Training and Research
PhD Programme Courses/classes - 2021/2022
Training offer to be defined
Probability (2021/2022)
Teacher
Not yet assigned
Credits
7.5
Language
English
Class attendance
Free Choice
Location
VERONA
Learning outcomes
Availability
The course is intended for 1st year students on PhD in Economics and Finance.
Pre-requisites
Introduction to mathematics, elementary statistical theory and elementary set theory. Basic knowledge of probability theory, as in: P. Newbold, W. Carlson, B. Thorne (2012), Statistics for Business and Economics, Pearson Higher Education, Chapters 3-5 (previous editions would be fine as well). Attendance at more advanced courses such as real analysis, probability, distribution theory and statistical inference would be desirable.
Objectives of the course
The purposes of this course are: (i) to explain, at an intermediate level, the basis of probability theory and some of its more relevant theoretical features; (ii) to explore those aspects of the theory most used in advanced analytical models in economics and finance. The topics will be illustrated and explained through many examples.
Program
Course content
1. Algebras and sigma-algebras, axiomatic definition of probability, probability spaces, properties of probability, conditional probability, Bayes theorem, stochastic independence for events.
2. Random variables, measurability, cumulative distribution functions and density functions.
3. Transformations of random variables, probability integral transform.
4. Lebesgue integral, expectation and variance of random variables, Markov inequality, Tchebycheff inequality, Jensen inequality, moments and moment generating function.
5. Multidimensional random variables, joint distributions, marginal and conditional distributions, stochastic independence for random variables, covariance and correlation, Cauchy-Schwartz inequality.
6. Bivariate normal distribution, moments, marginal and conditional densities.
7. Transformations of multidimensional random variables.
8. Convergence of sequences of random variables, weak law of large numbers and central limit theorem.
Textbook
S. Ross (2010). A First Course in Probability, 8th Edition. Pearson Prentice Hall.
Further readings
G. Casella, R. L. Berger (2002). Statistical Inference, Second edition. Duxbury Thompson Learning.
R. Durrett (2009). Elementary Probability for Applications. Cambridge University Press.
M. J. Evans, J. S. Rosenthal (2003). Probability and Statistics - The Science of Uncertainty. W. H. Freeman and Co.
G. Grimmett, D. Stirzaker (2001). Probability and Random Processes. Oxford University Press.
A. M. Mood, F. A. Graybill, D. C. Boes (1974). Introduction to the Theory of Statistics. McGraw-Hill.
P. Newbold, W. Carlson, B. Thorne (2012). Statistics for Business and Economics. Pearson Higher Education.
D. Stirzaker (2003). Elementary Probability. Cambridge University Press.
L. Wasserman (2004). All of Statistics. Springer.
Advanced readings
R. B. Ash, C. A. Doléans-Dade (2000). Probability and Measure Theory. Harcourt/Academic Press.
M. J. Schervish (1995). Theory of Statistics. Springer.
Bibliography
Examination Methods
A two-hour written paper at the end of the course.
PhD school courses/classes - 2021/2022
Please note: Additional information will be added during the year. Currently missing information is labelled as “TBD” (i.e. To Be Determined).
PhD students must obtain a specified number of CFUs each year by attending teaching activities offered by the PhD School.
First and second year students must obtain 8 CFUs. Teaching activities ex DM 226/2021 provide 5 CFUs; free choice activities provide 3 CFUs.
Third year students must obtain 4 CFUs. Teaching activities ex DM 226/2021 provide 2 CFUs; free choice activities provide 2 CFUs.
Registering for the courses is not required unless explicitly indicated; please consult the course information to verify whether registration is required or not. When registration is actually required, no confirmation e-mail will be sent after signing up.
Activities are also listed in the online calendar.
Teaching Activities ex DM 226/2021: Linguistic Activities
INFORMATION: ENGLISH FOR ACADEMIC PRESENTATION SKILLS [Arts and Humanities]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC PRESENTATION SKILLS [Law and Economics]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC PRESENTATION SKILLS [Life and Health Sciences - 1 st Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC PRESENTATION SKILLS [Life and Health Sciences - 2 nd Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC PRESENTATION SKILLS [Natural Sci. and Engineering-1st Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC PRESENTATION SKILLS [Natural Sci. and Engineering-2nd Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC WRITING SKILLS [Arts and Humanities]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC WRITING SKILLS [Law and Economics]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC WRITING SKILLS [Life and Health Sciences - 1 st Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC WRITING SKILLS [Life and Health Sciences - 2 nd Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC WRITING SKILLS [Natural Sci. and Engineering-1st Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC WRITING SKILLS [Natural Sci. and Engineering-2nd Session]
