STATISTICS FOR ASTRONOMY
Lecturer: Roberto Caimmi

The concept of probability from the standpoint of statistical mechanics. Random variable. Distribution. Expectation value. Median value. Variance. Absolute and relative frequence. The central limit theorem and related theorems. Experimental errors. General properties of punctual estimations. The method of the moments. The method of minimum variance. The method of maximum likehood. Likehood functions. Estimation of a single parameter. Simultaneous estimation of different parameters. Properties of maximum likehood estimators. Errors related to maximum likehood estimations. Special applications of the maximum likehood method. Indirect measures and error propagation. Confidence interval. Measure precision and accuracy. Ipotheses on distribution parameters. Test formulation. Simple and composite hypotheses. Hypothesis test in practice. Test on parameters of Gaussian istributions. Test on mean. Test on variance. T-test. F-test. Chi2-test. Control chart. Ordered data functions. Data elimination: Chauvenet's criterion. Examples. Mathematical and statistical models. Least square method. Linear relations. Interpolation along a straight line. Nonlinear relations. Gauss' method. Polynomial interpolation in presence of errors on the independent variable. Regression and correlation.