PhD prospective students

G4ZS MPhil/PhD Statistics applications for entry in 2020/21 are now open. 

The Department of Statistics is one of the world's leading centres of quantitative methods in the social sciences and has long been home to some of the world's most famous and innovative statisticians. Today, the department has an international reputation for the development of statistical methodology that has grown from its long history of active contributions to research and teaching in statistics. Our core research areas are social statistics, time series and statistical learning and risk and stochastics in insurance and finance. 

If you have any questions about our MPhil/PhD Statistics programme, please e-mail the research administrator

Research environment

The Department of Statistics at LSE is one of the oldest and most distinguished in the UK. It has a rich research portfolio covering core areas of statistical inference and real applications, particularly in the economic, financial and actuarial, social and industrial arenas. The close collaboration between departments, its London location and strong international partnerships are reflected in the research life of the Department of Statistics through the members of staff, PhD students, postdoctoral research fellows and the thriving visitor and seminar programmes. Research in the department is concentrated in the following areas and research proposals should normally be linked to one of these areas:

Social Statistics

PhD programmes of study in social statistics typically include both methodological development and the application of statistical methods to a social science field or to address new developments in social data, such as in sample surveys or social networks. Research topics may be identified in advance by the applicant or may be arrived at through communication with a potential supervisor. The relative emphasis on methodology/theory vs. application may vary.


Methodological areas of research include:

  • Latent variable modelling
  • Structural equation modelling
  • Multilevel modelling
  • Longitudinal data analysis
  • Causal modelling
  • Categorical data analysis
  • Measurement error
  • Missing data
  • Survey sampling
  • Model selection
  • Bayesian methods.

For more detail about potential supervisors and their areas of interest, see Social Statistics. If you are interested in applying to undertake PhD research in social statistics, you are welcome to contact one of these members of staff regarding a suitable topic for your research proposal.

Probability in Finance and Insurance 

PhD research in probability in finance and insurance encompasses many aspects of the discipline. Methodological and theoretical research is mainly guided by applications with the aid of both academic and industrial experts, covering topics of modern stochastic finance with an emphasis on insurance and financial mathematics.  Applications include pricing and hedging exotic products, counterparty risk, portfolio optimisation, risk management and insurance, risk transfer and securitisation, etc. 

Research topics may be identified in advance by the applicant or may be arrived at through communication with a potential supervisor. The relative emphasis on methodology/theory vs. application may vary. 

For more details about supervisors and their areas of research interests, please see the Probability in Finance and Insurance research group. You will find links to the web pages of individual members of staff here. If you are interested in applying to undertake PhD research in probability in finance and insurance, you are welcome to contact one of these members of staff regarding a suitable topic for your research proposal. 

Suggested research areas of PhD research projects include:

  • Energy markets
  • Excursions of Lévy processes and applications in finance and insurance
  • Financial market with frictions
  • Information asymmetry
  • Interface between insurance and finance
  • Model uncertainty quantification
  • Lévy processes
  • Optimal stopping
  • Point processes in insurance and credit risk
  • Quantile options and options based on occupation times
  • Stochastic analysis and its applications in financial mathematics
  • Stochastic control and analysis of partial differential equations in mathematical finance

This list of areas of research is indicative only and by no means exhaustive.

Time Series and Statistical Learning

PhD research in time series and statistical learning encompasses many aspects of these disciplines. We are keenly involved in both theoretical developments and practical applications. Current areas of interest include time series (including high-dimensional and non-stationary time series), data science and machine learning, networks (including dynamical networks), high-dimensional inference and dimension reduction, statistical methods for ranking data, spatio-temporal processes, functional data analysis, shape-constrained estimation, multiscale modelling and estimation and change-point detection.

Research topics may be identified in advance by the applicant or may be arrived at through communication with a potential supervisor. The relative emphasis on methodology/theory vs. application may vary.

