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At least 145 records · Page 8Linked to original sources
PubMed2006

On parameter estimation of chaotic systems via symbolic time-series analysis.

Symbolic time-series analysis is used for estimating the parameters of chaotic systems. It is assumed that a "target model" (i.e., a discrete- or continuous-time description of the data-generating mechanism) is available, but with unknown parameters. A time series, i.e., a noisy, finite sequence of a measured (output) variable, is given. The proposed method first prescribes to symbolize the time series, i.e., to transform it into a sequence of symbols, from which the statistics of symbols are readily derived. Then, a symbolic model (in the form of a Markov chain) is derived from the data. It allows one to predict, in a probabilistic fashion, the time evolution of the symbol sequence. The unknown parameters are derived by matching either the statistics of symbols, or the symbolic prediction derived from data, with those generated by the (parametrized) target model. Three examples of application (the Henon map, a population model, and the Duffing system) prove that satisfactory results can be obtained even with short time series.

Algorithms↗
PubMed1982

Role of longitudinal diffusion in the extravascular pulmonary space on parameter estimates derived from data of multiple indicator dilution.

A mathematical model of transcapillary exchange has been developed that considers in detail the role of axial diffusion in the extravascular tissue region on estimates of such physiological parameters as lung water (VE) and pulmonary capillary permeability-surface area products (PS), obtained from multiple indicator dilution studies. The experimental cases considered correspond to two animal models of pulmonary oedema in which the integrity of the pulmonary capillary membrane is disrupted and the effects of extravascular axial diffusion may be important. A novel feature of the computational scheme is the use of an Array Processor in the solution of the governing equations, initial and boundary conditions. Computer time is reduced to 2-3 min for parameter identification, thereby allowing a wide range of values for extravascular axial diffusion coefficients (D'/L2) to be studied at little computational expense. The results indicate that diffusion in the extravascular region does not influence parameter estimates for PS to urea. A statistical correlation is suggested between values for VE, PS to water, and D'/L2.

Animals↗
PubMed1998

Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation.

MOTIVATION: The simulation of biochemical kinetic systems is a powerful approach that can be used for: (i) checking the consistency of a postulated model with a set of experimental measurements, (ii) answering 'what if?' questions and (iii) exploring possible behaviours of a model. Here we describe a generic approach to combine numerical optimization methods with biochemical kinetic simulations, which is suitable for use in the rational design of improved metabolic pathways with industrial significance (metabolic engineering) and for solving the inverse problem of metabolic pathways, i.e. the estimation of parameters from measured variables. RESULTS: We discuss the suitability of various optimization methods, focusing especially on their ability or otherwise to find global optima. We recommend that a suite of diverse optimization methods should be available in simulation software as no single one performs best for all problems. We describe how we have implemented such a simulation-optimization strategy in the biochemical kinetics simulator Gepasi and present examples of its application. AVAILABILITY: The new version of Gepasi (3.20), incorporating the methodology described here, is available on the Internet at http://gepasi.dbs.aber.ac.uk/softw/Gepasi. html. CONTACT: prm@aber.ac.uk

Biochemistry↗
PubMed2006

Parameter estimation using Simulated Annealing for S-system models of biochemical networks.

MOTIVATION: High-throughput technologies now allow the acquisition of biological data, such as comprehensive biochemical time-courses at unprecedented rates. These temporal profiles carry topological and kinetic information regarding the biochemical network from which they were drawn. Retrieving this information will require systematic application of both experimental and computational methods. RESULTS: S-systems are non-linear mathematical approximative models based on the power-law formalism. They provide a general framework for the simulation of integrated biological systems exhibiting complex dynamics, such as genetic circuits, signal transduction and metabolic networks. We describe how the heuristic optimization technique simulated annealing (SA) can be effectively used for estimating the parameters of S-systems from time-course biochemical data. We demonstrate our methods using three artificial networks designed to simulate different network topologies and behavior. We then end with an application to a real biochemical network by creating a working model for the cadBA system in Escherichia coli. AVAILABILITY: The source code written in C++ is available at http://www.engg.upd.edu.ph/~naval/bioinformcode.html. All the necessary programs including the required compiler are described in a document archived with the source code. SUPPLEMENTARY INFORMATION: Supplementary material is available at Bioinformatics online.

Biochemistry↗
PubMed1985

A statistical comparison of parameter estimation for the Michaelis-Menten kinetics of human placental hexosaminidase.

