Probability & Statistics

UNIVERSITÀ DELLA SVIZZERA ITALIANA
A Mendrisio (Svizzera)

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  • Corso
  • Mendrisio (Svizzera)
Descrizione

Descrizione We treat the basic notions of discrete combinatorics and probability theory: Bernoulli trial, binomial coefficients, probability spaces, the probability function, random variables, expectation value, variance and covariance. Of central importance are the limit theorems such as the weak law of large numbers and the central limit theorem. These establish the link to statistics: In order to obtain a significant statement from a random sample, what is the necessary size of the sample? And if we have two or more different models that we can fit to the sample then which one is the "best"? And what does "best" means in this context? We discuss estimators and tests. Also based of the notions of probability, we discuss the basics of information theory such as entropy, conditional entropy, and mutual information. Theoretical concepts in the course will be illustrated with real-life examples from finance, climate research and medicine.

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Consultare
Mendrisio
Tessin, Svizzera
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Programma

Descrizione

We treat the basic notions of discrete combinatorics and probability theory: Bernoulli trial, binomial coefficients, probability spaces, the probability function, random variables, expectation value, variance and covariance. Of central importance are the limit theorems such as the weak law of large numbers and the central limit theorem. These establish the link to statistics: In order to obtain a significant statement from a random sample, what is the necessary size of the sample? And if we have two or more different models that we can fit to the sample then which one is the "best"? And what does "best" means in this context? We discuss estimators and tests. Also based of the notions of probability, we discuss the basics of information theory such as entropy, conditional entropy, and mutual information. Theoretical concepts in the course will be illustrated with real-life examples from finance, climate research and medicine.

REFERENCES

  • An introduction to probability theory and its applications / William Feller. - New York [etc.] : J. Wiley, 1968-1971
  • Elements of information theory [Archivio elettronico] / Thomas M. Cover, Joy A. Thomas. - Hoboken, N.J. : Wiley-Interscience, 2006


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