Estimation and setting starting values in ARMA algorithms

1993 ◽  
Vol 12 (1) ◽  
pp. 85-103 ◽  
Author(s):  
Zoran M. Šarić ◽  
Srbijanka R. Turajlić
Keyword(s):  
Starting Values

Comparison of two devices for measuring exercise transcutaneous oxygen pressures in patients with claudication

VASA ◽  
2015 ◽  
Vol 44 (5) ◽  
pp. 355-362 ◽  
Author(s):  
Marie Urban ◽  
Alban Fouasson-Chailloux ◽  
Isabelle Signolet ◽  
Christophe Colas Ribas ◽  
Mathieu Feuilloy ◽  
...  
Keyword(s):  
Oxygen Pressure ◽  
Optical Sensors ◽  
Chemical Sensors ◽  
Transcutaneous Oxygen ◽  
Starting Values ◽  
Two Systems ◽  
Transcutaneous Oxygen Pressure ◽  
New Sensors ◽  
Changes Over Time ◽  
Over Time

Abstract. Summary: Background: We aimed at estimating the agreement between the Medicap® (photo-optical) and Radiometer® (electro-chemical) sensors during exercise transcutaneous oxygen pressure (tcpO2) tests. Our hypothesis was that although absolute starting values (tcpO2rest: mean over 2 minutes) might be different, tcpO2-changes over time and the minimal value of the decrease from rest of oxygen pressure (DROPmin) results at exercise shall be concordant between the two systems. Patients and methods: Forty seven patients with arterial claudication (65 + / - 7 years) performed a treadmill test with 5 probes each of the electro-chemical and photo-optical devices simultaneously, one of each system on the chest, on each buttock and on each calf. Results: Seventeen Medicap® probes disconnected during the tests. tcpO2rest and DROPmin values were higher with Medicap® than with Radiometer®, by 13.7 + / - 17.1 mm Hg and 3.4 + / - 11.7 mm Hg, respectively. Despite the differences in absolute starting values, changes over time were similar between the two systems. The concordance between the two systems was approximately 70 % for classification of test results from DROPmin. Conclusions: Photo-optical sensors are promising alternatives to electro-chemical sensors for exercise oximetry, provided that miniaturisation and weight reduction of the new sensors are possible.

Digital Computer Analysis of Electrophoresis and Ultracentrifugation Patterns by a Sum of Gaussian-like Distributions

1975 ◽  
Vol 30 (5-6) ◽  
pp. 311-317 ◽  
Author(s):  
E Tränkle
Keyword(s):  
Distribution Function ◽  
Computer Analysis ◽  
Digital Computer ◽  
Fortran Program ◽  
Test Period ◽  
Starting Values ◽  
Overlapping Peaks ◽  
Molecular Components

Abstract Computer Analysis, Electrophoresis, Ultracentrifugation A Gaussian-like distribution function with three additional parameters is introduced which describes well the electrophoresis patterns of albumin, prealbumin and transferrin. Electrophoresis and ultracentrifugation patterns with 10-15 overlapping peaks are analyzed by means of the FORTRAN-program DIANA. One obtains the (relative) areas, positions and widths of the peaks. The analysis of a series of patterns proceeds in an automated way after the number of molecular components as well as starting values of the positions and the widths have been chosen in a test period.

Evaluation of Pettys Nonlinear Model in Wood Permeability Measurement

Holzforschung ◽  
2001 ◽  
Vol 55 (1) ◽  
pp. 82-86
Author(s):  
J. Lu ◽  
F. Bao ◽  
Y. Zhao
Keyword(s):  
Nonlinear Model ◽  
Gas Permeability ◽  
Optimization Algorithms ◽  
Optimization Techniques ◽  
Curvilinear Relationship ◽  
Grid Search ◽  
Permeability Measurement ◽  
Iterative Optimization ◽  
Starting Values ◽  
Least Squares Fit

