Statistical Methods in Experimental Particle Physics

10 Apr 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Introduction to ROOT: an open-source data analysis framework used in high energy physics.

17 Apr 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Introduction to the preliminary experiences: 1) Measurement of D0 meson lifetime using D0->Kpi decays and 2) Particle Identification with Ring-Imaging Cherenkov detector.

21 Apr 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Types of statistical inference. Probability and its operational definition. Kolomogorov axioms and its elementary consequences. The Bayesian view of probability. Conditional probability. Independence of two random variables. Bayes’s theorem. Probability density function of an observable and its properties. The Law of Large Numbers.

24 Apr 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Expectation value of a statistic. Distribution of a statistic. Moments of a probability distribution. Approximate computation of moments of a statistic. Moment Generating Function and examples. Characteristic Function. Paul Levy’s theorem.

28 Apr 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Central Limit Theorem and Gaussian probability density function. Derivation of probability density/mass function of binomial, poisson, exponential function. Functional inference: Likelihood Function (properties and examples).

30 Apr 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Data analysis laboratory assistance. Measurement of the D0 meson lifetime.

05 Maggio 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Likelihood function and inference. Inferential use of Bayes' theorem. Example of a Bayesian application (medical testing). Other uses of Bayes' formula. Subjective Bayesian inference. Likelihood principle. Sufficient statistic and examples. Sufficiency principle. Data reduction. Darmois' theorem. Fisher score and Fisher information. Properties of Fisher information.

08 Maggio 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Data analysis laboratory assistance. Measurement of the D0 meson lifetime.

12 Maggio 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Point estimation. Consistency, accuracy, and bias of estimators. Cramer-Rao inequality and the Minimum Variance Bound. Estimator efficiency. Cramer-Rao and sufficient statistics. Lehmann-Scheffè theorem. Example with an exponential probability density function (lambda vs. tau = 1/lambda).

15 Maggio 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Point estimation. LLN and consistent estimators. The method of moments and its properties/features. Generalization to implicit estimators. An important application: the Maximum Likelihood Estimator (MLE). MLE properties. Solving a Likelihood Fit in practice.

19 Maggio 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Likelihood fit of histograms. Case with fixed N (total number of events): multinomial distribution. Case with free N: Poisson distribution. Limit for infinitely small bins and Extended Unbinned Likelihood fit. Case with high statistics in each bin: Pearson's chi-square statistic. Least squares method and its properties. Gauss-Markov theorem.

21 Maggio 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Interval estimation vs. point estimation and the most common misconceptions. Bayesian interval estimation and credibility level. Classical interval estimation with Neyman construction, confidence level, and coverage. Sorting algorithms: ascending and descending in x, descending in probability (p-ordering). Examples with the Poisson distribution.

22 Maggio 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Interval estimation: the well-known flip-flopping problem. Interval estimation: the "empty interval" problem. Examples with the Poisson distribution (signal plus background) and with the Gaussian distribution. Feldman-Cousins "The Unified Approach". Likelihood Ratio (LR) and LR-ordering. Simplified extraction of confidence intervals. Definition of a pivotal quantity. Wilks' theorem and extraction of confidence intervals with lambda = -2log(LR).

26 Maggio 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Data analysis laboratory assistance. Measurement of the D0 meson lifetime.

28 Maggio 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Interval estimation by using the Likelihood function. Parabolic and non-parabolic log-likelihood function with one parameter with a Gaussian estimator. Profile likelihood regions in many parameters and asymptotic approximations. Profile Likelihood-Ratio ordering. Confidence regions with the presence of nuisance parameters. Plugin-in Method. A brief mention of the Supremum p-value Method.

29 Maggio 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Hypothesis testing. Simple and compound hypotheses. Critical region and acceptance region. Type I and Type II error probability. Significance level and power of a test. Statistical test properties (unbiasedness, consistency, Most Powerful, Uniform Most Powerful, Locally Most Powerful). Neyman-Pearson lemma and UMP test. LMP test. Likelihood ratio test. Example: Normal theory test vs. Sign test.

03 Giu 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Data analysis laboratory assistance. Introduction to the final experiment: Search for the tau+ -> phi mu+ decay.

04 Giu 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Goodness-of-fit tests. Properties of a GOF test statistic and definition of the p-value. How to combine multiple p-values. GOF tests from the LR statistic. Application of the LR test statistic to perform the GOF test of histograms (Poisson). Application of the LR test statistic to perform the GOF test of Gaussian fits (Pearson's Chi2 test). GOF tests of Gaussian fits with unknown variance (Student's t-test). Kolmogorov-Smirnov test.

05 Giu 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Data analysis laboratory assistance. Introduction to the final experiment: Search for the tau+ -> phi mu+ decay.

09 Giu 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Look-Elsewhere-Effect (LEE). Bonferroni adjustment. Local and global significance (or p-value) in the search for a rare signal (mass peak on background) in HEP. Gross-Vitels method.

10 Giu 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Data analysis laboratory assistance. Introduction to the final experiment: Search for the tau+ -> phi mu+ decay.

11 Giu 2026 (2h 00m)

MICHAEL JOSEPH Morello - Corso (attività didattica) - In presenza

Data analysis laboratory assistance. Introduction to the final experiment: Search for the tau+ -> phi mu+ decay.