# School of Mathematics

## Dr Robert G Aykroyd

Senior Lecturer

Statistics

### Contact details

Room: Satellite 10.18

Tel: +44 (0)113 3435167

Email: R.G.Aykroyd @ leeds.ac.uk

### Keywords

Applied statistics

Archaeological geophysics

Bayesian modelling

Electrical tomography

Image analysis

Inverse problems

Markov chain Monte Carlo methods

Variational Bayesian methods

## Research interests

My research interests are in the general area of applied statistics. Perhaps the main area being the use of Bayesian modelling approaches in image analysis and other inverse problems. Usually this involves the use of hyper-priors and prior parameter estimation. This has involved applications in archaeological geophysics, medical imaging (including PET & SPECT) and engineering applications of electrical tomography. Often estimation involves use of MCMC algorithms. I also have a strong interest in use of other numerical techniques such as finite element and boundary element methods. More fundamental work has looked at inhomogeneous Markov random field models, "phase change" properties of spatial auto-models, and approximations of normalizing constants in certain Markov random field models. I also have interest in Wavelet methods and kernel density methods. These have been applied in process monitoring, image analysis, forensic age estimation and climate reconstruction. I would like to start new work on variational Bayesian methods for inverse problems. If you are interested, then please get in touch.

## Current postgraduate students

Wafa Al Mohri (2013)

Nada Alfaer (2012)

Fatimah Alghamdi (2014)

Hassan Aljohani (2011)

## Publications

**Dyhoum TE; Aykroyd RG; Lesnic D ** *Solving the inverse three-dimensional continuous model of electrical resistance tomography using the method of fundamental solutions and the Markov chain Monte Carlo approach.*Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM11), 43-52 2017

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**Saulo H, Leão J, Leiva V, Aykroyd RG** Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data *Statistical Papers*, 1-25, 2017

DOI:10.1007/s00362-017-0888-6

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**Garcia-Papani F, Uribe-Opazo MA, Leiva V, Aykroyd RG** Birnbaum–Saunders spatial modelling and diagnostics applied to agricultural engineering data *Stochastic Environmental Research and Risk Assessment*, **31**, 105-124, 2017

DOI:10.1007/s00477-015-1204-4

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**Lillo C, Leiva V, Nicolis O, Aykroyd RG** L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data *Journal of Applied Statistics*, 1-23, 2016

DOI:10.1080/02664763.2016.1269729

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**Aykroyd RG; Alfaer N ** *A Bayesian approach to level-set based image segmentation with a prior sensitivity analysis*Stochastic and Data Analysis Methods and Applications in Statistics and Demography, 341-355 2016

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**Aykroyd RG** Generalized Student's t-distribution mixtures for autoradiographic image spread modelling. *Biom J*, **58**, 1021-1038, 2016

DOI:10.1002/bimj.201500067

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**Aykroyd RG, Alfaer N** Sequential models for time-evolving regression problems with an application to energy demand prediction *Stochastic Modelling and Applications*, **20**, 1-16, 2016

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**Dyhoum TE, Aykroyd RG, Lesnic D** Reconstructing rigid inclusions in the complete-electrode model of ERT In *Inverse Problems and Computational Mechanics (eds. L. Marin, L. Munteanu and V. Chiroiu), The Publishing House of the Romanian Academy, Bucharest, Romania.*, **2**, 73-102, 2016

**Aykroyd RG, Hidalgo-Silva H, Gomez-Trevino E** On the effect of Bayesian prior assumptions in the solution of geophysical inverse problems. In *Stochastic Modeling, Data Analysis and Statistical Applications. Editors: Filus L, Oliveira T, Skiadas CH*, 75-86, 2016

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**Aykroyd RG, Barber S, Miller LR** Classification of multiple time signals using localized frequency characteristics applied to industrial process monitoring *Computational Statistics and Data Analysis*, **94**, 351-362, 2016

DOI:10.1016/j.csda.2015.07.009

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**Hamed FMO, Aykroyd RG** Exploratory Methods for the Study of Incomplete and Intersecting Shape Boundaries from Landmark Data *Journal of Probability and Statistics*, **2016**, 1-9

DOI:10.1155/2016/1285026

**Aykroyd RG, Cattle BA, West RM** Statistical estimation of interface-boundary shapes from electrical impedance tomographic measurements *International Journal of Tomography and Simulation*, **29**, 2016

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**Aykroyd RG; Alfaer N ** *Bayesian object identification from image data using the level set method. In Proceedings of the 16th Applied Stochastic Models and Data Analysis, Piraeus, Greece, 30 Jun 2015 - 04 Jul 2015. Editors: Skiadas CH.*Stochastic Modelling and Applications, 13-20 2015

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**Aykroyd RG** Statistical image reconstruction. In *Industrial tomography: Systems and applications*, 2015

