Converting probabilities between time-intervals

This is the first in an irregular sequence of snippets about some of the slightly more technical aspects of uncertainty and risk assessment.  If you have a slightly more technical question, then please email me and I will try to answer it with a snippet.

Suppose that an event has a probability of 0.015 (or 1.5%) of happening at least once in the next five years. Then the probability of the event happening at least once in the next year is 0.015 / 5 = 0.003 (or 0.3%), and the probability of it happening at least once in the next 20 years is 0.015 * 4 = 0.06 (or 6%).

Here is the rule for scaling probabilities to different time intervals: if both probabilities (the original one and the new one) are no larger than 0.1 (or 10%), then simply multiply the original probability by the ratio of the new time-interval to the original time-interval, to find the new probability.

This rule is an approximation which breaks down if either of the probabilities is greater than 0.1. For example, to scale a probability of 0.04 in the next 5 years up to 20 years we cannot simply multiply by 4, because the result, 0.16 (or 16%), is larger than 0.1. In this case we have to use the proper rule, which is

p_new = 1 – (1 – p_orig)^(int_new / int_orig)

where ‘^’ reads ‘to the power of’. The example above becomes

p_new = 1 – (1 – 0.04)^(20 / 5) = 0.15 (or 15%).

So the approximation would have been 1 percentage point out in this case. The highlighted text in yellow can be pasted directly into a spreadsheet cell (the answer is 0.1507).

Of course it is unlikely to matter in practice whether the probability is 0.15 or 0.16.  But the difference gets bigger as the probabilities get bigger.  For example, it would definitely be a mistake to multiply a 0.25 one-year probability by 5 to find the five-year probability, because the result would be greater than 1.  Using the formula, the correct answer is a five-year probability of 0.76.

Blog post by Prof. Jonathan Rougier, Professor of Statistical Science.

Second blog in series here.
Third blog in series here.

Image: By Hovik Avetisyan [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons

