Statistics Group

Multivariate Statistics Research Group

Introduction  

Multivariate statistics is a major area of statistical endeavour, ranging from exploratory, graphical methods of multidimensional analysis to fundamental questions in probability theory and inference. Its applications range from archaeology to zoology, while its capabilities are continually being expanded by advances in computing.

Most members of the Group belong to this Research Group, reflecting the breadth of the area. The wide variety of current research interests is evident from the list of projects given below. Within this Group, Professors Critchley and Gower are internationally renowned leaders in the field.

This Group complements well the interests of the other two Statistics Research Group’s in Bayesian and Medical Statistics.

Aims and Objectives

• to stimulate and facilitate research into the theory and applications of multivariate statistical methods.
• to foster collaborative research, where appropriate.
• to draw attention to the large range of expertise the Statistics Group can call on in this area.

Membership

Internal members: 

External members:

Current Projects

Members of the Research Group are currently working on:

• multivariate Bayesian Forecasting and model selection (Faria)
• diagnostics and influence analysis (Critchley, Cook, Anaya)
• differential geometry in statistics (Critchley, Marriott, Anaya)
• analysis of distances and dissimilarities (Critchley, Gower)
• prior distribution assessment for multivariate models (Garthwaite)
• multivariate meta analysis (Garthwaite)
• biplots (Gower)
• Procrustes analysis (Gower)
• Australian inter-state migration (Gower, Constantine)
• multivariate beta and skew t distributions (Jones, Larsen)
• local dependence (Jones)
• multivariate dynamic linear models (Queen, Faria)
• superclassification (Taylor)
• market segmentation (Taylor)
• simple structure (Trendafilov, Vines, Critchley, Anaya)
   

Recent Publications

2009

Hannachi, A., Unkel, S., Trendafilov, N.T. and Jolliffe, I.T. (2009) Independent component analysis of climate data: A new look at EOF rotation, Journal of Climate, 2009, DOI: 10.1175/2008JCLI2571.1

Trendafilov, N.T. and Vines, K. (2009) Simple and interpretable discrimination, Computational Statistics and Data Analysis, 2009, 53, 979-989.

2008

2007

Anaya-Izquierdo, K. & Marriott, P.K. (2007) Local mixture models of exponential families. Bernoulli, 13, 623-640. 

Anaya-Izquierdo, K.A. & Marriott, P.K. (2007) Local mixtures of the exponential distribution. Annals of the Institute of Statistical Mathematics, 59, 111-134.

Arnold, G.M., Gower, J.C., Gardner, S. & LeRoux, N.J. (2007) Biplots of free-choice-profile data in generalized Procrustes analysis. Applied Statistics, 56, 445-458.

Banks, C.J., Brandon, M.A. & Garthwaite, P.H. (2006) Measurement of sea ice draft using upward looking ADCP on an autonomous underwater vehicle. Annals of Glaciology, 44, 211-216. 

Boente, G., Critchley, F., & Orellana, L. (2007) Influence functions for two families of robust estimators under proportional scatter matrices. Statistical Methods and Applications, 15, 295-327.

Crawford, J.R. & Garthwaite, P.H. (2007) Using regression equations built from summary data in the assessment of the individual case. Neuropsychology, 21, 611-621.

Crawford, J.R. & Garthwaite, P.H. (2007) Comparison of a single case to a control or normative sample in neuropsychology: development of a Bayesian approach. Cognitive Neuropsychology, 24, 343-372.

Crawford, J.R., Garthwaite, P.H. & Gault, C.B. (2007) Estimating the percentage of the population with abnormally low scores (or score differences) on standardized neuropsychological test batteries: a generic method with applications. Neuropsychology, 21, 419-430. 

Jones, M.C. (2007) Connecting distributions with power tails on the real line, the half line and the interval. International Statistical Review, 75, 58-69.

Jones, M.C. (2007) On a class of distributions defined by the relationship between their density and distribution functions. Communications in Statistics − Theory and Methods, 36, 1835-1843.