To enable the most effective method of kinetic discrimination between a group of isozymes such as those of human placental hexosaminidases (HEX), three methods estimating the parameters of the Michaelis-Menten equation were evaluated. Computer-simulated experiments were performed under various conditions. They indicated that, in the presence of constant absolute or relative errors, the method of unweighted nonlinear least squares yielded slightly more precise and accurate parameters than the method of the direct linear plot. Parameters calculated from the Lineweaver-Burk plot were very imprecise and inaccurate. The direct linear plot was comparatively resistant to outlier observations; however, only when outliers were substantial did the method become superior to nonlinear least squares. The calculation of a confidence limit is necessary for the evaluation of any resulting differences in the kinetic parameters for a set of isozymes. This can easily be calculated from either the Lineweaver-Burk plot or the nonlinear least-squares method. However, those calculated from the Lineweaver-Burk plot are biased, especially at higher levels of experimental errors. Therefore, the nonlinear least-squares method is the one most suited for the discrimination of a group of enzymes based on their kinetic parameters.

Computers↗
PubMed1998

Parameter estimation and confidence intervals for Xe-CT ventilation studies: a Monte Carlo approach.

Xenon-enhanced computed tomography (Xe-CT) is a technique for the noninvasive measurement of regional pulmonary ventilation from the washin and/or washout time constants of radiodense stable xenon gas, determined from serial computed tomography scans. Although the measurement itself is straightforward, there is a need for methods for the estimation of variability and confidence intervals so that the statistical significance of the information obtained may be evaluated, particularly since obtaining repeated measurements is often not practical. We present a Monte Carlo (MC) approach to determine the 95% confidence interval (CI) for any given measurement. This MC method was characterized in terms of its unbiasedness and coverage of the CI. In addition, 10 identical Xe-CT ventilation runs were performed in an anesthetized dog, and the time constant was determined for several regions of varying size in each run. The 95% CI, estimated from these repeated measurements as the mean +/- 2 x SE, compared favorably with the CI obtained by the MC approach. Finally, a simulation was performed to compare the performance of three imaging protocols in estimating model parameters.

Animals↗
PubMed2004

The maxslope taxometric procedure: mathematical derivation, parameter estimation, consistency tests.

This article first explains concepts in taxometrics, including the meaning of "taxon" in relation to taxometric procedures. It then mathematically develops the MAXSLOPE procedure of Grove and Meehl which relies on nonlinear regression of one taxometric indicator variable on another. Sufficient conditions for MAXSLOPE's validity are set forth. The relationship between the point of maximum regression slope (MAXSLOPE point) and the HITMAX cut, i.e., the point on a variable which, if used as a diagnostic cut-off score, yields maximum classification accuracy, is analyzed. A sufficient condition is given for the MAXSLOPE point to equal the HITMAX cut; however, most distributions have different MAXSLOPE and HITMAX points. Equations and an algorithm are spelled out for making a graphical test for the existence of a taxon, estimating taxometric parameters, and conducting consistency tests; the latter serve as stringent checks on the validity of a taxonic conjecture. The plausibility of assumptions made, in deriving MAXSLOPE equations, is discussed, and the qualitative effects of violations of these assumptions are explained.

Classification↗
PubMed1998

Genetic parameter estimates for carcass and yearling ultrasound measurements in Brangus cattle.

Carcass measurements of 12th-rib fat thickness (CARCFAT), longissimus muscle area (CARCLMA), and weight (CARCWT) on 2,028 Brangus and Brangus-sired fed steers and heifers, as well as yearling weights (YWT) and ultrasound measures of 12th-rib fat thickness (USFAT) and longissimus muscle area (USLMA) on 3,583 Brangus bulls and heifers were analyzed to estimate genetic parameters. Data were analyzed using a six-trait animal model and an average information REML algorithm. The model included fixed effects for contemporary group and breed of dam, covariates for age at slaughter or measurement, and random animal and residual effects. Heritabilities for CARCFAT, CARCLMA, CARCWT, USFAT, USLMA, and YWT were .27+/-.05, .39+/-.05, .59+/-.06, .11+/-.03, .29+/-.04, and .40+/-.04, respectively. Genetic correlations between CARCFAT and USFAT, CARCLMA and USLMA, and CARCWT and YWT were .69+/-.18, .66+/-.14, and .61+/-.11, respectively. The favorable and moderately strong genetic correlations between carcass measurements and similar yearling breeding-animal ultrasound measurements indicate that such measurements of 12th-rib fat and longissimus muscle area are useful in predicting genetic values for carcass leanness and longissimus muscle area. Selection using yearling ultrasound measurements of breeding cattle should result in predictable genetic improvement for carcass characteristics. Inclusion of yearling ultrasound measurements for fat thickness and longissimus muscle area should enhance national cattle evaluation programs.

Adipose Tissue↗
PubMed1989

Estimating parameters of growth curves of bulls.

