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381. http://hea-www.harvard.edu/AstroStat/astro193/HW6-03-02-2015.pdf
Homework 6 March 2, 2015 Due on March 13, 2015 This is a simple fit of a straight line to noisy data as in the HW 4 y a + bx = , i i where a and b are the unknown parameters. ... 2) Plot the data and do an "eyeball" estimate (i.e., no fancy mathematical calculations, but explain how you arrived at your answers) of the parameters a, b, nd and . a a b , (3) Use the answers in part (1) to set the initial values of the input parameters. ... 4) Repeat [3] for different values of the step size. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/HW6-03-02-2015.pdf -- 56.3 Кб -- 02.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/HW6-03-02-2015.pdf -- 56.3 Кб -- 02.03.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/HW6-03-02-2015.pdf -- 56.3 Кб -- 02.03.2015
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382. http://hea-www.harvard.edu/AstroStat/astro193/AS_March2.pdf
MCMC Theory Astro 193, March 2 Today Ї Reminder from the previous classes: Ї Likelihood and Maximum Likelihood Ї Bayesian Inference Ї Markov Chains Ї Basic MCMC Ї Jumping Rules Ї The Metropolis Sampler Ї The Metropolis-Hastings Sampler Ї Gibbs Likelihood and ML Ї Likelihood Functions: Ї P(data | ... d) likelihood (d | prior () d- data - parameters Ї Combine current and previous knowledge Ї Define the likelihood function Ї Describe the posterior probabilty distribution via MCMC simulations. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/AS_March2.pdf -- 363.9 Кб -- 01.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_March2.pdf -- 363.9 Кб -- 01.03.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_March2.pdf -- 363.9 Кб -- 01.03.2015
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383. http://hea-www.harvard.edu/PINTofALE/pro/linerem.pro
... NOTE: if not given, LAMDA is taken to be SPEC and ; the array indices are taken to be LAMDA ; ;keywords ; sig [INPUT] error at each point; if not given, the ; errors are taken to be 1+sqrt( abs (SPEC)+0.75). ; nsigma [INPUT; default: 4] multiple of SIG to consider ; as a threshold for detection of features ; cell [INPUT] 1D filter to use in computing the background ; * default is [1,1,0,0,0,1,1] ; * if scalar, then [IC+1,ICC,IC+1], where ...
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Ссылки http://hea-www.harvard.edu/PINTofALE/pro/linerem.pro -- 7.6 Кб -- 27.02.2015
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384. http://hea-www.harvard.edu/AstroStat/astro193/AS_slides_Feb.25.pdf
Parameter Estimation Astro 193, Feb.25 Non-linear Models Ї Define 2 and determine the best-fit parameters Ї No simple analytical solution Ї Involves iterative minimization of 2 Methods Ї Ї Ї Ї Levenberg-Marquardt Gradient methods Simplex Monte Carlo Comparison of the Methods Levenberg-Marquardt Ї Calculates derivatives of a statistics function over the parameter space of the function . ... Niter = 7 Comparison of the Methods Simplex Intercept vs. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/AS_slides_Feb.25.pdf -- 137.8 Кб -- 26.02.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_slides_Feb.25.pdf -- 137.8 Кб -- 26.02.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_slides_Feb.25.pdf -- 137.8 Кб -- 26.02.2015
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385. http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_feb25.pdf
... Working through Homework 5 Bayesian Probability Theory MCMC basics Homework 6 Homework 5 1. ... No guarantee of good coverage properties (because of priors), unlike frequentist confidence intervals ( the true value is contained 90% of the time for CIs calculated in this manner when the experiment is repeated ) frequentist vs Bayesian Bayesian Data are fixed and parameters have uncertainties Uncertainty is range in parameter values that encompass a certain probability Prior ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_feb25.pdf -- 114.1 Кб -- 26.02.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_slides_feb25.pdf -- 114.1 Кб -- 26.02.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_slides_feb25.pdf -- 114.1 Кб -- 26.02.2015
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386. http://hea-www.harvard.edu/AstroStat/astro193/AS_Feb.23.pdf
