Statistical modelling
Introduction to probabilistic and statistical modelling of risk


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” or “machine learning”, to use related and more trendy terms) 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)
View on Slideshare

Python notebook on basic statistics

Python notebook on coins and dice

Python notebook on probability distributions

Brief reminder on statistics

Handout (PDF)

Interactive examples of probability distributions

Interactive HTML5 demo

Analyzing data with Python

Lecture slides (PDF)

Exercise (Python notebook) on descriptive statistics

Python notebook on simple descriptive statistics

Python notebook on analysis and curve fitting for weather data

Python notebook on analysis of speed of light measurements

Python notebook on analysis of earthquake data

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

In these course materials, applications are presented using the NumPy and SciPy libraries for the Python programming language. You can try out our computational notebooks using free online services such as MyBinder, Google Colab notebooks or Microsoft Azure notebooks.

Other resources

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

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