Parameters were estimated for nonlinear growth curves for bulls of five straightbred and 20 crossbred breed-types produced in two generations of a diallel. The primary intent of this study was to use the estimates obtained for mature size and maturing rate to define male growth in manner that would be appropriate for use in the Texas Agricultural Experiment Station (TAES) Beef Cattle Simulation Model. The results that were obtained from the nonlinear regressions made on the male growth data indicated that the relation between the mature sizes of males and females of the same breed-type is consistent with the assumption for that relation contained in the model (a ratio of 1.5). However, the inverse relationship between mature size and maturing rate that is assumed in the model was not consistent with the results of the present study. That contradiction presumably arose due to the different environment imposed on the males relative to their female counterparts. This condition prohibits direct application of the results of this study because live weights cannot be directly related to the principal growth curve contained in the model. However, such a relationship can be developed when information regarding the composition of bulls considered in this study becomes available.

Age Factors↗
PubMed1983

Parameter estimation for nonlinear models with emphasis on compartmental models.

Techniques are described for the estimation of parameters in nonlinear models. When implemented in computer programs, these techniques will reduce programming effort, facilitate inference about implicit functions of parameters, and allow a more general variance-covariance structure. The techniques seem particularly useful for the analysis of data from stochastic compartmental models. They are illustrated by an example.

Models, Theoretical↗
PubMed1981

Application of jackknife procedures to inter-experiment comparisons of parameter estimates for the Michaelis-Menten equation.

The jackknife procedure is introduced as a means of making comparisons among Michaelis-Menten parameter estimates for six different experimental conditions. In addition to providing a solution to the general inter-experimental comparison problem, the jackknife procedure will provide valid parameter estimates even when some of the assumptions usually required for statistical analysis are violated, e.g., the random errors are not normally distributed and the variances are not homogeneous. Other recent variations of the jackknife have also been introduced and briefly investigated: (i) the linear jackknife, which is more efficient computationally, and (ii) the weighted jackknife, which reduces the influence of design points (substrate concentrations) that have an excessive influence on the precision of parameter estimates.

Benzphetamine↗
PubMed2002

Respirometry-based on-line model parameter estimation at a full-scale WWTP.

This paper describes part of a project to develop a systematic approach to knowledge extraction from on-line respirometric measurements in support of wastewater treatment plant control and operation. The paper deals with the following issues: (1) test of the implementation of an automatic set-up consisting of a continuous laboratory respirometer integrated in a mobile trailer with sampling and dosing equipment, and data-acquisition and communication system; (2) assessment of activated sludge/sewage characteristics from sludge respirograms by model parameter estimation; (3) comparison of the parameter estimates with regular plant data and information obtained from supplementary wastewater respirograms. The paper describes the equipment and some of its measuring results from a period of one week at a large-scale wastewater treatment plant. The measurements were evaluated in terms of the common activated sludge modelling practice. The automatic set-up allowed reliable measurements during at least one week. The data were used to calibrate two different version of the model, and independent parameter estimates were obtained.

Bioreactors↗
PubMed2001

The dependence of viral parameter estimates on the assumed viral life cycle: limitations of studies of viral load data.

Estimation of viral parameters, such as the basic reproductive number (R0) and infected cell life span, is central to the quantitative study of the within-host dynamics of viral diseases such as human immunodeficiency virus, hepatitis B or hepatitis C. As these parameters can rarely be determined directly, they are usually estimated indirectly by fitting mathematical models to viral load data. This paper investigates how parameter estimates obtained by such procedures depend on the assumptions made concerning the viral life cycle. It finds that estimates of the basic reproductive number obtained using viral load data collected during the initial stages of infection can depend quite sensitively on these assumptions. The use of models which neglect the intracellular delay before virion production can lead to severe underestimates of R0 and, hence, to overly optimistic predictions of how efficacious treatment must be in order to prevent or eradicate the disease. These results are also of importance for attempts at estimating R0 from similar epidemiological data as there is a correspondence between within-host and between-host models. Estimates of the life span of infected cells obtained from viral load data collected during drug treatment studies also depend on the assumptions made in modelling the virus life cycle. The use of more realistic descriptions of the life cycle is seen to increase estimates of infected cell life span, in addition to providing a new explanation for the shoulder phase seen during drug treatment. This study highlights the limitations of what can be learnt by fitting mathematical models to infectious disease data without detailed independent knowledge of the life cycle of the infectious agent.

Antiviral Agents↗
PubMed1999

Kinetic parameter estimation from compartment models using a genetic algorithm.

