Evaluating the risk of rare events

How much should you worry about an asteroid crashing into the museum where you work, destroying  the collections that you care for? Perhaps it would be better to worry about something more familiar, such as a flood? The Evening Standard recently warned that a "23ft wave threatens London ...", surely that's a worry? Or what about fire, earthquake, riots, bombs, bird flu? There are plenty of possible future events you could worry about. If they occurred at the right place, at the right time, with sufficient severity, they could cause catastrophic irreversible damage to your collections or to your museum business.

Risk is a function of probability and consequence. It only takes pessimism and a vivid imagination to conceive of catastrophic consequences. However it takes a bit more work, some research, some maths and a confident approach to uncertainty, to estimate the actual likelihood of that event. When you have an estimate of the probability you can decide whether its worth the bother of worrying.

Almost by definition, the future is uncertain. We can reduce that uncertainty to some extent but never remove it completely. We make assumptions about the future on a daily basis, starting with the belief that there will actually be a new day. It seems that we can, almost unconsciously, build models of the future, working with different levels of certainty and degrees of confidence. From my own direct experience as a commuter I know that a train service has run between Cambridge and London for the last thirty years. I believe, although I have never sought to confirm it, that the service started more than a century ago. If I need to work in London tomorrow I can be confident that the station and track will still be there, and only slightly less confident that there will be a train. I use my own experience to judge how long the journey will take, but I could use the timetable and the rail company's statistics on punctuality to make an estimate. It is very rare that the train arrives exactly on time, but arriving within a few minutes of the scheduled time is very common. I accommodate that degree of uncertainty in my journey plan. Severe unannounced delays are sufficiently rare that I do not make contingency plans. My own long experience of commuting, and my memory of news reports, suggest that fatal rail crashes are rare enough that the benefit of travel totally overwhelms any worry about dying prematurely.

A formal risk assessment for something more important than arriving late for a meeting in London would have to use the same mixture of experience, knowledge and belief to construct a useful picture of the future. The fundamental question is still "to what extent can the pattern of past incidents inform predictions of future events?". Scientific induction relies explicitly on the belief that the past informs the future. For systems that are not too complex, this belief is usually justified. But it is still possible to lose money trying to predict exactly the outcome of very simple mechanistic events such as rolling dice. If you want to forecast the effects of climate change, or to predict the use of nuclear weapons by terrorists, you may not feel that you can use much of the wealth of historic data about related events. It would do me little good to consult a ten year old train timetable to plan tomorrow's journey.

My research in the last few years has centred on decision-making in the face of uncertainty. I have been studying the use of the precautionary principle to guide action where there are fears of great and irreversible harm, and there is also great uncertainty about likelihood or possible mechanism. As part of this study I attended a conference at the Royal Society in London on "Flood risk in a changing climate". There I saw a poster by a hydrologist who wanted people to understand that "A record-breaker is not a trend-setter". This seemed a useful bit of advice which enlightened my concerns about current perceptions of environmental risks. The associated maths seemed potentially understandable. I determined to contact the author, Max Beran. We started an intermittent exchange of emails which eventually resulted in a determination to organise a workshop on the evaluation of rare event risks. For me this was to be an opportunity to get further exposure to the maths that relates past frequency to future probability. For Max it was an opportunity to transfer his knowledge to a different discipline.

This workshop was held at the V&A in March. The audience consisted of RCA/V&A students and about 16 conservation professionals invited from institutions around the UK (and one from Holland). My role was to place the day's teaching within the context of growing interest in the study of risk to collections, exemplified by the work of Stefan Michalski and Robert Waller. Max gave an elementary introduction to extreme value theory. The participants were introduced to various ways of extracting information from data. The interpretation of 'return period' was explained using the example of the 1966 Florence flood. The Poisson distribution was demonstrated using information about UK earthquakes. The Gumbel distribution was used to calculate the probability of  a flood at the British Library's newspaper archive at Colindale. In a less mathematical fashion I discussed the use and limitations of historic data for predicting the occurrence of fires in museums, terrorist attacks aimed at museums and airplane crashes on top of museums. The day ended with a discussion about the possible effects of global climate change on environmental risk factors. There are plans for a repeat workshop in the autumn.

Should you worry about the asteroid? On the NASA web page about asteroid and comet impact hazards the answer to the question "Is the earth targeted for an Impact?" is "Not that we know of". It is instructive to ponder the nature of the historic evidence on which this assertion is based.