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361. http://hea-www.harvard.edu/AstroStat/astro193/Loader_locfit_tutorial.pdf
... Locfit is a software package performing local regression, likelihood and related smoothing procedures. ... Our example uses the ethanol dataset, studied extensively in Cleveland (1993), and fits a local quadratic model: > fit.et <- locfit(NOx~E, data=ethanol, + alpha=0.5) > plot(fit.et, get.data = T) Three arguments are given to the locfit() funcLocal regression was applied in a variety of fields in tion. ... Figure 1 shows the (Cleveland and Devlin 1988). plot of the fit. ... Visualizing Data. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/Loader_locfit_tutorial.pdf -- 158.4 Кб -- 06.04.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/Loader_locfit_tutorial.pdf -- 158.4 Кб -- 06.04.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/Loader_locfit_tutorial.pdf -- 158.4 Кб -- 06.04.2015
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362. http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_apr06.pdf
Astro 193 : 2015 Apr 6 Ї Follow-up Ї Ї Ї Ї Ї p-value vs Linear smoothing edge effects Kernel Density Estimation locfit HW 10 Ї Ї Signal Processing: Fourier Transforms Signal Processing: Wavelets Kernel Density Estimation Ї A kernel K(x) is a non-negative real-valued function such that xR dx K(x) = 1 ; E[x] = x R dx x K(x) = 0 ; E[x2] = xR dx x K(x) Ї The Kernel density estimator for a ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_apr06.pdf -- 271.6 Кб -- 06.04.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_slides_apr06.pdf -- 271.6 Кб -- 06.04.2015
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363. http://hea-www.harvard.edu/AstroStat/astro193/HW10_dueApr15.pdf
... The data are from the symbiotic system RT Cru observed with the Chandra X-ray Observatory, and are at http://hea-www.harvard.edu/AstroStat/AY193/rtcru_times.txt Ї Plot the general cross-validation score (GCV) as a function of the bandwidth Plot the histogram at the optimal binning, as well as at bin sizes half and twice the optimal bin size for comparison. Determine the optimal smoothing scale to smooth 2-D paired data. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/HW10_dueApr15.pdf -- 21.2 Кб -- 06.04.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/HW10_dueApr15.pdf -- 21.2 Кб -- 06.04.2015
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364. http://hea-www.harvard.edu/AstroStat/astro193/AS_slides_april6.pdf
Fourier Transforms Astro193 April 6, 2015 Fourier Transforms Applications Ї Ї Ї Ї Filtering Convolution and Deconvolution Correlation and Autocorrelation Power Spectrum RR Lyrae lightcurve and Fourier modes Examples: Boxcar 1 2T 0 -T 0 T 0 t /T 0 Time-bandwidth product: Uncertainty principle: The shorter the signal the broader the spectrum. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/AS_slides_april6.pdf -- 336.8 Кб -- 06.04.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_slides_april6.pdf -- 336.8 Кб -- 06.04.2015
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365. http://hea-www.harvard.edu/AstroStat/astro193/AS_slides_apr1.pdf
Fourier Transforms Astro193 March 30, 2015 Definitions Some function f(t) then: "Forward" "Reverse" Temporal FT Spatial FT f(t) sec <--> radians/sec f(x) meters <--> radians/m The Fourier Transform and its Applications by Ronald N. Bracewell Definitions Some function f(t) then: "Forward" "Reverse" Temporal FT Spatial FT f(t) sec <--> radians/sec f(x) meters <--> radians/m Note no 2 factor x = time --> seconds S frequency --> cycles/sec= Hz Reversible? What's this? sinc function Examples Boxcar Impulse
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/AS_slides_apr1.pdf -- 400.3 Кб -- 01.04.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_slides_apr1.pdf -- 400.3 Кб -- 01.04.2015
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366. http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_apr01.pdf
Ї Ї Ї Ї Spearman's and Kendall's Class on Apr 10 Gibbs sampler acceptance rates: third time's the charm Adaptive MCMC Ї Ї Bias- Variance Tradeoff / Kernel Density Estimation Signal Processing: Fourier Transforms Adaptive MCMC Ї Run a chain for a short number of iterations in the kth block with modified step size (Hyungsuk Tak) compute acceptance rate if 0.4/npar, inflate step size by f+=e+min{ 0.07 ,1/k} if 0.2/npar, deflate step ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_apr01.pdf -- 62.7 Кб -- 01.04.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_slides_apr01.pdf -- 62.7 Кб -- 01.04.2015
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367. http://hea-www.harvard.edu/AstroStat/astro193/HW_8+9_dueApr8.pdf
Homework Problems 8 and 9 Note: The Kernel Density estimation problem that was mentioned in class has been postponed. HW 8 (Bootstrap): Use bootstrap techniques to compute the mean and variance of the fit parameters for data used in HW 6 (MCMC). HW 9 (Fourier Transforms): Compute the FT of the functions f(x) = exp(-|x|/) f(x) = exp(-ax?)
