Practical Statistics Lectures for Physicists 
Louis Lyons (Oxford)

May 5 - May 10, 2005


These lectures emphasise the practical aspects of using Statistics to
derive results from experimental data in an efficient manner. Many
examples are used to illustrate the ideas. The level is suitable for PhD
students with some experience of statistics, but they should also be
interesting for post-docs and others too. 


INTRODUCTION 
Probability. Conditional probability. Bayes and Frequentism.
Independence.  Estimating variance
Combining results. Paradox. 'Extra theoretical input is good for you'. 

LEARNING TO LOVE THE ERROR MATRIX
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. 
Maximum likelihood: 
      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 fit. Do's and don't's with likelihoods.
Least squares: 
       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. 

GOODNESS OF FIT and HYPOTHESIS TESTING 
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 hypotheses: THE
paradox. 
Problems with sparse data. Other goodness of fit tests. 
Kinematic fitting:
      What is it?  Why do it?  How do we do it? Toy example.  HEP
examples. 

BAYES and FREQUENTISM 
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).  Neutrino oscillations. 
Summary table. 

MONTE CARLO 
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. 

TOPICS FROM PARTICLE PHYSICS 
BLUE technique. 
Limits. 
Techniques for systematics. 
Estimates of significance. 
Neural networks.
Blind analyses.