Jones, M.C. & Henderson, D.A. (2007) Kernel-type density estimation on the unit interval. Biometrika, 94, 977-984.

Jones, M.C. & Yu, K. (2007) Improved double kernel local linear quantile regression. Statistical Modelling, 7, 377-389.

Pewsey, A., Lewis, T. & Jones, M.C. (2007) The wrapped t family of circular distributions. Australian and New Zealand Journal of Statistics, 49, 79-91.

Trendafilov, N.T. & Jolliffe, I.T. (2007) DALASS: variable selection in discriminant analysis via the LASSO. Computational Statistics and Data Analysis, 51, 3718-3736.

2006

Al-Awadhi, S.A. & Garthwaite, P.H. (2006) Quantifying expert opinion for modelling fauna habitat distributions. Computational Statistics, 21, 121-140.

Albers, C.J., Jansen, C.R., Kok, J., Kuipers, O.P. & van Hijum, S.A.F.T. (2006) SIMAGE: simulation of DNA-microarray gene expression data. BMC Bioinformatics, 7, Article 205 (‘highly accessed’)

Basu, S. Basu, A. & Jones, M.C. (2006) Robust and efficient parametric estimation for censored survival data. Annals of the Institute of Statistical Mathematics, 58, 341-355. 

Crawford, J.R. & Garthwaite, P.H. (2006) Comparing patients' predicted test scores from a regression equation with their obtained scores: a significance test and point estimate of abnormality with accompanying confidence limits. Neuropsychology, 20, 259-271.

Crawford, J.R. & Garthwaite, P.H. (2006) Methods of testing for a deficit in single-case studies: Evaluation of statistical power by Monte Carlo simulation. Cognitive Neuropsychology, 23, 877-904.

Crawford, J.R. & Garthwaite, P.H. (2006) Detecting dissociations in single-case studies: Type 1 errors, statistical power and classical versus strong dissociation. Neuropsychologia, 44, 2249-2258.

Crawford, J.R., Garthwaite, P.H., Azzalini, A., Howell, D.C. & Laws, K.R. (2006). Testing for a deficit in single-case studies: Effects of departures from normality. Neuropsychologia, 44, 666-677.

Gower, J.C. (2006) Statistica data analytica est et aliter. Statistica Neerlandica, 60, 124-134.  

Gower, J.C. (2006). An application of the modified Leverrier-Faddeev algorithm to the singular value decomposition of block-circulant matrices and the spectral decomposition of symmetric block-circulant matrices. Computational Statistics and Data Analysis, 50, 89-106.  

Gower, J.C., Gardner, S. & LeRoux, N.J. (2006). A synthesis of canonical variate analysis, generalised canonical correlation and Procrustes analysis. Computational Statistics and Data Analysis, 50, 107-134.

Gower, J.C. & Greenacre, M.J. (book in preparation) Analysis of Distance.

Gower, J.C. & Ngouenet, R.F. (under consideration) Prediction with non-linear biplots.

Hannachi, A, Jolliffe, I.T., Stephenson, D.B & Trendafilov, N.T. (2006) In search of simple structures in climate: Simplifying EOFs. International Journal of Climatology, 26, 7-28.

Jones, M.C. (under consideration) A bivariate t distribution with marginals on different degrees of freedom.

Jones, M.C. (2006) A note on rescalings, reparametrizations and classes of distributions. Journal of Statistical Planning and Inference, 136, 3730-3733.

Jones, M.C., Williams-Thorpe, O., Potts, P.J. & Webb, P.C. (2006) Using field-portable XRF to assess geochemical variations within and between dolerite outcrops of Preseli, South Wales. Geostandards and Geoanalysis Research, 29, 251-269.

Nowell, D.A.G., Jones, M.C. & Pyle, D.M. (2006) Episodic Quaternary volcanism in France and Germany. Journal of Quaternary Science, 21, 645-675.

Potts, P.J., Bernadini, F., Jones, M.C., Williams-Thorpe, O. & Webb, P.C. (2006) Effects of weathering on in situ portable X-ray fluorescence analyses of geological outcrops: dolerite and rhyolite outcrops from the Preseli Mountains, South Wales. X-Ray Spectrometry, 35, 8-18.

