DOCTORAL STUDIES IN STATISTICS

This web-page is created to support the initiative for development of a PhD program in Statistics. The initiative is a joint undertaking of the Mathematics Departments at the Universities of Zagreb and Osijek, and it is financially supported by NZZ – Croatian Science Foundation. Because of the advances in computer generated data in almost all fields, the need for the understanding and use of statistical analyses has become essential. This need led to the development of a doctoral program in statistics that would serve the country by contributing to domestic and regional research, and to development and business potential.

The idea to create such a program in Croatia has been welcomed by many people in local academia, businesses and official institutions. Moreover, this idea has received a warm welcome by many distinguished scientists from abroad, some of whom joined our international advisory board.

The main goals of this program are:

  1. Developing the use of statistics in cross disciplinary fields:

Providing education for researchers in multidisciplinary areas;

Creating an environment of scientific collaboration within academia;

Creating a fruitful ground for joint projects with businesses and state institutions.

  1. Training of statisticians and users of statistics:

Providing scientific education of future statisticians;

Developing a framework for continuous education of professional statisticians;

Improving the standards of teaching statistics.

The envisioned PhD program will follow the ideas of the Bologna process. In particular, we encourage the mobility of students and teachers. Moreover, we aim to provide an open curriculum with a high degree of electives.

Special attention will be dedicated to the development of theoretical statistics, and to applications:

Applications in Business and Finance

Applications in the Biological and Medical Sciences

Applications in the Industrial and Engineering Sciences

It is our intention that the students and the faculty of our doctoral studies cooperate closely with interested local industrial and business organizations. Hence, in parallel with the doctoral studies, we plan to provide a program of Specialist Studies in Statistics. Such an additional program should attract people working in research and development departments of various businesses and official institutions. This program should also provide a basis for (partial) self-financing of the PhD program.

INITIATIVE GROUP

The following faculty will form the working group behind this initative:

M. Huzak, (head) Department of Mathematics, University of Zagreb

H. Sikic, Department of Mathematics, University of Zagreb

M. Bensic, Department of Mathematics, University of Osijek

B. Basrak, Department of Mathematics, University of Zagreb

V. Saric, Department of Mathematics, University of Zagreb

DOCTORAL STUDIES IN STATISTICS

The studies are designed to provide students with intensive training in theoretical and applied statistics. The studies will be supported by various academic institutions in Croatia. Statisticians and probabilists in the Department of Mathematics of The Universities in Zagreb and Osijek are the main organizers. The quality of postgraduate teaching reflects internationally recognized level of mathematical education at both of these institutions. The research expertise of international guest faculty as well as local staff members will secure that the students are provided with up-to-date training in statistics. Because this program in mathematical and applied statistics is certain to have a beneficial impact on local industry and science, there are many indications that excellent prospects for employment will be available for future graduates.

The program will, in particular, introduce students to modern ideas of computational statistics such as nonparametric, Bayesian and regression models. It is designed to be accessible to students with degrees in a variety of quantitative disciplines: for example, mathematics, physics, computer science, engineering, economics, biology.

In addition to theoretical statistics, several areas of applications will be emphasized:

  1. Biostatistics and Bioinformatics
  2. Industrial and Financial Statistics
  3. Statistics Engineering

TENTATIVE SKETCH OF THE PROGRAMME

  1. THEORETICAL CORE SUBJECTS
  1. Introduction to Probability (45 hours)

(CLT, characteristics functions, conditional prob. etc.)

Stochastic processes I (30 hours)

(Random walk, Markov chains, AR(1), Poisson, GI/G/1 and ruin process)

Statistical software and data (15 hours)

(SAS, Splus/R, Statistica)

  1. Mathematical Statistics (45 hours)
  1. Large Sample Theory *(45 hours)

* Large Sample Theory is also listed as an elective, and could be in the core or as an elective.

  1. APPLIED CORE SUBJECTS
  1. Applied Statistics I (30 hours)

(concepts of statistics, descripitive statistics, regression ANOVA, contingency tables,…)

  1. Applied Statistics II (30 hours)

(general linear models, K-S test, rank tests, Bayesian analysis)

  1. Computer Intensive Statistics (30 hours)

(Bootstrap, Permutation test, Importance sampling, bagging, MCMC,…)

4. Multivariate analysis (45 hours)

(multivariate normal distribution, principal components, clustering)

  1. ELECTIVES (students will choose five or six topics courses of approximately 30 hours each)
  1. Nonparametric methods
  2. Time Series Analysis
  3. Design of Experiments
  4. Categorical Data
  5. Data Mining/Statistical Learning
  6. Large Sample Theory
  7. Advanced Probability
  8. Stochastic processes II
  9. Computational Biology
  1. SPECIAL TOPICS
  1. Biostatistics
  2. Populations Genetics
  3. Survival Analysis
  4. Clinical Trials Design
  5. Design of Experiments
  6. Financial Stochastics
  7. Risk Analysis
  8. Reliability and Quality Control
  9. Extreme Value Theory
  10. Pychometrics
  11. Probabilistic Combinatorics

The special topics lectures will be provided depending on the interests and needs of the students. They are likely to be of shorter duration, as in a workshop or summer school.

An important ingredient in the program is an applied project that may be considered as a mini-thesis. The final phase is a doctoral dissertation written under the supervision of the faculty.