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Colloquia
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| December 18, 2008, 10:00 am |
Jeanette Simino |
| December 8, 2008, 2:00 pm |
Wenhao Gui |
| December 4, 2008, 11:00 am |
Shuva Gupta |
| November 21, 2008, 10:10 am |
Dr. Jinfeng Zhang, Department of Statistics, FSU |
| November 14, 2008, 10:10 am |
Dr. Armin Schwartzman, Department of Biostatistics, Harvard University |
| November 7, 2008, 10:10 am |
Lanjia Lin |
| November 6, 2008, 11:00 am |
Dr. Stuart Lipsitz, Brigham and Women's Hospital, Harvard Medical School |
| October 31, 2008, 10:10 am |
Dr. Eric Chicken, Department of Statistics, FSU |
| October 24, 2008, 10:10 am |
Andrada Ivanescu |
| October 17, 2008, 2:30 pm |
Moeti Ncube |
| October 17, 2008, 10:10 am |
Dr. Fred Huffer, Department of Statistics, FSU |
| October 10, 2008, 10:10 am |
Prabhakar Chalise |
| October 6, 2008, 3:30 pm |
Warren Thompson |
| October 3, 2008, 10:10 am |
Dr. Richard Bertram, Department of Mathematics and Program in Neuroscience, FSU |
| September 26, 2008, 10:10 am |
Dr. Joshua Gert, Department of Philosophy, FSU |
| December 18, 2008 |
| Jeanette Simino |
| Dissertation Defense - Discrimination and calibration of prognostic survival models |
| December 18, 2008 10:00 am |
| Conference Room, OSB 210E |
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| Clinicians employ prognostic survival models for diseases such as coronary heart disease and cancer to inform patients about risks, treatments, and clinical decisions (Altman and Royston 2000). These prognostic models are not useful unless they are valid in the population to which they are applied. There are no generally accepted algorithms for assessing the validity of an external survival model in a new population. Researchers often invoke measures of predictive accuracy, the degree to which predicted outcomes match observed outcomes (Justice et al. 1999). One component of predictive accuracy is discrimination, the ability of the model to correctly rank the individuals in the sample by risk. A common measure of discrimination for prognostic survival models is the concordance index, also called the c-statistic or Harrell's C. We utilize the concordance index to determine the discrimination of Framingham-based Cox and Log-logistic models of coronary heart disease (CHD) death in cohorts from the Diverse Populations Collaboration, a collection of studies that encompasses many ethnic, geographic, and socioeconomic groups. Pencina and D'Agostino presented a confidence interval for the concordance index when assessing the discrimination of an external prognostic model. We perform simulations to determine the robustness of their confidence interval when measuring discrimination during internal validation. The Pencina and D'Agostino confidence interval is not valid in the internal validation setting because their assumption of mutually independent observations is violated. We compare the Pencina and D'Agostino confidence interval to a bootstrap confidence interval that we propose that is valid for the internal validation. We specifically discern the performance of the interval when the same sample is used to both fit and determine the validity of a prognostic model. The framework for our simulations is a Weibull proportional hazards model of CHD death fit to the Framingham exam 4 data.
We then focus on the second component of accuracy, calibration, which measures the agreement between the observed and predicted event rates for groups of patients(Altman and Royston 2000). In 2000, van Houwelingen introduced a method called validation by calibration to allow a clinician to assess the validity of a well-accepted published survival model on his/her own patient population and adjust the published model to fit that population. Van Houwelingen embeds the published model into a new model with only 3 parameters which helps combat the overfitting that occurs when models with many covariates are fit on datasets with a small number of events. We explore validation by calibration as a tool to adjust models when an external model over- or underestimates risk. Van Houwelingen discusses the general method and then focusses on the proportional hazards model. There are situations where proportional hazards may not hold, thus we extend the methodology to the Log-logistic accelerated failure time model. We perform validation by calibration of Framingham-based Cox and Log-logistic models of CHD death to cohorts from the Diverse Populations Collaboration. Lastly, we conduct simulations that investigate the power of the global Wald validation by calibration test. We study its power to reject an invalid proportional hazards or Log-logistic accelerated failure time model under various scale and/or shape misspecifications. |
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| December 8, 2008 |
| Wenhao Gui |
| Essay Defense - Adaptive series estimators for copula densities |
| December 8, 2008 2:00 pm |
| 110 OSB |
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| Copulas are the functions linking univariate marginals to their joint
distribution function. They measure the dependence among components of
random vectors and are a popular tool in multivariate modeling. In this
essay, we propose a new nonparametric method to estimate copula density
functions. The proposed estimators are based on orthogonal series,
including hard thresholding and soft thresholding for sparse epresentations. Under mild conditions, the asymptotic properties of estimators are proved. A
