Difference between revisions of "Forest Error Analysis for the Physical Sciences"

From New IAC Wiki
Jump to navigation Jump to search
Line 30: Line 30:
  
 
=Propagation of Uncertainties=
 
=Propagation of Uncertainties=
 +
 +
 +
= Chi-Square=
 +
 +
Root fundtion to evaluate meaning of Chi-square
 +
 +
P-value
 +
<pre>
 +
Double_t Prob(Double_t chi2, Int_t ndf)
 +
Computation of the probability for a certain Chi-squared (chi2)
 +
and number of degrees of freedom (ndf).
 +
 +
Calculations are based on the incomplete gamma function P(a,x),
 +
where a=ndf/2 and x=chi2/2.
 +
 +
P(a,x) represents the probability that the observed Chi-squared
 +
for a correct model should be less than the value chi2.
 +
 +
The returned probability corresponds to 1-P(a,x),
 +
which denotes the probability that an observed Chi-squared exceeds
 +
the value chi2 by chance, even for a correct model.
 +
 +
</pre>
 +
--- NvE 14-nov-1998 UU-SAP Utrecht
  
 
=References=
 
=References=

Revision as of 22:51, 17 September 2009

Class Admin

Forest_ErrorAnalysis_Syllabus

Homework

Homework is due at the beginning of class on the assigned day. If you have a documented excuse for your absence, then you will have 24 hours to hand in the homework after being released by your doctor.

Class Policies

http://wiki.iac.isu.edu/index.php/Forest_Class_Policies

Instructional Objectives

Course Catalog Description
Error Analysis for the Physics Sciences 3 credits. Lecture course with computation requirements. Topics include: Error propagation, Probability Distributions, Least Squares fit, multiple regression, goodnes of fit, covariance and correlations.

Prequisites:Math 360.

Course Description
The course assumes that the student has very limited experience with the UNIX environment and C/C++ programming. Homework problems involve modifying and compiling example programs written in C++.

Systematic and Random Errors

Reporting Uncertainties

Notation

X \pm Y = X(Y)

Statistical Distributions

Binomial

Poisson

Gaussian

Lorentzian

Propagation of Uncertainties

Chi-Square

Root fundtion to evaluate meaning of Chi-square

P-value

Double_t Prob(Double_t chi2, Int_t ndf)
 Computation of the probability for a certain Chi-squared (chi2)
 and number of degrees of freedom (ndf).

 Calculations are based on the incomplete gamma function P(a,x),
 where a=ndf/2 and x=chi2/2.

 P(a,x) represents the probability that the observed Chi-squared
 for a correct model should be less than the value chi2.

 The returned probability corresponds to 1-P(a,x),
 which denotes the probability that an observed Chi-squared exceeds
 the value chi2 by chance, even for a correct model.

--- NvE 14-nov-1998 UU-SAP Utrecht

References

1.) "Data Reduction and Error Analysis for the Physical Sciences", Philip R. Bevington, ISBN-10: 0079112439, ISBN-13: 9780079112439

CPP programs for Bevington

Bevington programs

2.)An Introduction to Error Analysis, John R. Taylor ISBN 978-0-935702-75-0