Trendafilov, N.T. (2006) The dynamical system approach to multivariate data analysis. Journal of Computational and Graphical Statistics, 15, 628-650.

Trendafilov, N.T. & Jolliffe, I.T. (2006) Projected gradient approach to the numerical solution of the SCoTLASS. Computational Statistics and Data Analysis, 50, 242-253.

Williams-Thorpe, O., Jones, M.C., Potts, P.J. & Webb, P.C. (2006) Preseli dolerite bluestones: Axe-heads, Stonehenge monoliths, and outcrop sources. Oxford Journal of Archaeology, 25, 29-46. 

Woodward, A., Hunter, J., Ixer, R., Maltby, M., Potts, P.J., Webb, P.C. Watson, J.S. & Jones, M.C. (2005) Ritual in some early Bronze Age gravegoods. The Archaeological Journal, 162, 31-64.

Woodward, A., Hunter, J., Ixer, R., Roe, F., Potts, P.J., Webb. P.C., Watson, J.S. & Jones, M.C. (2006) Beaker age bracers in England: Sources, function and use. Antiquity, 80, 530-543.

2005

Alberts, R., Fu. J., Swertz, M.A., Lubbers, L.A., Albers, C.J., Jansen, R.C. (2005).  Combining microarrays and genetic analysis, Briefings in Bioinformatics. 6:2, 135-146

Van Hijum, S.A.F.T., De Jong, A., Baerends, R.J.S., Karsens, H.A., Kramer, N.E., Den Hengst, C.D., Albers, C.J., Kok, J., Kuipers, O.P. (2005).  A generally applicable validation scheme for the assessment of factors involved in reproducibility and quality of DNA-microarray data, BMC Genomics, 6:77

2004

Critchley, F., Schyns, M., Haesbroeck, G., Kinns, D., Atkinson, R.A. & Lu, G. (2004) The case sensitivity function approach to diagnostic and robust computation: a relaxation strategy.  In COMPSTAT: Proceedings in Computational Statistics, ed: J. Antoch, pp. 113-125.

Critchley, F. & Marriott, P. (2004) Data informed influence analysis.  Biometrika, 91, 125-140.

Garthwaite, P.H. & Crawford, J.R. (2004).  The distribution of the difference between two t-variates and application to a test for dissociations.  Biometrika, 91, 987-994.

Gower, J.C. (2004) The geometry of biplot scaling.  Biometrika, 91,  705-714.

Gower, J.C. (2004) Classifying classification problems.  In Comptes Rendus des Iles Rencontres de la Societe Francophone de Classification, eds: M. Chavent, O. Dordan, C.C. Lacomblez, M. Langlais & B. Patouille, pp. 41-47.

Gower, J.C. & Dijksterhuis, G.B. (2004) Procrustes Problems.  Oxford University Press.

Jones, M.C. (2004) Families of distributions arising from distributions of order statistics.  Discussion paper.  Test, 13, 1-43.

Jones, M.C. (2004) On some expressions for variance, covariance, skewness and kurtosis.  Journal of Statistical Planning and Inference, 126, 97-106.

Jones, M.C. (2004) The Mobius distribution on the disc.  Annals of the Institute of Statistical Mathematics, 56, 733-742.

Jones, M.C. & Larsen, P.V. (2004) Multivariate distributions with support above the diagonal.  Biometrika, 91, 975-986.

Signorini, D.F. & Jones, M.C. (2004) Kernel estimators for univariate binary regression.  Journal of the American Statistical Association, 99, 119-126.

Wang, D.Q., Critchley, F. & Liu, I. (2004) Diagnostic analysis and perturbations in a clustered sampling model.  Communications in Statistics – Theory and Methods, 33, 2709-2721.

2003

Critchley, F. (2003) On ziggurats and dendrograms. In Between Data Science and Applied Data Analysis (eds M Schader, W Gaul & M Vichi), Springer, 191-200.

