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Colloquia
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| May 1, 2009, 1:30 pm |
Shuva Gupta |
| April 30, 2009, 2:00 pm |
Wenhao Gui |
| April 24, 2009, 10:10 am |
Vernon Lawhern and Dr. Wei Wu, Department of Statistics, FSU |
| April 22, 2009, 3:30 pm |
Michael Crane |
| April 10, 2009, 10:10 am |
Dr. Alan Yuille, Department of Statistics, UCLA |
| April 8, 2009, 9:45 am |
Lanjia Lin |
| April 3, 2009, 10:10 am |
Dr. Michael Black, Department of Computer Science, Brown University |
| March 27, 2009, 10:10 am |
Dr. David Gilbert, Department of Biological Science, FSU |
| March 25, 2009, 11:05 am |
Nikolay Balov |
| March 23, 2009, 3:30 pm |
Yang Liu |
| March 20, 2009, 10:10 am |
Dr. Frits Ruymgaart, Department of Mathematics and Statistics, Texas Tech University |
| March 16, 2009, 3:30 pm |
Dr. Robert Kass, Department of Statistics, Carnegie Mellon University |
| March 6, 2009, 10:10 am |
Dr. Yiyuan She, Department of Statistics, FSU |
| February 27, 2009, 10:10 am |
Dr. Yiyuan She, Department of Statistics, FSU |
| February 13, 2009, 10:10 am |
Dr. Jinfeng Zhang, Department of Statistics, FSU |
| February 6, 2009, 10:10 am |
Dr. Adrian Barbu, Department of Statistics, FSU |
| 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 |
| May 1, 2009 |
| Shuva Gupta |
| Dissertation Defense - A Study of the Asymptotic Properties of Lasso Estimates for Correlated Data |
| May 1, 2009 1:30 pm |
| OSB 210E, Conference Room |
|
| In this thesis we investigate post-model selection properties of L1 penalized weighted
least squares estimators in regression models with a large number of variables M and
correlated errors. We focus on correct subset selection and on the asymptotic distribution of the penalized estimators. In the simple case of AR(1) errors we give conditions under which correct subset selection can be achieved via our procedure. We then provide a detailed generalization of this result to models with errors that have a weak-dependency structure (Doukhan 1996). We also explore various special cases of weak dependence and show what the theorem translates to in these special cases. We then use estimates of the concentration matrix in the minimization criterion and investigate the results when the LASSO estimates are calculated from the altered criterion function. In all cases, the number M of regression variables is allowed to exceed the sample size n. We further investigate the asymptotic distribution of our estimates, when M < n, and show that under appropriate choices of the tuning parameters the limiting
distribution is multivariate normal. This generalizes to the case of correlated errors the
result of Knight and Fu (2000), obtained for regression models with independent errors. |
| Back To Top |
| April 30, 2009 |
| Wenhao Gui |
| Dissertation Defense - Adaptive series estimators for copula densities |
| April 30, 2009 2:00 pm |
| OSB 210E, Conference Room |
|
| In this thesis, based on an orthonormal series expansion, we propose a new
nonparametric method to estimate copula density functions. We propose
estimators of the variance of the estimated basis coefficients and
establish their consistency. We derive the asymptotic distribution of the
estimated coefficients under mild conditions on the copula density. Based
on this result, we derive an oracle inequality for the copula density
estimator. We propose a stop rule for selecting the number of coefficients
used in the series and we prove that this rule minimizes the mean
integrated squared error. In addition, we consider hard and soft
thresholding techniques for sparse representations. We obtain oracle
inequalities that hold with prescribed probability for various norms of
the difference between the copula density and our estimator. A simulation
study indicates that our method is extremely easy to implement and works
very well, and it compares favorably to the popular kernel based copula
density estimator, especially around the boundary points, in terms of mean
squared error. Finally, we have applied our method to an insurance
dataset. We reach the same conclusion as the parametric methods in the
literature and as such we provide additional justification for the use of
the developed parametric model. |
| Back To Top |
| April 24, 2009 |
| Vernon Lawhern and Dr. Wei Wu, Department of Statistics, FSU |
| Motor cortical decoding using improved generalized linear models |
| April 24, 2009 10:10 am |
| 110 OSB |
|
| Classical generalized linear models (GLMs) have been developed for modeling and decoding neural activity in the motor cortex. These models are based on various forms of Poisson or non-Poisson processes, and provide a reasonable characterization between neural activity and motor behavior. However, they lack a description of other movement-related terms, such as joint angles at the shoulder and elbow, muscular activation, and the subject's attention span. We propose to represent these important, yet unknown states into the GLM model as one multi-dimensional hidden state in the spiking rate density function. The system state in this new model includes two parts: one is the observable behavioral state such as the hand motion, and the other is the hidden state. We tested this new method in two experimental datasets. The results show that the new method significantly improves the model-fitting over the classical GLM model. Moreover, it provides more accurate decoding, while keeping real-time efficiency. These results suggest that this method could contribute as a useful tool to neural prosthetics. |
| Back To Top |
| April 22, 2009 |
| Michael Crane |
| Essay Defense - Nonparametric Estimation of 3D Projective Shapes |
| April 22, 2009 3:30 pm |
| 110 OSB |
