Department of Mathematical Sciences

Norwegian University of Science and Technology (NTNU)

Room: 1222, Sentralbygg II

Phone: +47 735 91699

Email: daniel.simpson@math.ntnu.no

Skype: dp.simpson

- Gaussian random fields, Gaussian Markov random fields and Stochastic partial differential equations
- Fast approximate inference
- Modelling nonstationarity
- Applying modern numerical linear algebra to large problems in statistics
- Numerical methods for fractional diffusion equations
- Krylov subspace methods
- The numerical solution of structured population models
- Mathematical models of Chlamydia

- Doctor of Philosophy (2006–2009)
Queensland University of Technology, Brisbane, Queensland, Australia

Supervisor: Professor Ian Turner.

Associate Supervisor: Professor Tony Pettitt.

- Bachelor of Applied Science (Mathematics – Honours) (2003-2005)
Queensland University of Technology, Brisbane, Queensland, Australia

- MA8704 - Probability Theory and Asymptotic Methods (Autumn 2010)
- Reading course on Bayesian theory and model selection. (Autumn 2012) --- Email me if you're interested!

- Åke Brännström, Linus Carlsson and Daniel Simpson, On the convergence of the Escalator Boxcar Train, Submitted October 2012. (arXiv:1210.1444)
- Thiago G. Martins, Daniel Simpson, Finn Lindgren and Håvard Rue, Bayesian computing with INLA: new features, Preprint in Statistics, No. 10/2012, NTNU, 2012.
- Yu Ryan Yue, Daniel Simpson, Finn Lindgren and Håvard Rue, Bayesian adaptive smoothing spline using stochastic differential equations, Preprint in Statistics, No. 8/2012, NTNU, 2012.
- Erlend Aune and Daniel Simpson, The use of systems of stochastic PDEs as priors for multivariate models with discrete structures , Preprint in Statistics, No. 7/2012, NTNU, 2012.
- Erlend Aune, Daniel Simpson and Jo Eidsvik, Parameter estimation in high dimensional Gaussian distributions, Preprint in Statistics, No. 5/2012, NTNU, 2012. ( Old version , Prepared for the ISI conference, Dublin, 2011).
- Daniel Simpson, Janine Illian, Finn Lindgren, Sigrunn H. Sørbye and Håvard Rue, Going off grid: Computationally efficient inference for log-Gaussian Cox processes, Preprint in Statistics No. 10/2011, NTNU, 2011. (Code for simulated examples)
- Dann Mallet, Masoumeh Bagher-Oskouei, Anna Charisse Farr, Daniel Simpson and Kelly-Jean Heymer, A mathematical model of chlamydial infection incorporating spatial movement of chlamydial particles.

- Michela Cameletti, Finn Lindgren, Daniel Simpson and Håvard Rue. Spatio-temporal modeling of particulate matter concentration through the SPDE approach. AStA Advances in Statistical Analysis, Online, 16 May, 2012. (Preprint version)
- Daniel Simpson, Finn Lindgren and Håvard Rue, Think continuous: Markovian Gaussian models in spatial statistics, Spatial Statistics, Volume 1, pp. 16–29, 2012. (Preprint in Statistics No. 9/2011, NTNU, 2011).
- Daniel Simpson, Finn Lindgren and Håvard Rue, In order to make spatial statistics computationally feasible, we need to forget about the covariance function , Environmetrics, Volume 23, No. 1, p. p65–74, 2012. ( Preprint in Statistics No. 16/2010, NTNU, 2010.)
- C.M. Strickland, D.P. Simpson, I.W. Turner, R. Denham, K.L. Mengersen. Fast Bayesian Analysis of Spatial Dynamic Factor Models for Multi-temporal Remotely Sensed Imagery, Journal of the Royal Statistical Society Series C, Volume 60, No. 1, pp. 109--124, January 2011.
- I.W. Turner, M. Ilic, D.P. Simpson. A Restarted Lanczos Approximation to Functions of a Symmetric Matrix. IMA Journal on Numerical Analysis, Volume 30, No. 4, pp. 1044--1061, 2010.
- D.P. Simpson, I.W. Turner, and A.N. Pettitt. Sampling from a Gaussian Markov random field conditioned on linear constraints. ANZIAM J., 48 (CTAC2006) pp. C1041–C1053, 2008.

- Daniel Simpson, Finn Lindgren and Håvard Rue, Fast approximate inference with INLA: the past, the present and the future, Prepared for the ISI conference, Dublin, 2011.
- D.P. Simpson, M. Ilic and I.W. Turner. A generalised matrix transfer technique for the numerical solution of fractional-in-space partial differential equations>. 2009.
*(Note. June, 2012: This is a nice piece of analysis that, for various reasons, probably won't be published. It's used extensively in my PhD thesis, where the practical bits are also tackled. To be brutally honest, this is not very well written! It really is much better in the thesis.)* - D.P. Simpson, I.W. Turner, A.N. Pettitt. Fast Sampling from a Gaussian
Markov random field using Krylov subspace approaches. 2008.
*(Note. June, 2012: This is a nice paper that languished too long as a techreport. Everything in it can be found in more detail in my PhD thesis. We are (with Chris Strickland) working on an improved version of this idea (see talk below), however this version will never be published. I agree with most of the things in it, except that it turned out that the Extended Krylov Subspace Method actually worked better than shift-and-invert. A (very!) detailed comparison is in my thesis, which you should read :p)*

- Abandoning the Cholesky factorisation: Efficient sampling from large Gaussian random vectors (Poster presented at the Structure and Uncertainty workshop, University of Bristol, September 2012)
- Approximating Gaussian random fields by Gaussian Markov random fields: A decade on (Workshop on Latent Gaussian Models, Trondheim, 2012)
*(While it is unclear from the (terrible terrible) title, this is a talk on new Krylov subspace methods for sampling from large Gaussian random fields. It comes with it's own Spotify playlist!! [Warning: Songs chosen for their titles/first lines/last lines rather than cohesion as a playlist. That being said, I will stand by Magic Dance until the very end!])* - INLA Course: Spatial Statistics and Stochastic PDEs (Norwegian Statistical Conference, 2011) (R files, Slides from full INLA course in Helsinki with a different spatial statistics section )
- Complex point processes without grids or pain (Joint talk [!!] with Janine Illian) (Workshop on Bayesian Inference for Latent Gaussian Models with Applications, Zurich, 2011)
- Numerical linear algebra for large spatial models (URE Meeting, December 2010)
- The mathematical modelling of Chlamydia: Simple models of a complex process (Student Seminar, October 2010)
- Fast approximate inference and spatio-temporal modelling: Stochastic partial differential equations and INLA (EMS, Piraeus, August 2010)
- Constructing spatial random fields: Stochastic partial differential equations and INLA (Queensland University of Technology, July 2010)
- Approximate inference for Bayesian smoothing problems on bounded domains: Stochastic partial differential equations and INLA (NORDSTAT, Voss, June 2010)
- Matrix function methods for fractional partial differential equations, (NTNU, March 2010)
- Exploiting structure when sampling from a Gaussian Markov random field: Three unusual methods for GMRF calculations (NTNU, February, 2010)
- The Numerical Solution of Structured Population Models (Student Seminar, October 2010)
- A practical error bound for the Lanczos approximation to a certain class of completely monotone functions, (IMA Conference on Numerical Linear Algebra and Optimization, Birmingham, 2007)