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PubMed2006

Parameter estimation of an asymmetric vocal-fold system from glottal area time series using chaos synchronization.

In this paper, we apply an iterative parameter adaption scheme based on chaos synchronization to estimate system parameters of the asymmetric vocal folds from glottal area time series. The original asymmetric vocal-fold system associated with recurrent laryngeal paralysis shows chaotic vibrations with positive Lyapunov exponents. Aperiodic glottal area time series from the original system will be applied as the feedback variable coupling the simulative and the original vocal-fold systems. The parameter adaption technique based on chaos synchronization is employed to manipulate the simulative system parameters. The chaotic vibrations, system parameters, and the bifurcation diagram of the original vocal-fold system can be exactly reproduced in the simulative system, and the two chaotic systems can be synchronized. Furthermore, the effects of noise, sampling rate, and equation difference due to nonlinear spring terms on vocal-fold parameter estimations are investigated. Despite large noise perturbations, large equation differences, and low sampling rate, the parameter adaption scheme can effectively estimate the original vocal-fold system parameters. This study provides a theoretical base to apply chaos synchronization to estimate the vocal-fold system parameters from the glottal area data and show its potential application in laryngeal physiology.

Algorithms↗
PubMed1999

Parameter Estimation for the Constant Capacitance Surface Complexation Model: Analysis of Parameter Interdependencies.

Results of extensive application of the 2-pK constant capacitance surface complexation model (CCM) to surface charge data of a range of minerals in 0.1 M electrolytes are summarized where the program FITEQL has simultaneously been used to study the interdependence of the involved optimized parameters. To illustrate representative results, surface complexation and goodness of fit parameters are given as a function of the capacitance value (C). For all (ca. 150) tested data sets, one of three patterns is observed, two of which do not allow a unique parameter set to be obtained. The results indicate that the optimized site density parameter is relatively insensitive to a wide variation of C; optimized site density is rather low in this range of (higher) C and tends toward maximum proton uptake in the respective data set which in turn will be close to sometimes experimentally observed saturation levels. At low and with further decreasing C a steep increase of site density may occur; in this case, DeltapKa strongly increases after a DeltapKa minimum. Alternatively at low C, DeltapKa may continue to decrease and site density decreases simultaneously after a site density maximum. The observed patterns can be explained by the constraint of C on the electrostatic correction factor. Linear correlation coefficients (which are very useful parameters but do not receive much attention) show that in the region of low C, the optimized parameters become fully correlated, which finally causes nonconvergence in parameter optimization. In the region where the optimized site density is not significantly affected by a decrease in C the optimized parameters are more weakly correlated. When site concentration is co-optimized high correlation between adjustable parameters suggests that it is preferable to have an estimate for this parameter. Overall, it can be stated that substantial difficulties were observed in the effort to obtain unique (and thus meaningful) parameters for the CCM in about 60% of the data sets treated. Copyright 1999 Academic Press.

Journal Article↗
PubMed1986

Parameter estimation for ligand binding systems kinetics applied to 1,25-dihydroxycholecalciferol.

A mathematical analysis of the kinetics of the hormone-receptor interaction was applied to the 1,25-dihydroxycholecalciferol-intestinal receptor system. The exact analytical solution and the numerical integration of the kinetic equation were installed in a Statistical Analysis System (SAS) computer program to estimate the rate constants of the reaction. Estimates of the parameters obtained by these two methods are similar, demonstrating that the numerical integration can be combined with the nonlinear regression procedure for least-squares parameter fitting using a simple SAS program. This enables estimation of kinetics rate constants when the kinetic equation cannot be solved analytically. The ratio of the rate constants (ka/kd) found by the nonlinear procedure is close to the independently determined equilibrium (Scatchard) constant in the nonlinear analysis.

Animals↗
PubMed2001

The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows.

A structural identifiability analysis is performed on a mathematical model for the coupled transmission of two classes of pathogen. The pathogens, classified as major and minor, are aetiological agents of mastitis in dairy cows that interact directly and via the immunological reaction in their hosts. Parameter estimates are available from experimental data for all but four of the parameters in the model. Data from a longitudinal study of infection are used to estimate these unknown parameters. A novel approach and application of structural identifiability analysis is combined in this paper with the estimation of cross-protection parameters using epidemiological data.