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/HW_8+9_dueApr8.pdf -- 39.5 Кб -- 01.04.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/HW_8+9_dueApr8.pdf -- 39.5 Кб -- 01.04.2015
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368. http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar30.pdf
... improvement in likelihood for M overwhelms the penalty of shrunk parameter space 2 2 Non-parametric tests Ї Comparing distributions Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling Mann-Whitney U test Kruskal-Wallis ANOVA Wald-Wolfowitz Higher Criticism ? Ї Correlation tests Pearson's coefficient Spearman's Kendall's Comparing distributions Ї One-sample test X = {x, i=1 N} Is the sample drawn from a specified distribution F0(X)? Two-sample test X (1) = {x i, i=1.. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar30.pdf -- 141.1 Кб -- 30.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_slides_mar30.pdf -- 141.1 Кб -- 30.03.2015
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369. http://hea-www.harvard.edu/AstroStat/astro193/scientificamerican0689-86.pdf
... Whereas the Fourier transform involves real and imaginary numbers and a complex sum of sinus oidal functions, the Hartley transform involves only real numbers and a real sum of sinusoidal functions. ... Hartley gave up the directIon of his SCIENTIFIC AMERICAN June 1989 ? 1989 SCIENTIFIC AMERICAN, INC 93 THE FOURIER AND HARTlEY TRANSFORMS The Fourier and Hartley transforms convert functions of time into functions of frequency that encode phase and amplitude information. ... THE HARTLEY TRANSFORM. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/scientificamerican0689-86.pdf -- 957.7 Кб -- 30.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/scientificamerican0689-86.pdf -- 957.7 Кб -- 30.03.2015
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370. http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar25.pdf
... , Jain, and Prosper, 2010, Phys.Rev. D, 82, 034002 http://journals.aps.org/prd/abstract/10.1103/PhysRevD.82.034002 Ї Ї improper priors what is important about the prior taking the likelihood to posterior ? ensures full parameter space is accounted for (frequentist analyses, optimize over parameter space) HW7 : Poisson Aperture Photometry NB photons are collected in a source-free region of area AB, and NS photons are collected in a region ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar25.pdf -- 326.8 Кб -- 25.03.2015
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371. http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar23.pdf
... generates irreproducible results, Nature Methods 12, 179 http://www.nature.com/nmeth/journal/v12/n3/full/nmeth.3288.html Ї Ї Ї Source Detection Survival Analysis Upper Limits Source Detection Ї The process of source detection is an application of p-value based null hypothesis rejection Background usually estimated locally, and multiple tests are made on ... Why is this not an upper limit? ... Set the max probability of a false detection, (e.g., =0.003 for a "3" detection) 3. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar23.pdf -- 242.2 Кб -- 23.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_slides_mar23.pdf -- 242.2 Кб -- 23.03.2015
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372. http://hea-www.harvard.edu/AstroStat/astro193/vlk_frequentist_rebuttal_mar11.pdf
Frequentist Rebuttal Ї Useful illustration of blind reliance on p-value, but no actual frequentist would set up such an experiment aside: set up to confirm impossible things; can be a unicorn detector Hypothesis test must control for power. This one purports to detect solar neutrino luminosity, but fails to detect in 35/36 cases. Low power! Must set appropriate sample size/rate to overcome low power problem. 12 How many samples? 10 per year per 10 billion stars, so 310 per 12 day. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/vlk_frequentist_rebuttal_mar11.pdf -- 32.9 Кб -- 12.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/vlk_frequentist_rebuttal_mar11.pdf -- 32.9 Кб -- 12.03.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/vlk_frequentist_rebuttal_mar11.pdf -- 32.9 Кб -- 12.03.2015
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373. http://hea-www.harvard.edu/AstroStat/astro193/AS_slides_march11.pdf
Model Selection Astro193, March 9 Steps in Hypothesis Testing 1/ Set up 2 possible exclusive hypotheses - two models : M0 ґ null hypothesis ґ formulated to be rejected M1 ґ an alternative hypothesis, research hypothesis 2/ Specify a priori the significance level 3/ Choose a test which: - has the required power - approximates the conditions - finds what is needed to obtain the sampling The model with the largest value provides the best description of the data. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/AS_slides_march11.pdf -- 663.1 Кб -- 11.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_slides_march11.pdf -- 663.1 Кб -- 11.03.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_slides_march11.pdf -- 663.1 Кб -- 11.03.2015
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374. http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar11.pdf
... Given a sample X = {X1, X2, .. ... For large NB, (2) (NB) Bootstrap mean is same as sample estimate, B = (1/NB) Bootstrap variance is same as standard error on (X), ?B = (1/(NB-1)) k=1.. ... Cannot bootstrap a bootstrap! standard deviation of bootstrap estimates standard error of sample estimate Jackknife Ї Ї aka "Leave-one-out" Figure out the robustness of an estimate from a sample by computing the estimate for all subsamples, leaving one out each time Given =fn(Xi), i=1..n, compute -k = fn-1(X1,.....