Deploying and Servicing a Seismic Network in Central Italy

From a scientific point of view, the seismicity that is hitting Central Italy presents itself as an unmissable opportunity for seismologists to analyse the triggering and the evolution of an earthquake sequence. From the tens of instruments installed in the affected area, a huge amount of data is being collected. Such a well-recorded sequence will allow us to produce a comprehensive seismic catalogue of events. On this big quantity of data, new algorithms will be developed and tested for the characterisation of even the smallest earthquakes. Moreover, they will enable the validation of more accurate and testable statistical and physics-based forecast models, which is the core objective of my Ph.D. project.
Seismicity map of the Amatrice-Norcia sequence updated 5 November 2016.
The Central Apennines are one of the most seismically hazardous areas in Italy and in Europe. Many destructive earthquakes have occurred throughout this region in the past, most recently the 2009 MW = 6.4 L’Aquila event. On August 24th, just 43 km North of the 2009 epicentre, an earthquake of magnitude 6.0 occurred and devastated the villages of Amatrice and Accumuli, leading to 298 fatalities, hundreds of injured and tens of thousands people affected. The mainshock was followed, in under an hour, by a MW = 5.4 aftershock. Two months later, on October 26th, the northern sector of the affected area was struck by two earthquakes of magnitude 5.4 and 5.9, respectively, with epicentres near the village of Visso. To make things even worse, on October 30th the city of Norcia was hit by a magnitude 6.5 mainshock, which has been the biggest event of the sequence to date and the strongest earthquake in Italy in the last 36 years. Building collapses and damages were very heavy for many villages and many historical heritage buildings have reported irreparable damages, such as the 14th century St. Benedict cathedral. Luckily, the has been no further fatalities since the very first event of August 24.
St. Benedict cathedral (Norcia), erected in the late 14th century and completely destroyed after the Mw 6.5 earthquake of October 30th.
Immediately after the first big event, an emergency scientific response team was formed by the British Geological Survey (BGS) and the School of GeoSciences at the University of Edinburgh, to support the rapid deployment of high-accuracy seismometers in collaboration with the Istituto Nazionale di Geofisica e Vulcanologia (INGV). The high detection capabilities, made possible by such a dense network, will let us derive a seismic catalogue with a great regional coverage and improved magnitude sensitivity. This new, accurate, catalogue will be crucial in developing operational forecast models. The ultimate aim is to understand the potential migration of seismic activity to neighbouring faults as well as the anatomy of the seismogenic structure and to shed light into the underlying physical processes that produce the hazard.
Thanks to the quick response of the National Environmental Research Council (NERC) and SEIS-UK, 30 broadband stations have been promptly dispatched from Leicester and arrived in less than 48 hours in Rome. There, a group of 9 people composed by INGV and BGS seismologists, technicians and Ph.D. students (including myself) from University of Bristol, Dublin Institute for Advanced Study (DIAS) and University of Ulster were ready to travel across the Apennines to deploy this equipment. The first days in Rome were all about planning; the location of each station was carefully decided so as to integrate the existing Italian permanent and temporary networks in the most appropriate way. After having performed the ‘huddle test’ in the INGV, which involves parallel checking of all the field instrumentation in order to ensure its correct functioning, we packed all the equipment and headed to the village of Leonessa, a location considered safe enough to be used as our base camp (despite the village being damaged and evacuated after the 30th October event).
Preparing instrumentation for the huddle test in one of INGV’s storage rooms.
In order to optimise time and resources, and to start recording data as soon as possible, we decided to split in 3 groups so that we could finish our work between the end of August and the first week of September. Each seismic station is composed of a buried sensor, a GPS antenna, a car battery, a regulator and two solar panels. The current deployment will stay for 1 year and will be collecting data continually. Each sensor had to be carefully buried and levelled to guarantee the highest quality of recording, which was a strenuous challenge when the ground was quite rocky!
Typical setting of our deployed stations. On the left, the buried sensor. Its cables, buried as well, connect it to the instrumentation inside the black box (a car battery, and a regulator). On the right, the solar panel (a second one was added in October service) and the white GPS antenna.
Aside from the scientific value of the expedition, the deployment week was a great opportunity to get to know each other, share opinions, ideas and, of course, get some training in seismology! At the end, we managed to install 24 stations around an area of approximately 2700 km2.
As this type of seismic station didn’t have telemetry, each needed to be revisited to retrieve data. For this purpose, from October 17th, David Hawthorn (BGS) and I flew to Italy again and stayed there for the following ten days to service the seismometers and to do the first data dump. Our goals were also  to check the quality of the first month of recordings, to add a second solar panel where needed, and to prepare the stations for the forthcoming winter. To do that, a lot of hammering and woodworking was needed. We serviced all the sites, raising the solar panels and GPS antennas on posts, which were securely anchored to the ground, to prevent snow from covering them. The stations were all in good conditions, with just minor damages due to some very snoopy cows.
David Hawthorn (BGS) servicing the stations – A second solar panel was added. Panels and GPS antennas were raised on posts anchored to the ground through timbers.
Dumping data from the stations using a netbook and specific hard drive.
On October 26, just the night before leaving for Rome, we experienced first-hand the frightening feeling of a mainshock just below our feet. Both the quakes of that evening surprised us while we were inside a building; the rumble just few seconds before the quake was shocking and the shaking was very strong. Fortunately, there were no severe damages in Leonessa but many people in the village refused to spend the night in their own houses. Also, it was impressive to see the local emergency services response: only a few minutes after the first quake, policemen were already out to patrol the inner village checking for any people experiencing difficulties.
The small village of Pescara del Tronto suffered many collapses and severe damages after the 24 August earthquakes. View from the motorway above.
Throughout our car transfers from one site to another we frequently found roads interrupted by a building collapse or by a landslide, but we could also admire the mountains with a mantle of beautiful autumnal colours and the spectacular landscapes offered by the Apennines, like the Monte Vettore, the Gran Sasso (the highest peak in the Apennines) and the breath-taking Castelluccio plain near Norcia.
View of the Norcia plain, near to the 24th August magnitude 5.4 and the 30th October magnitude 6.5 epicentres.
View of the Castelluccio plain. This picture was taken from the village of Castelluccio, just 5 days before it was totally destroyed by the magnitude 6.5 mainshock.
From my point of view, I learned a lot and really enjoyed this experience. I feel privileged to have started my Ph.D. in leading institutions like the University of Bristol and the BGS and, at the same time, to be able to spend time in my home country (yes, I am Italian…) with such interesting scientific questions. What I know for sure is that we will be back there again.

Blog written by Simone Mancini, 1st year Ph.D. student, University of Bristol and British Geological Survey.

Brexit: can research light the way?

What could Brexit mean for UK science? What impact will it have on UK fisheries? Could Brexit be bad news for emissions reductions? These were just some questions discussed at a Parliamentary conference last week, organised by the Parliamentary Office of Science and Technology (POST), the Commons Library and Parliament’s Universities Outreach team.

MPs researchers, Parliamentary staff and academic researchers from across the country came together to consider some of the key policy areas affected by the UK’s decision to leave the EU.

Why does academic research matter to Parliament?

Given the unchartered waters that Parliament is facing as the UK prepares to withdraw from the EU, it is more important than ever that Parliamentary scrutiny and debate is informed by robust and reliable evidence.