Animals↗
PubMed1979

Selection of optimal model for the DNA histogram by analysis of error of estimated parameters.

The ability of four different mathematical models of the DNA histogram to give accurate estimates for the fractions of cells in G1, S, and G2 + M has been investigated. The models studied differ in the form and number of parameters of the function used to represent cells in S-phase. Results obtained from simulated DNA histograms suggest that the standard deviations of the model parameters increase exponentially with the width of the G1 and G2 + M peaks of the histogram. Error analysis is presented as a method to select a model of optimal complexity in relation to the resolution provided by the data in a given set of DNA histograms. Introduction of additional parameters improves the agreement between model and data but may result in a less well-posed model. A model with an optimal number of parameters can therefore be found that will yield parameter estimates with the smallest possible standard deviations.

Cell Cycle↗
PubMed2002

Algorithm for vector autoregressive model parameter estimation using an orthogonalization procedure.

We review the derivation of the fast orthogonal search algorithm, first proposed by Korenberg, with emphasis on its application to the problem of estimating coefficient matrices of vector autoregressive models. New aspects of the algorithm not previously considered are examined. One of these is the application of the algorithm to estimate coefficient matrices of a vector autoregressive process with time-varying coefficients when multiple realizations of the said process are available. Computer simulations were also performed to characterize the statistical properties of the estimates. The results show that even for shorter time series the algorithm works well and obtains good estimates of the time-varying parameters. Statistical characterization indicates that the standard deviation of the estimates decreases as 1 square root N (N being the length of the time series), a typical behavior of least-squares estimators. Another key aspect of the approach, which has previously been considered, is its direct extension to the parameter estimation of vector nonlinear autoregressive models. Nonlinear terms can be added to the model and the same algorithm can be applied to effectively estimate their associated parameters. Using chaotic time series generated from the Lorenz equations, the algorithm produces a model that captures the nonlinear structure of the data and exhibits the same chaotic attractor as that of the original system.

Algorithms↗
PubMed1986

A mathematical model of survival kinetics. II. Parameter estimation.

Procedures for the estimation of the four parameters of a new mathematical model of survival and mortality kinetics are given. A formulation of the model has been found which had the advantage of maintaining three of four parameters independent of the unit chosen for the age; in addition, two of these parameters have values falling in a narrow range, even when the model is applied to rather different curves. Since, in any problem of this type, the initial estimate of the parameters plays a major role in the achievement of good final estimates, some simple methods of estimation are indicated based upon the characteristics of the function. The initial estimates may enter three different types of procedures; the best one can be chosen according to the precision of the initial estimates. The method is capable of fitting both survivorship and dying functions directly to the empirical data. An interactive approach to the computer facilities has been used as at each step the operator has to decide whether or not to apply a corrective factor. Goodness of fit, usually high, is estimated by chi 2 test.

Aging↗
PubMed1988

The Gemini conundrum--a problem of unpairable data: statistical comparison of ratios each derived from two separately estimated parameters.

In biological studies it may be necessary to compare ratios of two separately estimated parameters under test and control conditions. Since it is not always possible technically to obtain paired data for the two parameters, how does one take account of their variances? By extending previously described approximations in a modified t-test we present a BASIC computer program which may be used to solve this problem.

Algorithms↗
PubMed2001

A new algorithm for autoregression moving average model parameter estimation using group method of data handling.

A new algorithm for autoregresive moving average (ARMA) parameter estimation is introduced. The algorithm is based on the group method of data handling (GMDH) first introduced by the Russian cyberneticist, A. G. Ivakhnenko, for solving high-order regression polynomials. The GMDH is heuristic in nature and self-organizes into a model of optimal complexity without any a priori knowledge about the system's inner workings. We modified the GMDH algorithm to solve for ARMA model parameters. Computer simulations have been performed to examine the efficacy of the GMDH and comparison of the GMDH is made to one of the most accurate and one of the most widely used algorithms, the fast orthogonal search (FOS) and the least-squares methods, respectively. The results show that in some cases with noise contamination and incorrect model order assumptions, the GMDH performs better than either the FOS or the least-squares methods in providing only the parameters that are associated with the true model terms.