Gower, J.C. & de Rooij, M. (2003) A comparison of the multidimensional scaling of triadic and dyadic distances. Journal of Classification, 20, 115-136.

Gower, J.C. (2003) Unified biplot geometry. In Developments in Applied Statistics (eds A. Ferligoj & A. Mrvar), Department of Social Sciences, University of Ljubljana, 3-22.

Gower, J.C. (2003) Visualisation in multivariate and multidimensional data analysis. In Bulletin of the International Statistical Institute, 54, 101-104.

In-Sun, N., Mengersen, K. & Garthwaite, P.H. (2003) Multivariate meta-analysis. Statistics in Medicine, 22, 2309-2333.

Jones, M.C. & Faddy, M.J. (2003) A skew extension of the t distribution, with applications. Journal of the Royal Statistical Society, Series B, 65, 159-174.

Jones, M.C. & Koch, I. (2003) Dependence maps: local dependence in practice. Statistics and Computing, 13, 241-255.

Park, B.U., Jeong, S.O., Jones, M.C. & Kang, K.H. (2003) Adaptive variable location kernel density estimators with good performance at boundaries. Journal of Nonparametric Statistics, 15, 61-75.

de Rooij, M. & Gower, J.C. (2003) The geometry of triadic distances. Journal of Classification, 20, 181-220.

Wang, D.Q., Critchley, F. & Smith, P.J. (2003) Multiple set deletion measures and masking in regression. Communications in Statistics - Theory and Methods, 32, 407-413.

2002

Albers, C.J. & Schaafsma, W. (2002)  Estimating a density by adapting an initial guess', Computational Statistics and Data Analysis, 42:1/2, 27-36

Critchley, F., Marriott, P. & Salmon, M. (2002) On preferred point geometry in statistics. Journal of Statistical Planning and Inference, 102, 229–245.

Critchley, F. (2002) What is the dimension of a dendrogram? In Proceedings of the 9^th Congress of the French Classification Society, Toulouse, 35–38.

Critchley, F. (2002) Discussion of  ‘Recent advances in dimension reduction for regression’. 2002 Proceedings of American Statistical Association meeting,  New York: American Statistical Association. [CD–ROM]

Jolliffe, I.T., Uddin, M. & Vines, S.K. (2002) Simplified EOFs – three alternatives to rotation. Climate Research, 20, 271–279.

Jones, M.C. (2002) Marginal replacement in multivariate densities, with application to skewing spherically symmetric distributions. Journal of Multivariate Analysis, 81, 85–99.

Jones, M.C. (2002) A dependent bivariate t distribution with marginals on difference degrees of freedom. Statistics and Probability Letters, 56, 163–170.

Jones, M.C. (2002) Student’s simplest distribution. The Statistician, 51, 41–49.

Jones, M.C. (2002) The complementary beta distribution. Journal of Statistical Planning and Inference, 104, 329–337.

Jones, M.C. (2002) On fractional uniform order statistics. Statistics and Probability Letters, 58, 93–96.

Jones, M.C. (2002) On Khintchine’s theorem and its place in random variate generation. The American Statistician, 56, 304–307.

Jones, M.C. & Balakrishnan, N (2002) How are moments and moments of spacings related to distribution functions? Journal of Statistical Planning and Inference, 103, 377–390.

Park, B.U., Kim, W.C. & Jones, M.C. (2002) On local likelihood density estimation. Annals of Statistics, 30, 1480–1495.

Prescott, G.J. & Garthwaite, P.H. (2002) A simple analysis of misclassified binary data with a validation sub–study. Biometrics, 58, 454–458.

2001

Al-Awadhi, S.A. & Garthwaite, P.H. (2001) Prior distribution assessment for a multivariate normal distribution: An experimental study. Journal of Applied Statistics, 28, 5–23.

Critchley, F., Atkinson, R.A., Lu, G. & Biazi, E. (2001) Influence analysis based on the case sensitivity function. Journal of the Royal Statistical Society, Series B, 63, 307–323.

