Research overview

• Transposable data
  Many statistical data matrices have both many rows and many columns. Often both rows and columns correspond to entities of interest (e.g. proteins and genes or movies and customers) instead of being IID. It is not just p>n because in these problems you could argue which dimension has p and which has n levels. So questions arise as to how to bootstrap, cross-validate and visualize such data. For example:
  • Transposable data course notes
  • How to bootstrap (with Dean Eckles).
  • How to cross-validate (with Patrick Perry).
  • A copula plot to visualize incidence matrices (with Justin Dyer).

• Empirical likelihood
  Much of statistical inference is organized around the likelihood function. That usually requires an unpleasant assumption that the data come from one of the popular parametric families. Empirical likelihood uses a data determined likelihood function to avoid this. There is no loss of power up to second order asymptotics and it can either win or lose compared to the true likelihood at third order.
  • Web page for the book
  • 1988 Biometrica paper at JSTOR for univariate mean
  • 1990 Annals of Statistics paper at JSTOR for multivariate mean
  • 1991 Annals of Statistics paper at JSTOR for linear models
  • Escaping the convex hull EJS (with Sarah Emerson)

• Monte Carlo and quasi-Monte Carlo
  Monte Carlo integration typically gets a root mean square error of O(n^-1/2). Quasi-Monte Carlo (QMC) sampling uses deterministic points more uniformly distributed than random ones, and it gets an error of O(n^(-1+epsilon)) for any epsilon>0. Randomizing the QMC points (while preserving their uniformity) allows replication based error estimates. It can also bring error cancellation leading to RMSE O(n^(-3/2 + epsilon)).
  • Monte Carlo course
  • Variance of scrambled net quadrature at JSTOR
  • Conditions for which RQMC can reach O(n^(-3/2+epsilon)) RMSE at JSTOR
  • QMC for MCMC with Seth Tribble and with Su Chen and Josef Dick
  • Effective dimension with Russ Caflisch and Bill Morokoff (paywalled)
  • Generalized Sobol' indices at arXiv

• Bioinformatics
  The following papers are motivated by large data problems in biology. Most of the work was done with the Stuart Kim lab or as followup on theoretical holes that became evident in that work.
  • Plaid models with Laura Lazzeroni.
  • A gene recommender for completing partially known clusters (with Kim lab). It is a kind of supervised correlation.
  • The AGEMAP project (with Kim lab and Kevin Becker's lab at the National Institute on Aging).
  • Another look at Karl Pearson's meta-analysis wrongly thought for over 50 years to be inadmissible. It actually beats Fisher's test on certain alternatives, when the null hypotheses tend to be violated in the same direction as each other.
  • Aging in the human kidney and muscle with the Kim lab.
  • For correlated hypothesis tests this paper finds the variance of the number of false dscoveries.