Parameter Estimation Astro 193, Feb.23 Today Ї Ї Ї Ї Maximum Likelihood Best fit and goodness of fit 2 and non-linear models Minimization (optimization) methods Likelihood Ї Function of model parameters and the data. For the fixed data set - it is only a function of parameters. Finding best-fit => maximize likelihood or minimize 2 Goodness of Fit Ї Ї Ї Ї How good is the fit? 2 minimization gives the measure of goodness of fit if the measurement errors are Gaussian (normally distributed). ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/AS_Feb.23.pdf -- 92.2 Кб -- 23.02.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_Feb.23.pdf -- 92.2 Кб -- 23.02.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_Feb.23.pdf -- 92.2 Кб -- 23.02.2015
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387. http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_feb23.pdf
... Poisson З З З p(k|) = (1/k!) k e- mean = , variance = Gehrels' approximations (1986 ApJ 303, 336) З З +1 = 1+{k+0.75} -1 = {k-0.25} i З characteristic function is exp [(e -1)] Pois ( + ) = Pois () + Pois () Gamma З З З З p(; , ) = / () -1 e- 0, 0, 0; Poisson for =1 and =k+1 mean = /, variance = / 2 = meanВ/ variance , = mean / variance Normal З З З Distribution of summary statistics Normal ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_feb23.pdf -- 100.9 Кб -- 23.02.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_slides_feb23.pdf -- 100.9 Кб -- 23.02.2015
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388. http://hea-www.harvard.edu/AstroStat/astro193/VLK_feb18.pdf
MI dof -- yes, the square is outside dof = (N-1) (1 + (N/(N+1))(Wii/Bii)) 2 Ї Ї Ї Ї least-squares fitting and HW 4 Moments and intervals Random Numbers Binomial , Poisson , Gamma, Normal, ?, Student's t Moments Ї Mm = x p(x) dx or Mm = x p(x) M0=1, mean=M1, variance=M2-M 2 1 m m Ї Moment Generating Function e f(x) Mm = M/x x m m Ї Characteristic Function () = e f(x) dx (i) /k! M f(x) = d e -ix iz k k (i) /k! M k k ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_feb18.pdf -- 206.4 Кб -- 18.02.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_feb18.pdf -- 206.4 Кб -- 18.02.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_feb18.pdf -- 206.4 Кб -- 18.02.2015
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389. http://hea-www.harvard.edu/AstroStat/astro193/HW5_dueFeb25.pdf
AY 193 Homework 5 : Sampling Due Feb 25 1. Generate 10,000 Poisson random deviates each using rejection sampling for the cases =1,10,100 (do NOT use builtin methods except to get draws from a uniform distribution). ... Plot histograms of the distributions and overplot the corresponding density distributions 3. Compute means of 10 consecutive random deviates from the samples from [1] and make histogram plots of the distributions of the means. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/HW5_dueFeb25.pdf -- 26.2 Кб -- 18.02.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/HW5_dueFeb25.pdf -- 26.2 Кб -- 18.02.2015
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390. http://hea-www.harvard.edu/AstroStat/astro193/HW3.pdf
... Astro 193 : HW 3 Ї NH = 3.07?0.02, 3.07?0.04, 3.18?0.04, 3.07?0.04, 2.93?0.06, 3.10?0.055, 2.90?0.035, 2.94?0.035, 2.74?0.025 = 1.84?0.01, 2.09?0.07, 2.06?0.015, 1.91?0.015, 1.92?0.015, 1.90?0.02, 2.28?0.15, 1.77?0.025, 1.91?0.025, 1.78?0.015, 1.84?0.015, 1.76?0.01 <NH> = 3.00 ; NH Ї Ї Ї Ї Ї = 0.15 < > = 1.92 ; = 0.17 WNH = 0.00165 ; BNH = 0.0179 ; TNH = 0.0215 ; dof NH = 9.39 W = 0.00253 ; B = 0.0236 ; T = 0.0281; dof = 13.29 <NH> T <> individual measurements with error bars B W inflation factor ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/HW3.pdf -- 280.2 Кб -- 11.02.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/HW3.pdf -- 280.2 Кб -- 11.02.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/HW3.pdf -- 280.2 Кб -- 11.02.2015
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391. http://hea-www.harvard.edu/AstroStat/astro193/AS_notes_feb11.pdf
