COURSE OBJECTIVES:
To enable a student to apply basic statistical methods in geophysical context and to critically examine the obtained results.
COURSE CONTENT
Elements of probability, conditional probability, Bayes theorem, Bayes factor, the persistence as conditional probability. Random variables and vectors, mathematical expectation, joint, marginal and conditional distributions, independence. Descriptive statistics. Empirical distributions and parameter fitting. Some theoretical distributions with application in
geophysics. Hypothesis testing. Simple and multiple linear regression with geometrical interpretation. Bivariate normal distribution. Basics of time series analysis. Tests for data homogeneity.
LEARNING OUTCOMES
Students will be able to:
- define and discuss basic probability terms
- distinguish types of random variables and describe their properties
- apply mathematical expectation in practice
- relate the independence of random variables with the intuitive idea of independence
- relate properties of random variables with statistical attributes of empirical data sets
- explain and apply methods for parameter estimation
- define and recognize the applicability of theoretical probability distributions
- critically apply statistical tests
- explain and apply the method of linear regression using the geometrical representation.
LEARNING MODE:
- attending lectures, study of literature and lecture notes
- analyzing examples, solving of assigned problems
- doing homework based on small sets of real data
TEACHING METHODS:
- presentation, discussion
- problems to be solved by student himself
METHODS OF MONITORING AND VERIFICATION:
Preliminary, written and oral exam.
Conditions for Obtaining a Signature:
Regular class attendance, submission, and revision of all homework as needed.
Method of Knowledge Assessment and Examination:
Two midterms with a possible oral exam or a written and oral exam.
Each midterm consists of one computational and two theoretical tasks. The midterm lasts 90 minutes, and a minimum of 50% of the points is required to pass. A student who successfully passes both midterms may take the oral exam and potentially achieve a higher grade (the next one).
Students who do not pass the midterms must take both a written and oral exam. The written exam consists of two computational and three theoretical tasks, lasts 135 minutes, and requires a minimum of 50% of the points to pass. The oral exam consists of two to three questions covering the entire curriculum.
Grading for Midterms and Written Exam is determined based on the percentage of correct answers:
50 - 62%: Sufficient (2)
63 - 75%: Good (3)
76 - 88%: Very Good (4)
89 - 100%: Excellent (5)
The final grade is based on the grades from the midterms or from both the written and oral parts of the exam.
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