratified TMLE and the performance of inverse probability weighted (IPW) estimators using simulations. Concepts are illustrated using an example in which the aim is to estimate the causal effect of delayed switch following immunological failure of first line antiretroviral therapy among HIV-infected patients. Data from the International Epidemiological Databases to Evaluate AIDS, Southern Africa are analyzed to investigate this question using both TML and IPW estimators. Our results demonstrate practical advantages of the pooled TMLE over an IPW estimator for working marginal structural models for survival, as well as cases in which the pooled TMLE is superior to its stratified counterpart. PMID:25909047

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

NASA Technical Reports Server (NTRS)

Webster, L.

1976-01-01

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

Maximum Likelihood Shift Estimation Using High Resolution Polarimetric SAR Clutter Model

NASA Astrophysics Data System (ADS)

Harant, Olivier; Bombrun, Lionel; Vasile, Gabriel; Ferro-Famil, Laurent; Gay, Michel

2011-03-01

This paper deals with a Maximum Likelihood (ML) shift estimation method in the context of High Resolution (HR) Polarimetric SAR (PolSAR) clutter. Texture modeling is exposed and the generalized ML texture tracking method is extended to the merging of various sensors. Some results on displacement estimation on the Argentiere glacier in the Mont Blanc massif using dual-pol TerraSAR-X (TSX) and quad-pol RADARSAT-2 (RS2) sensors are finally discussed.

PyEvolve: a toolkit for statistical modelling of molecular evolution.

PubMed

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

2004-01-05

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