Basic Model Fitting Astro 193: Feb 9 Ї Ї Ї Ї Likelihood Model Linear regression Best fit Likelihood Ї Ї Ї How likely is our measurement? Measured quasar luminosity at (1.2 ? 0.3)*1045 erg/sec Gaussian probability - N(?,) => (1.2e45, 0.3e45) Ї How likely we will obtain the same measurement next time. Log Likelihood Ї Repeated measurements xi = (x1.....xn) : constant statistics Simple Model Ї Linear model - f(x) = ax +b Ї Statistics Minimize: Simple Model Ї Linear model - f(x) = ax +b Maximize likelihood
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/AS_notes_feb11.pdf -- 150.9 Кб -- 11.02.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_notes_feb11.pdf -- 150.9 Кб -- 11.02.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_notes_feb11.pdf -- 150.9 Кб -- 11.02.2015
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392. http://hea-www.harvard.edu/AstroStat/astro193/Tsujimoto+2011_AA_G21.5.pdf
A A 525, A25 (2011) DOI: 10.1051/0004-6361/201015597 c ESO 2010 Astronomy Astrophysics Cross-calibration of the X-ray instruments onboard the Chandra, INTEGRAL, RXTE, Suzaku, Swift, and XMM-Newton observatories using G21.5 ґ 0.9 M. Tsujimoto1 , M. Guainazzi2 , P.P.Plucinsky3 , A.P.Beardmore4 ,M. Ishida1 , L. Natalucci5 , J. L. L. Posson-Brown3 , A. M. Read4 ... Data 3.3. ... 2008), G21.5ґ0.9 was also used to compare the power-law index and flux in 2ґ10 keV band using the same data set. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/Tsujimoto+2011_AA_G21.5.pdf -- 1949.9 Кб -- 09.02.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/Tsujimoto+2011_AA_G21.5.pdf -- 1949.9 Кб -- 09.02.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/Tsujimoto+2011_AA_G21.5.pdf -- 1949.9 Кб -- 09.02.2015
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393. http://hea-www.harvard.edu/AstroStat/astro193/Rdemo.txt
193 getwd() #shows which directory you are in help.start() #pops up a browser window with online help apropos( FITS ) # FITSio is crucial for astronomers library( FITSio ) #load the FITSio library ? FITSio #get help about FITSio ls() #what is available a - c(1,1,2,3,5,8,13) #define an array ls() #now should see a str(a) #what does a look like? summary (a) #statistical summary of a # sequences ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/Rdemo.txt -- 2.4 Кб -- 04.02.2015
[ Сохраненная копия ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/Rdemo.txt -- 2.4 Кб -- 04.02.2015
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394. http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_Feb4.pdf
... What is R? Ї Ї Statistical computing environment programmable/scriptable C-like language (similar to matlab, IDL) Huge number of analysis packages, written for and by statisticians Ї Ї Where to get it from? Ї http ://www.r-project.org/ Recommended reading: Tutorial on AstroStatistics and R http ://hea-www.harvard.edu/AstroStat/Tutorial2014/ Some functionalities of R arithmetic linear algebra bootstrap resampling empirical distribution tests exploratory data ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_Feb4.pdf -- 299.6 Кб -- 04.02.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_slides_Feb4.pdf -- 299.6 Кб -- 04.02.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_slides_Feb4.pdf -- 299.6 Кб -- 04.02.2015
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395. http://hea-www.harvard.edu/AstroStat/astro193/HW_feb4.pdf
... 3. g = ln(a)-ln(b) Homework 3.2 : G21.5 Tsujimoto et al. ... 93ґ3. 01ґ3. 98ґ3. 05ґ3. 11ґ3. 95ґ3. 08ґ3. 05ґ3. 04) 12) 09) 16) 22) 06) 20) 09) 1. 1. 1. 1. 1. 1. 1. 1. 83 85 82 84 88 81 88 84 2.99 2.99 3.07 (3.03ґ3.11) 3.18 (3.14ґ3.22) 3.07 (3.03ґ3.11) 2.99 2. 2. 2. 3. 2. 3. 88ґ3. 83ґ2. 98ґ3. 08ґ3. 87ґ2. 05ґ3. 07) 98) 13) 25) 99) 16) 2.09 2.05 1.91 1.92 1.90 2.28 1. 1. 1. 1. 1. 1. 77 77 90 93 77 91 2.90 (2.87ґ2.94) 2.94 (2.91ґ2.98) 2.74 (2.72ґ2.77) 2.99 (2.98ґ3.00) 2.99 1.78 1.84 1.76 ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/HW_feb4.pdf -- 99.9 Кб -- 04.02.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/HW_feb4.pdf -- 99.9 Кб -- 04.02.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/HW_feb4.pdf -- 99.9 Кб -- 04.02.2015
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396. http://hea-www.harvard.edu/AstroStat/astro193/AS_notes_feb2.pdf
