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Research

In recent past, my research has focused on the following broad themes:

  • Modeling high-dimensional (multivariate) time series and spatial fields
  • Extremal behavior of dynamical systems modeling physical phenomena
  • Sampling and streaming algorithms in connection to “big data”
  • Modeling scaling and self-similar phenomena

    • These themes are discussed in greater detail below.

    Modeling high-dimensional (multivariate) time series and spatial fields: Here is a sample of recent and current works in this area:

    1. “Two sample tests for high-dimensional autocovariances” (with C. Baek, K. Gates and B. Leinwand). Computational Statistics and Data Analysis, 153 (2021), 107067.
    2. “Stationary subspace analysis of nonstationary covariance processes: eigenstructure description and testing” (with M. Pourahmadi and R. Sundararajan), Bernoulli, 27 (2021), pp. 381–418.
    3. “Periodic dynamic factor models” (with C. Baek and R. Davis). Electronic Journal of Statistics, 12 (2018), pp. 4377–4411.
    4. “Sparse seasonal and periodic vector autoregressive modeling” (with C. Baek and R. Davis). Computational Statistics and Data Analysis 106 (2017), pp. 103-126.
    5. “Modeling bivariate long-range dependence with general phase” (with S. Kechagias), Journal of Time Series Analysis, 41 (2020), pp. 268-292t.
    6. “Multivariate count time series with flexible autocovariances” (with J. Livsey, S. Kechagias and R. Lund). The Annals of Applied Statistics, 12 (2018), pp. 408–431.
    7. “Smoothing windows for the synthesis of Gaussian stationary random fields using circulant matrix embedding” (with H. Helgason and P. Abry). Journal of Computational and Graphical Statistics 23 (2014), pp. 616–635.

    The topics of interest include: sparse modeling with regularization (lasso and variants), dimension reduction with factor models, change points, non-linear models, classification and clustering, and others. The data for which the methods are explored and developed come from Economics and Finance, Psychology, Neuroscience, Environmental Sciences, Geophysics. Current collaborators in this area include: R. Davis (Columbia), K. Gates (UNC, Psychology and Neuroscience), R. Lund (UC Santa Cruz), and former PhD students C. Baek (Sungkyunkwan University, Korea) and S. Kechagias (SAS Institute).

    Extremal behavior of dynamical systems modeling physical phenomena: This research direction has been pursued in collaboration with researchers in US Navy, and more specifically the NSWC Carderock Division (NSWCCD), Maryland, where I spent 10-weeks as a senior fellow of the ONR summer faculty program a number of years. One basic problem of interest in this area concerns understanding extreme motions of a ship, which we have studied from various angles, including statistics, stochastic dynamics and differential equations, naval architecture and others. Here is a sample of past and current work:

    1. “Pitfalls of data-driven peaks-over-threshold analysis: perspectives from extreme ship motions,” Probabilistic Engineering Mechanics, 60 (2020), 103053.
    2. “On extreme value properties of vertical bending moment” (with T. Sapsis, K. Weems and V. Belenky), Proceedings of the 33rd Symposium on Naval Hydrodynamics, 2020.
    3. “On extending multifidelity uncertainty quantification methods from non-rare to rare problems” (with B. Brown), Proceedings of 17th Intl. Ship Stability Workshop, Helsinki, Finland, 2019.
    4. “Distribution tail structure and extreme value analysis of constrained piecewise linear oscillators” (with V. Belenky, D. Glotzer and T. Sapsis). Probabilistic Engineering Mechanics, 57 (2019), pp. 1-13.
    5. “Confidence intervals for exceedance probabilities with application to extreme ship motions” (with D. Glotzer, V. Belenky, B. Campbell and T. Smith). Revstat, 15 (2017), pp. 537–563.
    6. “Application of the envelope peaks over threshold (EPOT) method for probabilistic assessment of dynamic stability” (with V. Belenky and B. Campbell). Ocean Engineering 120 (2016), pp. 298–304.
    7. “Split-time / critical derivative value approach for evaluation of probability of capsizing of a ship in irregular waves” (with V. Belenky, K. Weems and K. Spyrou). The 7th International Conference on Computational Stochastic Mechanics (CSM-7), Santorini, Greece, 2014.

    The data of interest in these applications come from ship motions (generated by high-fidelity computer codes or gathered in the “field”), satellite and buoy measurements of wave heights. Main collaborators in this area include: V. Belenky, K. Weems and T. Smith (all at NSWCCD of US Navy), T. Sapsis (MIT), and a former PhD student D. Glotzer (Meredith College).

    Sampling and streaming algorithms in connection to “big data”: My previous work in this area focused on understanding how various methods to sample packets in Internet traffic can be used to infer characteristics of the underlying original traffic, more specifically, the so-called flow size and duration distributions. More recently, I have also been looking into problems on sampling and streaming large graphs (networks). Data of interest in these applications come from Internet traffic, and social, www and other networks. Here is a sample of works on these topics:

    1. “Sampling methods and estimation of triangle count distributions in large networks” (with N. Antunes and T. Guo), Network Science (2021).
    2. “Sampling-based estimation of in-degree distribution with applications to directed complex networks” (with N. Antunes, S. Bhamidi, T. Guo and B. Wang), Journal of Computational and Graphical Statistics (2021).
    3. “Regularized inversion of flow size distribution” (with N. Antunes and G. Jacinto), INFOCOM, 2019.
    4. “Skampling for the flow duration distribution” (with N. Antunes and D. Veitch), Proceedings of 29th International Teletraffic Congress, Genoa, Italy, 2017.
    5. “Estimation of flow distributions from sampled traffic” (with N. Antunes). ACM Transactions on Modeling and Performance Evaluation of Computing Systems, 1 (2016), Article No. 11.
    6. “Semi-stable non-Gaussian limits arising in sampling of finite renewal processes” (with R. Chaudhuri). Bernoulli, 22 (2016), pp. 1055–1092.
    7. “Probabilistic sampling of finite renewal processes” (with N. Antunes). Bernoulli 17 (2011), pp. 1285–1326.

    My collaborators include N. Antunes (Algarve, Portugal), D. Veitch (University of Technology Sydney), S. Bhamidi (UNC).

    Modeling scaling and self-similar phenomena: This theme was the main driver of my research efforts since receiving PhD and joining the department in 2002. These efforts have concluded with a comprehensive monograph on the subject and another smaller specialized textbook:

    1. Long-Range Dependence and Self-Similarity (with M. S. Taqqu). Cambridge University Press, 688 pages, 2017.
    2. Stable Self-Similar Processes with Stationary Increments (with M. S. Taqqu). Springer-Briefs, 135 pages, 2017.

    I obviously like this area and still dabble in it with this or that project.