Statistics Syllabus, Spring Semester 2020

Budapest Semesters in Mathematics

Prerequisite: Undergraduate Calculus and Basic Probability

Course description: Statistics teaches us how to behave in the face of uncertainties, according to the famous mathematician, Abraham Wald. Roughly speaking, we will learn strategies of treating chances in everyday life. The main concept is that our inference is based on a randomly selected sample from a large population, and hence, our observations are treated as random variables. Applications are also discussed, mainly on a theoretical basis, but we make the students capable of solving numerical exercises by choosing the most convenient method for a given real-life problem.

Topics:

1. Short introduction to probability theory (sample spaces, random variables, notable distributions, Bayes rule, laws of large numbers, Central Limit Theorem).

2. Descriptive study of data. Statistical sample, basic statistics, histograms.

3. Basic concepts of testing hypotheses and estimation theory.

4. Methods of point estimation, properties of the estimators, confidence intervals.

5. Inferences about a population, sampling statistics, theory and applications.

6. Parametric inference, comparing two treatments (z, t, F tests).

7. Nonparametric inference: Wilcoxon test and sign test.

8. Analyzing categorized data (contingency tables), chi-square test.

9. Introduction to linear models: regression analysis (linear regression, correlation, model fitting) and analysis of variance.

10. If time permits, we will cover the following topics too: sufficiency, efficiency, consistency, Neyman-Fisher factorization, Neyman-Pearson theorem.

Text: G. K. Bhattacharyya, R. A. Johnson: Statistical Concepts and Methods, Wiley.

C. R. Rao: Statistics and Truth, World Scientific, 1997 (only if you have a deeper interest in statistics).

Handouts: tables of notable distributions and percentile values of basic test distributions.

Assignments, grading: homeworks, midterm test, and final exam make up 40%, 20%, and 40% of the final grade, respectively. The final grade as the function of the total

(maximum 100) points is the following. Below 45: F, 46-49: D,

50-56: C+, 57-63: B-, 64-70: B, 71-77: B+, 78-84: A-, 85-91: A, 92-100: A+.

Contact details of lecturer:

Marianna Bolla, DSc, Univ. Prof.

Budapest University of Technology and Economics

Institute of Mathematics, 1111. Budapest, Egry József u. 1. Bldg. H5/2

Phone: 06-30-728-3679

E-mail: marib@math.bme.hu Homepage: http://www.math.bme.hu/~marib/bsm

If reading course, I will stay after the classes to answer possible questions. If requested, you can ask for extra appointment via e-mail or phone: Marianna Bolla