Initial Parameter Estimates Research Articles

Using otolith weight–age relationships to predict age based metrics of coral reef fish populations across different temporal scales

We assess the use of otolith weight to predict population age structure of an important harvested coral reef fish at different temporal scales up to 4 years, and explore the implications of age prediction for estimates of key fishery parameters. Fish age and otolith weight relationships were estimated for common coral trout, Plectropomus leopardus (Serranidae: Epinephelinae), at 24 coral reefs located in four different regions spanning 7° of latitude along the Great Barrier Reef of Australia from 1995 to 1999. We explored the robustness of predictions of population age structures from otolith weights where age structure in 1 year was derived from otolith weights using the age–otolith weight relationships derived in another year up to 4 years earlier. The accuracy of predictions of age structure varied depending upon the temporal scale over which the prediction was made. Predictive accuracy was highest for predictions in the same year as the age–otolith weight relationship was derived and worst at the longest scale, when predictions spanned 4 years. Predictions of age based on the age–otolith weight relationships generally overestimated the minimum age of a population and underestimated the maximum age. Mean predicted age was generally within ±1% difference of the mean observed age while mean predicted length at modal age (growth index) was largely within ±5% difference of mean observed length at modal age. Predicted age structures gave less accurate estimates of total mortality rate than those estimated from directly determined age structures. Fish age–otolith weight relationships generally predicted modal age within ±1 year at all temporal scales. These results have significance for making rapid, initial estimates of key parameters for long-term monitoring of tropical reef fish stocks, especially in circumstances where available resources are insufficient for a comprehensive program of direct age estimation.

Use of Bayesian Methods to Improve Prediction of Panicle and Shoot Blight Severity of Pistachio in California

ABSTRACT Panicle and shoot blight, caused by a Fusicoccum sp., is one of the major aboveground diseases of pistachio in California. The effects of temperature, number of continuous rainy days in April and May, irrigation system, and incidence of latent infection of the Fusicoccum sp. on severity of panicle and shoot blight of pistachio leaves and fruit have been quantified previously, using data collected from 1999 through 2001. A predictive model for leaves and another model for fruit with good explanatory power were generated. In 2003 and 2004, newly collected data were used to evaluate the two models with non-Bayesian and Bayesian methods. The 95% credible (i.e., confidence) intervals of initial (before modification with non-Bayesian and Bayesian methods) and updated parameter estimates were used to investigate their prognostic validity. In 2003, the non-Bayesian analysis resulted in all parameter estimates, with the exception of cumulative daily mean temperature from 1 June until harvest, having different 95% confidence intervals than the parameter estimates of the original models. In addition, the parameter estimates for drip irrigation for the leaf infection and the parameter estimates for drip irrigation and number of continuous rainy days in April and May for fruit infection were not statistically significant. With Bayesian methods, the reestimated model parameters had overlapping 95% credible intervals with the initial estimated parameters, except for the number of continuous rainy days in April and May. When the two sets of modified parameter estimates were used to predict disease severity, statistically significant (alpha = 0.05) differences between observed and predicted disease severities were found with non-Bayesian analysis for leaf infection in three locations and with Bayesian analysis for fruit infection in one orchard. The parameter estimates were modified again at the end of the 2004 season and were all statistically significant with both non-Bayesian and Bayesian methods. Both sets of parameter estimates gave predictions that were not significantly different from observed disease severity on leaves and fruit in all monitored orchards in 2004. In summary, Bayesian methods gave more consistent results when used to update parameter estimates with new information and yielded predictions not statistically different from observed disease severity in more cases than the non-Bayesian analysis.

A quantitative kinetic model for Al 2O 3:C: TL response to ionizing radiation

This paper presents a quantitative kinetic model for the important dosimetric material Al 2O 3:C. The model consists of two traps and two centers, and reproduces the experimental thermoluminescence (TL) vs. dose behavior, as well as the experimental variation of the optical absorption coefficient K with beta dose. Initial estimates of the kinetic parameters in the model are obtained either from published experimental data, or by using reasonable physical assumptions. Good agreement between the experimental data and calculations from the model are obtained for three different types of samples of alumina. This is achieved by keeping the trapping and recombination probabilities constant for all three samples, while the concentrations of the carriers are varied. The kinetic model provides also a quantitative description of the experimentally observed nonmonotonic behavior of the TL dose–response curves for all three samples.