Suggested research areas of PhD research projects include:

  • Big Data: analysing vast time series
  • Estimation of stochastic volatility models
  • Forecasting functional time series and classification
  • Financial econometrics
  • Functional time series analysis
  • Dimension reduction and factor modelling
  • High-dimension variable selection
  • High dimensional time series analysis
  • Multiscale methods in data analysis, including Unbalanced Haar, Haar-Fisz and Wild Binary Segmentation
  • Multiscale methods for image analysis
  • Nonparametric regression
  • Probabilistic prediction and risk management Randomised algorithms in time series analysis
  • Re-weighted iterative penalty methods for data smoothing
  • Spatio-temporal modelling
  • Variable selection

Please see the Time Series and Statistical Learning research group

The Centre for the Analysis of Time Series (CATS)

The Centre for the Analysis of Time Series (CATS) was established in 2000 and is based within the Department of Statistics at the LSE. CATS is at the frontier of time series analysis in many subject areas; ranging from the stochastic to the deterministic, from linearity to nonlinearity, from the parametric to the semi-parametric and the non-parametric. The research centre is interdisciplinary, working in partnership with industry and other academic institutions, and guided by application; the centre seeks practical solutions to real-world problems. CATS research in the climate change area is closely linked to that of the LSE's Grantham Research Institute on Climate Change and the Environment. Prospective PhD students can expect a lively and engaging course of study that will introduce new forecasting methods as well as develop the critical reasoning necessary to choose the most suitable tools for the task in hand.

CATS sits at a critical crossroads between the UK environmental science, UK industry and policy formation. At the forefront of international research in applied statistics and mathematics, CATS, under the direction of Professor Leonard Smith, is uniquely able to apply cutting edge developments in mathematics and statistics, developed either in-house or elsewhere, to the interpretation of environmental forecast simulations and communicate these results to industry. 

PhD programme

A PhD offers the chance to undertake a substantial piece of supervised work that is worthy of publication and which makes an original contribution to knowledge in a particular field.  

First year: MPhil

All students registering for a programme of study leading to a PhD begin under MPhil registration. The opportunity to upgrade this registration to PhD typically comes in the second year.

The following courses are mandatory:

•          ST505 Statistical Modelling and Data Analysis
•          ST552 Probability and Mathematical Statistics I
•          ST553 Probability and Mathematical Statistics II

Students are expected to attend courses suggested to them by their supervisor and perform well in any mandatory assessments. They should also complete any necessary training in research techniques and/or computing.

Throughout their first year students perform literature searches and become more familiar with their chosen research topic. By the end of the year they are expected to have written up an introductory chapter for their thesis, as well as any new results they may have obtained. Assessment by the supervisor is based on these. Students will be asked to present their research topics at the annual PhD presentation event.

All MPhil/PhD students at the London School of Economics have the opportunity to take advantage of research methodology courses provided by the Department of Methodology. Further courses are available at the London Graduate School in Mathematical Finance and the London Taught Course Centre (LTCC) . MPhil/PhD students are encouraged to make full use of these additional opportunities.

Second year: MPhil/PhD

In the second year students become more deeply involved with their research topic, producing and writing up new results. During this time students need to meet with supervisors on a regular basis to discuss their academic development and at some stage during the year there will be a formal review their progress.

Following the successful assessment of their work, students may be recommended for upgrade to PhD. Students should also be able to present their current research at departmental seminars and will be asked to present their research findings at the annual PhD presentation event. 

Third year: PhD

The third year demands considerable and rapid progress with research and a substantial part of the year should be spent consolidating material students have already assembled.

The role of the supervisor is to ensure the thesis is of a high standard. At the beginning of the fourth year students should submit their entry form for PhD examination and should be close to submitting their thesis. Students are encouraged to submit their thesis as early in the year as possible. 

Thesis Examination

When a thesis is nearly ready for submission, the supervisor will nominate a suitable internal examiner and external examiner. The internal examiner will be from the LSE or another college of the University of London, while the external examiner will be from another university. The appointed examiners will normally require at least two months to read a thesis once it has reached them. After the examiners have read the thesis, a date will be arranged for a viva examination. Students should expect to give a short presentation of their work and answer general questions on their area of research, as well as on the details of their thesis. Students may request the attendance of their supervisor at the viva, but the supervisor will speak only if asked to do so by the examiner.