Garthwaite, P.H. & Al-Awadhi, S.A. (2001) Elicitation of non-conjugate prior distributions for multivariate normal sampling. Journal of the Royal Statistical Society, Series B, 63, 95–110.

Jones, M.C. (2001) Multivariate t and beta distributions associated with the multivariate F distribution. Metrika, 54, 215–231

Jones, M.C. & Williams-Thorpe, O. (2001) An illustration of the use of an atypicality index in provenancing British stone axes. Archaeometry, 43, 1–18.

2000

Aucott, L.S., Garthwaite, P.H. & Curral, J. (2000) Regression methods for high-dimensional multicollinear data. Communications in Statistics: Simulation and Computation, 29, 1021–1037.

Cook, R.D. & Critchley, F. (2000) Identifying regression outliers and mixtures graphically. Journal of the American Statistical Association, 95, 781–794.

Critchley, F. & Wang, D.Q. (2000) Multiple deletion measures and conditional influence in regression. Communications in Statistics: Theory and Methods, 29, 2391–2404.

Critchley, F., Marriott, P.K. & Salmon, M.H. (2000) An elementary account of Amari’s expected geometry. Applications of Differential Geometry to Econometrics, Cambridge University Press, 294–315.

Critchley, F. (2000) On a framework for dissimilarity analysis. Data Analysis: Scientific Modeling and Practical Application, Springer-Verlag: Berlin. Gaul, W., Opitz, O. & Schader, M. (Eds.) 121–134. (Invited paper).

Gower, J.C. (2000) Rank-one and rank-two departures from symmetry. Computational Statistics and Data Analysis, 33, 177–188.

Queen, C.M. & Whitlock, M.E. (2000) Modelling a traffic network with missing data. Journal of Forecasting, 19, 561–574.

Vines, S.K. (2000) Simple principal components. Applied Statistics, 49, 441–451.

1999

Gower, J.C. & Krzanowski, W.J. (1999) Analysis of distance for structured multivariate data. Applied Statistics, 48, 505–19.

Gower, J.C., Meulman, J.J. & Arnold, G.M. (1999) Non-metric linear biplots. Journal of Classification, 16, 181–196.

Taylor, P.C. & Hand, D.J. (1999) Finding superclassifications with acceptable error rate. Journal of Applied Statistics, 26, 579–90.

1998

Al-Awadhi, S.A. & Garthwaite P.H. (1998) An elicitation method for multivariate normal distributions. Communications in Statistics: Theory and Methods 27, 1123–1142.

Gower, J.C. & Zielman, B. (1998) Orthogonality and its approximation in the analysis of asymmetry. Linear Algebra and its Applications, 278, 183–93.

Jones, M.C. (1998) Constant local dependence. Journal of Multivariate Analysis, 64, 148–55.

Vines, S.K. & Jones, M.C. (1998) Choosing the smoothing parameter for unordered multinomial data. Test, 7, 413–426.

1997

Critchley, F. & Fichet, B. (1997) On (super-) spherical distance matrices and two results from Schoenberg. Linear Algebra and its Applications, 251, 145–165.

1996

Critchley, F., Marriott, P.K. & Salmon, M.H. (1996) On the differential geometry of the Wald test with nonlinear restrictions. Econometrica, 64, 1213–1222.

Garthwaite, P.H. & Dickey, J.M. (1996) Quantifying and using expert opinion for variable-selection problems in regression. Chemometrics and Intelligent Laboratory Systems, 35, 1–43.

Garthwaite, P.H. (1996) Confidence intervals from randomization tests. Biometrics, 52, 1387–1393.

Gower, J.C. & Hand D.J. (1996) Biplots Chapman & Hall/CRC.

Jones, M.C. (1996) The local dependence function. Biometrika, 83, 899–904.

Queen, C.M. & Smith, J.Q. (1996) Bayesian models for sparse probability tables. Annals of Statistics, 24, 2178–2198.

Vines, S.K., Gilks, W.R. & Wild, P. (1996) Fitting Bayesian multiple random effects models. Statistics and Computing, 6, 337–346.

Last Updated August 2009