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Selected applications of probability and statistics

Code: 36931
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Bojan Basrak - Lectures
Lecturers: Nikolina Milinčević, mag. math. - Exercises
Load:

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES:
The main objective is to introduce to students basic probabilistic models and their applications in natural and social sciences. In particular, students will get acquainted with elements of statistical inference for selected stochastic models as well as with various applications of probabilistic modeling in sciences such as mathematical finance and molecular biology.

COURSE DESCRIPTION AND SYLLABUS:
The following topics will be discussed on the basis of various real-life examples
1. Descriptive statistics. Histogram and qq-plot. Comparing empirical and theoretical distribution.
2. Nonparametric statistics. Order statistics. Donsker theorem (without the proof) and Kolmogorov -Smirnov test. Goodness of fit.
3. Random permutations. Birthday problem. Permutation tests in statistics.
4. Independence. Coefficients of correlation. Linear regression. Copulas. Measuring dependence in statistical genetics and finance.
5. Linear and nonlinear regression. Parameter estimation and tests
6. Simulations. Simulating random variables from a given probability distribution. Monte Carlo methods.
7. Random walk. Simulating trajectories of random walk. Asymptotic behavior, recurrence and transience. Random walk as a model for stock price movements.
8. Time series. Chaotic dynamical systems. Logistic map. Comparison of random and deterministic dynamical systems with real-life data.
9. Poisson process. Homogenous Poisson process in one and two dimensions. Applications in actuarial mathematics and genetics.
10. Probabilistic modeling of biological sequences. Erdos-Reny theorem. Longest match between two DNA sequences.
11. Bayesian inference. A priori and a posteriori distributions. DNA evidence in court.
12. Computational statistics. Elements of nonparametric density estimation. Smoothing the histogram
Literature:
  1. G. R. Grimmett, D. R. Stirzaker: Probability and random processes
  2. D. Nolan, T. Speed: Stat Labs. Mathematical Statistics Through Applications
  3. S. Resnick: A probability path
  4. P. Dalgaard: Introductory Statistics with R
  5. D. Williams: Weighing the odds. A course in probability and statistics
Prerequisit for:
Enrollment :
Passed : Probability
5. semester
Izborni predmet 1, 2 - Regular study - Mathematics

6. semester
Izborni predmet 1, 2 - Regular study - Mathematics
Consultations schedule:

Content

Link to the course web page: https://web.math.pmf.unizg.hr/nastava/opvis/

 

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