Theory of Probability and Statistics
Faculty
Timo Koski
Ph.D., Professor of Mathematical Statistics, KTH Royal Institute of Technology, Stockholm
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
The aim of the course is to introduce basic theories and methods of pure probability theory at an intermediate level and their applications to chosen topics of theory of statistical inference and machine learning. No knowledge of measure and integration theory is required, and only bare first statements of that will be included in the course.
Techniques developed in this course are important in AI, time series analysis, financial analysis, signal processing, econometrics, and other branches of engineering and science. The course gives also a background and motivation for studies of advanced courses in probability and statistics.
Learning highlights
- 1. Computational skill in probability: Axioms of Probability; Distributions of probability theory; Conditional probability and Expectation; Martingales; Characteristic functions; Multivariate Gaussian; Probability generating functions; Convergence concepts of probability theory; Law of large numbers; Central limit theorem; Stationary stochastic processes; Wiener process; Ornstein-Uhlenbeck Process; Poisson process.
- 2. Application of A in theory of statistical inference and machine Learning: PAC-theory; Expected risk minimisation; Exponential families of distributions; Bayesian theory; Maximum Likelihood; Bias-Variance Decomposition of data science; Confidence intervals; Model choice in machine learning; Expectation maximisation algorithm; High-dimensional data.
Course outline
4 classes
Sigma-fields,
Probability space.
Axioms of probability calculus
Session 2
Some Theorems of Probability calculus.
Probability on propositional logic.
PAC-theory of machine learning
Session 3
Distribution functions.
Multivariate random variables
Session 4
Multivariate random variables.
Marginal density, Independence,
Density of a transformed random vector,
Exponential families of distributions
Prerequisites
This course is one of three in a wholistic series.
Students that have already taken MSL-111 and those with prior experience with HTML, CSS, and Javascript building simple web pages will be good candidates for this module.
Ph.D at Abo Akademi University in Finland. Teaching & research positions in Sweden: at Lulea University of Technology, Linkoping University, KTH Royal Institute of Technology (current position). Visiting researcher at University of North Carolina at Chapel Hill, Louisiana State University at Baton Rouge, UTIA of Czech Academy of Sciences, University of Warsaw, Institute of Advanced Study at Aalto University, Visiting lecturer and researcher at University of Helsinki, University of Turku, University of Makerere. Author (co-author) of three monographs.
Has worked in signal processing, biomathematics and genetics groups.
See full profileApply for this course
Theory of Probability and Statistics
by Timo Koski
Total hours
45 Hours
Dates
Feb 18 - Mar 08, 2019
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
Complete the form below to kickstart your application
Schedule your Harbour.Space interview
If successful, get ready to join us on campus
FAQ
Will I receive a certificate after completion?
Yes. Upon completion of the course, you will receive a certificate signed by the director of the program your course belonged to.
Do I need a visa?
This depends on your case. Please check with the Spanish or Thai consulate in your country of residence about visa requirements. We will do our part to provide you with the necessary documents, such as the Certificate of Enrollment.
Can I get a discount?
Yes. The easiest way to enroll in a course at a discounted price is to register for multiple courses. Registering for multiple courses will reduce the cost per individual course. Please ask the Admissions Office for more information about the other kinds of discounts we offer and what you can do to receive one.