Exercises and tools for probabilistic analysis
MATERIAL FOR THE COURSE OF “APPLIED STATISTICS AND PROBABILITY ANALYSIS”
On this page you may find links to learning material for the course “Applied Statistics and Probability Analysis”, which is taught by Prof. Jalayer, ETRiS’ coordinator, at at the University of Naples Federico II (more information on the right column).
This Ph.D.-level course strives to introduce elementary concepts in probability. The main aspect that distinguishes this course is that it is inspired by the concept of probability as extended logic (see E. T. Jaynes 2003, Probability Theory: the Logic of Science).
The objective of this course is to introduce the essential concepts and tools that a researcher may encounter in his/her problem-solving. The course begins by providing elementary concepts in probability theory. Next, the students are going to get to know the different types of probability distributions and their statistics. Specifically, the Poisson family of distributions, Normal and Lognormal distributions will be discussed thoroughly. Furthermore, the probabilistic model of linear regression will be described. Finally, the standard Monte Carlo Simulation method will be introduced. Emphasis is placed on showing the application of probabilistic concepts in real research examples.
The lecture notes and the solutions to the sample problems may be found on the course repository, and are released under the following DOI:
Notebooks on Google Colab:
Lecture 2, Problem 1 – Lecture 2, Problem 2 – Lecture 2, Problem 3 – Lecture 2, Problem 4 – Lecture 2, Problem 5
Lecture 3, Problem 2.6
Lecture 6, Problem 1 – Lecture 6, Problem 2 – Lecture 6, Problem 3
SOME USEFUL EXTRA READING
Here are links to some useful textbooks in applied probability and statistics and structural reliability analysis:
Probability, Statistics, and Decision for Civil Engineers, J.R. Benjamin and C.A. Cornell, Dover Edition, 2014
Bayesian Inference in Statistical Analysis, G.E.P. Box and G.C. Tiao, John Wiley and Sons, 2011
An introduction to the theory of point processes: volume I: elementary theory and methods, D.J. Daley, D. Vere-Jones, Springer New York, 2003
Structural Reliability Methods, O.D. Ditlevsen, H.O. Madsen, John Wiley and Sons, 1996