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PubMed1997

Multiple Parameter Estimation in an Adaptive Psychometric Method: MUEST, an Extension of the QUEST Method

An extension of the so-called QUEST method of Watson and Pelli (1979, 1983) is proposed. In contrast to the traditional QUEST method, the new method, the MUEST method, offers the possibility of simultaneously estimating more than one parameter of a parametric representation of the psychometric function. Knowledge about more parameters gives a higher guarantee of obtaining correct threshold values. The basic extension itself is analytically quite modest and can be explained in a few sentences. However, the involved additional techniques, like the placing of stimulus levels, require a more extensive description, which is presented here. Copyright 1997 Academic Press. Copyright 1997 Academic Press

Journal Article↗
PubMed1992

A relation between the Akaike criterion and reliability of parameter estimates, with application to nonlinear autoregressive modelling of ictal EEG.

The Akaike minimum information criterion provides a means to determine the appropriate number of lags in a linear autoregressive model of a time series. We show that the Akaike criterion is closely related to the reliability estimates of successively determined parameters of a linear autoregressive (LAR) model. A similar criterion may be applied to determine whether the addition of a nonlinear term to an LAR model provides a statistically significant improvement in the description of the time series. As an example, we use this method to identify quadratic contributions to a nonlinear autoregressive characterization of a typical 3/s spike and wave seizure discharge.

Data Interpretation, Statistical↗
PubMed2000

Nonlinear regression in parameter estimation from polarographic signals

In this work we describe a detailed treatment of polarographic data curves, including error analysis, by means of nonlinear least-squares in its standard form (or resorting to the errors in variables model). Error estimates for the related parameters are additionally verified by Monte-Carlo simulation and resampling techniques.

Journal Article↗
PubMed1998

A Metropolis Monte Carlo implementation of bayesian time-domain parameter estimation: application to coupling constant estimation from antiphase multiplets.

The Bayesian perspective on statistics asserts that it makes sense to speak of a probability of an unknown parameter having a particular value. Given a model for an observed, noise-corrupted signal, we may use Bayesian methods to estimate not only the most probable value for each parameter but also their distributions. We present an implementation of the Bayesian parameter estimation formalism developed by G. L. Bretthorst (1990, J. Magn. Reson. 88, 533) using the Metropolis Monte Carlo sampling algorithm to perform the parameter and error estimation. This allows us to make very few assumptions about the shape of the posterior distribution, and allows the easy introduction of prior knowledge about constraints among the model parameters. We present evidence that the error estimates obtained in this manner are realistic, and that the Monte Carlo approach can be used to accurately estimate coupling constants from antiphase doublets in synthetic and experimental data.

Algorithms↗
PubMedDate not supplied

Arterial windkessel parameter estimation: a new time-domain method.

We developed and validated a new, more accurate, and easily applied method for calculating the parameters of the three-element Windkessel to quantitate arterial properties and to investigate ventriculoarterial coupling. This method is based on integrating the governing differential equation of the three-element Windkessel and solving for arterial compliance. It accounts for the interaction between characteristic impedance and compliance, an important phenomenon that has been ignored by previously implemented methods. The new integral method was compared with four previously published methods as well as a new independent linear least-squares analysis, using ascending aortic micromanometric and volumetric flow measurements from eight dogs. The parameters calculated by the new integral method were found to be significantly different from those obtained by the previous methods but did not differ significantly from maximum likelihood estimators obtained by a linear least-squares approach. To assess the accuracy of parameter estimation, pressure and flow waveforms were reconstructed in the time domain by numerically solving the governing differential equation of the three-element Windkessel model. Standard deviations of reconstructed waveforms from the experimental ensemble-averaged waveforms, which solely reflect the relative accuracy of the Windkessel parameters given by the various methods, were calculated. The new integral method invariably yielded the smallest error. These results demonstrate the improved accuracy of our new integral method in estimating arterial parameters of the three-element Windkessel.

Animals↗
PubMed1978

Program to estimate parameters of linear systems without numerical differentiation.

