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Advanced Statistics

  • Course name: Advanced Statistics
  • Course number: DS-03
  • Area of instruction: Math

Administrative details

  • Faculty: Computer Science and Engineering
  • Year of instruction: 1st year of MSc
  • Semester of instruction: 2nd semester
  • No. of Credits: 5 ECTS
  • Total workload on average: 180 hours overall
  • Frontal lecture hours: 2 hours per week.
  • Frontal tutorial hours: 0 hours per week.
  • Lab hours: 2 hours per week.
  • Individual lab hours: 2 hours per week.
  • Frequency: weekly throughout the semester.
  • Grading mode: letters: A, B, C, D.

Course outline

The course covers substantially two topics: most of the course (about 80%) is about nonparametric statistics, especially with reference to non parametric tests and bootstrap; then the courses discusses Gamma analysis and sequence analysis (20%). For the labs, Python is used together with its statistical packages.

Expected learning outcomes

  • To understand the problems related to analyse statistically data not distributed normally
  • To know the more recent computationally-intensive techniques that can help to describe samples and to infer properties of populations in absence of normality
  • To identify situations when the data is on nominal scales so alternative techniques should be use, and act accordingly.
  • To be able to run experiment to evaluate hypotheses for situation of scarce data, distributed non normally, on different kinds of scales.

Programming related learning outcomes

  • None.

Required background knowledge

Fundamental knowledge of statistics, including parametric tests, (multilinear) regression, logistic regression, and inference.

Prerequisite courses

It is recommended that the students have passed all the courses of a BS in Computer Engineering, Electrical Engineering, Computer Science, or Applied Mathematics, and then have taken specific courses in Empirical Methods.

Detailed topics covered in the course

  • Review of basic concepts (Bernoulli and binomial distributions, convergence, statistical hypothesis testing)
  • Estimation of the CDF
  • Jackknife
  • Bootstrap. Bootstrap Confidence Intervals.
  • Smoothing: General Concepts
  • Nonparametric Regression
  • Nonparametric Classification
  • Kernels
  • Gamma Analysis
  • Sequence Analysis

Textbook

Reference material

Required computer resources

Students should have laptops. A Mac or Window’s PC capable of running a scientific python development environment.

Evaluation

  • Weekly Assignments (10%)
  • Mid-term exam (20%)
  • Final written exam (30%)
  • Final oral exam (35%)
  • Participation (5%)