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  • JOURNAL ARTICLE
    Battey H, 2017,

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

    , Bernoulli, Vol: 23, Pages: 3166-3177, ISSN: 1350-7265
  • JOURNAL ARTICLE
    Bennedsen M, Lunde A, Pakkanen MS, 2017,

    Hybrid scheme for Brownian semistationary processes

    , Finance and Stochastics, Vol: 21, Pages: 931-965, ISSN: 1432-1122

    We introduce a simulation scheme for Brownian semistationary processes, whichis based on discretizing the stochastic integral representation of the processin the time domain. We assume that the kernel function of the process isregularly varying at zero. The novel feature of the scheme is to approximatethe kernel function by a power function near zero and by a step functionelsewhere. The resulting approximation of the process is a combination ofWiener integrals of the power function and a Riemann sum, which is why we callthis method a hybrid scheme. Our main theoretical result describes theasymptotics of the mean square error of the hybrid scheme and we observe thatthe scheme leads to a substantial improvement of accuracy compared to theordinary forward Riemann-sum scheme, while having the same computationalcomplexity. We exemplify the use of the hybrid scheme by two numericalexperiments, where we examine the finite-sample properties of an estimator ofthe roughness parameter of a Brownian semistationary process and study MonteCarlo option pricing in the rough Bergomi model of Bayer et al. (2015),respectively.

  • JOURNAL ARTICLE
    Bodenham DA, Adams NM, 2017,

    Continuous monitoring for changepoints in data streams using adaptive estimation

    , STATISTICS AND COMPUTING, Vol: 27, Pages: 1257-1270, ISSN: 0960-3174
  • JOURNAL ARTICLE
    Chandna S, Walden AT, 2017,

    A Frequency Domain Test for Propriety of Complex-Valued Vector Time Series

    , IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 65, Pages: 1425-1436, ISSN: 1053-587X
  • JOURNAL ARTICLE
    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
  • JOURNAL ARTICLE
    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.

  • JOURNAL ARTICLE
    Pakkanen MS, Sottinen T, Yazigi A, 2017,

    On the conditional small ball property of multivariate Lévy-driven moving average processes

    , Stochastic Processes and their Applications, Vol: 127, Pages: 749-782, ISSN: 0304-4149

    © 2016 Elsevier B.V. We study whether a multivariate Lévy-driven moving average process can shadow arbitrarily closely any continuous path, starting from the present value of the process, with positive conditional probability, which we call the conditional small ball property. Our main results establish the conditional small ball property for Lévy-driven moving average processes under natural non-degeneracy conditions on the kernel function of the process and on the driving Lévy process. We discuss in depth how to verify these conditions in practice. As concrete examples, to which our results apply, we consider fractional Lévy processes and multivariate Lévy-driven Ornstein–Uhlenbeck processes.

  • JOURNAL ARTICLE
    Zhang Q, Filippi S, Gretton A, Sejdinovic Det al., 2017,

    Large-Scale Kernel Methods for Independence Testing

    , Statistics and Computing, ISSN: 1573-1375

    Representations of probability measures in reproducing kernel Hilbert spacesprovide a flexible framework for fully nonparametric hypothesis tests ofindependence, which can capture any type of departure from independence,including nonlinear associations and multivariate interactions. However, theseapproaches come with an at least quadratic computational cost in the number ofobservations, which can be prohibitive in many applications. Arguably, it isexactly in such large-scale datasets that capturing any type of dependence isof interest, so striking a favourable tradeoff between computational efficiencyand test performance for kernel independence tests would have a direct impacton their applicability in practice. In this contribution, we provide anextensive study of the use of large-scale kernel approximations in the contextof independence testing, contrasting block-based, Nystrom and random Fourierfeature approaches. Through a variety of synthetic data experiments, it isdemonstrated that our novel large scale methods give comparable performancewith existing methods whilst using significantly less computation time andmemory.

  • JOURNAL ARTICLE
    Zhuang L, Walden AT, 2017,

    Sample Mean Versus Sample Frechet Mean for Combining Complex Wishart Matrices: A Statistical Study

    , IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 65, Pages: 4551-4561, ISSN: 1053-587X
  • CONFERENCE PAPER
    Bakoben M, Adams N, Bellotti A, 2016,

    Uncertainty aware clustering for behaviour in enterprise networks

    , 16th IEEE International Conference on Data Mining (ICDM), Publisher: IEEE, Pages: 269-272, ISSN: 2375-9232
  • JOURNAL ARTICLE
    Bakoben M, Bellotti A, Adams N, 2016,

    Improving clustering performance by incorporating uncertainty

    , PATTERN RECOGNITION LETTERS, Vol: 77, Pages: 28-34, ISSN: 0167-8655
  • JOURNAL ARTICLE
    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.

