Illustrative: the exceedance probability of a hazard as a sheet, return-period isolines and simulated events

Risk Academy, led by the Nexus Consortium · Course catalogue · Risk Science and Methods

Quantitative Risk Analysis

Quantitative risk analysis and statistics

Quantitative risk analysis and statistics, taught twice over: as the working methods of the field and as its frontier since 2024, with labs on the Academy's tools, open data and the Nexus Standards.

Core course Frontier course

The discipline

01Core course · L2 Intermediate

Quantitative risk analysis and statistics: foundations and practice

This area covers the quantitative core of risk analysis: probability and return periods, loss metrics such as average annual loss and exceedance probability curves, Monte Carlo simulation, dependence, extreme value analysis, Bayesian updating and the programming tools used to apply them, together with the limits of qualitative matrices.

Level
L2 Intermediate
Study time
about 24 hours (planning estimate)
Status
In authoring
Prerequisites
An L1 course in the area, or an entry review

Why now

Loss records from secondary perils inform the tail and frequency assumptions used in loss metrics and exceedance curves. Munich Re, Climate change presses on: Devastating wildfires and intense thunderstorms exacerbate losses for insurers, 13 January 2026

Learning outcomes

  1. Define exceedance probability and the other key terms of the discipline and use them correctly in a written case
  2. Explain probability and return periods and loss metrics and exceedance curves with a worked example and its source
  3. Apply the discipline's method to a documented case and explain each result with its source
  4. Analyse a named case against monte Carlo simulation, stating evidence, date and limits

Modules

  1. Probability and return periods
    • Probability and return periods
    • Loss metrics and exceedance curves
    • Monte Carlo simulation
  2. Dependence and correlation
    • Dependence and correlation
    • Extreme value analysis
    • Bayesian updating
  3. Risk analytics programming
    • Risk analytics programming
    • Qualitative tools and their limits
  4. Lab: the discipline's method
    • Losses above a chosen threshold arrive at a rate and follow a generalised Pareto law whose shape parameter sets how heavy the tail is; rate, scale and shape together give the loss at any return period, and the shape, more than any other number, decides what a retention or a limit should be.
    • Work the method through a documented case and explain each result
    • Read the method's sources and stated values

Labs with Academy tools

Nexus Standards

Teaches

  • NRS-C2 Risk assessment method
  • NRS-C9 Risk models, methods and validation
  • NRS-M1 Method fabric: Universal mathematics and statistics

Relies on

  • NS-1 The UNI and the artefact catalogue
  • NS-16 UNI application profile (how articles, documents, code, data, APIs and interfaces carry the UNI)
  • NRS-C1 Risk vocabulary and ontology
  • NRS-C8 Evidence, uncertainty and provenance

Assessment

  • 40%Lab recordWork the discipline's method through a documented case and explain each result with its source and date
  • 40%Case memoApply the discipline's methods to a named place or organisation, stating evidence and limits
  • 20%Key terms checkShort answers on the key terms, marked against the definitions

Delivery

  • Self-paced online, with the labs in the browser
  • Cohort study over six to eight weeks, with a weekly lab review
  • Co-delivered with a partner institution, inside its own courses

Partner on this course

  • Co-teach a module and bring a current case from your work
  • Host a cohort for your learners, with your own schedule and review
  • Contribute a lab: a dataset your institution publishes openly, or a model
  • Review the course content and its references before it opens
  • Translate the course and adapt its cases to your region

How institutions and experts take part

In the Academy LMS

Course on the learning platform
Intermediate, 4 topics
Cohort group
A community group for each cohort of learners
Achievement
Recorded on completion of the assessed work

References

  1. Munich Re, Climate change presses on: Devastating wildfires and intense thunderstorms exacerbate losses for insurers, 13 January 2026
  2. Coles, An Introduction to Statistical Modeling of Extreme Values, 2001
  3. Embrechts, Klüppelberg and Mikosch, Modelling Extremal Events for Insurance and Finance, 1997
  4. Pickands, Statistical inference using extreme order statistics, Annals of Statistics, 1975
02Live map

Hazards and exposure in Italy

Flood water, active fires and surface heat beside population and night-time lights, over Italy.

The interactive map needs JavaScript; the layer list and sources are below.

Layers 3

Hazards and exposure

Latest available

NASA GIBS / EOSDIS · ASTER GDEM (METI, NASA) · Blue Marble (NASA) · © OpenStreetMap contributors (ODbL) · Natural Earth

Loading the latest NASA imagery.

Drag to move. Ctrl or ⌘ and scroll, pinch or the buttons to zoom; hover for the values under the pointer; reset returns to the region.

Hazards and exposure, framed on Italy.Satellite and model products as NASA publishes them, each with its own date. They are indicators, not assessments of any place.