Credits: 2,5
Language: English
Teaching Activities ex DM 226/2021: Research management and Enhancement
SEMINARIO AVANZATO SULLE RISORSE BIBLIOTECARIE PER LA RICERCA [Arts and Humanities]
Credits: 2,5
Language: Italian
Teacher: Donatella Boni
SEMINARIO AVANZATO SULLE RISORSE BIBLIOTECARIE PER LA RICERCA [Law and Economics]
Credits: 2,5
Language: Italian
Teacher: Luisella Zocca
SEMINARIO AVANZATO SULLE RISORSE BIBLIOTECARIE PER LA RICERCA [Scientific Area]
Credits: 2,5
Language: Italian
Teacher: Elena Scanferla
Teaching Activities ex DM 226/2021: Statistics and Computer Sciences
INTRODUCTION TO PROBABILITY (MODULE I)
Credits: 1
Language: English
Teacher: Marco Minozzo
INTRODUCTION TO PROBABILITY (MODULE II)
Credits: 1
Language: English
Teacher: Marco Minozzo
BASIC LEVEL STATISTICS
Credits: 2,5
Language: English
INTRODUCTION TO STATISTICAL INFERENCE
Credits: 1
Language: English
Validità e affidabilità delle misure e dei test diagnostici
Credits: 0,5
Language: English
Teacher: Alessandro Marcon
BASIC LEVEL STATISTICS
Credits: 2,5
Language: Italian
Statistical analysis with R - module I
Credits: 1
Language: Italian
Teacher: Erica Secchettin
Generalized linear models: logistic regression, loglinear model, Poisson model
Credits: 2
Language: English
Teacher: Lucia Cazzoletti
Disegno dello studio nella ricerca osservazionale e sperimentale
Credits: 1,5
Language: English
Teacher: Alessandro Marcon
Calcolo della numerosità campionaria in funzione di una precisione o potenza statistica prefissata
Credits: 1
Language: English
Teacher: Giuseppe Verlato
Introduzione alla meta-analisi per la ricerca biomedica (revisione della letteratura, raccolta dei dati, costruzione del database)
Credits: 1
Language: English
Teacher: Giuseppe Verlato
Applicazioni della meta-analisi in campo epidemiologico e medico
Credits: 1
Language: English
Teacher: Giuseppe Verlato
Analisi di sopravvivenza: test log-rank, curve di sopravvivenza di Kaplan-Meier, modello di regressione di Cox
Credits: 1,5
Language: English
Teacher: Simone Accordini
Applicazioni della meta-analisi al campo epidemiologico o biomedico
Credits: 1
Language: English
Teacher: Giuseppe Verlato
INTERMEDIATE STATISTICS [Recommended for Human Sciences]
Credits: 2,5
Language: English
INTERMEDIATE STATISTICS [Tutti i corsi di studio]
Credits: 2,5
Language: English
Introduzione alla meta-analisi focalizzata sulla ricerca medica (revisione della letteratura, raccolta dei dati)
Credits: 1
Language: English
Statistical analysis with R - module II
Credits: 2
Language: Italian
Teacher: Erica Secchettin
Teaching Activities: Free choice
PROTECTING PSYCHOLOGICAL WELL-BEING IN THE PHD PROGRAM: WHAT DO WE NEED TO CONSIDER FOR BEING A GOOD SCIENTIST: BEST PRACTICE AND THE ETHICS OF SCIENCE
Credits: 1
Language: inglese
Teacher: Paola Cesari
QUANDO LA RICERCA SI FA ETICA (PERCORSO ORGANIZZATO E FINANZIATO DAL TEACHING AND LEARNING CENTER DI UNIVR)
Credits: 2
Language: Italian
Teacher: Roberta Silva
IMPARA IL MARKETING DIGITALE
Credits: 1,5
Language: English
Italian Poetry abroad
Credits: 1
Language: Italiano
Teacher: Massimo Natale
COSTRUISCI IL TUO BUSINESS MODEL CANVAS
Credits: 1,5
Language: English
APPROCCI E METODOLOGIE PARTECIPATIVE NELLA RICERCA CON GLI ATTORI DEL TERRITORIO
Credits: 1,5
Language: Italian
Teacher: Cristiana Zara
DOING INTERVIEWS IN QUALITATIVE RESEARCH
Credits: 1,5
Language: English
Teacher: Chiara Sità
LA COMUNICAZIONE UMANISTICA: OPPORTUNITA' E RISCHI
Credits: 1
Language: Italiano
DIFFERENTIAL DIAGNOSIS OF DEMYELINATING DISEASES OF THE CENTRAL NERVOUS SYSTEM
Credits: 2
Language: English
Teacher: Alberto Gajofatto
IL SONNO E I SUOI DISTURBI: FOCUS SULLE PARASONNIE E I DISTURBI DEL MOVIMENTO IN SONNO
Credits: 1
Language: English
Teacher: Elena Antelmi
IMAGING TECHNIQUES FOR BODY COMPOSITION ANALYSIS
Credits: 1
Language: English
Teacher: Carlo Zancanaro
OPEN SCIENCE: THE MIGHTY STICK AGAINST "BAD" SCIENCE
Credits: 2
Language: English
Teacher: Alberto Scandola
THE EMPIRICAL PHENOMENOLOGICAL METHOD (EPM): THEORETICAL FOUNDATION AND EMPIRICAL APPLICATION IN EDUCATIONAL AND HEALTHCARE FIELDS
Credits: 2
Language: English
THE PATHWAY OF OXYGEN: CAUSE OF HYPOXEMIA
Credits: 1
Language: English
Teacher: Carlo Capelli
Faculty
045 802 8102
simona.fiore@univr.it
tamara.fioroni@univr.it
cecilia.mancini@univr.it
andrea.mazzon@univr.it
martina.menon@univr.it
marcella.veronesi@univr.it
giorgio.vocalelli@univr.it
PhD students
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Guidelines for PhD students
Below you will find the files that contain the Guidelines for PhD students and rules for the acquisition of ECTS credits (in Italian: "CFU") for the Academic Year 2023/2024.
Documents
| Title | Info File |
|---|---|
Dottorandi: linee guida generali (2023/2024)
|
pdf, it, 245 KB, 26/02/24 |
|
PhD students: general guidelines (2023/2024)
|
pdf, en, 245 KB, 26/02/24 |
