Seminar Schedule
Seminars are held on Thursdays from 4:00 p.m.  5:00 p.m. in GriffinFloyd 100 unless otherwise noted.
Refreshments are available before the seminars from 3:30 p.m.  4:00 p.m. in GriffinFloyd Hall 230.
Date  Speaker  Comments  

Jan 22 (Tue)  Dawn Woodard (Duke)  Convergence of Parallel and Simulated Tempering on Multimodal Distributions 

Feb 7  Guilherme Rocha (Berkeley)  Designing Penalty Functions for Grouped and Hierarchical Selection  
Feb 12 (Tue)  Omar De la Cruz (Chicago)  A geometric approach in the analysis of biological data  
Feb 14  Bodhisattva Sen (U Mich)  Bootstrap in some Nonstandard Problems  
Feb 28  Lie Wang (U Penn)  A Difference Based Method in Nonparametric Function Estimation  
Mar 27  Xiaogang Su (UCF)  
Apr 3  Sanat Sarkar (Temple)  A Review of Results on False Discovery Rate  
Apr 11 (Fri)  Arthur Berg (UF)  Nonparametric Estimation at a Semiparametric Rate  UF/FSU Colloquium (in Tallahassee) 
Apr 17  Alan Agresti (UF)  PseudoScore Confidence Intervals for Categorical Data Analyses 
Convergence of Parallel and Simulated Tempering on Multimodal Distributions 
Dawn Woodward (Duke) Sampling methods such as Markov chain Monte Carlo are ubiquitous in Bayesian statistics, statistical mechanics, and theoretical computer science. However, when the distribution being sampled is multimodal many of these techniques require long running times to obtain reliable answers. In statistics, multimodal posterior distributions arise in model selection problems, mixture models, and nonparametric models among others. Parallel and simulated tempering (PT and ST) are Markov chain methods that are designed to sample efficiently from multimodal distributions; we address the extent to which this is achieved. We obtain general bounds on the convergence rate of PT and ST. We then use these bounds to evaluate the running time of PT and ST as a function of the parameter dimension, for multimodal examples including several normal mixture and discrete Markov random field distributions. We categorize the distributions into those for which PT and ST are rapidly mixing, meaning that the running time increases polynomially in the parameter dimension, and those for which PT and ST are torpidly mixing, meaning that the running time increases exponentially. 
Designing Penalty Functions for Grouped and Hierarchical Selection 
Guilherme Rocha (Berkeley) More recently, penalization by the L1norm (lasso) has enjoyed a lot of attention. L1penalized estimates are cheaper to compute (convex optimization) and lead to more stable model estimates than their L0 counterparts. In this talk, I will present the Composite Absolute Penalties (CAP) family of penalties. CAP penalties allow given grouping and hierarchical relationships between the predictors to be expressed. They are built by defining groups of variables and combining the properties of norm penalties at the across group and within group levels. Grouped selection occurs for nonoverlapping groups. Hierarchical variable selection is reached by defining groups with particular overlapping patterns. Under easily verifiable assumptions, CAP penalties are convex: an attractive property from a computational standpoint. Within this subfamily, unbiased estimates of the degrees of freedom (df) exist so the regularization parameter is selected without crossvalidation. Simulation results show that CAP improves on the predictive performance of the LASSO for cases with p>>n and misspecified groupings. This is joint work with Peng Zhao and Bin Yu. 
A geometric approach in the analysis of biological data 
Omar De la Cruz (Chicago) This approach leads in a natural way to the problem of manifold learning. We will present a new approach to this problem, and describe a way to integrate manifold learning with more traditional statistical procedures, like regression, as a way to obtain more easily interpretable inferences. In particular, after learning the geometry of a manifold underlying the overall distribution of the data, one can use that manifold as a "generalized predictor" in regression analyses. This is useful in at least two ways: First, it makes it possible to establish which coordinates contribute significantly to the geometric structure (in the cell cycle case, one can establish or verify the annotation of genes as cycle regulated). Second, it makes it possible to adjust for the influence of the geometric structure, in order to more accurately measure other properties of the individuals. For example, in studies of gene expression in single cells, adjusting for the cell cycle allows a more accurate estimation of other characteristic (e.g., finding cell subpopulations). In our second example, we show how this can be used to adjust for population structure in genetic association studies, as a nonlinear generalization of the approach based on principal components. 