Data: NASA GIBS · ASTER GDEM · Blue Marble · © OpenStreetMap contributors · Natural Earth · NASA EONET · U.S. Geological SurveySources and licences

  • We acknowledge the use of imagery provided by services from NASA's Global Imagery Browse Services (GIBS), part of NASA's Earth Science Data and Information System (ESDIS). Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). NASA open data
  • We acknowledge the use of imagery provided by services from NASA's Global Imagery Browse Services (GIBS), part of NASA's Earth Science Data and Information System (ESDIS). Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). NASA open data
  • VIIRS near-real-time products (flood, land surface temperature, snow cover, corrected reflectance), NASA LANCE; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). NASA open data
  • NASA Fire Information for Resource Management System (FIRMS), VIIRS 375 m active fire product, NASA LANCE; vector tiles via NASA GIBS. Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). NASA open data
  • Center for International Earth Science Information Network (CIESIN), Columbia University. 2018. Gridded Population of the World, Version 4 (GPWv4): Population Density, Revision 11. NASA Socioeconomic Data and Applications Center (SEDAC). Licensed under CC BY 4.0. Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). doi:10.7927/H49C6VHW. CC BY 4.0
  • VIIRS Black Marble night-time lights, NASA Goddard Space Flight Center; distributed by the NASA Level-1 and Atmosphere Archive and Distribution System (LAADS DAAC); imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). NASA open data
  • MODIS and VIIRS atmosphere products, NASA LANCE and LAADS DAAC; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). NASA open data
  • ASTER GDEM is a product of METI and NASA (ASTER Global Digital Elevation Model V003, NASA LP DAAC); imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). Cite as: NASA/METI/AIST/Japan Spacesystems and U.S./Japan ASTER Science Team (2019). ASTER Global Digital Elevation Model V003. doi:10.5067/ASTER/ASTGTM.003. NASA open data
  • Made with Natural Earth. Free vector and raster map data @ naturalearthdata.com. Public domain
  • © OpenStreetMap contributors (ODbL), via NASA GIBS (coastlines, boundaries, roads and place names). Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). ODbL
  • Blue Marble, NASA Earth Observatory; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). NASA open data
  • Context on the globe and flat map: coastlines, boundaries, roads and place names from NASA GIBS reference layers (OpenStreetMap data, ODbL, © OpenStreetMap contributors); Blue Marble imagery as an optional base; 3D terrain and the elevation read-out from the ASTER GDEM elevation colour index (5 m to 200 m classes, exaggerated for legibility). Boundaries are drawn as published and imply no position on any territory.
  • Globe: MapLibre GL JS 6.9.1, BSD-3-Clause, © MapLibre contributors.
  • Live events: NASA Earth Observatory Natural Event Tracker (EONET); events are indicative and keep their original source links.
  • Live: NASA EONET Events are indicative, not authority warnings.
  • Live: U.S. Geological Survey Events are indicative, not authority warnings.
  • NASA GIBS: We acknowledge the use of imagery provided by services from NASA's Global Imagery Browse Services (GIBS), part of NASA's Earth Science Data and Information System (ESDIS).
  • River discharge forecast, 30 days with range (GloFAS via Open-Meteo): Contains modified Copernicus Emergency Management Service information 2026; not a flood warning.
  • Weather data by Open-Meteo.com (https://open-meteo.com/), licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/).
  • Optional layers (10 sources in the layer list: live, forecast, observed and context) print their provider credit on the map and here when switched on; forecasts are model output and derived indices are estimates.

Layers and dates

  • Flood water, 3-day composite: VIIRS Global Flood Product, NASA LANCE · 14 Oct 2026
  • Active fires and thermal anomalies: VIIRS NOAA-20 375 m (FIRMS), NASA LANCE FIRMS · 13 Oct 2026
  • Population density, 2020: Population: CIESIN, Columbia University, Gridded Population of the World v4.11 (2018), NASA SEDAC, CC BY 4.0 · static
  • Land surface temperature, day, 8-day composite: VIIRS NOAA-20 Level 3, 8-day, NASA LANCE · 14 Sep 2026
  • Night-time lights, daily: VIIRS Black Marble (VNP46A2), NASA LAADS DAAC · 12 Oct 2026
  • Aerosol optical depth, daily: VIIRS NOAA-20 Deep Blue AOD, NASA LANCE · 13 Oct 2026

03How learning runs

How learning runs, as a process you can run

Select a scenario and press Play: course, pathway, practice, faculty, cells and record.

04What is changing

Frontier course · L3 advanced, programme courses and standards

Quantitative risk analysis and statistics: frontier methods

The methods, data, tools and studies that changed quantitative risk analysis and statistics between 2024 and 2026, taught by reproducing them on open data.

Level
L3 Advanced
Study time
about 28 hours (planning estimate)
Status
Planned
Prerequisites
Quantitative risk analysis and statistics: foundations and practice; Working knowledge of a scripting language (Python or R) for the labs

Why now

Loss records from secondary perils inform the tail and frequency assumptions used in loss metrics and exceedance curves. Munich Re, Climate change presses on: Devastating wildfires and intense thunderstorms exacerbate losses for insurers, 13 January 2026

Learning outcomes

  1. Explain what changed in quantitative risk analysis and statistics since 2024 and cite the studies, data or rules behind each change
  2. Reproduce Munich Re put 2025 natural catastrophe losses at USD 224 billion on open data and state the uncertainty of the result
  3. Evaluate a 2024 to 2026 study: its question, data, method, limits and what it changes for practice
  4. Design an analysis that combines a frontier method with the faculty's instruments, and justify each choice