Kinetic parameters were estimated from a three-compartment fluorodeoxyglucose model with three rate constants using a genetic algorithm. The performance of the genetic algorithm was investigated by simulation studies, in which brain time-activity data (TAD) were generated using cited mean values of rate constants and the plasma TAD obtained from positron emission tomographic studies. The accuracy of kinetic parameter estimation using the genetic algorithm was compared with that using the non-linear least-squares (NLSQ) method. The margin of error in the parameters estimated using the genetic algorithm tended to be smaller than that obtained by the NLSQ method. Although not statistically significant at a noise level of 5% in the brain TAD, the difference between the two methods became significant for all parameters at a noise level of 15% or higher. Our results suggest that the genetic algorithm is a promising means of estimating kinetic parameters from compartment models, because it is more robust against statistical noise than the NLSQ method and it can be rendered highly parallel for processing.

Algorithms↗
PubMed2006

A decompositional approach to parameter estimation in pathway modeling: a case study of the Akt and MAPK pathways and their crosstalk.

Parameter estimation is a critical problem in modeling biological pathways. It is difficult because of the large number of parameters to be estimated and the limited experimental data available. In this paper, we propose a decompositional approach to parameter estimation. It exploits the structure of a large pathway model to break it into smaller components, whose parameters can then be estimated independently. This leads to significant improvements in computational efficiency. We present our approach in the context of Hybrid Functional Petri Net modeling and evolutionary search for parameter value estimation. However, the approach can be easily extended to other modeling frameworks and is independent of the search method used. We have tested our approach on a detailed model of the Akt and MAPK pathways with two known and one hypothesized crosstalk mechanisms. The entire model contains 84 unknown parameters. Our simulation results exhibit good correlation with experimental data, and they yield positive evidence in support of the hypothesized crosstalk between the two pathways.

Algorithms↗
PubMed1996

Error analysis on parameter estimates in the ligand-receptor model: application to parameter imaging using PET data.

Positron emission tomography and compartmental models allow the in vivo analysis of radioligand binding to receptor sites in the human brain. Benzodiazepine receptor binding was studied using a three-compartmental model and [11C]flumazenil. Four and five parameters were estimated from a single kinetic curve obtained with a multi-injection protocol, and parametric maps of receptor density and of the individual kinetic parameters were created with four-pixel sampling of the experimental images. The coefficient of variation on each estimated model parameter was calculated using the diagonal elements of the covariance matrix. However, these estimates are valid only under some statistical hypotheses which are not always verified with PET data. Thus, in order to verify the validity of the coefficient of variation of each parameter calculated with the covariance matrix, these results have been compared with the more rigorous statistical results provided by a Monte Carlo simulation. The study showed a negligible difference between the results obtained by the two methods for a low noise level in time-concentration curves encountered using large ROIs. However, this bias becomes less negligible when the noise level is high and some estimations of the coefficients of variation were unacceptable (> 100%) with the five-parameter model. Such difficulties did not occur with the four-parameter model which led to parametric images with good quality and acceptable estimates of coefficients of variation (less than 20% in about 75% of the ROIs).

Brain↗
PubMed2001

A comparison of generalized linear mixed model procedures with estimating equations for variance and covariance parameter estimation in longitudinal studies and group randomized trials.

Response data in longitudinal studies and group randomized trials are gathered on units that belong to clusters, within which data are usually positively correlated. Therefore, estimates and confidence intervals for intraclass correlation or variance components are helpful when designing a longitudinal study or group randomized trial. Data simulated from both study designs are used to investigate the estimation of variance and covariance parameters from the following procedures: for continuous outcomes, restricted maximum likelihood (REML) and estimating equations (EE); for binary outcomes, restricted pseudo-likelihood (REPL) and estimating equations (EE). We evaluate these procedures to see which provide valid and precise estimates as well as correct standard errors for the intraclass correlation coefficient or variance components. REML seems the better choice for estimating terms related to correlation for models with normal outcomes, especially in group randomized trial situations. Results for REML and EE are mixed when outcomes are continuous and non-normal. With binary outcomes neither REPL nor EE provides satisfactory estimation or inference in longitudinal study situations, while REPL is preferable for group randomized trials.

Cluster Analysis↗
PubMed2003

GGUMLINK: a computer program to link parameter estimates of the generalized graded unfolding model from item response theory.

The generalized graded unfolding model (GGUM) is an item response theory (IRT) model that implements symmetric, nonmonotonic, single-peaked item characteristic curves. The GGUM is appropriate for measuring individual differences for a variety of psychological constructs, especially attitudes. Like other IRT models, the location and scale (i.e., the metric) of parameter estimates from the GGUM are data dependent. Therefore, parameter estimates from alternative calibrations will generally not be comparable, even when responses to the same items are analyzed. GGUMLINK is a computer program developed to reexpress parameter estimates from two separate GGUM calibrations in a common metric. In this way, the results from separate calibrations of model parameters can be compared. GGUMLINK can secure a common metric by using one of five methods that have recently been generalized to the GGUM. The GGUMLINK executable program is available free and may be downloaded from http://www.education.umd.edu/EDMS.

Calibration↗