Data Analysis Using the Method of Least Squares by John Wolberg

By John Wolberg

The most popular approach to info research of quantitative experiments is the strategy of least squares. usually, notwithstanding, the entire strength of the strategy is ignored and intensely few books care for this topic on the point that it merits. the aim of knowledge research utilizing the tactic of Least Squares is to fill this hole and contain the kind of info required to assist scientists and engineers practice the strategy to difficulties of their particular fields of curiosity. moreover, graduate scholars in technology and engineering doing paintings of experimental nature can take advantage of this publication. relatively, either linear and non-linear least squares, using experimental mistakes estimates for information weighting, systems to incorporate past estimates, technique for choosing and testing models, prediction research, and a few non-parametric tools are mentioned.

Show description

Read or Download Data Analysis Using the Method of Least Squares PDF

Best measurements books

Numerical and Practical Exercises in Thermoluminescence

"Thermoluminescence (TL) is a well-established approach that's everyday in dosimetric and relationship functions. even if a number of very good reference books exist which record either the theoretical and experimental elements of TL, there's a basic loss of books that care for the categorical numerical and useful facets of studying TL information.

Introduction to contact mechanics

Advent to touch Mechanics, moment variation is a gradual advent to the mechanics of strong our bodies in touch for graduate scholars, put up doctoral contributors, and the start researcher. This moment version keeps the introductory personality of the 1st with a spotlight on fabrics technological know-how as certain from immediately strong mechanics conception.

501 Measurement Conversion Questions (Learning Express)

This e-book serves readers who are looking to increase the dimension and conversion abilities they should be triumphant in school and on checks. the 10 sections of this ebook make sure that readers perform numerous questions together with perimeter, quarter, quantity, and angles. With over 500 perform questions, this ebook is an important instrument for college kids who have to increase their math abilities to cross tests very easily.

Close Range Photogrammetry: Principles, Techniques and Applications

An authoritative advisor and the 1st accomplished glossy textual content in this topic in English; provided the acclaimed Karl Kraus Medal via ISPRS

Extra resources for Data Analysis Using the Method of Least Squares

Example text

2. 2) In this equation, Xi (italicized) is the measured value of the ith independent variable and xi is the computed value. 1. In that equation capital X (unitalicized) represents the vector of independent variables. 1 is valid even if the uncertainties in the x variables are not negligible. All that is required is a modified form of the weighting function used to determine the values of wi. 4 Xi is unitalicized because it represents the vector of the independent variables. 3 represents the scalar independent variable.

An alternative class of methods to find a “best” set of ak's is to use an intelligent search within a limited range 38 Chapter 2 THE METHOD OF LEAST SQUARES of the unknown parameter space. , TV04). 2, we noted that regardless of the choice of the objective function, a weight wi is specified for each point. The "weight" associated with a point is based upon the relative uncertainties associated with the different points. Clearly, we must place greater weight upon points that have smaller uncertainties, and less weight upon the points that have greater uncertainties.

Let us use the notation bk as the prior estimate of ak and σ bk as the uncertainty associated with this prior estimate. In the statistical literature these prior estimates are sometimes called Bayesian estimators. (This terminology stems from the work of the Reverend Thomas Bayes who was a little known statistician born in 1701. 6) If there is no Bayesian estimator for a particular ak the value of σ bk is set to infinity. Regardless of the choice of objective function and scheme used to determine the weights wi, one must then determine the values of the p unknown parameters ak that minimize S.

Download PDF sample

Rated 4.45 of 5 – based on 10 votes