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**Aykroyd RG, Lesnic DL, Karageorghis A** A fully Bayesian approach to shape estimation of objects from tomography data using MFS forward solutions *International Journal of Tomography and Simulation*, **28**, 1-21, 2015

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**Aykroyd RG; Hidalgo-Silva H; Gomez-Trevino E ** *Bayesian reconstruction of subsurface conductivity from geosounding data*3rd Stochastic Modeling Techniques and Data Analysis, 91-98 2014

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**Aykroyd RG, Hamed FMO** Horizon Detection in Seismic Data: An Application of Linked Feature Detection from Multiple Time Series *Advances in Statistics*, **2014**

DOI:10.1155/2014/548070

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**Aykroyd RG, Al-Gezeri SM** 3D modeling and depth estimation in archaeological geophysics *Chilean Journal of Statistics*, **5**, 19-35, 2014

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**Dyhoum TE, Lesnic D, Aykroyd RG** Solving the complete-electrode direct model of ERT using the boundary element method and the method of fundamental solutions *Electronic Journal of Boundary Elements*, **12**, 26-71, 2014

**Aykroyd RG, Lesnic D, Karageorghis A** A Bayesian approach for shape estimation of objects In *4th Inverse Problems, Design and Optimization Symposium (IPDO 2013)*, 1-10, 2013

**Lucy D, Robertson I, Aykroyd RG, Pollard AM** Estimates of uncertainty in the prediction of past climatic variables *APPLIED GEOCHEMISTRY*, **23**, 2961-2965, 2008

DOI:10.1016/j.apgeochem.2008.04.008

**Aykroyd RG, Cattle BA** A boundary-element approach for the complete-electrode model of EIT illustrated using simulated and real data *INVERSE PROBL SCI EN*, **15**, 441-461, 2007

DOI:10.1080/17415970600795337

**Aykroyd RG, Cattle BA** A flexible statistical and efficient computational approach to object location applied to electrical tomography *STAT COMPUT*, **16**, 363-375, 2006

DOI:10.1007/s11222-006-9619-x

**Romanowski A, Grudzien K, Aykroyd RG, Williams RA** Advanced statistical analysis as a novel tool to pneumatic conveying monitoring and control strategy development *PARTICLE&PARTICLE SYSTEMS CHARACTERIZATION*, **23**, 289-296, 2006

DOI:10.1002/ppsc.200601059

**Aykroyd RG, Soleimani M, Lionheart WRB** Conditional Bayes reconstruction for ERT data using resistance monotonicity information *MEAS SCI TECHNOL*, **17**, 2405-2413, 2006

DOI:10.1088/0957-0233/17/9/006

**Grudzien K; Romanowski A; Aykroyd RG; Williams RA; Mosorov V ** *Parametric modelling algorithms in electrical capacitance tomography for multiphase flow monitoring*Perspective Technologies and Methods in MEMS Design, 100-106 2006

**Goodwin DA; Barber S; Aykroyd RG ** *Modelling and predicting flow regimes using wavelet representations*Wavelet Applications in Industrial Processing IV, U33-U40 2006

DOI:10.1117/12.692645

**Grudzien K; Romanowski A; Aykroyd RG; Williams RA ** *A novel approach to pneumatic conveying monitoring and control strategy development*4th World Congress on Industrial Process Tomography, 886-891 2005

**Soleimani M; Aykroyd RG; Freear S; Lionheart WRB; Podd FJW ** *Multi-modal data fusion for enhanced imaging applied to 3D ERT with ultrasound time of flight data*4th World Congress on Industrial Process Tomography, Aizu, Japan 2005

**West RM, Meng S, Aykroyd RG, Williams RA** Spatial-temporal modeling for electrical impedance imaging of a mixing process *REV SCI INSTRUM*, **76**, 2005

DOI:10.1063/1.1947882

**Grudzien K; Romanowski A; Sankowski D; Aykroyd RG; Williams RA ** *Advanced statistical computing for capacitance tomography as a monitoring and control tool*5th International Conference on Intelligent Systems Design and Applications (ISDA 2005), 49-54 2005

**West RM; Soleimani M; Aykroyd RG; Lionheart WRB ** *MCMC algorithm acceleration using a hybrid linearised/non-linear forward problem strategy applied to the bayesian analysis of 3d ERT data*4th World Congress in Industrial Process Tomography, 570-575 2005

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**Aykroyd RG; Soleimani M; Lionheart WRB ** *Full shape reconstruction from partial ert monotonicity information using a Bayes-Mcmc approach*4th World Congress in Industrial Process Tomography, 697-702 2005

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**Goodwin DA; Aykroyd RG; Barber S ** *Modelling and predicting flow regimes using wavelet representations of ERT data*4th World Congress on Industrial Process Tomography 2005