Summary To calculate the effective radii of two conductive elements in series in wood specimens by using the gas permeability measurement, the four parameters from the curvilinear relationship of superficial specific permeability against reciprocal mean pressure as illustrated in Petty's model must be evaluated. This paper describes a detailed procedure for obtaining such parameters by using the least-squares fit calculated from a statistical analysis system (SAS) program. Three different iterative optimization algorithms and starting points were used separately to fit the Petty's nonlinear model based on the same experimental data from one specimen of birch. The estimate of the parameters: A = 35.38 darcy, B = 80.51 darcy, l = 0.19 darcy atm, m = 6.34 darcy atm was recommended for the fitted model. Compared to the results on the estimate of parameters obtained in the previous papers, this estimate for the parameters was a global minimum, thus it was a refinement and more accurate. Since the Gauss-Newton method resulted in almost the same convergence results for all the three sets of starting values with the least iterations in the evaluation, it was the preferred optimization algorithm both for simplicity and accuracy in solving the Petty's model. Because the same solutions for all three iterative optimization algorithms were obtained by using two different sets of starting points produced from the grid search, a grid search seemed to be very helpful for finding reasonable starting values for various iterative optimization techniques.

A modified Runge-Kutta method

SIMULATION ◽  
1968 ◽  
Vol 10 (5) ◽  
pp. 221-223 ◽  
Author(s):  
A.S. Chai
Keyword(s):  
Error Estimate ◽  
Linear Combination ◽  
Experimental Results ◽  
The Other ◽  
New Method ◽  
Kutta Method ◽  
Starting Values ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
A Minor

It is possible to replace k2 in a 4th-order Runge-Kutta for mula (also Nth-order 3 ≤ N ≤ 5) by a linear combination of k1 and the ki's in the last step, using the same procedure for computing the other ki's and y as in the standard R-K method. The advantages of the new method are: It re quires one less derivative evaluation, provides an error estimate at each step, gives more accurate results, and needs a minor change to switch to the RK to obtain the starting values. Experimental results are shown in verification of the for mula.

scholarly journals Rayleigh Quotient Methods for Estimating Common Roots of Noisy Univariate Polynomials

2019 ◽  
Vol 19 (1) ◽  
pp. 147-163 ◽  
Author(s):  
Alwin Stegeman ◽  
Lieven De Lathauwer
Keyword(s):  
Eigenvalue Problem ◽  
Simulation Study ◽  
Rayleigh Quotient ◽  
Tensor Algebra ◽  
Symbolic Algebra ◽  
Starting Values ◽  
New Methods ◽  
Sylvester Matrix ◽  
Univariate Polynomials ◽  
The Common

AbstractThe problem is considered of approximately solving a system of univariate polynomials with one or more common roots and its coefficients corrupted by noise. The goal is to estimate the underlying common roots from the noisy system. Symbolic algebra methods are not suitable for this. New Rayleigh quotient methods are proposed and evaluated for estimating the common roots. Using tensor algebra, reasonable starting values for the Rayleigh quotient methods can be computed. The new methods are compared to Gauss–Newton, solving an eigenvalue problem obtained from the generalized Sylvester matrix, and finding a cluster among the roots of all polynomials. In a simulation study it is shown that Gauss–Newton and a new Rayleigh quotient method perform best, where the latter is more accurate when other roots than the true common roots are close together.

A LINEAR CORRELATION OF PROTON CHEMICAL SHIFTS IN SOME ALKYL CHLORIDES AND HYDROCARBONS WITH THE OCCUPATION NUMBER OF THE HYDROGEN ORBITALS

1965 ◽  
Vol 43 (12) ◽  
pp. 3188-3192 ◽  
Author(s):  
F. Hruska ◽  
G. Kotowycz ◽  
T. Schaefer
Keyword(s):  
Linear Correlation ◽  
Occupation Number ◽  
Chemical Shifts ◽  
The Self ◽  
Starting Values ◽  
Occupation Numbers ◽  
Self Consistent ◽  
Consistent Group ◽  
Proton Chemical Shifts ◽  
Group Orbital

A linear correlation exists between the proton shifts of some alkyl chlorides and some hydrocarbons and the occupation numbers of the hydrogen 1s orbitals in the C—H bonds. The occupation numbers are those given by the self-consistent group orbital and bond electronegativity method. The application of this correlation to the prediction of starting values for occupation numbers, to the derivation of bond anisotropies in ethylene and acetylene, and to the prediction of hydrogen-bonded shifts of C—H protons is discussed.

