The Global Centre for Risk and Innovation (GCRI)

Risk Academy, a Nexortium programmeFaculty of Risk Science and Methods

The shared methods of risk analysis, with their limits stated

Faculty of Risk Science and Methods

Every risk figure rests on a rate, a distribution, a sample and a decision rule, and each carries an uncertainty that has to be written down.

Open the twin builder See the departments

risksacademy.comrisk-sciencefaculty

Risk Science and Methods: departments, disciplines and courses. Drawn as uncertainty bands.

Open, 3
In preparation, 19
Approved for authoring, 6

From the Academy atlas and the curriculum: primary courses only; numbers mark departments.

Twin builder and simulatorThe central Apennines: L'Aquila, Amatrice and Norcia4 twin generators, 8 layers, 4 instruments

disciplines in 4 departments: 17
courses open now, 19 in preparation: 3
reference earthquakes, M6.2 to M6.6: 3

Twin figures for the central Apennines: L'Aquila, Amatrice and Norcia, counted from its layers at their stated dates.

Twin builder and simulator.

The faculty's twin of L'Aquila on the planet map, the globe and in 3D. Pick a generator, switch layers, run the instruments; every layer prints its provider and date.

The central Apennines: L'Aquila, Amatrice and Norcia, Italy. 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 with WebGL once its data and library have been checked.

Terrain 24 to 2,805 m
3 reference earthquakes, M6.2 to M6.6
Earthquakes M4.5 and above, past week (live): live, loads in the twin
USGS ShakeMap intensity contours: live, loads in the twin

Credits and dates per layer are listed under the stage. Relief in the twin is exaggerated ×1.5 for legibility.

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 with WebGL once its data and library have been checked.

Distribution fitter (magnitude-frequency)

The Gutenberg-Richter relation fitted by maximum likelihood to a sample of magnitudes, with the cumulative magnitude-frequency curve, the b-value and its standard error, and a completeness magnitude the learner moves to watch the fit move.

The box's catalogue layer waits for its register row, so the fitter runs on the past week's world feed of M4.5 and above (one request to the plan's fixed URL on your press, never polled here) and on the three reference events for the method. Move the completeness magnitude and watch the fit move; the standard error is printed with every value.

Completeness magnitude4.5 Mw

Reference events Three main shocks, M6.2 to M6.6: the estimator is shown on them for the method only; a fit needs a complete catalogue.

Reading	Value
Magnitudes in the extract	M6.3, M6.2, M6.6
Completeness magnitude used	M6.0 (the extract holds main shocks only)
Maximum-likelihood b-value	1.04, standard error 0.6 with n = 3: an illustration of the estimator only, three events say nothing about the regional b-value
Inter-event times	7.4 years, 0.2 years (too few for an exponential fit)

A fit to a sample; its standard error is printed. The box's catalogue layer is pending, so the fitter runs on the past week's world feed of M4.5 and above, read once on the learner's press, and shows the estimator on the three reference events for the method only. A fit to a sample, with its standard error. Catalogue pending: the past week's world feed stands in. Method: Gutenberg, B. and Richter, C. F. (1944), Frequency of earthquakes in California, Bulletin of the Seismological Society of America 34; Aki, K. (1965), Maximum likelihood estimate of b in the formula log N = a - bM and its confidence limits, Bulletin of the Earthquake Research Institute 43; Utsu, T. (1966), A statistical significance test of the difference in b-value between two earthquake groups, Journal of Physics of the Earth 14.

Return-period calculator

The annual rate of events at or above a threshold magnitude from the Gutenberg-Richter relation, the return period and the probability of at least one event in an exposure time under a Poisson process, with the rate, the b-value, the threshold and the time on sliders.

The rate, the b-value, the threshold and the exposure time are on sliders; the rate and b-value start as declared teaching values (not estimates for the box) and take the fitter's values when a fit is made. The calculator shows the difference between a return period and the probability of at least one event in a lifetime.

Annual rate of M4.5 and above0.2 per year

b-value1 per magnitude unit

Threshold magnitude6 Mw

Exposure time50 years

Poisson model With 0.2 events of M4.5 and above a year and b = 1, M6 and above has a return period of 158 years and a 27 percent chance of occurring at least once in 50 years (declared teaching values).

Reading	Value
Annual rate of M at or above the threshold	0.006 per year
Return period	158 years
Probability of at least one in 50 years	27 percent
Probability in one year	0.6 percent

A Poisson teaching model: clustering (aftershocks) is not modelled, and the rate and b-value are declared teaching values until the fitter supplies a fit from a sample of thirty or more; not a hazard assessment for any site. A Poisson teaching model, without clustering. Not a hazard assessment for any site. Method: Cornell, C. A. (1968), Engineering seismic risk analysis, Bulletin of the Seismological Society of America 58(5), 1583-1606.

Monte Carlo sampler (the uncertainty field)

Synthetic earthquakes drawn from the magnitude-frequency model over the box, the intensity at every hexagonal cell from a published prediction equation with its sigma, and the probability per cell that an intensity threshold is reached in the exposure time, drawn on the terrain with its sampling error.

Change the prior and resample: the field is redrawn on the terrain of the open twin as hexagonal cells of 1.4 km side (about the H3 resolution 7 area), with the sampling error in the read-out; the ShakeMap contours of the three reference events show what one realisation looked like.

b-value1 per magnitude unit

Maximum magnitude7 Mw

Annual rate of M4.5 and above0.2 per year

Intensity threshold7 MMI

Samples2000 events

Baseline field Probability of intensity 7 and above at least once in 50 years: highest cell 0.27, mean 0.2 over 156 cells of 4 km side, from 2,000 synthetic events (teaching surface, not a hazard map).

