Statistical modelling
Introduction to probabilistic and statistical modelling of risk


Overview

The exponential
probability distribution Risk analysis is sometimes based on the analysis of data concerning a hazardous event, such as the occurrence of an earthquake, or the exceedance of a threshold. This analysis is based on statistical modelling, most often with computer tools. When the risk analyst puts her data scientist hat on, she collects data (measurements, observations) from various sources and inputs them into the computer, obtains a general overview of the data and its distribution, and builds a statistical model which attempts to reproduce properties of the underlying phenomena. After checking that the statistical model is a good fit for the observations, she can generate various risk metrics and quantify the level of uncertainty in the predictions.

Statistical modelling (or “data science”, to use a related and more trendy term) is an important part of risk analysis and safety in various engineering areas (mechanical engineering, nuclear engineering), in the management of natural hazards, in quality control, and in finance.

This submodule is a part of the risk analysis module.

Learning objectives

Upon completion of this submodule, you should be able to:

  • Analyze data using descriptive statistics and graphical tools

  • Fit a probability distribution to data (estimate distribution parameters)

  • Express various risk measures as statistical tests

  • Determine quantile measures of various risk metrics

  • Build flexible models to allow estimation of quantities of interest and associated uncertainty measures

  • Select appropriate distributions of random variables/vectors for random phenomena

Course material

Statistics and risk modelling with Python

Lecture slides (PDF)
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Python notebook on basic statistics

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Python notebook on coins and dice

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Python notebook on probability distributions

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Brief reminder on statistics

Handout (PDF)

Interactive examples of probability distributions

Interactive HTML5 demo

Analyzing data with Python

Lecture slides (PDF)

Python notebook on simple descriptive statistics

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Python notebook on analysis and curve fitting for weather data

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Python notebook on analysis of speed of light measurements

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Python notebook on analysis of earthquake data

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Python notebook on Semmelweis’s work on risk reduction in hospitals

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In these course materials, applications are presented using the NumPy and SciPy libraries for the Python programming language.

Other resources

We recommend the following sources of further information on this topic:

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