SPATIAL AND TEMPORAL PATTERNS OF WITHIN-TREE COLONIZATION BY DENDROCTONUS FRONTALIS (COLEOPTERA: SCOLYTIDAE)

1978 ◽  
Vol 110 (11) ◽  
pp. 1213-1232 ◽  
Author(s):  
W. Scott Fargo ◽  
Robert N. Coulson ◽  
Paul E. Pulley ◽  
Don N. Pope ◽  
Claude L. Kelley
Keyword(s):  
Loblolly Pine ◽  
Nonlinear Function ◽  
Temporal Sequence ◽  
Dendroctonus Frontalis ◽  
Spatial And Temporal Patterns ◽  
Starting Values ◽  
Frequency Histogram ◽  
Modeling Process ◽  
Standing Trees ◽  
Colonization Process

AbstractWithin-tree colonization by Dendroctonus frontalis infesting loblolly pine, Pinus taeda L., was investigated. Two components of the colonization process were studied: the establishment of attacking adults (ATK) and the ensuing construction of egg galleries (GL). Data on the two variables were taken from standing trees beginning at the time of initial attack and continuing for 14 consecutive days.The spatial and temporal sequence of ATK was described for 1.5 m intervals along the infested bole for the duration of the process. A three parameter nonlinear function was used to describe the data. The pattern of attack was also described as an average process for the entire tree using the same model. A frequency histogram encompassing the range in variation for peak ATK from 134 trees was prepared to provide starting values for simulation purposes.The spatial and temporal sequence of GL construction was described using essentially the same approach as employed for ATK. The modeling process was complicated by loss or obscuring of GL from the radiograph by omission errors and foraging by Monochamus spp. and other associates. GL construction was also described as an average function for the entire tree and the rate of GL construction was defined. A frequency histogram of peak GL was prepared from data on 54 trees for use in selecting starting values for simulation purposes.Numerical relationships between ATK and GL were defined by combining the data on ATK and cumulative expected GL.

Velocity models for routine earthquake monitoring at volcanoes: from deterministic to Bayesian

2021 ◽  
Author(s):  
Jeremy Pesicek ◽  
Trond Ryberg ◽  
Roger Machacca ◽  
Jaime Raigosa
Keyword(s):  
Velocity Structure ◽  
Full Range ◽  
Earthquake Location ◽  
Monitoring Networks ◽  
Unknown Parameters ◽  
Widespread Application ◽  
Starting Values ◽  
Velocity Models ◽  
Earthquake Locations ◽  
Station Corrections

<p>Earthquake location is a primary function of volcano observatories worldwide and the resulting catalogs of seismicity are integral to interpretations and forecasts of volcanic activity.  Ensuring earthquake location accuracy is therefore of critical importance.  However, accurate earthquake locations require accurate velocity models, which are not always available.  In addition, difficulties involved in applying traditional velocity modeling methods often mean that earthquake locations are computed at volcanoes using velocity models not specific to the local volcano.   </p><p>Traditional linearized methods that jointly invert for earthquake locations, velocity structure, and station corrections depend critically on having reasonable starting values for the unknown parameters, which are then iteratively updated to minimize the data misfit.  However, these deterministic methods are susceptible to local minima and divergence, issues exacerbated by sparse seismic networks and/or poor data quality common at volcanoes.  In cases where independent prior constraints on local velocity structure are not available, these methods may result in systematic errors in velocity models and hypocenters, especially if the full range of possible starting values is not explored.  Furthermore, such solutions depend on subjective choices for model regularization and parameterization.</p><p>In contrast, Bayesian methods promise to avoid all these pitfalls.  Although these methods traditionally have been difficult to implement due to additional computational burdens, the increasing use and availability of High-Performance Computing resources mean widespread application of these methods is no longer prohibitively expensive.  In this presentation, we apply a Bayesian, hierarchical, trans-dimensional Markov chain Monte Carlo method to jointly solve for hypocentral parameters, 1D velocity structure, and station corrections using data from monitoring networks of varying quality at several volcanoes in the U.S. and South America.  We compare the results with those from a more traditional deterministic approach and show that the resulting velocity models produce more accurate earthquake locations.  Finally, we chart a path forward for more widespread adoption of the Bayesian approach, which may improve catalogs of volcanic seismicity at observatories worldwide. </p>

Starting values in estimation of cointegrating vectors with restrictions

2001 ◽  
Vol 8 (8) ◽  
pp. 521-524
Author(s):  
Johan Lyhagen ◽  
Lars Forsberg
Keyword(s):  
Starting Values
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