Lent Term 2014 – Mike Irwin
This short course will give an overview and an introduction to several examples of statisticaltechniques that are commonly used in Astronomy.
- Overview, why statistics?, basic deﬁnitions, characteristic functions, probability anderrors, properties of some common distributions, estimating location and scale
- Combining variables - error propogation, Central Limit theorem, random numbers, Bayes' theorem, Rayleigh distribution, likelihood of identiﬁcations in catalogues, order statistics and NN distributions, correlation and covariance.
- Introduction to time series analysis - statistics of Fourier transforms, Shannon's sampling theorem, periodicity estimation. Combination of signals, convolution (smearing, blurring), optimal detection of signals/objects, cross-correlation (radial velocities)
- Bayes theorem again, parameter estimation/model ﬁtting, Maximum Likelihood estimators, Least-Squares, optimal spectral extraction, numerical techniques for model ﬁtting.
- Conﬁdence intervals & Hypothesis testing: correlation tests, KS, Chisq, binned -vunbinned data, information criteria, which model ? how many parameters ? low detection rates.
- Processing CCD data, direct imaging and spectroscopy, aliasing and Shannon's sampling theorem, interpolation, stacking. Image detection and parameterisation
- Introduction to digital image processing methods: ﬁltering, direct methods, Fourier methods; Wiener ﬁlters, entropy and information, image restoration.
- Multivariate analysis and Classiﬁcation - PCA, ICA, ANNs, linear discriminants, genetic algorithms.
Page last updated: 15 October 2013 at 12:04