At the conclusion of the viva, examiners will usually inform candidates of the unofficial outcome of the examination. In the best circumstances the thesis will be accepted without change or subject only to minor corrections. Once these are made, an electronic copy (PDF format) must be submitted and official confirmation of the award will follow. In less ideal circumstances a student might be required to undertake more substantial revision of their thesis or an award of MPhil maybe be decreed instead. In some cases a thesis may be rejected completely.

Please note that the maximum period of full-time registration is four years.


Each student is assigned a first and second supervisor with whom they meet frequently to discuss their research. There is also plenty of opportunity to participate in poster presentations, give seminars and attend advanced training and conferences.

Entry requirements

All applicants should have completed a taught MSc containing a substantial statistical component, usually with a distinction, plus an undergraduate degree of good standing. There is also an English language requirement for all applicants for whom English is not their first language. The British Council's International English Language Testing System (IELTS) is an accepted qualification. Applicants should already have or expect to gain a minimum score of 7.0 in the IELTS.

More information about English language tests.

International students should consult the graduate prospectus for details of equivalent qualifications. Please see Graduate Admissions


Application Process

We recommend that you apply online as this is the quickest and cheapest method. Please refer to Graduate Admissions for further information.

When applying, you should provide evidence of your ability to undertake independent research and state your research topic as accurately as possible on a separate sheet. Your research proposal should address the following questions:

  • What is your general topic?
  • What questions do you want to answer?
  • What is the key literature and its limitations?
  • What are the main hypotheses of the work?
  • What methodology do you intend to use?
  • What theoretical/conceptual framework will you adopt?
  • What are your case studies, if any, and what are your case selection criteria?
  • What previous research have you undertaken in this field?

Most applicants will have little or no prior experience of research and therefore we do not expect a fully-developed research proposal. We are assessing the potential of the applicant for research and the chosen topic. The following is a guideline of what to emphasise in the proposal:

  • A research question rather than a very broad research topic
  • Be specific, to aid selectors to assess the suitability of the topic for PhD study
  • A statement of how the proposed research builds on earlier research on the topic, with reference to two or three key papers
  • Demonstrate your understanding of the area and the need for further research
  • Selectors will look for a sense of the merits of your approach
  • Most topics will involve an application of the proposed methods to a substantive research question. Give a brief outline of this question and explain how it will benefit from tis particular approach
  • Be specific about the training and skills you have to undertake the proposed research (do not simply list courses attended: this information is already available in the CV and transcripts)

Your proposal should be approximately 1,500 words in length. MPhil/PhD applications that are received without a research proposal that addresses these questions will not be considered.

In addition, you should submit a personal statement of between 1,000 and 1,500 words, describing your academic interests and your purpose and objectives in undertaking a doctoral research degree. Your personal statement should also explain why you have chosen LSE.

Your personal statement should provide the following:

  • A clear sense of why you wish to undertake a PhD
  • What you hope to gain from PhD study
  • Why have chosen this particular topic?
  • Details of prior research experience - for example, an undergraduate and/or MSc project
  • To what extent did the project involve independent thinking?
  • Why have to chosen to apply to this department rather than another statistics department?
  • If you have discussed your research proposal with a member of academic staff prior to the submission of your application, why do you consider that person to be an appropriate supervisor for your research?

You should also submit a scanned copy of a marked assignment or a research paper/report, ideally from your most recent programme of study.

Further guidance about completing your application.

There are three possible start dates; in October, January and March/April. If the final result of your taught postgraduate degree is not published before the end of September your entry date should be the following January or later.

The application process begins in October and continues until all places are filled. We strongly recommend that you apply by the end of December for entry in October of the following year. We endeavour to assess applications as quickly as possible, but you should allow at least eight weeks from the date on which you submit your application. If you apply outside of term time it will take considerably longer for your application to be assessed. 

