Peter D. Hoff

  1. Marginally Specified Priors for Nonparametric Bayesian Estimation.

    Authors: Peter D. Hoff, David B. Dunson, David C. Kessler
    Subjects: Methodology
    Abstract

    Prior specification for nonparametric Bayesian inference involves the
    difficult task of quantifying prior knowledge about a parameter of high, often
    infinite, dimension. Realistically, a statistician is unlikely to have informed
    opinions about all aspects of such a parameter, but may have real information
    about functionals of the parameter, such the population mean or variance.

  2. Small-Sample Behavior of Novel Phase I Cancer Trial Designs.

    Authors: Assaf P. Oron, Peter D. Hoff
    Subjects: Methodology
    Abstract

    Novel dose-finding designs, using estimation to assign the best estimated
    maximum- tolerated-dose (MTD) at each point in the experiment, most commonly
    via Bayesian techniques, have recently entered large-scale implementation in
    Phase I cancer clinical trials. We examine the small-sample behavior of these
    "Bayesian Phase I" (BP1) designs, and also of non-Bayesian designs sharing the
    same main "long-memory" traits (hereafter: LMP1s).

  3. Information bounds for Gaussian copulas.

    Authors: Peter D. Hoff, Jon A. Wellner, Xiaoyue Niu
    Subjects: Statistics
    Abstract

    Often of primary interest in the analysis of multivariate data are the copula
    parameters describing the dependence among the variables, rather than the
    univariate marginal distributions. Since the ranks of a multivariate dataset
    are invariant to changes in the univariate marginal distributions, rank-based
    procedures are natural candidates as semiparametric estimators of copula
    parameters. Asymptotic information bounds for such estimators can be obtained
    from an asymptotic analysis of the rank likelihood, i.e. the probability of the
    multivariate ranks.

  4. A Mixed Effects Model for Longitudinal Relational and Network Data, with Applications to International Trade and Conflict.

    Authors: Peter D. Hoff, Anton H. Westveld
    Subjects: Methodology
    Abstract

    The focus of this paper is an approach to the modeling of longitudinal social
    relational or network data. Such data arise from measurements on pairs of
    objects or actors made at regular temporal intervals, resulting in a social
    network for each point in time. In this article we represent the network and
    temporal dependencies with a random effects model, resulting in a stochastic
    process defined by a set of stationary covariance matrices.

  5. Separable covariance arrays via the Tucker product, with applications to multivariate relational data.

    Authors: Peter D. Hoff
    Subjects: Methodology
    Abstract

    Modern datasets are often in the form of matrices or arrays,potentially
    having correlations along each set of data indices. For example, data involving
    repeated measurements of several variables over time may exhibit temporal
    correlation as well as correlation among the variables. A possible model for
    matrix-valued data is the class of matrix normal distributions, which is
    parametrized by two covariance matrices, one for each index set of the data. In
    this article we describe an extension of the matrix normal model to accommodate
    multidimensional data arrays, or tensors.

  6. A Statistical View of Learning in the Centipede Game.

    Authors: Peter D. Hoff, Anton H. Westveld
    Subjects: Methodology
    Abstract

    In this article we evaluate the statistical evidence that a population of
    students learn about the sub-game perfect Nash equilibrium of the centipede
    game via repeated play of the game. This is done by formulating a model in
    which a player's error in assessing the utility of decisions changes as they
    gain experience with the game. We first estimate parameters in a statistical
    model where the probabilities of choices of the players are given by a Quantal
    Response Equilibrium (QRE) (McKelvey and Palfrey, 1995, 1996, 1998), but are
    allowed to change with repeated play.

  7. Convergence of Nonparametric Long-Memory Phase I Designs.

    Authors: Assaf P. Oron, Peter D. Hoff
    Subjects: Methodology
    Abstract

    We examine Phase I cancer clinical trial designs that use toxicity estimates
    based on all available data at each dose-allocation decision, but refrain from
    employing parametric models or Bayesian decision rules. We show that one such
    design family, called here "interval designs", converges almost surely to the
    maximum tolerated dose under fairly general conditions. Another family called
    "point designs" does not converge.

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