Modeling the hydrologic response of groundwater dominated wetlands to transient boundary conditions: Implications for wetland restoration

A variably-saturated groundwater model, based on that of Freeze [Freeze, R.A., 1971. Three-dimensional, transient, saturated–unsaturated flow in a groundwater basin. Water Resources Research 7, 347–366.], was used to analyze the details of surface–groundwater interaction and resulting hydroperiods of a site undergoing wetland restoration (the Lake Station Wetland Restoration Site in Northwest Indiana, USA). The three-dimensional groundwater flow model couples the saturated and unsaturated zones through the use of van Genuchten’s [van Genuchten, M.T., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44, 892–898.] characteristic equations. Initial estimates of hydraulic parameters were refined through a calibration exercise aimed at minimizing the discrepancy between simulated and measured water levels in seven wells within the study. Numerical simulations using the calibrated model, and driven by annual time series of rainfall and potential evaporation, were used to generate hydroperiod maps of surface saturation and root-zone saturation over a three-year period of study. This allowed identification of regularly saturated areas that would support hydric plants, as well as more rarely saturated areas that would require more dry tolerant species or additional hydrological remediation. The simulations also revealed the critical roles that topography, rainfall history, and antecedent conditions play in the hydrology of degraded wetlands that have been targeted for restoration.

An info‐gap approach to power and sample size calculations

AbstractPower and sample size calculations are an important but underutilised component of many ecological investigations. A key problem with these calculations is the need to estimate or guess the effect size and error variance (the design parameters) prior to the actual data collection. Furthermore, calculations associated with statistical power and sample size are invariably predicated on normal distribution theory. While the central limit theorem ensures the applicability of normal‐based inference for reasonably large sample sizes, the impact of violations of this assumed distributional form in the context of power and sample size determinations is rarely considered. This paper uses information‐gap theory to provide sample size guidelines that are robust to uncertainties associated with both the design parameters and distributional form. A simple information‐gap approach is developed for one‐ and two‐sided hypothesis tests. The model results quantify the extent to which minimum power demands can be protected from uncertainty by taking additional samples, and demonstrate the importance of the combined effects of standard deviation/effect size ratio and assumed distribution in these considerations. Info‐gap theory does not eliminate the need for an initial estimate or best guess of the design parameters or the specification of a parametric distribution from which to compute power. It does, however, measure the degree of insurance provided by additional samples in the face of uncertainties in each of these. Copyright © 2006 John Wiley & Sons, Ltd.

A Library of Eclipsing Binary Light-Curves: Fast Initial Parameters Estimation, and on the Uniqueness of the Inverse Problem

In order to improve the light curve solutions we suggest to use a new approach. A library of the Fourier-coefficients (up to 20th term) of (several millions of) light curves was constructed each of the light curves has different input parameters. A light curve solution is made in a very fast way: its discrete Fourier-transform yields not more than some simple number which are compared to the Fourier-coefficients in the library. A chi-squared test can help us to estimate very good initial parameters for the differential correction analysis. The library can also be used to study the uniqeness problem of the light curve solutions. Here we investigated the uniqueness of the spot solution of SV Cam.

A refined algorithm for multisensor image registration based on pixel migration

Multimodality image registration via pixel migration is a powerful approach. However, it suffers from a serious problem--the global maximum on the sum of squared gradient magnitude (SSG) surface does not correspond to the correct solution of registration. To solve the problem, we partition the search space into feasible and infeasible regions. The genetic algorithm (global optimizer) is used to obtain a good initial estimate of registration parameters and followed by a fast refining with Powell's approach (local optimizer). The experimental results demonstrate that the use of this modified pixel migration algorithm on multisensor image registration is very effective.