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar11.pdf -- 147.3 Кб -- 11.03.2015
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375. http://hea-www.harvard.edu/AstroStat/astro193/ulim_Kashyap+ApJ_2010_719_900.pdf
... It should not be confused with confidence intervals or other estimates of source intensity. ... The confidence interval is the result of inference on the source intensity, while the upper limit is a measure of the power of the detection process. ... Note that unlike the confidence interval, which depends strongly on the number of observed source counts, nS , the upper limit is fixed once the detection threshold S (which depends on B ) and the minimum detection probability min are specified. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/ulim_Kashyap+ApJ_2010_719_900.pdf -- 745.5 Кб -- 09.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/AstroStat/etc/ulim_kvcfsx_apj2010_719_900.pdf -- 745.5 Кб -- 09.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/etc/ulim_kvcfsx_apj2010_719_900.pdf -- 745.5 Кб -- 09.03.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/AstroStat/etc/ulim_kvcfsx_apj2010_719_900.pdf -- 745.5 Кб -- 09.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/etc/ulim_kvcfsx_apj2010_719_900.pdf -- 745.5 Кб -- 09.03.2015
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376. http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar09.pdf
parameter estimates and variances Bayesian Gaussian Aperture Photometry -- updated notes Ї Model Selection Model Selection Ї Ї Ї Ї Ї p-values and Hypothesis Tests Type I, Type II, and other errors Analysis Design Upper Limits Hypothesis Tests , Likelihood Ratio Tests , and posterior predictive pvalues Odds ratios, Bayes Factors AIC/BIC/DIC/WAIC/HQIC/MDL Ї Ї p-values Ї Ї p=Pr(T T(D)|H) What ... The difference between significant and not significant is not significant." ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar09.pdf -- 142.6 Кб -- 09.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_slides_mar09.pdf -- 142.6 Кб -- 09.03.2015
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377. http://hea-www.harvard.edu/AstroStat/astro193/AS_slides_March-4.pdf
Bias and Measurement Errors Astro193, March 4 2015 Measurement Error Effects Ї Blurring and broadening distribution of quantities Ї Measured is broadly scattered in comparison to True Ї Impacts statistical inference: Ї Biased measurements Ї Smeared out any trends in the data ґ the separation in the True is not present in the Measured Brandon Kelly 2011 , Measurement ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/AS_slides_March-4.pdf -- 223.2 Кб -- 06.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/AS_slides_March-4.pdf -- 223.2 Кб -- 06.03.2015
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378. http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar04.pdf
... Product of two Gaussians Ї g = N(?,2) N(?,2) exp [-(x-?)?/2? - (x-?)?/2?] Ї ? = (??+??) / (?+?) ; ? = ?? / (?+?) for , ? ? and Ї g = (1/2) exp [-(x-?)?/2?] (1/2(?+?)) exp [(?-?)?/2(?+?)] Bayesian Aperture Photometry (Gaussian) Ї Measurements: Background in an area AB = rAS: fB ? B M ( Source + Background ) in an area AS: fM ? Ї Priors: p(b) = N(b;f0B,0B?) p(s) = N(s;f0S,0S?) Ї Likelihoods: f(fB,B|b,r) exp [-(rb-fB)?/2B?] ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar04.pdf -- 89.4 Кб -- 06.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/VLK_slides_mar04.pdf -- 89.4 Кб -- 06.03.2015
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379. http://hea-www.harvard.edu/AstroStat/astro193/HW7_dueMar13.pdf
Homework 7 : Bayesian Aperture Photometry (Poisson ) Due : 13 Mar The goal of this assignment is to make you familiar with the mechanics of Bayesian analysis. We will use the familiar setting of aperture photometry to develop a simple Poisson model to estimate the intensity of a source. ... A: Consider the case where NB photons are collected in a source-free region of size AB pixels, and NS photons are collected in a region of size AS that includes a source. ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/HW7_dueMar13.pdf -- 63.6 Кб -- 05.03.2015
[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/HW7_dueMar13.pdf -- 63.6 Кб -- 05.03.2015
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[ Текст ] Ссылки http://hea-www.harvard.edu/astrostat/astro193/HW7_dueMar13.pdf -- 63.6 Кб -- 05.03.2015
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380. http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar02.pdf
... You pick door A (say). ... Suppose the probability that the prize is behind door X is represented as X, and the datum is D = Monty opens door B. Then, p(X|D) = p(X) p(D|X) / p(D) prior probability p(X) = 1/3 likelihood p(D|A) = 1/2, p(D|B) = 0, p(D|C) = 1 Normalize p(D ... p(B|D) = p(B) p(D|B) / p(D) = 0 p(A|D) = p(A) p(D|A) / p(D) = (1/6)/(1/2) = 1/3 p(C|D) = p(C) p(D|C) / p(D) = (1/3)/(1/2) = 2/3 MCMC Theory MCMC in practice MCMC in practice Ї Ї Ї Ї Ї one by one, or all at once? ...
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Ссылки http://hea-www.harvard.edu/AstroStat/astro193/VLK_slides_mar02.pdf -- 240.8 Кб -- 02.03.2015
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