**Goodwin DA; Barber S; Aykroyd RG ** *Modelling and predicting flow regimes using wavelet representations of ERT data*Quantitative Biology, Shape Analysis, and Wavelets, 134-137 2005

**Aykroyd RG; Cattle BA; West RM ** *A boundary element approach for real-time monitoring and control from electrical resistance tomographic data*4th World Congress in Industrial Process Tomography, 637-642 2005

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**Grudzien K; Romanowski A; Williams RA; Aykroyd RG; West RM; Meng S ** *Application of the Bayesian approach to powder flow investigation*3rd International Symposium on Process Tomography, 72-76 2004

**West RM, Aykroyd RG, Meng S, Williams RA** Markov chain Monte Carlo techniques and spatial–temporal modelling for medical EIT *Physiological Measurement*, **25**, 181-194, 2004

DOI:10.1088/0967-3334/25/1/025

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**Aykroyd RG; Barber S; Mardia KV ** *Bioinformatics, Images, and Wavelets*. Leeds University Press 2004

**Nason G, Moulines E, Robert CP, Andrieu C, Stoffelen A, Paul D, Abramovich F, Aykroyd RG, West RM, Meng S, Butucea C, Cavalier L, Davy M, De Canditiis D, Golubev Y, Hoffman RN, Khabie-Zeitoune E, Munk A, Ruymgaart FH, Olhede SC, Tsybakov A, Wahba G, Johnstone IM, Kerkyacharian G, Picard D, Raimondo M, Wolfe PJ, Godsill SJ, Ng WJ, Haario H, Laine M, Lehtinen M, Saksman E, Tamminen J, Cornford D, Csato L, Evans DJ, Opper M** Dicussion on the meeting on 'Statistical approaches to inverse problems *J ROY STAT SOC B*, **66**, 627-652, 2004

**Goodwin DA; Barber S; Aykroyd RG ** *Wavelet packet modelling of seismic data*Bioinformatics, Images, and Wavelets, 126-129 2004

**West RM; Meng S; Aykroyd RG; Williams RA ** *Spatial-temporal modelling for electrical impedance imaging of a mixing process*The 3rd World Congress on Industrial Process Tomography, 226-232 2003

**Aykroyd RG; Mardia KV; Langdon MJ ** *Stochastic Geometry, Biological Structure and Images*. Leeds University Press 2003

**Aykroyd RG, Mardia KV** A wavelet approach to shape analysis for spinal curves *J APPL STAT*, **30**, 605-623, 2003

DOI:10.1080/0266476032000053718

**Aykroyd RG** Approximations for Gibbs distribution normalising constants *STAT COMPUT*, **12**, 391-397, 2002

**Romanowski A; Grudzien K; Aykroyd RG; Williams RA; West RM; Meng S ** *An introduction to the Bayesian/MCMC approach as a recently developed methodology for tomographic data analysis*3rd International Symposium on Process Tomography, 134-138 2002

**Aykroyd RG; Mardia KV; Mcdonnell P ** *Statistics of large datasets - functional and image data, bioinformatics and data mining*. Leeds University Press 2002

**Lucy D, Aykroyd RG, Pollard M** Nonparametric calibration for age estimation *Royal Statistical Society. Journal. Series C: Applied Statistics*, **51**, 183-196, 2002

DOI:10.1111/1467-9876.00262

**Lucy D, Aykroyd RG, Pollard M** Commentary on Munoz JI, Suarez-Penaranda JM, Otero XL, Rodriguez-Calvo MS, Costas E, Miguens X, Concheiro L. A new perspective in the estimation of postmortem interval (PMI) based on vitreous (k+) *Journal of Forensic Sciences*, **46**, pp.1527, 2001

**Aykroyd RG, Lucy D, Pollard AM, Carter AHC, Robertson I** Temporal variability in the strength of proxy-climate *Geophysical Research Letters*, **28**, 1559-1562, 2001

DOI:10.1029/2000GL012570

**Aykroyd RG, Haigh JGB, Allum GT** Bayesian methods applied to survey data from archeological magnetmetry *Journal of the American Statistical Association*, **96**, 64-76, 2001

DOI:10.1198/016214501750332983

**Kent JT, Mardia KV, Aykroyd RG, Morris RJ** Functional models of growth for landmark data In *Proceedings in Functional and Spatial Data Analysis*, 109-115, 2001

**Zimeras S, Aykroyd RG** Neighbourhood structure estimation of images using hierarchical testing *Electronics Letters*, **35**, 2188-2189, 1999

DOI:10.1049/el:19991476

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**Morris RJ; Kent JT; Mardia KV; Fidrich M; Aykroyd RG; Linney A ** *Analysing growth in faces*INTERNATIONAL CONFERENCE ON IMAGING SCIENCE, SYSTEMS, AND TECHNOLOGY, PROCEEDINGS, 404-410 1999