Applicants who are nominated by the selectors for possible admission to the MPhil/PhD programme will be interviewed by members of the academic staff of the department before any final decision is reached regarding entry, either in person or by Skype. More than one interview might be conducted.  

Informal Application Enquiries

Places on our MPhil/PhD programme are limited and we strongly recommend that you submit your full application and supporting documents to the Graduate Admissions Office as early as possible. However, you may wish to first send an informal application email to the research administrator to enquire about making a formal application within the area of your research interests and to check about the availability of potential supervisors.

To do this, please submit the following documents:

  • A brief research proposal that clearly states the specific areas of your proposed research
  • A brief personal statement that states your academic interests and your purpose and objectives in undertaking doctoral research study. You should also state your reason for applying to the Department of Statistics at LSE
  • An up-to-date CV (curriculum vitae)
  • Academic transcripts covering your study to date

Your informal application documents will be forwarded to appropriate members of academic staff for consideration and the research administrator will communicate the recommendation back to you as soon as possible.

If a formal application is invited, this should be made to the Graduate Admissions Office in accordance with the normal application procedure.


Fees and Postgraduate Funding

If your application is successful you must make sure that you have made adequate financial provision for your programme of study. Under no circumstances will LSE be able to help you register without sufficient finance. At the time of application the Department will ask you to provide a brief outline of your funding strategy, indicating what steps you have taken or intend to take to secure adequate funding for your studies. Although some funding is offered by LSE, this is very limited and there is considerable competition for it. Please refer to the Financial Support Office for full details.

LSE PhD Studentships and Economic and Social Research Council (ESRC) Studentships

Each year LSE offers a limited number of full scholarships for new PhD students. The scholarships cover fees and living expenses for four years. They are available for UK/EU (ESRC only) and international students undertaking research in any LSE discipline, with annual renewal subject to satisfactory academic performance at the School.  Scholarships are awarded strictly on academic merit and research potential. To be considered for one of these scholarships you must submit your application, including all supporting documentation, by the deadline quoted on the Financial Support Office website.

There is a deadline date set for the receipt of applications (with all required supporting documents) by the Graduate Admission Office. Applicants who submit by this date will, subject to the availability of places, be considered by the department for nomination for an LSE PhD Scholarship: The first deadline date is 10 January 2020 (final date 27 April 2020). However, we strongly recommend applications are submitted as early as possible.

ESRC funding to LSE includes studentship provision. With the mutual emphasis on economics and social sciences, ESRC is a major sponsor of LSE research. From 2011, only institutions that hold the status of Doctoral Training Centres (individual institutions and some consortia of a number of universities) will be able to hold ESRC studentships. LSE has been awarded Doctoral Training Centre status and has a total of 36 studentships per year to spread across disciplines.

The Graduate Prospectus gives an indication which programmes are eligible for funding.

The deadline date set for the receipt of applications (with all required supporting documents) by the Graduate Admissions Office is 10 January 2020. Eligible applicants who submit their application by this date will, subject to the availability of places, be considered by the department for nomination for an ESRC studentship.

Statistics PhD Scholarship

The Department of Statistics offers one scholarship to a 2019/20 offer holder covering fees and living expenses for four years. This scholarship is available for a home UK/EU or international student undertaking research in any statistics discipline, with annual renewal subject to satisfactory academic performance. The scholarship is awarded strictly on academic merit and research potential. To be considered for one of these scholarships you must submit your application, including all supporting documentation, by 10 January 2020.

Teaching Opportunities

Many of our research students take part-time graduate teaching assistant posts in the department teaching undergraduate Statistics classes and marking. Students usually undertake teaching responsibilities after their first year of study.


International students

International students who require a visa to study in the United Kingdom should refer to the Office of the Immigration Services Commissioner (OISC) (external link) and to the LSE's International Student Visa Advice Team (ISVAT) website.


LSE PhD Academy

The PhD Academy is a bespoke space for LSE doctoral students. 

Contact details

For general information on the MPhil/PhD programme and advice about academic requirements and research opportunities in the Department of Statistics please contact the research administrator.