Astro 193 AS cture 2 Notes Feb.2, 2015 Le Measurements in Astronomy 1/ Telescope and Detectors: In the past the optical detectors were photographic plates. ... Count data follow the isson distributions Po . ... The data a is usually treated as ussian (Normal) e. Ga typ 2/ Calibration Calibration is a measurement of the instrument characteristics. ... Calibration measurements improve when more data has been collected and the data can be reprocessed to account for the new calibration information. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/AS_notes_feb2.pdf -- 128.2 Кб -- 03.02.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_notes_feb2.pdf -- 128.2 Кб -- 03.02.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_notes_feb2.pdf -- 128.2 Кб -- 03.02.2015
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397. http://hea-www.harvard.edu/PINTofALE/pro/munge_list.pro
... WAVE may be (any combination of):- ; exact match -- "WVL" ; inexact match -- "WVL +- dW" or "WVL ? , and // -- the last is treated as ; scribbles to go into the NOTES field of the ID) ; * if no IDs are found, WVL is flagged as UNKNOWN ; * emissivities of IDs not attached to any WVL are returned in LNSTR ; ;subroutines ; RD_LIST ; RD_ LINE ; SYMB2ZION ; LAT2ARAB ; FOLD_IONEQ ; RD_IONEQ ; READ_IONEQ ; CAT_LN ; LINEFLX ; GETABUND ; WHEE ; IS_KEYWORD_SET ; ;history ; vinay ...
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Ссылки http://hea-www.harvard.edu/PINTofALE/pro/munge_list.pro -- 11.6 Кб -- 30.01.2015
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398. http://hea-www.harvard.edu/AstroStat/astro193/Week1-Jan28.pdf
Astron 193 Lecture 2, Jan.28, 2015 NOTES 1/ Data vs. ... 4/ Data Storage View Your Data Software to read the data files rrent Astronomy Formats FITS inary with standards, Cu b defined keywords, but may become not good enough for large data of the future LOFAR, SKA in radio, LSST ds9 display the data mage gui, but also access to catalogs download and image the files i event files contain all the information about the observation photons , energy, arrival times ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/Week1-Jan28.pdf -- 84.0 Кб -- 29.01.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/Week1-Jan28.pdf -- 84.0 Кб -- 29.01.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/Week1-Jan28.pdf -- 84.0 Кб -- 29.01.2015
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399. http://hea-www.harvard.edu/AstroStat/astro193/Lee+2011_apj_731_2_126.pdf
... Printed in the U.S.A. ACCOUNTING FOR CALIBRATION UNCERTAINTIES IN X-RAY ANALYSIS : EFFECTIVE AREAS IN SPECTRAL FITTING Hyunsook Lee1 , Vinay L. Kashyap1 , David A. van Dyk2 , Alanna Connors3 , Jeremy J. Drake1 , Rima Izem4 ... This method is implemented using recently codified Chandra effective area uncertainties for low-resolution spectral analysis and is verified using both simulated and actual Chandra data. ... Effect of calibration uncertainty on fitted parameters and error bars. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/Lee+2011_apj_731_2_126.pdf -- 2913.9 Кб -- 28.01.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/AstroStat/etc/calerr_Lee+2011apj731p126.pdf -- 2913.9 Кб -- 28.01.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/Lee+2011_apj_731_2_126.pdf -- 2913.9 Кб -- 28.01.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/AstroStat/etc/calerr_Lee+2011apj731p126.pdf -- 2913.9 Кб -- 28.01.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/Lee+2011_apj_731_2_126.pdf -- 2913.9 Кб -- 28.01.2015
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400. http://hea-www.harvard.edu/AstroStat/astro193/HW_jan28.txt
Astro 193 Homework 2 28-jan-2015 Due Mon Feb 2, 2015 The goal is to measure the count rates [counts/second] of individual sources in an X-ray dataset of the Orion Nebula Cluster. ... For each selected source, define a region in which to collect source counts. ... For each selected source, define a region in which to collect background counts. ... The background counts scaled to under the source is (area_source/area_background)*(measured_background) Report the source counts and the errors. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/HW_jan28.txt -- 2.8 Кб -- 28.01.2015
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[ Сохраненная копия ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/HW_jan28.txt -- 2.8 Кб -- 28.01.2015
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