**Graduate program in Statistics**

This is a program that aims to form Masters and Ph.D's in the field of Statistics. The students are selected among candidates with a solid knowledge base in Statistics/Mathematics coming from Brazil and abroad, after a rigorous selection process (summer class, curriculum and letter of recommendation for Master's Degree; curriculum and letter of recommendation for Ph.D's Degree). The program received grade 5 in the last CAPES evaluation. All professors accredited to the program are active researchers (for accreditation, Articles 22 and 23 in the Regulation demand that the professor present a regular and recent scientific production).

The focus of the Master's Degree program is to form professionals in Probability, Statistics and their applications. The student graduated in these programs must be able to act both professionally (consulting, industry, etc.) and academically (teaching and research).One of the main goals of the Ph.D's Degree program is the formation of leaderships in Probability and Statistics research, to work preferably as professors in universities and research centers. The quality of the defended Ph.D. thesis must be in a level compatible with the best international specialized journals.The curriculum of the Master's and the Ph.D's Degrees is composed of a variety of courses in Mathematical Statistics, Statistical Methods, Probability and Stochastic Processes.

**Master's Degree**

In order to obtain the title of Master, the student must meet the following requirements:

- Be approved in the mandatory courses: Probability (MI401), Statistical Inference (MI402), Statiscal Methods (MI404);
- Obtain at least 22 credits in courses from the Elegible Courses for Master's Degree list, chosen in agreement with his/her advisor;
- Be approved in the English Proficiency Exam (reading);
- Be approved in the
**Masters Qualification**Exam; - Elaborate and defend the Masters Dissertation.
- The minimal and maximal duration for the Master's course are 12 and 36 months, respectively.
- Masters Qualification

__Master' Degree:__

The student must pass the Qualification Exam conducted within 12 months from the date of enrollment. The Exam shall consist of two written tests: Probability (about the contents of the course MI401 and Statistical Inference (about the contents of the course MI402).Each one of these tests shall be held twice a year on dates defined by the SCPGE.

**MI401 - Probability**

T:60 E:30 L:0 S:0 C:6 P:3__Program:__ Probability spaces. Discrete and Continuous random variables. Conditional distribution. Conditional expectation. Generator functions. Convergence of random variables. Inequalities. Law of large numbers. Central limit theorem.

__Bibliography__: Grimmett, G.R. e Stirzaker, D.R., Probability and Random Processes. Oxford Science Publications, James, B. R. Probabilidade: um curso a nível intermediário. Projeto Euclides. IMPA.

**MI402 - Statistical Inference**

T:60 E:30 L:0 S:0 C:6 P:2__Program:__ Statistical models. Statistics and parameters. Sufficiency. Exponential family. Estimation methods: method of moments, method of least squares and maximum likelihood. Comparison of estimators: principle of optimality, minimum-variance unbiased estimators, inequality of information. Confidence intervals and hypothesis tests. Likelihood-ratio-test. Optimal tests. Neyman-Pearson lemma. Introduction to decision theory. Notions in Bayesian procedures.

__Bibliography__: Rohatagi, V.K., An Introduction to Probability Theory and Mathematical Statistics., John Wiley, New York, 1976. Casella, G. e Berger, R.L, Statistical Inference, Wadsworth & Brooks, California, 1990.

__Ph.D.:__

The Ph.D. Qualification Exam shall consist of two steps. The first one shall consist of a written test, about the contents of the courses Intermediate Probability (MI659) and Advanced Inference (MI677).

This test will be held once or twice a year, on dates defined by the SCPGE. In this first step, the student must obtain approval within 24 months from his/her enrollment. The second step of the Qualification Exam will consist of an oral dissertation about a specific subject of the student's thesis. Regarding this second step, the student must obtain approval within 36 months from his enrollment.

**Ph.D.**

In order to obtain the title of Ph.D., the student must attend the following requirements:

- Be approved in the mandatory courses: Advanced Inference (MI677) and Intermediate Probability (MI659);
- Obtain at least 24 credits in courses from the Elegible Courses for Master's Degree list, chosen in agreement with his/her advisor. From these 24 credits, at least 16 must be obtained in Eligible Courses for Ph.D.;
- Be approved in the English Proficiency Exam (written).
- Be approved in the two steps of the Ph.D. Qualification Exam;
- Elaborate and defend the Ph.D thesis.

The minimal and maximal duration for the Ph.D. course are 24 and 72 months, respectively.