Reading	Value
Source zone	the whole box, locations uniform; depths uniform between the reference events' depths
Prior	rate 0.2 per year of M4.5 and above, b = 1, maximum magnitude M7, intensity threshold 7, 50 years (declared teaching values)
Samples	2,000 synthetic events, seed fixed at build
Highest cell probability	0.27 (sampling error of the exceedance fraction up to 0.004)
Mean cell probability	0.2

A teaching probabilistic surface, not a hazard map: the source zone is the whole box, the rate and the maximum magnitude are declared teaching values on the sliders, and the published GEM map's row is pending. Every parameter is on screen and the sampling error is printed; the ShakeMap contours of the three reference events are drawn beside the field as what one realisation looked like. A teaching surface, not a hazard map. Sampling error printed with every field. Method: Cornell (1968); Allen, T. I., Wald, D. J. and Worden, C. B. (2012), Intensity attenuation for active crustal regions, Journal of Seismology 16; McGuire, R. K. (2004), Seismic Hazard and Risk Analysis, EERI monograph MNO-10.

Scenario tree

A decision tree with a decision node (act now or wait) and a chance node (the event comes or not), solved by backward induction for the expected value of each branch and the value of perfect information, with the probability and the consequence values on sliders.

A two-branch tree with one chance node: move the probability and the three consequence values (relative loss units, 0 to 100) and watch the preferred branch and the value of perfect information change. The probability starts from the calculator; the consequence values are declared teaching values and nothing in the twin supplies them.

Probability of the event6 percent

Cost of acting now20 units

Loss if the event comes after acting30 units

Loss if the event comes after waiting100 units

Backward induction Act now: -21.8; wait: -6; the preferred branch is to wait and perfect information would be worth 3 (declared teaching values).

Node	Value
Chance node	an M6 and above event within 10 years, p = 0.06 from the calculator's teaching values
Act now (retrofit)	cost 20, loss if the event comes 30: expected value -21.8
Wait	no cost, loss if the event comes 100: expected value -6
Preferred branch	wait
Value of perfect information	3
Probability at which the branches tie	0.29

A teaching tree on learner inputs: the probability starts from the return-period calculator and the consequence values are declared teaching values in relative loss units; no consequence value is supplied by the twin. A teaching tree on learner inputs. Method: Raiffa, H. (1968), Decision Analysis: Introductory Lectures on Choices under Uncertainty, Addison-Wesley; Howard, R. A. (1966), Decision analysis: applied decision theory, Proceedings of the Fourth International Conference on Operational Research.

The map loads from this site as it nears the view (MapLibre 6.9.1, checked by hash).

What the faculty teaches.

On the central Apennines, where L'Aquila 2009, Amatrice 2016 and Norcia 2016 stand on the terrain, the stage carries four methods: a Gutenberg-Richter fit with its standard error, a return-period calculator after Cornell (1968), a Monte Carlo sampler that draws a probability field on hexagonal cells with its sampling error, and a scenario tree solved by backward induction, read under ISO 31000:2018 and ISO/IEC 31010:2019. A graduate can fit, sample, decide and communicate with the uncertainty on the page.

Faculty of Risk Science and Methods groups 17 disciplines into 4 departments. 3 of the 22 courses whose primary discipline is here are open for enrolment and the rest are in preparation; all of them are taught on the Risk Academy main site, so your record stays in one place.

A graduate can

Fit a magnitude-frequency or loss distribution to a sample by maximum likelihood, print its standard error and say when the sample is too small to call the fit an estimate.
Convert a rate into a return period and into the probability of at least one event in a lifetime, and explain to a non-specialist why the two are not the same number.
Build a probabilistic surface by Monte Carlo sampling with every parameter and the sampling error on screen, and say why it is a teaching surface and not a hazard map.
Solve a decision tree by backward induction, compute the value of perfect information and show how a changed probability moves the preferred branch.
Read an index, a model or a dataset against its provenance, licence and validation record and write the finding a board, a regulator or a planner can act on.

4 departments, 17 disciplines.

Numbered as on the faculty figure at the top of the page. Each card counts the department's disciplines and the courses whose primary discipline is there.

Disciplines by status.

Each discipline once, in its department. A mark is one primary course, filled when it is open.

Where the field is moving.

Emerging areas, the technologies changing practice and the bodies that set the field's methods, from the faculty's expert review. Named for orientation; none of them endorses the Academy.

What is changing now.

The newest developments cited on the faculty's discipline pages, sources checked on 16 October 2026. Each links to its discipline and its source.

The faculty hub.

News and research as they are published, per discipline, with the faculty's other tools.

Where to start, and where it leads.

The faculty's entry course, then its flagship pathways and the Academy flagship in Nexus-Based Risk Management.

3 open, 19 in preparation.

Courses with their primary discipline in this faculty. Open courses link to the catalogue; the others are listed so you can plan.

The standards it teaches toward.

The Nexus Standards subsites whose standards the faculty's disciplines teach, by the Academy's proposed mapping.

Where these subjects are practised.

Where the faculty practises.

Nexus programmes that span faculties.

Each programme joins disciplines from more than one faculty and is hosted by an institute on the main site; it is listed on every faculty it spans.

Technology, Society and RiskSpace and foodStudies how satellite positioning and Earth observation support, and expose, food production and food security monitoring.3 disciplines in 3 faculties

Institutes that convene the faculty.

Institute

Institute for Nexus-Based Risk Management

The institute is the cross-faculty home of Nexus-Based Risk Management, the Academy's paradigm.

Terms used on this page.

Around Faculty of Risk Science and Methods.

Faculty of Risk Science and Methods

Start in one department.

Each department lists its disciplines, courses and pathways; each discipline its scope, labs, technology and key terms.

Open Department of Risk Management Browse the course catalogue