|
| This talk is about analysis of invariants of a 3D configuration from its 2D
images in pictures of this configuration, without requiring any
restriction for the camera positioning relative to the scene pictured. We
mention some of the main results found in the literature. The methodology
used is nonparametric, manifold based combined with standard computer
vision reconstruction techniques. More specifically, we use asymptotic
results for the extrinsic sample mean and the extrinsic sample covariance
to construct bootstrap confidence regions for mean projective shapes of 3D
configurations. |
| Back To Top |
| April 10, 2009 |
| Dr. Alan Yuille, Department of Statistics, UCLA |
| Recursive Compositional Models |
| April 10, 2009 10:10 am |
| 110 OSB |
|
| Recursive Compositional Models (RCMs) are a class of probability models designed to detect, recognize, parse, and segment visual objects and label visual scenes. They take into account the statistical and computational complexities of visual patterns. The key design principle is recursive compositionality. Visual patterns are represented by RCMs in a hierarchical form where complex structures are composed of more elementary structures. Probabilities are defined over these structures exploiting properties of the hierarchy (e.g. long range spatial relationships can be represented by local potentials). The compositional nature of this representation enables efficient learning and inference algorithms. Hence the overall architecture of RCMs provides a balance between statistical and computational complexity. HOST: Dr. Adrian Barbu |
| Back To Top |
| April 8, 2009 |
| Lanjia Lin |
| Dissertation Defense - Association Models for Clustered Data with Binary and Continuous Responses |
| April 8, 2009 9:45 am |
| 499 Dirac Science Library Seminar Room |
|
| This dissertation develops novel single random effect models as well as bivariate correlated random effects model for clustered data with mixed bivariate responses. Logit and identity link functions are used for the binary and continuous responses. For the ease of interpretation of the regression effects, random effect of the binary response has bridge distribution so that the marginal model of mean of the binary response after integrating out the random effect preserves the logistic form. And the marginal regression function of the continuous response preserves the linear form. Within-cluster and within-subjects associations could be measured by our proposed models. Fully parametric and semi-parametric Bayesian methods as well as maximum likelihood method are illustrated for model analysis. In the semiparametric Bayesian model, normality assumption of the regression error for the continuous response is relaxed by using a nonparametric Dirichlet Process prior. Robustness of the correlated bivariate random effects model using ML method to misspecifications of regression function as well as random effect distribution is investigated by simulation studies. The Bayesian and likelihood methods are applied to a developmental toxicity study of ethylene glycol in mice. |
| Back To Top |
| April 3, 2009 |
| Dr. Michael Black, Department of Computer Science, Brown University |
| Predicting Human Body Shape Under Clothing |
| April 3, 2009 10:10 am |
| 110 OSB |
|
| We propose a method to estimate the detailed 3D shape of a person from images of that person wearing clothing. The approach exploits a model of human body shapes that is learned from a database of over 2000 range scans. We show that the parameters of this shape model can be recovered independently of body pose. We further propose a generalization of the visual hull to account for the fact that observed silhouettes of clothed people do not provide a tight bound on the true 3D shape. With clothed subjects, different poses provide different constraints on the possible underlying 3D body shape. We consequently combine constraints across pose to more accurately estimate 3D body shape in the presence of occluding clothing. Finally we use the recovered 3D shape to estimate the gender of subjects and then employ gender-specific body models to refine our shape estimates. Results on a novel database of thousands of images of clothed and "naked" subjects, as well as sequences from the HumanEva dataset, suggest the method may be accurate enough for biometric shape analysis in video.
This is joint work with Alexandru Balan.
Project page: http://www.cs.brown.edu/~alb/scapeClothing/
Related ECCV paper: http://www.cs.brown.edu/~black/Papers/balanECCV08.pdf.
HOST: Dr. Wei Wu |
| Back To Top |
| March 27, 2009 |
| Dr. David Gilbert, Department of Biological Science, FSU |
| Epigenomics, Mathematics and Stem Cells |
| March 27, 2009 10:10 am |
| 110 OSB |
|
| I will begin with an informal discussion of how modern technical
advances have transformed biomedical research from the study of one
gene or one protein at a time to the study of all genes and proteins
in each and every experiment. These huge data sets hold great promise
but are now the rate-limiting step for the mathematically challenged
molecular biologist. I will then describe one of these great promises
in a bit more detail- the ability to transform any cell type into any
other cell type to regenerate diseased or deteriorating tissue-and how
our research on chromosome structure and replication relates to this
problem. HOST: Dr. Jinfeng Zhang |
| Back To Top |
| March 25, 2009 |
| Nikolay Balov |
| Dissertation Defense - Covariance on Manifolds |
| March 25, 2009 11:05 am |
| HCB 315 |
|
| With ever increasing complexity of observational and theoretical data models, the sufficiency of the classical statistical techniques, designed to be applied only on vector quantities, is challenged.
