Probability. Conditional probability. Bayes and Frequentism. Independence. Estimating variance. Combining results. Paradox. 'Extra theoretical input is good for you'.
Reminder of 1-D Gaussian (and student's t). Uncorrelated and correlated Gaussians in 2-D. Error matrix via 2-D Gaussian.
Understanding error matrix and inverse error matrix. Estimating error matrix elements.
Simple calculations using the error matrix: z = f(x,y).
Change of variables. General transformation. Physics examples.
Combining results: the BLUE approach.
Parameter Determination (Point Estimates and Ranges)
Philosophy. To normalise. Should parameter ranges be physical?
Method of moments.
What it is. Likelihoods and pdf’s. Understanding likelihoods: resonance. Error estimates and coverage. Example of lifetime determination. Extended likelihood. Unbinned and binned likelihoods. Likelihood and goodness of it.
Which errors? Example of straight line fit. Use of orthogonal functions. How many terms to include?
Correlated measurements. Errors on x and y.
Summary of different techniques.
S and chi-squared. Degrees of freedom. Chi-squared distributions and tail areas: how to impress your colleagues.
What it is and what it is not. Errors of first and second kind. Comparing hypothesis: THE paradox.
Problems with sparse data. Other goodness of fit tests.
What is it? Why do it? How do we do it? Toy example. HEP examples.
Bayes’ Theorem. For frequentists. For Bayesians. Bayesian prior and posterior.
Examples: Tossing a coin. Particle identification. Peasant and dog.
Prob(data | theory) .ne. Prob(theory | data): Mistaken statements. Unseen person.
Neyman construction: Coverage. Problems. Importance of ordering rule.
Why Feldman and Cousins? Empty intervals. Unified limits. Flip-flop. Simple examples (Gaussian, Poisson).
Integration examples. Why do it? Non-uniform distributions (weighting, hit and miss, clever methods, special examples). Correlated variables. Typical HEP examples. Garden of Eden problem.
Techniques for systematics.
Estimates of significance.