  • JOURNAL ARTICLE
    Bodenham DA, Adams NM, 2016,

    A comparison of efficient approximations for a weighted sum of chi-squared random variables

    , STATISTICS AND COMPUTING, Vol: 26, Pages: 917-928, ISSN: 0960-3174
  • CONFERENCE PAPER
    Evangelou M, Adams NM, 2016,

    Predictability of NetFlow data

    , 14th IEEE International Conference on Intelligence and Security Informatics - Cybersecurity and Big Data (IEEE ISI), Publisher: IEEE, Pages: 67-72
  • JOURNAL ARTICLE
    Filippi S, Holmes C, 2016,

    A Bayesian nonparametric approach to testing for dependence between random variables

    , Bayesian Analysis, ISSN: 1931-6690

    Nonparametric and nonlinear measures of statistical dependence between pairsof random variables are important tools in modern data analysis. In particularthe emergence of large data sets can now support the relaxation of linearityassumptions implicit in traditional association scores such as correlation.Here we describe a Bayesian nonparametric procedure that leads to a tractable,explicit and analytic quantification of the relative evidence for dependence vsindependence. Our approach uses Polya tree priors on the space of probabilitymeasures which can then be embedded within a decision theoretic test fordependence. Polya tree priors can accommodate known uncertainty in the form ofthe underlying sampling distribution and provides an explicit posteriorprobability measure of both dependence and independence. Well known advantagesof having an explicit probability measure include: easy comparison of evidenceacross different studies; encoding prior information; quantifying changes independence across different experimental conditions, and; the integration ofresults within formal decision analysis.

  • JOURNAL ARTICLE
    Filippi S, Holmes CC, Nieto-Barajas LE, 2016,

    Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures

    , Electronic Journal of Statistics, Vol: 10, Pages: 1807-1828, ISSN: 1935-7524

    We present a novel Bayesian nonparametric regression model for covariates XX and continuous response variable Y∈RY∈R. The model is parametrized in terms of marginal distributions for YY and XX and a regression function which tunes the stochastic ordering of the conditional distributions F(y|x)F(y|x). By adopting an approximate composite likelihood approach, we show that the resulting posterior inference can be decoupled for the separate components of the model. This procedure can scale to very large datasets and allows for the use of standard, existing, software from Bayesian nonparametric density estimation and Plackett-Luce ranking estimation to be applied. As an illustration, we show an application of our approach to a US Census dataset, with over 1,300,000 data points and more than 100 covariates.

  • CONFERENCE PAPER
    Flaxman S, Sejdinovic D, Cunningham JP, Filippi Set al., 2016,

    Bayesian Learning of Kernel Embeddings

    , UAI'16

    Kernel methods are one of the mainstays of machine learning, but the problemof kernel learning remains challenging, with only a few heuristics and verylittle theory. This is of particular importance in methods based on estimationof kernel mean embeddings of probability measures. For characteristic kernels,which include most commonly used ones, the kernel mean embedding uniquelydetermines its probability measure, so it can be used to design a powerfulstatistical testing framework, which includes nonparametric two-sample andindependence tests. In practice, however, the performance of these tests can bevery sensitive to the choice of kernel and its lengthscale parameters. Toaddress this central issue, we propose a new probabilistic model for kernelmean embeddings, the Bayesian Kernel Embedding model, combining a Gaussianprocess prior over the Reproducing Kernel Hilbert Space containing the meanembedding with a conjugate likelihood function, thus yielding a closed formposterior over the mean embedding. The posterior mean of our model is closelyrelated to recently proposed shrinkage estimators for kernel mean embeddings,while the posterior uncertainty is a new, interesting feature with variouspossible applications. Critically for the purposes of kernel learning, ourmodel gives a simple, closed form marginal pseudolikelihood of the observeddata given the kernel hyperparameters. This marginal pseudolikelihood caneither be optimized to inform the hyperparameter choice or fully Bayesianinference can be used.

  • JOURNAL ARTICLE
    Lee SMS, Young GA, 2016,

    Distribution of likelihood-based p-values under a local alternative hypothesis

    , BIOMETRIKA, Vol: 103, Pages: 641-652, ISSN: 0006-3444
  • JOURNAL ARTICLE
    Lukkarinen J, Pakkanen MS, 2016,

    Arbitrage without borrowing or short selling?

    , Mathematics and Financial Economics, Vol: 11, Pages: 263-274, ISSN: 1862-9679

    We show that a trader, who starts with no initial wealth and is not allowedto borrow money or short sell assets, is theoretically able to attain positivewealth by continuous trading, provided that she has perfect foresight of future asset prices, given by a continuous semimartingale. Such an arbitrage strategy can be constructed as a process of finite variation that satisfies a seemingly innocuous self-financing condition, formulated using a pathwiseRiemann-Stieltjes integral. Our result exemplifies the potential intricacies offormulating economically meaningful self-financing conditions in continuoustime, when one leaves the conventional arbitrage-free framework.