This paper describes a computer program for estimating the parameters of a linear differential equation systen with constant coefficients by use of a nonlinear least-squares method. For minimization the sum of squares of an existing standard program, the Gauss-Newton gradient procedure, is employed. The differential equation system is solved by the Taylor expansion method. The advantage of this approach is that the derivatives with respect to the parameters are available without numerical differentiation. Therefore the inaccuracy inherent in numerical differentiation and the problem of choosing the modification of the parameters are eliminated. The given procedure is applicable for all the first order gradient methods. The presented method was tested with generated data from a four-compartmental model.

Computers↗
PubMed1981

Twin-family studies of perceptual speed ability. II. Parameter estimation.

Offspring of monozygotic (MZ) twins form half-ships that permit a direct test of maternal effects and differentiate several sources of between-family environmental variance. Combined with conventional twin data, these genetic half-sibships provide a unique data set for estimating sources of variation in quantitative traits. To illustrate, genetic and environmental parameters were estimated for Identical Pictures Test data obtained from children of MZ twin parents and an (approximate) age-matched cohort of like-sex twins. Analyses of variance of the data, standardized for age and sex, yield 12 mean squares to which gene-environment models were fit. Maximum-likelihood estimation revealed a complete absence of maternal influences and shared environmental effects; a simple two-parameter model, assuming random mating and attributing variation in test scores to additive genes and within-family environment, adequately accounts for the familial data.

Adolescent↗
PubMedDate not supplied

Parameter estimation for a prosthetic ankle.

The mechanical parameters of a model of an energy storage and return ankle prosthesis are estimated for normal level walking by means of an optimization procedure. The walking cycle is divided into six fields, such that the power does not change sign within each field; the transition between successive fields occurs at zero power. The optimal spring stiffness as a function of time, is found by optimizing a quadratic cost function to minimize the difference between the estimated ankle moments and the moments in normal walking. The optimization is subjected to four continuous constraints within each field and to two continuity constraints for the transitions between successive fields. The time-varying spring stiffness and the implications of additional external energy are discussed and are presented as recommendations for the designer.

Ankle Joint↗
PubMedDate not supplied

Innovations in bayes and empirical bayes methods: estimating parameters, populations and ranks.

By formalizing the relation among components and 'borrowing information' among them, Bayes and empirical Bayes methods can produce more valid, efficient and informative statistical evaluations than those based on traditional methods. In addition, Bayesian structuring of complicated models and goals guides development of appropriate statistical approaches and generates summaries which properly account for sampling and modelling uncertainty. Computing innovations enable implementation of complex and relevant models, thereby substantially increasing the role of Bayes/empirical Bayes methods in important statistical assessments. Policy-relevant statistical assessments involve synthesis of information from a set of related components such as medical clinics, geographic regions or research studies. Typical assessments include inference for individual parameters, synthesis over the collection of components (for example, the parameter histogram) and comparisons among parameters (for example, ranks). The relative importance of these goals depends on the context. Bayesian structuring provides a guide to valid inference. For example, while posterior means are the 'obvious' and optimal estimates for individual components under squared error loss, their empirical distribution function (EDF) is underdispersed and never valid for estimating the EDF of the true, underlying parameters. Effective histogram estimates result from optimizing a loss function based in a distance between the histogram and its estimate. Similarly, ranking observed data usually produces poor estimates and ranking posterior means can be inappropriate. Effective estimates should be based on a loss function that caters directly to ranks. Using examples of 'borrowing information', shrinkage and the variance/bias trade-off we motivate Bayes and empirical Bayes analysis. Then, we outline the formal approach and discuss 'triple-goal' estimates with values that when ranked produce optimal ranks, for which the EDF is an optimal estimate of the parameter EDF and such that the values themselves are effective estimates of co-ordinate-specific parameters. We use basic models and data analysis examples to highlight the conceptual and structural issues.

Animals↗
PubMed1987

Identifiability: the first step in parameter estimation.

The observations in an experiment define a set of observational parameters that are functions of the basic kinetic parameters of the model of the system. The problem of identifiability is concerned with whether the observational parameters uniquely specify the basic kinetic parameters. As such, it depends only on the functional relation between the two levels of parameters and not on errors of observation and the estimation procedure. It should be checked before doing the experiment. Given initial estimates of the basic kinetic parameters, identifiability can be checked, in a local sense, from data generated by simulating the experiment on the model.

