Importance Sampling for Computing Extremes

Extreme climate events such as prolonged heatwaves, heavy rainfall, and severe windstorms with return periods of hundreds of years or more have severe impacts when they occur. In August 2003, a 10-day heatwave resulted in 2,000 deaths in the UK and more than 70,000 deaths in western Europe (Robine et al. 2008). In winter 2013/2014, rainfall over the UK led to significant damage with 18,700 insurance claims, and clean-up costs of over &pound;1 billion in the Thames River valley (Thompson et al. 2017). More recently, the record-setting UK heatwave of July 2022 led to an estimated 850 excess deaths over a 2-day period (Kendon 2022, Mitchell &amp; Lo 2022).<br /> <br /> Therefore, predicting the occurrence of such critical events is of paramount practical interest to several sectors. Particularly, it would help to make alerts by detecting possible hazards. This is crucial at both national (measures adaptation) and international (policy and strategy design) levels.<br /> <br /> The question is why do not we rely on historical data to predict these extremes? Obviously, historical data are too short to give reliable predictions for events with a return period longer than a few decades. To surmount this challenge, researchers in climate and weather science traditionally turn to extreme value modelling as their conventional approach. However, due to the limited number of observations on the tails, large errors can result from extrapolating the extreme value statistical distribution.<br /> <br /> An alternative approach is to use climate models to provide a much larger sample of events, potentially providing a more accurate estimate of return periods. Running a large ensemble from climate models is shown to be efficient, as Thomson et al. 2017 have shown that the 2013/2014 extreme rainfall and flooding could have been anticipated. However, the approach presented in Thompson et al. 2017 is computationally expensive for extreme events with a return period of hundred years, which requires running the climate model long enough to get a sample in the rare/extreme region (Ragone et al. 2018). More specifically, a substantial number of samples needs to be generated by the model to get a &ldquo;relevant/important&rdquo; sample, i.e., a sample that belongs to the rare set of interest.

<p><strong>Project description and objectives:</strong></p> <p>Importance sampling is a very popular technique that, when appropriately used, can dramatically reduce the computational effort when computing extreme event return periods (Kroese et al. 2011). The core concept involves performing a change in the probability measure such that we sample more in the region of interest. The crucial challenge lies in determining this change of measure to yield substantial computational savings.&nbsp; Despite the continuous advances in the development of importance sampling schemes, its adoption among climate researchers remains relatively limited (Ragone et al. 2018, Ragone et al. 2021).</p> <p>This proposal aims to develop computationally efficient importance sampling schemes for the computation of extreme climate events. The project comprises the following objectives:</p> <ul> <li>Initially, the student will design an importance sampling scheme tailored to a relatively simple yet crucial probabilistic rainfall model. This serves as a foundational step before delving into more complex climate models.</li> <li>The second objective entails the development of an efficient importance sampling scheme for estimating return periods in scenarios where dynamics evolves according to the simple yet chaotic Lorenz climate model. The Lorenz model comprises a system of coupled stochastic differential equations, necessitating a change of measure in trajectory/path space.</li> <li>Once the student has acquired proficiency in employing importance sampling for two relatively straightforward climate models, the overarching goal is to implement importance sampling techniques within a complex real climate model from the Met Office. The objective is to draw similar conclusions as those presented in Thompson et al. (2017) in a computationally efficient manner.</li> </ul> <p><strong>References:</strong></p> <ul> <li>JM Robine et al. Death toll exceeded 70,000 in Europe during the summer of 2003.&nbsp;Comptes Rendus Biologies,&nbsp;331(2008), 171&ndash;178, https://doi.org/&nbsp;<a href="https://doi.org/10.1016/j.crvi.2007.12.001">1016/j.crvi.2007.12.001</a></li> <li>F Ragone et al. Computation of extreme heat waves in climate models using a large deviation algorithm.&nbsp;Proceedings of the National Academy of Sciences of the USA,&nbsp;115&nbsp;(2018), 24&ndash;29,&nbsp;https://doi.org/10.1073/pnas.171264511</li> <li>V Thompson et al. High risk of unprecedented UK rainfall in the current climate.&nbsp;Nature Communications,&nbsp;8&nbsp;(2017), 107, https://doi.org/10.1038/s41467-017-00275-3.</li> <li>DP Kroese,&nbsp;<a href="https://onlinelibrary.wiley.com/authored-by/">T Taimre and&nbsp;</a><a href="https://onlinelibrary.wiley.com/authored-by/">ZI Botev</a>. Handbook of Monte Carlo Methods.&nbsp;Wiley Series in Probability and Statistics. Wiley, 2011,&nbsp;<a href="https://doi.org/10.1002/9781118014967">https://doi.org/1002/9781118014967</a>.</li> <li>M Kendon, Unprecedented extreme heatwave, July 2022. Met Office report. https://www.metoffice.gov.uk/binaries/content/assets/metofficegovuk/pdf/weather/learn-about/uk-past-events/interesting/2022/2022_03_july_heatwave_v1.pdf.</li> <li>DM Mitchell and Y T E Lo. Downplaying the catastrophic health impact of heatwaves costs lives.&nbsp;The BMJ,&nbsp;378&nbsp;(2022),&nbsp;<a href="https://doi.org/10.1136/bmj.o1940">https://doi.org/10.1136/bmj.o1940</a></li> </ul>

<p style="text-align:start; margin-bottom:24px">Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University&#39;s website</a>.Please state clearly in the Planned Course of Study section that you are applying for&nbsp;<em><strong>PhD Statistics FT,</strong></em>&nbsp;in the research information section&nbsp;that the research degree you wish to be considered for is&nbsp;<em><strong>Variance Reduction Technique for Rare Events Simulations</strong></em>&nbsp;as well as&nbsp;<a href="https://eps.leeds.ac.uk/faculty-engineering-physical-sciences/staff/12206/dr-nadhir-ben-rached">Dr Nadhir Ben Rached</a>&nbsp;as your proposed supervisor and&nbsp;and in the finance section, please state clearly&nbsp;<em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p style="text-align:start; margin-bottom:24px">If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p style="text-align:start; margin-bottom:24px"><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p style="text-align:start; margin-bottom:24px">Applications will be considered on an ongoing basis. &nbsp;Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p style="text-align:start; margin-bottom:24px">Please note that you must provide the following documents in support of your application by the closing date of 3 April 2024 for Leeds Opportunity Research Scholarship or 8 April 2024 for Leeds Doctoral Scholarship:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<p><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK</strong>&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a>, <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a>&nbsp;and and&nbsp;<a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship">School of Mathematics Scholarships</a>.&nbsp;&nbsp;<a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK</strong> &ndash; The&nbsp;<a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a>&nbsp;is available to nationals of China (now closed for 2024/25 entry). The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Important:&nbsp;</strong> Any costs associated with your arrival at the University of Leeds to start your PhD including flights, immigration health surcharge/medical insurance and Visa costs are not covered under this studentship.</p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For general enquiries about applications, contact our Doctoral College Admissions by email to&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a></p> <p>For questions about the research project, contact Dr Nadhir Ben Rached by email to&nbsp;<a href="mailto:n.benrached@leeds.ac.uk">n.benrached@leeds.ac.uk</a></p>