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Astronomical Data Analysis: Lecture Notes on Coding, FITS, Errors and Measurement (UCF, Fa, Study notes of Astronomy

University of Central Florida (UCF)Astronomy

Lecture notes from the university of central florida's (ucf) advanced astronomical data analysis course (ast 5765/4762) in fall 2009. The notes cover topics such as coding with fits, errors, illegitimate, systematic, and random errors, and measurement concepts. Students are introduced to the importance of understanding different types of errors and their impact on astronomical data analysis.

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Uploaded on 02/24/2010

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UCF Physics: AST 5765/4762: (Advanced) Astronomical Data Analysis
Fall 2009 Lecture Notes: 8. Coding, FITS, Errors
1 Check In: 10:30 — 10:35:, 5 min
•Questions before we start?
2 Astronomical Data: 10:35 — 10:50, 15 min
•What is FITS?
•Reading FITS files
•Reading header variables
•Adding/modifying header variables
•Writing FITS files
3 Illegitimate, Systematic, and Random Errors: 10:50 — 11:00,
10 min
•A measurement is the best estimate of a quantity in terms of accepted units.
•Three types of measurement error: illegitimate, systematic, and random
•Illegitimate error: a fundamental problem in the methods or assumptions (think you’re
doing one thing, really doing another)
•Find and fix!
–Check yourselves! Most homework errors are in this category.
–We’re particularly picky in this course to prepare you for doing this in real science.
–Mars Polar Lander English vs. Metric goof
•Systematic error: predictable difference between data and measurement
•Quantify and remove.
–A non-quantified systematic error can kill a measurement
–Must always estimate the unquantifiable error conservatively
–Any experimental plan must show how it will quantify and remove systematic errors
well enough to get the accuracy needed.
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Download Astronomical Data Analysis: Lecture Notes on Coding, FITS, Errors and Measurement (UCF, Fa and more Study notes Astronomy in PDF only on Docsity!

UCF Physics: AST 5765/4762: (Advanced) Astronomical Data Analysis

Fall 2009 Lecture Notes: 8. Coding, FITS, Errors

1 Check In: 10:30 — 10:35:, 5 min

  • Questions before we start?

2 Astronomical Data: 10:35 — 10:50, 15 min

  • What is FITS?
  • Reading FITS files
  • Reading header variables
  • Adding/modifying header variables
  • Writing FITS files

3 Illegitimate, Systematic, and Random Errors: 10:50 — 11:00,

10 min

  • A measurement is the best estimate of a quantity in terms of accepted units.
  • Three types of measurement error: illegitimate, systematic, and random
  • Illegitimate error: a fundamental problem in the methods or assumptions (think you’re doing one thing, really doing another)
  • Find and fix! - Check yourselves! Most homework errors are in this category. - We’re particularly picky in this course to prepare you for doing this in real science. - Mars Polar Lander English vs. Metric goof
  • Systematic error: predictable difference between data and measurement
  • Quantify and remove. - A non-quantified systematic error can kill a measurement - Must always estimate the unquantifiable error conservatively - Any experimental plan must show how it will quantify and remove systematic errors well enough to get the accuracy needed.

- Usually this is a major portion of any proposal (lack of this is a “red flag” for a bad proposal)

  • Random error: differences between data and measurement that can only be described prob- abilistically
  • Quantify, propagate through equations/analysis - Called the “noise” - Parameterized by the data’s standard deviation - Error bars in astronomy are 1σ (3σ in biology) - Minimize by repeated measurement
  • Figure of merit for all measurements: Signal-to-noise ratio (S/N or SNR or SN)

S/N =

final value of corrected measurement random error in that value

4 What’s in a Measurement?: 11:00 — 11:10, 10 min

  • Attempt measurement of a person’s height with tape measure bouncing on my shoe
  • Have class call out all effects affecting the measurement and classify as illigitimate, system- atic, or random
  • What if stick was actually in half-inches, not centimeters, but we didn’t notice?

5 Terms: 11:10 — 11:20, 10 min

  • Language of probability is precise , due to the subtleties involved. Be careful!
  • accuracy : closeness to truth
  • precision : ability to make small distinctions
  • (draw 2 charts like Bevington fig 1.1)
  • significant figures (1000. vs. 1000)
  • error : difference between measurement and truth (usually don’t know)
  • estimate (of error, mean, std. dev., etc.) best attempt to quantify ( vs. true value)
  • uncertainty : amount by which 2 measurements could differ and not be recognized as dif- ferent
  • standard error : estimate of 1σ (standard deviation) spread in measurements
  • significant difference : different by several times the uncertainty (3 or preferably more)
  • mean : x¯ =

∫ (^) ∞ −∞ xp(x)dx

  • median : P (x < median) = P (x > median) = 1/ 2
  • mode : max(p(x))
  • variance : σ^2 =

∫ (^) ∞

−∞

(x − ¯x)^2 p(x)dx (4)

  • mean is also the expected value of x = 〈x〉
  • variance is the expected value of (x − μ)^2 , the square of the deviations from the mean
  • standard deviation : σ
  • population : all possible measurements of a system, proportionally represented (often infi- nite in number)
  • draw : one measurement of system
  • sample : a set of draws
  • estimate mean, std. dev., etc. from sample

8 Estimates of Mean, etc.: 11:40 — 11:45, 5 min

  • All estimates use discrete formulae: can’t take an infinite number of measurements!
  • Estimate the mean and standard deviation of the parent distribution from a sample:
  • mean ¯x =

N

∑ xi (5)

  • standard deviation s^2 =

N − m

∑ (xi − x¯)^2 (6)

  • Factor of (^) N −^1 m takes into account effect of degrees of freedom, makes it work for low N.