  • JOURNAL ARTICLE
    Nieto-Reyes A, Battey H, 2016,

    A Topologically Valid Definition of Depth for Functional Data

    , Statistical Science, Vol: 31, Pages: 61-79, ISSN: 0883-4237
  • CONFERENCE PAPER
    Noble J, Adams NM, 2016,

    Correlation-based Streaming Anomaly Detection in Cyber-Security

    , 16th IEEE International Conference on Data Mining (ICDM), Publisher: IEEE, Pages: 311-318, ISSN: 2375-9232
  • JOURNAL ARTICLE
    Pakkanen MS, Réveillac A, 2016,

    Functional limit theorems for generalized variations of the fractional Brownian sheet

    , Bernoulli, Vol: 22, Pages: 1671-1708, ISSN: 1350-7265

    We prove functional central and non-central limit theorems for generalizedvariations of the anisotropic d-parameter fractional Brownian sheet (fBs) forany natural number d. Whether the central or the non-central limit theoremapplies depends on the Hermite rank of the variation functional and on thesmallest component of the Hurst parameter vector of the fBs. The limitingprocess in the former result is another fBs, independent of the original fBs,whereas the limit given by the latter result is an Hermite sheet, which isdriven by the same white noise as the original fBs. As an application, wederive functional limit theorems for power variations of the fBs and discusswhat is a proper way to interpolate them to ensure functional convergence.

  • CONFERENCE PAPER
    Plasse J, Adams N, 2016,

    Handling Delayed Labels in Temporally Evolving Data Streams

    , 4th IEEE International Conference on Big Data (Big Data), Publisher: IEEE, Pages: 2416-2424
  • CONFERENCE PAPER
    Rubin-Delanchy P, Adams NM, Heard NA, 2016,

    Disassortativity of Computer Networks

    , 14th IEEE International Conference on Intelligence and Security Informatics - Cybersecurity and Big Data (IEEE ISI), Publisher: IEEE, Pages: 243-247
  • JOURNAL ARTICLE
    Schneider-Luftman D, Walden AT, 2016,

    Partial Coherence Estimation via Spectral Matrix Shrinkage under Quadratic Loss

    , IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 64, Pages: 5767-5777, ISSN: 1053-587X
  • CONFERENCE PAPER
    Whitehouse M, Evangelou M, Adams NM, 2016,

    Activity-based temporal anomaly detection in enterprise-cyber security

    , 14th IEEE International Conference on Intelligence and Security Informatics - Cybersecurity and Big Data (IEEE ISI), Publisher: IEEE, Pages: 248-250
  • JOURNAL ARTICLE
    Bender C, Pakkanen MS, Sayit H, 2015,

    Sticky continuous processes have consistent price systems

    , Journal of Applied Probability, Vol: 52, Pages: 586-594, ISSN: 1475-6072

    Under proportional transaction costs, a price process is said to have aconsistent price system, if there is a semimartingale with an equivalentmartingale measure that evolves within the bid-ask spread. We show that acontinuous, multi-asset price process has a consistent price system, underarbitrarily small proportional transaction costs, if it satisfies a naturalmulti-dimensional generalization of the stickiness condition introduced byGuasoni [Math. Finance 16(3), 569-582 (2006)].

  • JOURNAL ARTICLE
    Cohen E, Kim D, Ober RJ, 2015,

    The Cramer Rao lower bound for point based image registration with heteroscedastic error model for application in single molecule microscopy

    , IEEE Transactions on Medical Imaging, Vol: 34, Pages: 2632-2644, ISSN: 1558-254X
  • JOURNAL ARTICLE
    DiCiccio TJ, Kuffner TA, Young GA, 2015,

    Quantifying nuisance parameter effects via decompositions of asymptotic refinements for likelihood-based statistics

    , Journal of Statistical Planning and Inference, Vol: 165, Pages: 1-12, ISSN: 1873-1171

    Accurate inference on a scalar interest parameter in the presence of a nuisance parameter may be obtained using an adjusted version of the signed root likelihood ratio statistic, in particular Barndorff-Nielsen’s R∗ statistic. The adjustment made by this statistic may be decomposed into a sum of two terms, interpreted as correcting respectively for the possible effect of nuisance parameters and the deviation from standard normality of the signed root likelihood ratio statistic itself. We show that the adjustment terms are determined to second-order in the sample size by their means. Explicit expressions are obtained for the leading terms in asymptotic expansions of these means. These are easily calculated, allowing a simple way of quantifying and interpreting the respective effects of the two adjustments, in particular of the effect of a high dimensional nuisance parameter. Illustrations are given for a number of examples, which provide theoretical insight to the effect of nuisance parameters on parametric inference. The analysis provides a decomposition of the mean of the signed root statistic involving two terms: the first has the property of taking the same value whether there are no nuisance parameters or whether there is an orthogonal nuisance parameter, while the second is zero when there are no nuisance parameters. Similar decompositions are discussed for the Bartlett correction factor of the likelihood ratio statistic, and for other asymptotically standard normal pivots.

  • JOURNAL ARTICLE
    DiCiccio TJ, Kuffner TA, Young GA, Zaretzki Ret al., 2015,

    STABILITY AND UNIQUENESS OF p-VALUES FOR LIKELIHOOD-BASED INFERENCE

    , STATISTICA SINICA, Vol: 25, Pages: 1355-1376, ISSN: 1017-0405

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