Algorithms↗
PubMed1998

Parameter Estimation for the Triple Layer Model. Analysis of Conventional Methods and Suggestion of Alternative Possibilities.

The 2-pK one-site triple layer model (TLM) is one of the most popular surface complexation models (SCMs). The present paper deals with parameter estimation for this model. It is shown that there is a need for new, reliable estimation techniques for TLM parameters. The existing methods are not convincing. In the present paper this becomes evident from application to theoretical data, which unfortunately never yields the expected parameters, be it with graphical or numerical approaches. A possible alternative method is proposed, which uses systems with differences in points of zero charge to determine the inner layer capacitance and the pristine point of zero charge for theoretical and experimental data. This method is based on a simple equation for the isoelectric point. Application of the approach to three sets of experimental surface charge data showed that it is possible to decide if the TLM is a reasonable model for a certain system. The equation for the point of zero net proton charge could in principle be applied in a similar way, but would involve some assumption(s) about the results of electrokinetic measurements. No knowledge about site density is required in such approaches. An equation for the point of zero surface potential was found to be at present too complex to be used in a similar way since it involves the site density parameter. Reliable methods might have a promising perspective insofar as they would in principle allow the prediction of parameters for a wide range of sorbents. The alternative approach suggested in this paper can in principle be applied to other SCMs (both single site 1-pK and 2-pK), which account for electrolyte adsorption. Copyright 1998 Academic Press.

Journal Article↗
PubMed1979

A program package for simulation and parameter estimation in pharmacokinetic systems.

A set of programs is presented which has been developed for parameter estimation and simulation of models arising from pharmacokinetic applications. The programs can accommodate linear and nonlinear models with multiple inputs and multiple outputs. When the model is defined by differential equations, non-uniform repetitive dosage regimens can be handled. The model may also be entered in integrated form when single dose studies or uniform multiple dose studies are being considered. The programs employ a variable-step, variable-order integration routine to solve the model differential equations, and the Nelder-Mead simplex procedure to determine the parameter values which minimize a weighted least squares criterion. The programs have been written for an interactive time-sharing environment with the experimental data and model equations stored in files for future use.

Computers↗
PubMed2007

Sizing a trial to alter the trajectory of health behaviours: methods, parameter estimates, and their application.

Group-randomized trials often involve repeat observations on the same participants. When there are no more than two observations from each participant, standard mixed-model regression methods for a pretest-posttest design can be used. When there are more than two observations from each participant, random coefficients models may be useful. This paper describes the random coefficients analysis appropriate to data from an extended nested cohort design and presents the methods for power analysis and sample size calculations based on that analysis. We provide estimates for the parameters required for those calculations for a number of adolescent health behaviours. We also show how the estimates can be used to plan a future trial.

Adolescent↗
PubMed2006

Salmonella Dublin infection in young dairy calves: transmission parameters estimated from field data and an SIR-model.

In this study we used field data collected from October 2001 to January 2002 to estimate number of days of faecal excretion of Salmonella Dublin bacteria and time to seroconversion in infected calves below the age of 180 days. Based on these estimates all calves in four endemically infected dairy herds were grouped into the following infection states: susceptible (S), infectious (I) and resistant/recovered (R). Resistant calves had either acquired maternal antibodies through colostrum or they have recovered from previous infection and had a high level of antibodies directed against Salmonella Dublin possibly protecting them from becoming infected again until the level of antibodies had decreased to sufficiently low levels. Using the antibody measurements and faecal excretion periods, it was possible to assign the most likely infection state to each calf per week of the study period. Estimates of transmission parameter, beta, were obtained from a generalised linear model relating the number of new infections to the proportion of susceptible and infectious calves per week. From beta, the reproduction ratio R at steady state and the basic reproduction ratio R(0) were estimated for each herd and across herds. The R(0) denotes the average number of new infections caused by one infectious individual that is introduced to a fully susceptible population. The point estimates for R(0) ranged from 1.1 to 2.7 in the study herds. However, the confidence intervals were wide. Data were too limited to show possible significant differences in the parameters between the study herds. However, the tendency in the data suggested that there may be important differences. Across herds the R(0) was close to two suggesting that on average one infectious calf will produce two new infectious calves when introduced into a fully susceptible population under typical Danish dairy production systems. Further, the analyses indicated that environmental contamination from infectious calves plays an important role in transmitting Salmonella Dublin between calves.