Modules

  1. Munich Re put 2025 natural catastrophe losses at USD 224 billion
    • Munich Re estimated 2025 overall losses at about USD 224 billion and insured losses at USD 108 billion, with non-peak perils causing about USD 166 billion, above long-term inflation-adjusted averages.
    • Loss records from secondary perils inform the tail and frequency assumptions used in loss metrics and exceedance curves.
    • Munich Re, 13 January 2026
  2. Rapid attribution quantified fire weather change behind Los Angeles fires
    • World Weather Attribution estimated the extreme fire weather of January 2025 is about a 1-in-17-year event in today's climate, about 35 per cent more likely than in a 1.3 degree cooler climate, using reanalysis and an eleven-model ensemble.
    • It shows return periods shifting under warming, so stationary statistics fitted to past records can understate current hazard.
    • World Weather Attribution, 28 January 2025
  3. Copernicus found 2024 the first calendar year above 1.5 degrees
    • Copernicus reported 2024 was the warmest year on record, about 1.60 degrees above pre-industrial, the first calendar year above 1.5 degrees, while noting the Paris limit is assessed over multi-decade averages.
    • Shifting baselines matter for choosing reference periods and detrending data before estimating hazard probabilities.
    • Copernicus Climate Change Service, 10 January 2025
  4. Reproduction lab
    • Extend the discipline's method with one frontier method and compare its results
    • State the uncertainty and the limits of the result
    • Peer review against a shared checklist

Labs with Academy tools

Nexus Standards

Teaches

  • NRS-C2 Risk assessment method
  • NRS-C9 Risk models, methods and validation
  • NRS-M1 Method fabric: Universal mathematics and statistics

Relies on

  • NS-1 The UNI and the artefact catalogue
  • NS-16 UNI application profile (how articles, documents, code, data, APIs and interfaces carry the UNI)
  • NRS-C1 Risk vocabulary and ontology
  • NRS-C8 Evidence, uncertainty and provenance

Assessment

  • 50%Method reproductionReproduce one frontier method on open data and state the uncertainty of the result
  • 30%Study reviewA critical review of a 2024 to 2026 study: question, data, method, limits, what it changes
  • 20%Peer reviewReview two other learners' reproductions against a shared checklist

Delivery

  • Self-paced online, with the labs in the browser
  • Cohort study over six to eight weeks, with a weekly lab review
  • Co-delivered with a partner institution, inside its own courses

Partner on this course

  • Co-teach a module and bring a current case from your work
  • Host a cohort for your learners, with your own schedule and review
  • Contribute a lab: a dataset your institution publishes openly, or a model
  • Review the course content and its references before it opens
  • Translate the course and adapt its cases to your region

How institutions and experts take part

In the Academy LMS

Course on the learning platform
Expert, 4 topics
Cohort group
A community group for each cohort of learners
Achievement
Recorded on completion of the assessed work

References

  1. Munich Re, Climate change presses on: Devastating wildfires and intense thunderstorms exacerbate losses for insurers, 13 January 2026
  2. World Weather Attribution, Climate change increased the likelihood of wildfire disaster in highly exposed Los Angeles area, 28 January 2025
  3. Copernicus Climate Change Service, Copernicus: 2024 is the first year to exceed 1.5°C above pre-industrial level, 10 January 2025
  4. Coles, An Introduction to Statistical Modeling of Extreme Values, 2001
  5. Embrechts, Klüppelberg and Mikosch, Modelling Extremal Events for Insurance and Finance, 1997
  6. Pickands, Statistical inference using extreme order statistics, Annals of Statistics, 1975
05Take part

Take part in the work

Start from who you are.

06Questions

Questions, answers and key terms

Is the course free?
Yes. Every course and learning material of Risk Academy, led by the Nexus Consortium, is free to study, self-paced or with a cohort. Ordinary participation has no fee; paid work, internships and fellowships are separate arrangements.
What does completing a course give me?
A completion record: the course, its version, the date and what was assessed, private by default and shared by you. It stacks into discipline, department and programme achievements. A record states what was studied and assessed and does not certify competence; it is not a licence, a professional title or an employment status.
Where do the data and the places come from?
Every faculty teaches on a twin of a real place built from open data; each layer carries its provider, licence and date, and every result on the Academy states its source. Maps and figures are indicators for teaching, never an assessment of a place.
How do I take part beyond the course?
Form a competence cell of three to seven people, study a shared pathway, take a supervised assignment in the National Working Groups, or bring a cohort from your institution. For organisations.

Key terms

Term

Exceedance probability

The probability that a loss or hazard exceeds a given level in a period.

Term

Average annual loss

The expected loss per year averaged over many years.

Term

Monte Carlo simulation

Estimating outcomes by sampling many random scenarios from input distributions.

Term

Extreme value theory

Statistical theory for the behaviour of the largest or smallest values.

ReportsContribute

Contribute evidence from this page.

Reports is the Consortium's quarterly publication. What you know about this subject can become evidence, a case or a correction in the next edition, credited to you and published under CC BY 4.0 where it is your own work.

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