Office: B0.24
Email: matthew.dunlop (at) warwick.ac.uk

About Me

I'm a fourth year MASDOC student supervised by Prof. Andrew Stuart and Dr. Marco Iglesias. My PhD thesis is available here. In 2015 I was president of the Warwick SIAM Student Chapter.

Current Research

I am working in the area of Bayesian inverse problems. This includes work in

• Groundwater flow: determination of subsurface permeability from noisy pressure head measurements. In particular we are interested in recovery of the geometry of the interfaces separating different materials, rock types, etc.
• Electrical impedance tomography (EIT): an imaging technique using boundary voltage and current measurements to determine the internal structure of a body. Approaches used include a hierarchical Bayesian level set method.
• Multiplicative noise in Bayesian inversion: noise is often modelled as additive, though there are applications where the magnitude of the noise will be proportional to the size of the measurement. We look at conditions under which the posterior distribution exists and demonstrate some posterior consistency.

Papers

• M. M. Dunlop, M. A. Iglesias, A. M. Stuart, Hierarchical Bayesian level set inversion (submitted) [arXiv]
• M. M. Dunlop, A. M. Stuart, MAP estimators for piecewise continuous inversion (Inverse Problems) [arXiv] [IP]
• M. M. Dunlop, A. M. Stuart, The Bayesian formulation of EIT: analysis and algorithms (submitted) [arXiv]

Selected Talks/Posters

• SIAM Conference on Uncertainty Quantification (UQ16), 5th - 8th April 2016 (EPFL)
  Talk: The Bayesian formulation of EIT [pdf]
  Talk: Hierarchical Bayesian level set inversion [pdf] [movie 1] [movie 2]
• PMPM and UK InterPore Joint Annual Meeting 2016, 14th January 2016 (ICMS)
  Poster: Hierarchical Bayesian level set inversion [pdf]
• Sensitivity, Error and Uncertainty Quantification for Atomic, Plasma, and Material Data, 8th November 2015 (Stony Brook)
  Talk: Bayesian level set inversion [pdf]
• SIAM National Student Chapter Conference 2015, 29th May 2015 (Reading)
  Talk: The Bayesian formulation of EIT: analysis and algorithms [pdf] [movie 1] [movie 2]
  
• 4th CCA-MASDOC Student Conference, 17th April 2015 (Warwick)
  Talk: The Bayesian formulation of EIT: analysis and algorithms
• EQUIP Lunch Seminar, 23rd February 2015 (Warwick)
  Talk: MAP estimators for Bayesian inverse problems
• Warwick Applied PDEs Seminar, 11th November 2014 (Warwick)
  Talk: A multiplicative noise model for Bayesian inversion
• IPTA 2014 - Inverse Problems from Theory to Application, 27th August 2014 (@Bristol)
  Poster: Bayesian geometric inverse problems in groundwater flow [pdf]
• Reading-Warwick Data Assimilation Meeting, 13th May 2014 (Warwick)
  Talk: Bayesian geometric inverse problems in groundwater flow
• Warwick Postgraduate Seminar, 30th April 2014 (Warwick)
  Talk: Bayesian geometric inverse problems in groundwater flow [pdf]
• 3rd CCA-MASDOC Student Conference, 17th March 2014 (Cambridge)
  Talk: Bayesian geometric inverse problems in groundwater flow

Teaching

This year I am the TA for

• MA398 - Matrix Analysis and Algorithms

Previously I have been a TA for MA258 - Mathematical Analysis III and ST111/112 - Probability A & B. Additionally I have supervised groups of 1st year undergraduate students since 2011.

Academic Background

I completed an MMath degree at Warwick from 2008 - 2012, with a focus mainly on analysis and probability. My final year project was supervised by Dr. Xue-Mei Li, discussing the Malliavin calculus with applications to Hörmander's theorem and the Ornstein-Uhlenbeck process [pdf]. I stayed at Warwick to join the MASDOC DTC in 2012. Details of research from the MSc year can be found here.