Academic research is expected to meet rigorous standards of quality, independence and transparency. Although it is far from being the only source of evidence relevant to Parliament, it has vital role to play in the effective scrutiny of Government.

“Academics can help ensure that we get the best possible outcome for the British public through describing the state of knowledge, setting out comparative knowledge (whether in different territories or over time), and evaluating what’s happening as it plays out” said Penny Young, House of Commons Librarian, in her keynote speech.

Last week’s meeting showcased relevant UK academic research as well as giving participants the opportunity to hear the perspectives and concerns of different groups. With over 100 participants, the organisers made the wise decision to split us up into smaller groups to discuss specific policy areas.  This worked rather well, although most people would have liked to be in several groups at once!

What does the future hold for UK research?

In the session on science and research funding a mix of early career researchers and more seasoned academics set out their top issues. The discussion quickly moved beyond research funding. All the researchers agreed free movement of researchers between the UK, other parts of the EU, and beyond the EU, was a top priority.  Several researchers were concerned that the UK research community would become more isolated as a result of Brexit, making it more difficult to recruit and retain the best academic staff.

The group also discussed what kind of data we needed to gauge the impact of Brexit on UK research.  One researcher argued that if we wait until we have “hard data” – such as statistics on citations, publications and collaborations, it might be too late for decision-makers to intervene in any meaningful way.

Economic Impact of Brexit: New Models Needed

Researchers participating in the session on “trade relations and economic impact” highlighted that research on the economic impact of Brexit tends to focus on trade.  New models are needed that take trade into account, along with other relevant factors such as investment, migration and regulation. Participants also felt that more data on the local effects of trade deals would be useful to policymakers, but there are very few studies looking at such effects because of the many uncertainties involved.

Environment, agriculture and fisheries: ‘Cod Wars’?

What would the loss of subsidies under the Common Agricultural Policy mean for UK agriculture? Participants highlighted that areas such as horticulture and fisheries in particular could end up struggling with workforce retention. On a brighter note, one researcher thought there could be some financial gain for UK fisheries if the UK took back its Economic Exclusion Zone (EEZ), but warned of possible future “Cod Wars” if countries clashed over fishing rights.

Immigration: how many EU nationals live in the UK?

Participants in the immigration discussion group highlighted that we do not have reliable figures for how many EU nationals live in the UK. According to some estimates the figure is around 3 million, but this is based on survey data. More reliable data is needed to make informed policy decisions. Participants also highlighted that while most of the discussion around border control focuses on people, movement of goods across borders was also vitally important.

Energy and climate: who will drive emissions reductions targets?

The energy and climate group considered the impact of Brexit across Europe as a whole. The UK has been a strong driver for ambitious emissions reduction targets for the EU. Would other nations continue to drive such targets? Participants also speculated over whether UK would remain part of the European Emissions Trading Scheme and stay involved with some of the EU’s internal energy market regulatory bodies after Brexit.

Foreign and security policy

Participants covered a huge range of topics from UK-Irish relations to the future of NATO and drug trafficking and border control. The importance of learning lessons from history was a key theme in the session, whether it related to the future of NATO or to major treaty negotiations more generally.

What next…

These conversations were not based entirely on research evidence, not least because it there are simply too many uncertainties for research to answer all our questions on the impact of Brexit. In the end our discussions were based around a mix of anecdote, opinion, and ‘hard’ evidence. Overall it was a very enriching experience and we came away with lots of new contacts and ideas.

Many of the researchers said that they’d had relatively few opportunities to feed into policy discussions with parliament and government and that there needed to be many more meetings like this one!

This article was written for The House of Commons Library Blog Second Reading by Chandy Nath, acting Director of the POST and Cressida Auckland, a POST fellow.

Picture credit: Brexit Scrabble, by Jeff Djevdet; Creative Commons Attribution 2.0 Generic (CC by 2.0)

The Diamond Battery – your ideas for future energy generation

On Friday 25th November, at the Cabot Institute Annual Lecture, a new energy technology was unveiled that uses diamonds to generate electricity from nuclear waste. Researchers at the University of Bristol, led by Prof. Tom Scott, have created a prototype battery that incorporates radioactive Nickel-63 into a diamond, which is then able to generate a small electrical current.

Details of this technology can be found in our official press release here: http://www.bristol.ac.uk/news/2016/november/diamond-power.html.

Despite the low power of the batteries (relative to current technologies), they could have an exceptionally long lifespan, taking 5730 years to reach 50% battery power. Because of this, Professor Tom Scott explains:

“We envision these batteries to be used in situations where it is not feasible to charge or replace conventional batteries. Obvious applications would be in low-power electrical devices where long life of the energy source is needed, such as pacemakers, satellites, high-altitude drones or even spacecraft.