**Robertson I, Lucy D, Baxter L, Pollard AM, Aykroyd RG, Barker AC, Carter AHC, Switsur VR, Waterhouse JS** A kernel-based Bayesian approach to climatic reconstruction *Holocene*, **9**, 495-500, 1999

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**Aykroyd RG, Lucy D, Pollard AM, Roberts CA** Nasty, brutish, but not necessarily short: A reconsideration of the statistical methods used to calculate age at death from adult human skeletal and dental age indicators *American Antiquity*, **64**, 55-70, 1999

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**Aykroyd RG, Zimeras S** Inhomogeneous prior models for image reconstruction *Journal of the American Statistical Association*, **94**, 934-946, 1999

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**Allum GT, Aykroyd RG, Haigh JGB** Empirical Bayes estimation for archaeological stratigraphy *Royal Statistical Society. Journal. Series C: Applied Statistics*, **48**, 1-14, 1999

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**Wright DJ, Aykroyd RG, Chrystyn H** Rating clinical pharmacy interventions by clinical panels: which health professionals should be included? *BRITISH JOURNAL OF CLINICAL PHARMACOLOGY*, **46**, 278P-305P, 1998

**Aykroyd RG** Bayesian Estimation for Homogeneous and Inhomogeneous Gaussian Random Fields *IEEE Transactions on Pattern Analysis and Machine Intelligence*, **20**, 533-539, 1998

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**Aykroyd RG, Lucy D, Pollard AM, Solheim T** Technical note: Regression analysis in adult age estimation *American Journal of Physical Anthropology*, **104**, 259-265, 1997

DOI:10.1002/(SICI)1096-8644(199710)104:2<259::AID-AJPA11>3.0.CO;2-Z

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**Aykroyd RG, Haigh JGB, Zimeras S** Unexpected Spatial Patterns in Exponential Family Auto Models *Graphical Models and Image Processing*, **58**, 452-463, 1996

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**Lucy D, Aykroyd RG, Pollard AM, Solheim T** A Bayesian approach to adult human age estimation from dental observations by Johanson's age changes. *J Forensic Sci*, **41**, 189-194, 1996

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**AYKROYD RG** CALCULATION OF GUSTAFSON ERROR OF ESTIMATION *JOURNAL OF FORENSIC SCIENCES*, **40**, 925-925, 1995

**AYKROYD RG** PARTITION MODELS IN THE ANALYSIS OF AUTORADIOGRAPHIC IMAGES *APPLIED STATISTICS-JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C*, **44**, 441-454, 1995

DOI:10.2307/2986137

**Allum GT, Aykroyd RG, Haigh JGB** A new statistical approach to reconstruction from area magnetometry data *Archaeological Prospection*, **2**, 197-205, 1995

DOI:10.1002/1099-0763(199512)2:4<197::AID-ARP6140020403>3.0.CO;2-D

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**Aykroyd RG, Anderson CW** Use of the em algorithm for maximum likelihood estimation in electron microscope autoradiography *Biometrika*, **81**, 41-52, 1994

DOI:10.1093/biomet/81.1.41

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**Aykroyd RG, Green PJ** Global and Local Priors, and the Location of Lesions Using Gamma-Camera Imagery *Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, **337**, 323-342, 1991

DOI:10.1098/rsta.1991.0128

**Aykroyd RG, Anderson CW, Junger E, Williams MA** An improved analysis of experimental data from 125 I hot-line autoradiographs: allowing for the effects of background grains *Journal of Microscopy*, **162**, 271-278, 1991

DOI:10.1111/j.1365-2818.1991.tb03136.x

**Deidda D, Aykroyd RG, Tsoumpas C** Assessment of maximum a posteriori image estimation algorithms for reduced acquisition time medical positron emission tomography data In *Risk Analysis and Statistical Modelling*

Deidda D; Efthimiou N; Manber R; Thielemans K; Markiewicz P; Aykroyd RG; Tsoumpas C *Comparative Evaluation of Image Reconstruction Methods for the Siemens PET-MR Scanner Using the STIR Library*2016 Nuclear Science Symposium and Medical Imaging Conference

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**Dyhoum TE, Aykroyd RG, Lesnic D** Detection of Multiple Rigid Inclusions from ERT Data Using The Complete-Electrode Model *International Journal of Tomography and Simulation*

**Aykroyd RG, Aljohani H** Two-stage estimation in inverse problems using a combined wavelet thresholding and penalized maximum likelihood *Journal of Mathematics and Statistics*

**Aykroyd RG, Mahmoud MAW, Aljohani HM** Bayesian analysis using MCMC methods of record values based on a new generalised Rayleigh distribution *Stochastic Modeling and Applications*

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