Fingerprint matching based on global comprehensive similarity

This paper introduces a novel algorithm based on global comprehensive similarity with three steps. To describe the Euclidean space-based relative features among minutiae, we first build a minutia-simplex that contains a pair of minutiae as well as their associated textures, with its transformation-variant and invariant relative features employed for the comprehensive similarity measurement and parameter estimation, respectively. By the second step, we use the ridge-based nearest neighborhood among minutiae to represent the ridge-based relative features among minutiae. With these ridge-based relative features, minutiae are grouped according to their affinity with a ridge. The Euclidean space-based and ridge-based relative features among minutiae reinforce each other in the representation of a fingerprint. Finally, we model the relationship between transformation and the comprehensive similarity between two fingerprints in terms of histogram for initial parameter estimation. Through these steps, our experiment shows that the method mentioned above is both effective and suitable for limited memory AFIS owing to its less than 1k byte template size.

Modeling the Effects of Torsional Disorder on the Spectra of Poly- and Oligo-(p-phenyleneethynylenes)

The absorption spectra of phenyleneethynylene oligomers show an unusual change in shape with oligomer length. The unusual aspects of the spectra arise from rotation of the phenylene rings about the long axis of the oligomer. In the ground electronic state, the barrier to this rotation is low and the spectra in room temperature come from an ensemble of different structures. In the excited electronic state, the barrier to rotation is substantially higher, giving rise to strong nonlinear electron-phonon coupling. A multidimensional semiempirical model that includes these effects is developed for the photophysics of phenyleneethynylene oligomers. The ground-state energy is modeled with a molecular mechanics expression, and the excitation energy is modeled with an exciton model. Intermediate Neglect of Differential Overlap/Singles Configuration Interaction (INDO/SCI) calculations verify the exciton model and provide initial estimates of the model parameters. These parameters generate the qualitative features seen in experimental spectra. Inclusion of entropy effects from the multiple torsional coordinates is essential. Refinement of the parameters yields quantitative agreement with experiment. This agreement shows that coupling to torsional motion is a major factor in the spectroscopy and photophysics of these conjugated polymers.

Allele frequency misspecification: effect on power and Type I error of model-dependent linkage analysis of quantitative traits under random ascertainment

BackgroundStudies of model-based linkage analysis show that trait or marker model misspecification leads to decreasing power or increasing Type I error rate. An increase in Type I error rate is seen when marker related parameters (e.g., allele frequencies) are misspecified and ascertainment is through the trait, but lod-score methods are expected to be robust when ascertainment is random (as is often the case in linkage studies of quantitative traits). In previous studies, the power of lod-score linkage analysis using the "correct" generating model for the trait was found to increase when the marker allele frequencies were misspecified and parental data were missing. An investigation of Type I error rates, conducted in the absence of parental genotype data and with misspecification of marker allele frequencies, showed that an inflation in Type I error rate was the cause of at least part of this apparent increased power. To investigate whether the observed inflation in Type I error rate in model-based LOD score linkage was due to sampling variation, the trait model was estimated from each sample using REGCHUNT, an automated segregation analysis program used to fit models by maximum likelihood using many different sets of initial parameter estimates.ResultsThe Type I error rates observed using the trait models generated by REGCHUNT were usually closer to the nominal levels than those obtained when assuming the generating trait model.ConclusionThis suggests that the observed inflation of Type I error upon misspecification of marker allele frequencies is at least partially due to sampling variation. Thus, with missing parental genotype data, lod-score linkage is not as robust to misspecification of marker allele frequencies as has been commonly thought.

Robust regression for high throughput drug screening

Effective analysis of high throughput screening (HTS) data requires automation of dose–response curve fitting for large numbers of datasets. Datasets with outliers are not handled well by standard non-linear least squares methods, and manual outlier removal after visual inspection is tedious and potentially biased. We propose robust non-linear regression via M-estimation as a statistical technique for automated implementation. The approach of finding M-estimates by Iteratively Reweighted Least Squares (IRLS) and the resulting optimization problem are described. Initial parameter estimates for iterative methods are important, so self-starting methods for our model are presented. We outline the software implementation, done in Matlab and deployed as an Excel application via the Matlab Excel Builder Toolkit. Results of M-estimation are compared with least squares estimates before and after manual editing.

