nexustandards.com/digital-ai · 1 taught
Digital, Cyber and AI
NRS-C9 Risk models, methods and validation
1standard1discipline
Illustrative: the exceedance probability of a hazard as a sheet, return-period isolines and simulated events
Risk Academy, led by the Nexus Consortium · Risk Science and Methods · Department of Quantitative Risk Analysis
Rates, return periods, exceedance curves, Monte Carlo and the limits of matrices
Quantitative risk analysis and statistics
Quantitative risk analysis turns data into probabilities with their errors attached.
- Department
- Department of Quantitative Risk Analysis
- Courses
- In preparation
- Levels
- L2 Intermediate, L3 Advanced
- Labs
- Exposure lab, Trigger lab
- Probability and return periods
- Loss metrics and exceedance curves
- Monte Carlo simulation
- Dependence and correlation
- Extreme value analysis
- Bayesian updating
- Risk analytics programming
- Qualitative tools and their limits
Courses in development extend the scope to further subjects: Bayesian methods for risk; Compound-event statistics.
02Maps
Build a twin of any place
Search any place or open the world; the layers and generators follow quantitative risk analysis and statistics on the planet map, the globe and in 3D.
- Terrain 24 to 2,805 m
- 3 reference earthquakes, M6.2 to M6.6
- Earthquakes M4.5 and above, past week: read live when the 3D twin opens
- USGS ShakeMap intensity contours: read live when the 3D twin opens
Drag to move, right drag or Shift with a drag to turn and tilt, Ctrl with the wheel to zoom. Keyboard: arrows move, Shift with arrows turn and tilt, + and – zoom, 0 resets, V steps through the views, Escape clears.
Flat plan of the same data: relief, the three reference epicentres with magnitude and depth, and the numbers below; the sampler's figure shows one precomputed field with its parameters. The 3D twin opens on devices that can draw it, once its data and code have been checked.
The boundaries, names and designations shown do not imply any judgement on the legal status of any territory, or any endorsement or acceptance of such boundaries. Countries: Natural Earth (public domain).
03Live 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
Keyboard, with the map focused
Hold Ctrl or ⌘ and scroll to zoom
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
04The subject
The subject, methods and measures and debates and bodies
The field and its scope
For analysts, actuaries, engineers and modellers who need to turn data and judgement into probabilities, loss distributions and exceedance curves, and to know when a number should not be trusted.
Quantities and units
Methods and their limits
Each method is listed with what it assumes and where it fails.
What the field debates
Bodies that set practice, and the data they publish
Bodies and standards are named so learners can find and apply their published work; the Academy teaches their use and links to the publisher, and no affiliation is implied.
05The method
From losses above a threshold to a return level: the peaks-over-threshold chain and the shape that sets the tail
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.
Sources: Coles, An Introduction to Statistical Modeling of Extreme Values (2001); Embrechts, Klüppelberg and Mikosch, Modelling Extremal Events for Insurance and Finance (1997); Pickands, Statistical inference using extreme order statistics, Annals of Statistics (1975); Kaplan and Garrick, On the quantitative definition of risk, Risk Analysis (1981); Morgan and Henrion, Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis (1990).
06At a glance
At a glance, with 5 related topics
Quantitative risk analysis and statistics at a glance
risksacademy.comrisk-sciencediscipline
- Open, 0
- In preparation, 6
- Also taught here, 4
- Subtopics, 8
Nexus Standards it teaches and relies on
The Nexus Standards the discipline teaches toward, grouped by master standard, with the disciplines that teach each.
nexustandards.com/systemic-risk · 1 taught
Systemic Risks
NRS-C2 Risk assessment method
1standard1disciplinenexustandards.com/data · 1 taught
Data and Evidence
NRS-M1 Universal mathematics and statistics
1standard1discipline
Nexus Standards at the AcademyThe Academy proposes how each discipline teaches toward the Nexus Standards; the mapping is open for public review.
Research and tools
Research and preprints as they are published, by discipline, with the faculty's other tools.
The hub lists the newest research and preprints for Quantitative risk analysis and statistics, each with its source and date. Open the research hub
The methods it teaches
From the Academy's risk taxonomy: the discipline's own entries and those of its primary courses, with how many courses teach each.
What is changing now
Recent developments in quantitative risk analysis and statistics, each with its source; sources checked on 16 October 2026.
Courses in this discipline
Courses for this discipline are in development; until they open, study it through the connected courses and open lessons below.
Courses from connected disciplines that also teach this field
Each course has its primary discipline elsewhere and teaches this field as part of its scope.
07Labs
How the subject is practised in labs
| Lab | What you do in it | Courses using it |
|---|---|---|
| Exposure lab | Overlay people and assets with hazard footprints | 2 |
| Trigger lab | Set forecast thresholds, pre-agreed actions and messages | 1 |
08Console
How Quantitative risk analysis and statistics is taught, as a process you can run
Press Play to run this process from this page's own data.
09Learning
Learning, practice and connections
Achievements in this discipline
Pathways that teach it
Where the subject is practised
- The Global Centre for Risk and Innovation (GCRI Canada)Systemic Risk ManagementQuantitative and qualitative methods
- Methods and modelling
Field platforms of the ecosystem where the subject is studied and applied.
The Foundry system where it is practised
- FoundryNXS-GRX systemStatistical risk productsData room, Reports room
Foundry system pages describe what each system and its rooms are designed to do; the courses teach the methods these systems apply.
Across the ecosystem
10Take part
Take part in Risk Science and Methods
Start from who you are.
11References
Core references and where to begin
Start with Kaplan, then Morgan, then Cox.
12Questions
Questions, answers and key terms
Is study here 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 courses in quantitative risk analysis and statistics?
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.
Risk Academy
Related
Around Quantitative risk analysis and statistics
Quantitative risk analysis and statistics
Prepare with a related course
Open courses in connected disciplines teach the methods this discipline will build on.