“There are so many possible uses that we’re asking the public to come up with suggestions of how they would utilise this technology by using #diamondbattery.”

Since making the invitation, we have been overwhelmed by the number of amazing ideas you’ve been sharing on Facebook, Twitter and by email. In this blog, we take a brief look at some of the top suggestions to date, and offer some further information on what may and may not be possible.

10 of our favourite ideas (in no particular order!)

Medical devices
From ocular implants to pacemakers, and from insulin pumps to nanobots, it’s clear that there is a great deal of potential to make a difference to people’s lives in the medical field. Many devices must be implanted within the body, meaning long battery life is essential to minimise the need for replacements and distress to patients.

@rongonzalezlobo suggests that the #diamondbattery could power nanorobots which can be injected into a person or animal to sense and transmit information about the health of the individual to an external device. This could be particularly helpful to diabetes patients, for example.

 

@TealSkys also suggests they could be used to monitor vital signs in individuals in high-risk jobs such as explorers, military
professionals or miners.

 

@JulianSpahr suggests we also investigate ICDs (Implantable Cardioverter Defibrillators- small devices which can treat people with dangerously abnormal heart rhythms) and DBS (deep brain stimulation – a surgical procedure used to treat a variety of disabling neurological symptom most commonly the debilitating symptoms of Parkinson’s disease).
The opportunities for implantable #diamondbattery powered devices appear to be significant.

GPS trackers or Geo-markers
GPS trackers are rating highly so far, and could offer an opportunity for us to keep tabs on pets or valuable items without worrying about device batteries running out of charge. Implantable devices using a #diamondbattery would not need to be replaced, minimising discomfort to tracked animals. Indeed, @Boomersaurus suggests we could also use these for tagging animals in wildlife studies.

In addition to Geo-tagging/ tracking, some of you have suggested that the #diamondbattery could be used to power permanent geomarkers.

 

The Internet of Things
A major concern surrounding the new wave of ‘Internet of Things’ (IoT) technologies is the amount of power they might consume. IoT devices require a constant stream of power to transmit over wireless frequencies which could cause issues as these proliferate.

@CIMCloudOne suggests the #diamondbattery could become the new default for IoT devices in the future.

 

Safety and security
A number of you suggested that the #diamondbattery could be extremely useful in smoke detectors.

The US National Fire Protection Association states that 21% of home fire deaths resulted from fires in homes with no working smoke alarms, where around 46% of the alarms had missing or disconnected batteries. Dead batteries caused one-quarter (24%) of the smoke alarm failures.

If feasible, this suggestion from @StarhopperGames could therefore not only prevent annoying late-night battery beeps, but may also help avoid preventable death.

 

However, a question remains as to whether the battery would be sufficient to power the alarm (and not just the detector).
@idbacchus suggested we use the #diamondbattery to power Black Box transmitters in aeroplanes to ensure it is possible to track and record planes for safety reasons.

 

Remote sensing
Many corners of our planet are far from civilisation and are inaccessible, complex environments. If we are to study the seas, or mountains (or indeed, space) effectively over long periods, low-powered devices with long-life batteries are required.

Many of you called for the use of these batteries in sea and remote location studies:

 

 

Seismology and building resilience
Seismic sensors that are located underground could help us to detect early warnings for earthquake risk.

 

Additionally, small sensors housed within the foundations of buildings/ within building walls may also prove helpful for indoor environment sensing, structural resilience, heat etc.

Mechanical bees
Whilst this is possibly the most futuristic of all the suggestions, we felt that it warranted a mention for innovation! @TheSteveKoch suggests a low-power #diamond battery might be able to power mechanical bees in the future.

 

Watches
It’s often impossible to know when a watch battery is about to run out, and when it does, it can feel disastrous to the owner. Perhaps a #diamondbattery watch could help people around the world avoid those missed appoints and trains in the future.

 

Space exploration
Of course, when we send devices out into space we need to know that they have sufficient battery life and sufficient levels of resilience to maintain operations for long periods. @johnconroy and others noted the opportunities for space probes and radio transmitters on the moon:

 

Bringing the internet to new areas
Finally, whilst it’s currently unclear what the power requirements would be for this idea, deployment of low power UAVs in remote areas to deliver free internet sounds like a highly worthwhile cause.

 

If you are inspired by these ideas and think you might have a suggestion for future diamond battery uses, send us a tweet at
@cabotinstitute or @UoBrisIAC with the hashtag ‘#diamondbattery’.