Bootstrap in some Nonstandard Problems 
Bodhisattva Sen (U Mich) The talk will consider some issues with the consistency of different bootstrap methods for constructing confidence intervals in two nonstandard problems characterized by shape restricted estimation. The study of consistency of bootstrap methods in these problems is motivated by the problem of estimating dark matter distribution in Astronomy. The Grenander estimator, the nonparametric maximum likelihood estimator of an unknown nonincreasing density function f on [0, ∞), is a prototypical example of a class of shape constrained estimators that converge at rate cuberoot n. We focus on this example and illustrate different approaches of constructing confidence intervals for f(t_{0}), for 0 < t_{0} < ∞. It is claimed that the bootstrap estimate of the sampling distribution of the Grenander estimator, when generating bootstrap samples from the empirical distribution function (e.d.f.) or its least concave majorant (the maximum likelihood estimate), does not have any weak limit, conditional on the data, in probability. The other problem arises in Astronomy and is similar to the Wicksell's Corpuscle problem (1925, Biometrika). We observe (X_{1}, X_{2}), the first two coordinates of a three dimensional spherically symmetric random vector (X_{1}, X_{2}, X_{3}). Interest focuses on estimating F, the distribution function of X_{1}^{2} + X_{2}^{2} + X_{3}^{2}. This gives rise to an inverse problem with missing data. We propose two estimators of F and derive their limit distributions. Although the normalized estimators of F converge to a normal distribution, the nonstandard asymptotics involved with the nonstandard rate of convergence (n / log n)^{1/2}, cast doubt on the consistency of bootstrap methods. We focus on bootstrapping from the e.d.f. of data, and show that the estimates can be bootstrapped consistently. A comparison of the two examples sheds light on some of the reasons for the (in)consistency of bootstrap methods. 
A Difference Based Method in Nonparametric Function Estimation 
Lie Wang (U Penn) Variance function estimation and semiparametric regression are important problems in many contexts with a wide range of applications. In this talk I will present some new results on these two problems. A consistent theme is the use of a difference based method. I will begin with a minimax analysis of the variance function estimation in heteroscedastic nonparametric regression. The results indicate that, contrary to the common practice, it is often not desirable to base the estimator of the variance function on the residuals from an optimal estimator of the mean. Instead it is desirable to use estimators of the mean with minimal bias. The results also correct the optimal rate claimed in Hall and Carroll (1989, JRSSB). I will then consider adaptive estimation of the variance function using a wavelet thresholding approach. A datadriven estimator is constructed by applying wavelet thresholding to the squared firstorder differences of the observations. The variance function estimator is shown to be nearly optimally adaptive to the smoothness of both the mean and variance functions. Finally I will discuss a difference based procedure for semiparametric partial linear models. The estimation procedure is optimal in the sense that the estimator of the linear component is asymptotically efficient and the estimator of the nonparametric component is minimax rate optimal. Some numerical results will also be discussed. 
Subgroup Analysis via Recursive Partitioning 
Xiaogang Su (UCF) Subgroup analysis is an integral part of comparative analysis such as clinical trials. Its goal is to determine whether and how the effect of an investigational treatment varies across subpopulations. We propose an interaction tree (IT) procedure to help delineate the heterogeneity structure for the treatment effect. The proposed method automatically facilitates a number of objectively defined subgroups, in some of which the treatment effect may be found prominent while in others the treatment may have a negligible or even negative effect. We follow the standard CART (Breiman et al., 1984) methodology to construct trees. Important effectmodifiers for the treatment are also extracted via random forests of interaction trees. Both simulated experiments and an example on pay gap assessment between women and men are provided for illustration. 
A Review of Results on False Discovery Rate 
Sanat Sarkar (Temple) Multiple testing has become again a flourishing area of research due to its increased relevance in modern statistical investigations. As some of the notions of error used in traditional multiple testing procedures turn out to be too conservative while testing a large number of hypotheses, which is common in these investigations, alternative and more appropriate measures of error have been developed. Among these, the false discovery rate (FDR) and those related to it have received the most attention. In this talk, I will review results on the FDR. 
Nonparametric Estimation at a Semiparametric Rate 
Arthur Berg (UF) At the core of this talk is the use of infiniteorder kernels in a density estimation context with a specially tailored databased bandwidth selection algorithm. In particular, we will focus on the estimation of the polyspectrum from Time Series and the hazard function from Survival Analysis. Additionally, improvement gained in terms of deficiency [Hodges and Lehmann, 1970] in smoothing the empirical distribution function and the KaplanMeier estimator will also be detailed. The talk will be peppered with a familiar group representation related to the symmetries of the polyspectrum. 
PseudoScore Confidence Intervals for Categorical Data Analyses 
Alan Agresti (UF) This talk surveys confidence intervals that result from inverting score or pseudoscore tests for parameters summarizing categorical data. Such methods perform well, usually better than inverting Wald or likelihoodratio tests. For some models ordinary score inferences are impractical, such as when the likelihood function is not an explicit function of the model parameters. For such cases, we propose pseudoscore inference based on a Pearsontype chisquared statistic that compares fitted values for a working model with fitted values of the model when a parameter of interest takes a fixed value. For multinomial models, this interval simplifies to the largesample score interval when the model is saturated but otherwise can be much simpler to construct. Possible generalizations of the method include a quasilikelihood approach for discrete data. For small samples, `exact' methods are conservative inferentially, but inverting a score test using the midP value provides a sensible compromise. Finally, we briefly review a different pseudoscore approach that approximates the score interval for proportions and their differences with independent or dependent samples by adding pseudo data before forming simple Wald confidence intervals. 
Past Seminars
Fall 2007  
Spring 2007  Fall 2006  Spring 2006  Fall 2005 
Spring 2005  Fall 2004  Spring 2004  Fall 2003 
Spring 2003  Fall 2002  Spring 2002  Fall 2001 
Spring 2001  Fall 2000  Spring 2000  Fall 1999 