Designs and model effects definitions in the initial stage of a plant breeding program

The objective of this work was to compare the relative efficiency of initial selection and genetic parameter estimation, using augmented blocks design (ABD), augmented blocks twice replicated design (DABD) and group of randomised block design experiments with common treatments (ERBCT), by simulations, considering fixed effect model and mixed model with regular treatment effects as random. For the simulations, eight different conditions (scenarios) were considered. From the 600 simulations in each scenario, the mean percentage selection coincidence, the Pearsons´s correlation estimates between adjusted means for the fixed effects model, and the heritability estimates for the mixed model were evaluated. DABD and ERBCT were very similar in their comparisons and slightly superior to ABD. Considering the initial stages of selection in a plant breeding program, ABD is a good alternative for selecting superior genotypes, although none of the designs had been effective to estimate heritability in all the different scenarios evaluated.

MULTIPLE STRATEGIES FOR PARAMETER ESTIMATION VIA A HYBRID METHOD: A COMPARATIVE STUDY

In this paper, two different strategies are considered for application of a previously proposed hybrid method designed to parameter estimation. This method combines the feedforward neural networks ability to produce initial parameter estimates close to the true values with the fast convergence of the Levenberg-Marquardt method using such estimates. The first strategy is of general applicability, while the second one is intended for models having a structure defined by various blocks in series. The neuromuscular blockade model parameter estimation problem is taken as the case study for comparing the performances of the two strategies.

The integration of macromolecular diffraction data

The objective of any modern data-processing program is to produce from a set of diffraction images a set of indices (hkls) with their associated intensities (and estimates of their uncertainties), together with an accurate estimate of the crystal unit-cell parameters. This procedure should not only be reliable, but should involve an absolute minimum of user intervention. The process can be conveniently divided into three stages. The first (autoindexing) determines the unit-cell parameters and the orientation of the crystal. The unit-cell parameters may indicate the likely Laue group of the crystal. The second step is to refine the initial estimate of the unit-cell parameters and also the crystal mosaicity using a procedure known as post-refinement. The third step is to integrate the images, which consists of predicting the positions of the Bragg reflections on each image and obtaining an estimate of the intensity of each reflection and its uncertainty. This is carried out while simultaneously refining various detector and crystal parameters. Basic features of the algorithms employed for each of these three separate steps are described, principally with reference to the program MOSFLM.

Ultracompact AM Canum Venaticorum Binaries from the Sloan Digital Sky Survey: Three Candidates Plus the First Confirmed Eclipsing System

AM CVn systems are a rare (about a dozen previously known) class of cataclysmic variables, arguably encompassing the shortest orbital periods (down to about 10 minutes) of any known binaries. Both binary components are thought to be degenerate (or partially so), likely with mass transfer from a helium-rich donor onto a white dwarf, driven by gravitational radiation. Although rare, AM CVn systems are of high interest as possible Type Ia supernova progenitors and because they are predicted to be common sources of gravity waves in upcoming experiments such as the Laser Interferometer Space Antenna. We have identified four new AM CVn candidates from the Sloan Digital Sky Survey (SDSS) spectral database. All four show hallmark spectroscopic characteristics of the AM CVn class: each is devoid of hydrogen features and instead shows a spectrum dominated by helium. All four show double-peaked emission, indicative of helium-dominated accretion disks. Limited time series CCD photometric follow-up data have been obtained for three of the new candidates from the Astrophysical Research Consortium 3.5 m telescope; most notably, a 28.3 minute binary period with sharp, deep eclipses is discovered in one case, SDSS J0926+3624. This is the first confirmed eclipsing AM CVn, and our data allow initial estimates of binary parameters for this ultracompact system. The four new SDSS objects also provide a substantial expansion of the current critically small sample of AM CVn systems.

