Novel Methods for High-Dimensional Output Analysis for Agent-Based Models

We are looking for strong candidates to work on this exciting multidisciplinary project described below!

<p style="margin-bottom: 11px;"><strong>The challenge:</strong></p> <p>Agent-based models (ABMs) is a powerful computational approach for understanding complex systems. It focuses on modelling individual agents and their interactions, allowing emergent phenomena to arise from the bottom up (i.e. there are no equilibrium conditions to constrain the model outcomes, which are dynamic and evolving). In ABMs, agents are autonomous entities with defined behaviours and decision-making processes. These agents interact with each other and their environment according to specified rules, leading to complex system-level behaviours that often cannot be predicted from the individual components alone. This approach is particularly useful for studying social, economic, and environmental systems where heterogeneity, spatial and temporal aspects, and non-linear dynamics play crucial roles.</p> <p>The outputs of agent-based models are often high-dimensional due to the inherent complexity and richness of the systems they simulate. Each agent in the model can have multiple attributes that change over time, and the model typically tracks numerous variables at both the individual and aggregate levels. For instance, in our urban transition model (1,2), we might track each household's income, employment status, housing situation, and location, as well as neighbourhood-level variables like average property values and employment rates. Additionally, the model may generate time series data for multiple scenarios, further increasing the dimensionality. In our global trade model (3), we track multiple variables for each country agent, including import and export volumes for 91 different food commodities, as well as the consumption and nutritional intake of 15 different macro and micronutrients. This results in thousands of output variables for each simulation run. This high-dimensionality allows for a comprehensive analysis of the system but also presents challenges in terms of data visualisation, interpretation, and communication of results to stakeholders, but also presents significant challenges insensitivity analysis, calibration, and validation of the model.</p> <p>The high-dimensional outputs of agent-based models present significant challenges in several key areas of model development and analysis. Sensitivity analysis, which aims to understand how changes in input parameters affect model outcomes, becomes particularly complex with high-dimensional outputs. Traditional methods like one-at-a-time sensitivity analysis can be inadequate. Calibration and validation of agent-based models with high-dimensional outputs are particularly challenging. The process of fitting model parameters to match empirical data becomes increasingly difficult as the number of output variables grows. This is compounded by the fact that not all output variables may have corresponding empirical data for comparison. Lee et al. (2015)(4) discuss these challenges in the context of urban models, highlighting the need for advanced calibration techniques such as Bayesian inference and machine learning approaches. Validation faces similar hurdles, as assessing model performance across multiple dimensions simultaneously can be complex. Windrum et al. (2007)(5) propose various validation approaches for agent-based models, but note that the field still lacks standardised methods for dealing with high-dimensional outputs. These challenges underscore the need for innovative approaches in handling and interpreting the rich, but complex, data generated by agent-based models.</p> <p><strong>Proposed approach:</strong></p> <p>Since the outputs of ABMs are high dimensional variables, which make the sensitivity analysis, calibration and validation very complicated. A natural proposal is to cluster the outputs with high similarity, pick a few variables in each cluster and then perform sensitivity analysis, calibration and validation on these variables.</p> <p>The spatial and temporal property of the outputs of ABMs imply traditional multivariate clustering analysis methods might be inappropriate. Therefore, time series clustering and functional data clustering methods (6) will be utlised. Our proposed nonparametric clustering (7) designed for functional data can be implemented, however different distance (similarity measures) might have different performance for outputs of ABMs. So the clustering methods and similarity measures should be selected carefully, say by conducting extensive simulations. Notice that for high-dimensional variables with different units and domains, pre-processing such as registration and standardisation usually needs to be designed before implementing clustering methods.</p> <p>If sensitivity analysis based on selected variables is different from that based on original variables, sensitivity analysis methods should be adapted.</p> <p>Since we have to conduct sensitivity analysis, calibration and validation using selected variables. Then the following questions arise. How do we know we have selected the right ones? Is there any benchmark to measure against? These questions are to be explored in this project.</p> <p><strong>References:</strong></p> <p>1. Ge J, Furtado BA. Modelling urban transition with coupled housing and labour markets. Environment and Planning B:Urban Analytics and City Science. 2023 Jul 4;23998083231186623.</p> <p>2. Ge J, Furtado BA. Simulating urban transition in major socio-economic shocks. In IEEE; 2021. p. 1–10.</p> <p>3. Ge J, Polhill JG, Macdiarmid JI, Fitton N, Smith P, Clark H, et al. Food and nutrition security under global trade: arelation-driven agent-based global trade model. Royal Society open science. 2021;8(1):201587.</p> <p>4. Lee JS, Filatova T, Ligmann-Zielinska A, Hassani-Mahmooei B, Stonedahl F, Lorscheid I, et al. The complexities ofagent-based modeling output analysis. Journal of Artificial Societies and Social Simulation [Internet]. 2015 [cited 2024 Jul22];18(4). Available from: https://www.econstor.eu/handle/10419/230635</p> <p>5. Windrum P, Fagiolo G, Moneta A. Empirical Validation of Agent-Based Models: Alternatives and Prospects. Journal ofArtificial Societies and Social Simulation [Internet]. 2007;10(2). Available from: http://jasss.soc.surrey.ac.uk/10/2/8.html</p> <p>6. Zhang, M., & Parnell, A. (2023). Review of clustering methods for functional data. ACM Transactions on KnowledgeDiscovery from Data, 17(7), 1-34.</p> <p>7. Xie, M., Liu, H., & Houwing-Duistermaat, J. Nonparametric clustering for longitudinal functional data with the applicationto H-NMR spectra of kidney transplant patients. In Longitudinal functional data clustering. Theor Biol Forum 2021; 114 (1-2):15 (Vol. 28).</p>

