ADV ASTRONOMICAL DATA ANALYSIS
ADV ASTRONOMICAL DATA ANALYSIS AST 5765
University of Central Florida
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Date Created: 10/22/15
y x N M UCF Physics AST 57654762 Advanced Astronomical Data Analysis Fall 2009 Lecture Notes 8 Coding FITS Errors Check In 1030 1035 5 min 0 Questions before we start Astronomical Data 1035 1050 15 min 0 What is FITS 0 Reading FITS les 0 Reading header variables 0 Addingmodifying header variables 0 Writing FITS les Illegitimate Systematic and Random Errors 1050 1100 10 min 0 A measurement is the best estimate of a quantity in terms of accepted units 0 Three types of measurement error illegitimate systematic and random 0 Illegitimate error a fundamental problem in the methods or assumptions think you re doing one thing really doing another 0 Find and x 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 0 Systematic error predictable difference between data and measurement 0 Quantify and remove A nonquanti ed systematic error can kill a measurement Must always estimate the unquanti able 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 ag for a bad proposal Random error di erences 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 10 3a in biology Minimize by repeated measurement Figure of merit for all measurements Signaltonoise ratio SN or SNR or SN nal value of corrected measurement SN 1 random error in that value What s in 21 Measurement 1100 1110 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 halfinches not centimeters but we didn t notice Terms 1110 1120 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 g 11 signi cant gures 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 unceltajnty amount by which 2 measurements could differ and not be recognized as dif ferent standard error estimate of 10 standard deviation spread in measurements signi cant difference di erent by several times the uncertainty 3 or preferably more 6 Testing Theory 1120 1130 10 min An hypothesis or theory is clear decisive and positive but it is believed by no one but the man who created it Experimental findings on the other hand are messy inexact things which are believed by everyone except the man who did the work Harlow Shapley 0 Good theories predict measurable quantities 0 Do the measurement 0 If the measurements are within errors of the prediction the data support the theory at the level of their uncertainty 0 Is it true If it con icts with other theory it must provide a replacement or appeal to data that shows the other theory to be false It must not make predictions that are against the data not even one Do other predictions also t the data Then need better data Do other theories that depend on this one also work Usually need to wait to see if other theories appear Eventually theory becomes accepted if it passes these tests No theory is ever immune from being overturned later I Probability basics 1130 1140 10 min 0 Description of behavior of many identical independentlyprepared systems 0 Discrete vs continuous probability coin vs time interval 0 In the limit of large N everything appears continuous o Described by probability density function PDF that integrates to l 0 Do de nite integral over range to get probability 7 Px in range a 7 b pzd 2 L WW 1 3 mean i 30 pzdx median Px lt median Pz gt median 12 mode maxpx variance 4 mean is also the expected value of z variance is the expected value of x 7 2 the square of the deviations from the mean standard deviation 039 population all possible measurements of a system proportionally represented often in nite in number draw one measurement of system sample a set of draws estimate mean std dev etc from sample Estimates of Mean etc 1140 1145 5 min All estimates use discrete formulae can t take an in nite number of measurements Estimate the mean and standard deviation of the parent distribution from a sample mean 5 standard deviation 6 Factor of Niim takes into account effect of degrees of freedom makes it work for low N