SigrafW: An easy‐to‐use program for fitting enzyme kinetic data

SigrafW is Windows-compatible software developed using the Microsoft® Visual Basic Studio program that uses the simplified Hill equation for fitting kinetic data from allosteric and Michaelian enzymes. SigrafW uses a modified Fibonacci search to calculate maximal velocity (V), the Hill coefficient (n), and the enzyme-substrate apparent dissociation constant (K). The estimation of V, K, and the sum of the squares of residuals is performed using a Wilkinson nonlinear regression at any Hill coefficient (n). In contrast to many currently available kinetic analysis programs, SigrafW shows several advantages for the determination of kinetic parameters of both hyperbolic and nonhyperbolic saturation curves. No initial estimates of the kinetic parameters are required, a measure of the goodness-of-the-fit for each calculation performed is provided, the nonlinear regression used for calculations eliminates the statistical bias inherent in linear transformations, and the software can be used for enzyme kinetic simulations either for educational or research purposes. Persons interested in receiving a free copy of the software should contact Dr. F. A. Leone.

Initial condition and parameter estimation in physical 'on-off' processes by variational data assimilation

Initial condition and parameter estimation in physical 'on-off' processes by variational data assimilation

Graphical estimation of the dual-enzyme kinetic parameters for Cr(VI) reduction

Chromium(VI) (Cr(VI)) contamination of soil and groundwater is a major environmental concern. Bioreduction of Cr(VI) by Shewanella oneidensis MR-1 (MR-1) can be considered a feasible option to reduce the toxic and mobile Cr(VI) to the less toxic and less mobile chromium(III) (Cr(III)). The reaction rate expression for Cr(VI) reduction is nonlinear and the rate constants are evaluated by employing nonlinear optimization techniques. The outcome of the optimization techniques, in general, depends on the initial estimate of the kinetic parameters which is not always available. A graphical approach based on sound mathematical reasoning has been developed which is accurate, simpler to use, and can provide the best initial estimate for nonlinear optimization.

A hybrid genetic algorithm for estimating the equilibrium potential of an ion-selective electrode

Non-linear equations can be used to model the measured potential of ion-selective electrodes (ISEs) as a function of time. This can be done by using non-linear least squares regression to fit parameters of non-linear equations to an ISE response curve. In iterative non-linear least squares regression (which can be considered as local optimisers), the determination of starting parameter estimates that yield convergence to the global optimum can be difficult. Starting values away from the global optimum can lead to either abortive divergence or convergence to a local optimum. To address this issue, a global optimisation technique was used to find initial parameter estimates near the global optimum for subsequent further refinement to the absolute optimum. A genetic algorithm has been applied to two non-linear equations relating the measured potential from selected ISEs to time. The parameter estimates found from the genetic algorithm were used as starting values for non-linear least squares regression, and subsequent refinement to the absolute optimum. This approach was successfully used for both expressions with measured data from three different ISEs; namely, calcium, chloride and lead ISEs.

Inverse Analysis of Upward Water Flow in a Groundwater Table Lysimeter

The accuracy of numerical water flow models for the vadose zone depends on the estimation of the soil hydraulic properties. In this study, the hydraulic parameters for a silty clay soil in a large lysimeter were determined through inverse modeling of a fallow period with upward water flow from a shallow groundwater table. Parameter uniqueness was studied by simulating a hypothetical soil with known hydraulic properties under comparable conditions. Sensitivity analysis showed that the pressure head h(z,t), the volumetric water content θ(z,t), and the cumulative bottom flux Q(t) were least sensitive to the residual volumetric water content θr and the pore‐connectivity parameter λ in the van Genuchten–Mualem (VGM) model. Parameter response surfaces showed that least squares fitting with θ(z,t) data is more likely to result in a unique hydraulic parameter set than least squares fitting with h(z,t) or Q(t) data. With only θ(z,t) in the objective function, the least squares minimization algorithm was capable of finding the correct soil hydraulic parameters, provided that θr and λ were fixed and that multiple initial parameter estimates were used. The protocol that was developed for the hypothetical soil was subsequently applied to the actual groundwater table lysimeter. The soil hydraulic parameters for the lysimeter for two (x,y) locations were determined using θ(z,t) data as measured by capacitance sensors. The variability in the optimized inverse of the air‐entry value α and the saturated hydraulic conductivity Ks in the VGM model was relatively high because of the high parameter correlation between these parameters. The optimized soil hydraulic properties can be used to study capillary rise from the groundwater table.