Animals↗
PubMed2006

Parameter estimation in models combining signal transduction and metabolic pathways: the dependent input approach.

Biological complexity and limited quantitative measurements pose severe challenges to standard engineering methodologies for modelling and simulation of genes and gene products integrated in a functional network. In particular, parameter quantification is a bottleneck, and therefore parameter estimation, identifiability, and optimal experiment design are important research topics in systems biology. An approach is presented in which unmodelled dynamics are replaced by fictitious 'dependent inputs'. The dependent input approach is particularly useful in validation experiments, because it allows one to fit model parameters to experimental data generated by a reference cell type ('wild-type') and then test this model on data generated by a variation ('mutant'), so long as the mutations only affect the unmodelled dynamics that produce the dependent inputs. Another novel feature of the approach is in the inclusion of a priori information in a multi-objective identification criterion, making it possible to obtain estimates of parameter values and their variances from a relatively limited experimental data set. The pathways that control the nitrogen uptake fluxes in baker's yeast (Saccharomyces cerevisiae) have been studied. Well-defined perturbation experiments were performed on cells growing in steady-state. Time-series data of extracellular and intracellular metabolites were obtained, as well as mRNA levels. A nonlinear model was proposed and was shown to be structurally identifiable given data of its inputs and outputs. The identified model is a reliable representation of the metabolic system, as it could correctly describe the responses of mutant cells and different perturbations.

Algorithms↗
PubMed2004

From FNS to HEIV: a link between two vision parameter estimation methods.

Problems requiring accurate determination of parameters from image-based quantities arise often in computer vision. Two recent, independently developed frameworks for estimating such parameters are the FNS and HEIV schemes. Here, it is shown that FNS and a core version of HEIV are essentially equivalent, solving a common underlying equation via different means. The analysis is driven by the search for a nondegenerate form of a certain generalized eigenvalue problem and effectively leads to a new derivation of the relevant case of the HEIV algorithm. This work may be seen as an extension of previous efforts to rationalize and interrelate a spectrum of estimators, including the renormalization method of Kanatani and the normalized eight-point method of Hartley.

Algorithms↗
PubMed2006

Parameter estimation for the exponential-normal convolution model for background correction of affymetrix GeneChip data.

There are many methods of correcting microarray data for non-biological sources of error. Authors routinely supply software or code so that interested analysts can implement their methods. Even with a thorough reading of associated references, it is not always clear how requisite parts of the method are calculated in the software packages. However, it is important to have an understanding of such details, as this understanding is necessary for proper use of the output, or for implementing extensions to the model. In this paper, the calculation of parameter estimates used in Robust Multichip Average (RMA), a popular preprocessing algorithm for Affymetrix GeneChip brand microarrays, is elucidated. The background correction method for RMA assumes that the perfect match (PM) intensities observed result from a convolution of the true signal, assumed to be exponentially distributed, and a background noise component, assumed to have a normal distribution. A conditional expectation is calculated to estimate signal. Estimates of the mean and variance of the normal distribution and the rate parameter of the exponential distribution are needed to calculate this expectation. Simulation studies show that the current estimates are flawed; therefore, new ones are suggested. We examine the performance of preprocessing under the exponential-normal convolution model using several different methods to estimate the parameters.

Algorithms↗
PubMed1999

On the kinematic modelling and the parameter estimation of the human shoulder.

This paper presents some results on the modelling and the corresponding parameter estimation of the human shoulder. This system consists of the clavicle, the scapula, the humerus and the various joints between these bodies and the trunk through the sternum; it will be represented as a succession of a rotational joint between the sternum and the clavicle and a constant distance joint, representing the scapula between, the clavicle and the humerus head. The parameters of this system are the components of the position vectors of the joint characteristic points (the corresponding centres of the rotations). Experimental results are presented as well as a validation of the proposed model.

Acromioclavicular Joint↗