Computer Simulation↗
PubMed1994

CO2 control of breathing: parameter estimation and stability evaluation.

A method is developed to evaluate system stability for the CO2 control of breathing in individuals by using data from the dynamics of CO2 rebreathing and elimination. The theoretical basis of the method is a physiological model of the CO2 respiratory control system and an explicit stability index (SI). The SI is algebraically related to the model parameters: system volume (Vs), cardiac output (Q), circulatory transit time (ts), and controller gain (G). A sequential optimization scheme is shown to yield estimates of the model parameters by comparing the alveolar ventilation and PCO2 of the model output with corresponding experimental data. Model simulation of CO2 rebreathing and elimination with different parameter values demonstrate that all parameters except ts have significant effect on the outputs. Least-squares estimation of the parameters using model-generated data with added noise showed good precision for all parameters (except ts). This analysis is performed with parameter values chosen to produce overdamped and underdamped responses that would occur in normal and abnormal respiratory control systems, respectively. It is anticipated that SI values of the (overdamped) normal and (underdamped) abnormal systems differ by much more than the variation produced by imprecision of the parameter estimates. For this circumstance, the method is expected to be sensitive enough to distinguish normal from abnormal CO2 respiratory control of individual subjects.

Carbon Dioxide↗
PubMed2001

Evaluation of scatter compensation methods by their effects on parameter estimation from SPECT projections.

Three algorithms for scatter compensation in Tc-99m brain single-photon emission computed tomography (SPECT) were optimized and compared on the basis of the accuracy and precision with which lesion and background activity could be simultaneously estimated. These performance metrics are directly related to the clinically important tasks of activity quantitation and lesion detection, in contrast to measures based solely on the fidelity of image pixel values. The scatter compensation algorithms were (a) the Compton-window (CW) method with a 20% photopeak window, a 92-126 keV scatter window, and an optimized "k-factor," (b) the triple-energy window (TEW) method, with optimized widths of the photopeak window and the abutting scatter window, and (c) a general spectral (GS) method using seventeen 4 keV windows with optimized energy weights. Each method was optimized by minimizing the sum of the mean-squared errors (MSE) of the estimates of lesion and background activity concentrations. The accuracy and precision of activity estimates were then determined for lesions of different size, location, and contrast, as well as for a more complex Bayesian estimation task in which lesion size was also estimated. For the TEW and GS methods, parameters optimized for the estimation task differed significantly from those optimized for global normalized pixel MSE. For optimal estimation, the CW bias of activity estimates was larger and varied more (-2% to 22%) with lesion location and size than that of the other methods. The magnitude of the TEW bias was less than 7% across most conditions, although its precision was worse than that of CW estimates. The GS method performed best, with bias generally less than 4% and the lowest variance; its root-mean square (rms) estimation error was within a few percent of that achievable from primary photons alone. For brain SPECT, estimation performance with an optimized, energy-based, subtractive correction may approach that of an ideal scatter-rejection procedure.

Algorithms↗
PubMed2000

Parameter estimates for number of lambs born at different ages and for 18-month body weight of Rambouillet sheep.

Genetic parameters were estimated using REML with animal models for number of lambs born and 18-mo body weight in Rambouillet sheep. Number of lambs born was modeled either as repeated measurements on the same trait or as different traits at different ages. The original data for number of lambs born were separated according to age of the ewe into two classes: 2 and 3 yr, and older than 3 yr. Numbers of ewes with lambing records for the age classes were 653 and 466 with 1,106 and 1,118 records, respectively. For the data set that included all ages, the number of ewes was 684 with 2,224 records, and for 18-mo body weight the number of ewes measured was 557. For number of lambs born, the animal model included random genetic, permanent environmental, and residual environmental effects and fixed effects for age of ewe, year of lambing, and month of year of lambing. Lambing day within season was used as a covariate. For 18-mo body weight, year of birth of ewe was used as a fixed effect. Actual age in days when the ewe was weighed was used as a covariate. Estimates of heritability for number of lambs born by age group were .04, for 2- and 3-yr old ewes, and .06, for ewes greater than 3 yr old, from the two-trait (two age of ewe classes) analyses and .06 when all ages were included. Estimates of heritability for number of lambs born from the single-trait analyses were somewhat less than estimates from two-trait analyses. Estimate of genetic correlation between number of lambs born for the 2 and 3 yr and the >3 yr classes was near unity (1.00), which suggests that a repeated measures model for number of lambs born is adequate for making selection decisions. Estimate of genetic correlation between number of lambs born and 18-mo body weight was .35 with a heritability estimate of .48 for 18-mo body weight. The estimate of genetic correlation suggests that selection for increased number of lambs born would result in increased 18-mo body weight.