preliminary simulation study for different copula densities indicates that our method performs better than the kernel method, especially around the
boundary points, in terms of mean squared error. |
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| December 4, 2008 |
| Shuva Gupta |
| Essay Defense - A study of the asymptotic properties of LASSO estimates for correlated data |
| December 4, 2008 11:00 am |
| 110 OSB |
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| Here we present a theoretical study of the model selection properties and the asymptotic distribution of the LASSO($\ell_{1}$ penalized LS estimate ) when the observations are generated from a linear model with correlated errors. The model selection property is investigated when the observations are high dimensional (i.e, M>n) and assumed to follow a first order autoregressive process (AR(1)). We are also going to provide an outline as to how to generalize this result when the errors have a weak-dependency structure(Doukhan 1996). We also generalize the result of Knight and Fu (2000) when the errors are weakly dependent and find the asymptotic properties of the LASSO estimator. This result was proved when M is less than n (that is the number of parameters are fixed and do not exceed the number of observations). We finish our talk by present some ideas as to which way our future research shall be directed. This shall highlight some the shortcomings of the LASSO estimator how we plan to overcome it. We also present a novel application of our present research to the area of neuroscience. |
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| November 21, 2008 |
| Dr. Jinfeng Zhang, Department of Statistics, FSU |
| Biopolymer Structure Simulation and Optimization via Fragment Regrowth Monte Carlo |
| November 21, 2008 10:10 am |
| 110 OSB |
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| An efficient exploration of the configuration space of a biopolymer is essential for its structure modeling and prediction. We developed a new Monte Carlo method, Fragment Re-growth via Energy-guided Sequential Sampling (FRESS), which incorporates the idea of multigrid Monte Carlo into the framework of configurational-bias Monte Carlo and is suitable for chain polymer simulations. We tested FRESS on hydrophobic-hydrophilic (HP) protein folding models in both two and three dimensions. For the benchmark sequences, FRESS not only found all the minimum energies obtained by previous studies with substantially less computation time, but also found new lower energies for all the three-dimensional HP models with sequence length longer than 80 residues. I will also briefly discuss the potential applications of FRESS as a general Monte Carlo sampling and optimization method. |
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| November 14, 2008 |
| Dr. Armin Schwartzman, Department of Biostatistics, Harvard University |
| Inference for Eigenvalues and Eigenvectors of Gaussian Symmetric Matrices |
| November 14, 2008 10:10 am |
| OSB 110 |
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| This work presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of Diffusion Tensor Imaging data, where the observations are 3-by-3 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered here, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure. HOST: Dr. Anuj Srivastava. |
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| November 7, 2008 |
| Lanjia Lin |
| Essay Defense - Association Models for Clustered Data with Mixed Responses |
| November 7, 2008 10:10 am |
| 110 OSB |
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| We consider analysis of clustered data with mixed bivariate responses, i.e., where each member of the cluster has a binary and a continuous outcome. We propose a new bivariate random effects model which induces associations between the bianry and continuous responses. For the ease of interpretation of the regression effects, the marginal model of the binary response probability integrated over the random effects preserves the logistic form and the marginal regression function of the continuous response preserves the linear form. We implement maximum likelihood estimation of model parameters using standard
software such as PROC NLMIXED of SAS. Fully parametric and semiparametric Bayesian methods are also presented for model analysis. We illustrate our methodology by analyzing a developmental
toxicity study of ethylene glycol in mice using the three methods. |
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| November 6, 2008 |
| Dr. Stuart Lipsitz, Brigham and Women's Hospital, Harvard Medical School |
| Median Regression via the Box-Cox Transformation |
| November 6, 2008 11:00 am |
| OSB 110 |
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| Median regression is used increasingly in many different areas of applications. The usual median regression estimating equations (Basset and Koenker, 1982), derived from minimizing the least absolute deviations (LAD), are not a smooth function of the regression parameters and a solution is best obtained using a linear programming algorithm. Because the usual regularity conditions do not hold for these estimating equations, many of the appealing properties of standard maximum likelihood or quasi-likelihood estimation do not hold. As an alternative, we propose estimating the median regression parameters via Gaussian estimation after applying a Box-Cox transformation to both the outcome and the linear predictor. The proposed estimator is notably more efficient than the standard LAD estimator.