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Statistics FT</strong></em>, in the research information section that the research degree you wish to be considered for is <em><strong>Novel methods for high-dimensional output analysis for agent-based models</strong></em> as well as <a href="https://environment.leeds.ac.uk/geography/staff/2702/jiaqi-ge">Dr. Jiaqi Ge</a> and <a href="https://eps.leeds.ac.uk/maths/staff/4053/dr-haiyan-liu">Dr. Haiyan Liu</a> as your proposed supervisor <em><strong>and in the finance section, please state clearly the funding source that you are applying for, if you are self-funding or externally sponsored.</strong></em></p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p><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="margin-bottom:11px">Applications will be considered on an ongoing basis.  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 class="MsoNoSpacing"><strong>Please note that you must provide the following documents in support of your application by the closing date of Monday 6 January 2025 if applying for the China Scholarship Council-University of Leeds Scholarship, Monday 3 February 2025 if applying for Leeds Doctoral Scholarship or Tuesday 1 April 2025 for Leeds Opportunity Research Scholarship.</strong></p> <p><strong>If you are applying for the School of Mathematics Scholarship 2025/26, or with external sponsorship or you are funding your own study, please ensure you provide your supporting documents at the point you submit your application:</strong></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> – The <a href="https://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarship-2025-faculty-of-engineering-and-physical-sciences#:~:text=Key%20facts&text=One%20Leeds%20Doctoral%20Scholarship%20is,rata%20for%20part%2Dtime%20study.">Leeds Doctoral Scholarship</a> <strong>(closing date: Monday 3 February 2025)</strong>, <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> <strong>(closing date: Tuesday 1 April 2025)</strong> and <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship-2025-26">School of Mathematics Scholarship 2025/26</a> <strong>(open from October 2024)</strong> are available to UK applicants.</p> <p><strong>Non-UK</strong> – <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship-2025-26">School of Mathematics Scholarship 2025/26</a> <strong>(open from October 2024) </strong>are available to all International applicants.  The <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> <strong>(closing date: Monday 6 January 2025) </strong>is available to nationals of China. The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens.</p> <p><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>You will be responsible for paying the overtime fee in full in your writing up/overtime year (£320 in Session 2024/25), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award.</p> <p><strong>Important:</strong> Please note that that the award does <em><strong>not</strong></em> cover the costs associated with moving to the UK.  All such costs (<a href="https://www.leeds.ac.uk/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights etc) would have to be met by yourself, or you will need to find an alternative funding source. </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 style="margin-bottom:11px">For general enquiries about applications, contact our admissions team by email to <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. Jiaqi Ge ny email to <a href="mailto:j.ge@leeds.ac.uk">j.ge@leeds.ac.uk</a> or Dr. Haiyan Liu by email to  <a href="mailto:h.liu1@leeds.ac.uk">h.liu1@leeds.ac.uk</a>.</p>