Age Factors↗
PubMed1993

Metabolic pathway characterization from transient response data obtained in situ: parameter estimation in S-system models.

The actual values of internal metabolites and fluxes can be measured by a number of experimental techniques and they provide important information for evaluating the properties of a metabolic pathway in situ. In this paper we propose a strategy to properly exploit this information. The suggested approach permits estimation of a set of parameters on the whole system so that a useful model can be constructed and used to describe its components and systemic properties and to predict its behavior under new conditions. A simulated reference pathway is provided to validate this method and to show its utility in metabolic studies.

Animals↗
PubMed1988

Relationships among growth hormone and prolactin secretory parameter estimates in Holstein bulls and their predicted differences for lactational traits.

Selection of dairy sires is based on the production records of their female ancestors, half-sibs and daughters. No trait expressed by the sire is used. Concentrations of growth hormone (GH) and prolactin (PRL), hormones produced in both males and females that are fundamental in lactation, may be correlated with production. A study was conducted to determine whether measures of these hormones in the sire would be useful predictors of lactational ability of daughters. Blood samples were collected at 15-min intervals for 8 h from 26 Holstein bulls (5.5 yr of age) that had one progeny summary available. Plasma concentrations of GH and PRL were quantified and the mean and baseline concentrations and the frequency and mean amplitude of the secretory peaks were determined for each bull. Concentrations among these values and bulls' predicted differences (PD) were determined. Significant negative correlations were detected for frequency of GH peaks and PD for yield of milk, fat and protein; correlations were positive for PRL baseline concentrations and PD for fat and protein (P less than .10), and correlations were negative for frequency of PRL peaks and PD for milk, fat and protein (P less than .10). Addition of estimates of bull hormone secretory parameters to breeding values based on performance of relatives considerably improved the accuracy (R2) for predicting progeny performance from sire information. Certain characteristics of the patterns of GH and PRL secretion may be heritable and aid in identification of superior dairy animals.

Animals↗
PubMed1990

Transducer characterization from pressure amplitude distribution measurements using a Kalman filter as parameter estimation algorithm.

The amplitude and frequency contents of a received ultrasound pulse depends on the spatial pressure amplitude distribution of the sound field, as produced by the transducer in the medium, and on the position and orientation of the reflecting surface in this field. Often, the geometry of the reflecting surface and the acoustical properties of the medium are known or can be estimated. Then it is practical to determine the transducer parameters in order to calculate the distortion of a reflected ultrasound pulse. Apart from geometrical parameters such as size and mechanical focusing, the surface velocity amplitude distribution (SVAD) of a transducer is of major importance. For some transducer configurations this SVAD may be described with a limited number of parameters. This paper presents a method, based on a Kalman filter algorithm, to assess the transducer parameters by measurement of the spatial sound field pressure amplitude distribution in various planes for different emission frequencies. Comparison of the measured pressure amplitudes with those calculated using the estimated values of the parameters shows that this method yields reliable results.

Acoustics↗
PubMedDate not supplied

Identifiability and parameter estimation.

In experiments on biological systems one often cannot measure all state variables (compartments). Given a particular experiment of that type, a basic kinetic parameter may have no effect on the observations; such a parameter is an insensible parameter for that experiment. A parameter may influence the observations and not be uniquely determinable; such a parameter is nonidentifiable for that experiment. Only identifiable parameters can be estimated uniquely, by that experiment. I review the basic theory to check identifiability for a nominal value of a parameter (local identifiability), and present some examples of problems that may arise in estimation.

Kinetics↗