HOST: Dr. Debajyoti Sinha |
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| October 31, 2008 |
| Dr. Eric Chicken, Department of Statistics, FSU |
| Analysis of Water Flow in the Woodville Karst Plain |
| October 31, 2008 10:10 am |
| 110 OSB |
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| The Woodville Karst Plain includes a complex system of springs, underground rivers, and sinkholes with many unusual characteristics that at times are counterintuitive. Over the past several years, the subterranean flow in the Woodville Karst Plain has been studied extensively. Much of this analysis has been qualitative. Lately, quantitative analysis of this system has attempted to describe the influences on the flow, the physical properties of the system, and possible models for the network of underground channels. The methods used include known statistical modeling techniques as well as new methods developed specifically for this problem. |
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| October 24, 2008 |
| Andrada Ivanescu |
| Dissertation Defense - Revealing Sparse Signals in Functional Data |
| October 24, 2008 10:10 am |
| OSB 110 |
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| My dissertation presents a novel statistical method to estimate a sparse signal in functional data and to construct confidence bands for the signal. The methodology involves thresholding a least squares estimator, and the threshold level depends on the sources of variability that exist in this type of data. The proposed estimation method and the confidence bands successfully adapt to the sparsity of the signal. Supporting evidence is presented through simulations and applications to datasets.
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| October 17, 2008 |
| Moeti Ncube |
| Essay Defense - Stochastic models and inferences for commodity futures pricing |
| October 17, 2008 2:30 pm |
| OSB 110 |
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| Developing models that can adequately describe the evolution of a commodity is essential to the valuation of financial projects and instruments; here we focus on the class of reduced-form models within this literature and give a brief history of the important models extensions. We examine the estimation problems that exists with these models and propose an alternative estimation procedure that is fully automatic and produces optimal estimates. We compare our results with that of the Schwartz-smith model and apply our methodology to crude oil and natural gas data sets. For future work we propose extending the observations vector in the Schwartz-Smith model to incorporate options as well as futures prices. We will also examine the problem of identifiably, which has not been addressed in the current literature, and look into estimation techniques in the non-linear framework. |
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| October 17, 2008 |
| Dr. Fred Huffer, Department of Statistics, FSU |
| Bernoulli sequences and Poisson processes |
| October 17, 2008 10:10 am |
| OSB 110 |
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| Consider an infinite sequence of independent Bernoulli
trials where the probability of success on the i-th trial is 1/i.
What is the distribution of the number of pairs of consecutive
successes in this sequence? We give the answer to this and related
questions, and present a new approach (based on Poisson processes) for
proving these answers. This is joint work with Jayaram Sethuraman and
Sunder Sethuraman. |
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| October 10, 2008 |
| Prabhakar Chalise |
| Essay Defense - Time Scales in Epidemiological Analysis |
| October 10, 2008 10:10 am |
| OSB 110 |
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| October 6, 2008 |
| Warren Thompson |
| Essay Defense - Modeling Highly Correlated Data in Logistic Regression: A Comparison of Methods |
| October 6, 2008 3:30 pm |
| 108 OSB |
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| October 3, 2008 |
| Dr. Richard Bertram, Department of Mathematics and Program in Neuroscience, FSU |
| Mathematical Analysis of Bursting Electrical Activity in Nerve and Endocrine Cells |
| October 3, 2008 10:10 am |
| OSB 110 |
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| Nerve cells generate and transmit information in the form of electrical impulses. Similarly, endocrine cells secrete hormones in response to electrical impulses. These impulses are often clustered together into episodes or bursts, and there is evidence that bursts are more efficient at transmitting information and evoking hormone secretion than are evenly-spaced impulses. In this seminar I will discuss how mathematical modeling and analysis is used to understand the generation of bursting oscillations and to classify the different types of oscillations according to topological features. I will then discuss our current research that uses correlation patterns to allow us to determine the type of bursting pattern from an experimental measurement of electrical activity. |
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| September 26, 2008 |
| Dr. Joshua Gert, Department of Philosophy, FSU |
| Some Remarks on the Nature of Color |
| September 26, 2008 10:10 am |
| OSB 110 |
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| In this paper I explain and defend a pair of claims about the nature of color. First, colors should not be understood as identical to any of the physical or dispositional properties to which philosophers have traditionally sought to reduce them. Such an identification will give colors properties that they do not have. Second, we should distinguish sharply between color experiences and color properties in such a way that it is only color experiences that can be described by giving coordinates in the traditional three-dimensional color spaces. Colors themselves are what underlie patterns in variation in color experiences as viewing conditions change. |
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