Most of the members of this group are from the Statistics Section and Biomaths research group of the Department of Mathematics. Below you can find a list of research areas that members of this group are currently working on and/or would like to work on by applying their developed mathematical and statistical methods.

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    Avella M, Battey HS, Fan J, Li Qet al., 2018,

    Robust estimation of high-dimensional covariance and precision matrices

    , Biometrika, Vol: 105, Pages: 271-284, ISSN: 0006-3444

    High-dimensional data are often most plausibly generated from distributions with complex structure and leptokurtosis in some or all components. Covariance and precision matrices provide a useful summary of such structure, yet the performance of popular matrix estimators typically hinges upon a sub-Gaussianity assumption. This paper presents robust matrix estimators whose performance is guaranteed for a much richer class of distributions. The proposed estimators, under a bounded fourth moment assumption, achieve the same minimax convergence rates as do existing methods under a sub-Gaussianity assumption. Consistency of the proposed estimators is also established under the weak assumption of bounded2+ϵmoments forϵ∈(0,2). The associated convergence rates depend onϵ.

    Battey HS, Zhu Z, Fan J, Lu J, Liu Het al., 2018,

    Distributed testing and estimation in sparse high dimensional models.

    , Annals of Statistics, Vol: 46, Pages: 1352-1382

    This paper studies hypothesis testing and parameter estimation inthe context of the divide-and-conquer algorithm. In a unified likelihoodbased framework, we propose new test statistics and point estimatorsobtained by aggregating various statistics fromksubsamples of sizen/k, wherenis the sample size. In both low dimensional and sparsehigh dimensional settings, we address the important question of howlargekcan be, asngrows large, such that the loss of efficiency dueto the divide-and-conquer algorithm is negligible. In other words,the resulting estimators have the same inferential efficiencies andestimation rates as an oracle with access to the full sample. Thoroughnumerical results are provided to back up the theory.

    Aryaman J, Hoitzing H, Burgstaller JP, Johnston IG, Jones NSet al., 2017,

    Mitochondrial heterogeneity, metabolic scaling and cell death

    , BIOESSAYS, Vol: 39, ISSN: 0265-9247
    Aryaman J, Johnston IG, Jones NS, 2017,

    Mitochondrial DNA density homeostasis accounts for a threshold effect in a cybrid model of a human mitochondrial disease

    , BIOCHEMICAL JOURNAL, Vol: 474, Pages: 4019-4034, ISSN: 0264-6021
    Battey H, 2017,

    Eigen structure of a new class of covariance and inverse covariance matrices

    , Bernoulli, Vol: 23, Pages: 3166-3177, ISSN: 1350-7265
    Cox DR, Battey HS, 2017,

    Large numbers of explanatory variables, a semi-descriptive analysis

    , Proceedings of the National Academy of Sciences, Vol: 114, Pages: 8592-8595, ISSN: 0027-8424
    Fulcher BD, Jones NS, 2017,

    hctsa: A Computational Framework for Automated Time-Series Phenotyping Using Massive Feature Extraction

    , CELL SYSTEMS, Vol: 5, Pages: 527-+, ISSN: 2405-4712
    Griffié J, Shlomovich L, Williamson DJ, Shannon M, Aaron J, Khuon S, Burn LG, Boelen L, Peters R, Cope AP, Cohen EAK, Rubin-Delanchy P, Owen DMet al., 2017,

    3D Bayesian cluster analysis of super-resolution data reveals LAT recruitment to the T cell synapse

    , Scientific Reports, Vol: 7

    © 2017 The Author(s). Single-molecule localisation microscopy (SMLM) allows the localisation of fluorophores with a precision of 10-30 nm, revealing the cell's nanoscale architecture at the molecular level. Recently, SMLM has been extended to 3D, providing a unique insight into cellular machinery. Although cluster analysis techniques have been developed for 2D SMLM data sets, few have been applied to 3D. This lack of quantification tools can be explained by the relative novelty of imaging techniques such as interferometric photo-activated localisation microscopy (iPALM). Also, existing methods that could be extended to 3D SMLM are usually subject to user defined analysis parameters, which remains a major drawback. Here, we present a new open source cluster analysis method for 3D SMLM data, free of user definable parameters, relying on a model-based Bayesian approach which takes full account of the individual localisation precisions in all three dimensions. The accuracy and reliability of the method is validated using simulated data sets. This tool is then deployed on novel experimental data as a proof of concept, illustrating the recruitment of LAT to the T-cell immunological synapse in data acquired by iPALM providing ~10 nm isotropic resolution.

    Wills QF, Mellado-Gomez E, Nolan R, Warner D, Sharma E, Broxholme J, Wright B, Lockstone H, James W, Lynch M, Gonzales M, West J, Leyrat A, Padilla-Parra S, Filippi S, Holmes C, Moore MD, Bowden Ret al., 2017,

    The nature and nurture of cell heterogeneity: accounting for macrophage gene-environment interactions with single-cell RNA-Seq

    , BMC GENOMICS, Vol: 18, ISSN: 1471-2164
    Battey H, Feng Q, Smith RJ, 2016,

    Improving confidence set estimation when parameters are weakly identified

    , Statistics and Probability Letters, Vol: 118, Pages: 117-123, ISSN: 0167-7152

    © 2016 Elsevier B.V. We consider inference in weakly identified moment condition models when additional partially identifying moment inequality constraints are available. We detail the limiting distribution of the estimation criterion function and consequently propose a confidence set estimator for the true parameter.

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