Non-linear statistical analysis is an area of intensive research in recent years.
Despite of the impressive progress in this direction, however, a unified and consistent framework is still not present.
In this regard, the following work is an attempt to improve our understanding of random phenomena on non-Euclidean spaces.
More specifically, the motivating goal of the present dissertation is
to generalize the notion of distribution covariance,
which in standard settings is defined only in Euclidean spaces,
on manifolds with metric also known as Riemannian manifolds.
I introduce a tensor field structure, named covariance field,
that is consistent with the heterogeneous nature of manifolds
and not only describes the variability imposed by a distribution,
but in general provides alternative distribution representations.
The covariance field of a distribution combines distribution's density with
geometric characteristics of its domain and thus fills the gap between these two.
I present some of the properties of the covariance fields and argue that
they can be successfully applied to various statistical problems.
In particular, I provide a unified approach for defining parametric families of distributions on manifolds,
parameter estimation using regression analysis,
non-parametric statistical tests for comparing distributions and
interpolation between distributions.
Emphasized are several application areas where this new theory may have potential impact.
One of them is the branch of directional statistics,
with domain of influence ranging from geosciences to medical image analysis.
The fundamental level at which the covariance based structures are introduced,
opens new area for future research. |
| Back To Top |
| March 23, 2009 |
| Yang Liu |
| Dissertation Defense - Transformation Models for Survival Data Analysis and Applications |
| March 23, 2009 3:30 pm |
| 110 OSB |
|
| It is often assumed that all uncensored subjects will eventually experience the event of interest in standard survival models. However, in some situations when the considering event is not death, it will never occur for a proportion of subjects. Survival models with a cure fraction are becoming popular in analyzing this type of studies. We propose a generalized transformation model motivated by Zeng et al's (2006) transformed proportional time cure model. In our proposed model, fractional polynomials are used instead of the simple linear combination of the covariates. The proposed models give us more flexibility without loosing any good properties of the original model, such as asymptotical consistency and asymptotical normality of the regression coefficients. The proposed model will better fit the data where the relationship between a response variable and covariates is non-linear. We also provide a power selection procedure based on likelihood function. A simulation study is curried out to show the accuracy of the proposed power selection procedure. The proposed models are applied to coronary heart disease and cancer related medical data from both observational cohort studies and clinical trials. |
| Back To Top |
| March 20, 2009 |
| Dr. Frits Ruymgaart, Department of Mathematics and Statistics, Texas Tech University |
| Deconvolution and the ruin problem for unknown claims distributions |
| March 20, 2009 10:10 am |
| 110 OSB |
|
| The well-known insurance ruin problem is reconsidered. The ruin
probability is estimated in the case of an unknown claims density,
assuming a sample of claims is given. An important step in the
construction of the estimator is the application of a regularized version
of the inverse of the Laplace transform. A rate of convergence in
probability for the ISE is derived and some simulations are included. HOST: Dr. Victor Patrangenaru. |
| Back To Top |
| March 16, 2009 |
| Dr. Robert Kass, Department of Statistics, Carnegie Mellon University |
| Analysis of Neural Spike Train Data: Methods and Commentary |
| March 16, 2009 3:30 pm |
| 110 OSB |
|
| One of the most important techniques in learning about the functioning
of the brain has involved examining neuronal activity in laboratory
animals under varying experimental conditions. Neural information is
represented and communicated through series of action potentials, or
spike trains, and the central scientific issue in many studies
concerns the physiological significance that should be attached to a
particular neuron firing pattern in a particular part of the brain. In
addition, a major comparatively new effort in neurophysiology involves
the use of multielectrode recording, in which responses from dozens of
neurons are recorded simultaneously. Among other things, this has
made possible the construction of brain-controlled robotic devices,
which could benefit people whose movement has been severely impaired.
In my talk I will briefly outline the progress made, by many people,
over the past 10 years, highlighting some of the work my colleagues
and I have contributed. Part of my perspective comes from
the evolution of the international workshops "Statistical Analysis
of Neural Data", which I co-organized in 2002, 2004, 2006, and 2008.
I will try to emphasize general statistical ideas, but will also
indicate current status and future challenges. HOST: Dr. Wei Wu |
| Back To Top |
| March 6, 2009 |
| Dr. Yiyuan She, Department of Statistics, FSU |
| Thresholding-based Iterative Selection Procedures for Model Selection and Shrinkage |
| March 6, 2009 10:10 am |
| 110 OSB |
|
| A class of thresholding-based iterative selection procedures (TISP) is proposed for model selection and shrinkage. People have long before noticed the weakness of the convex $l_1$-constraint (or the soft-thresholding) in wavelets and have designed many different forms of nonconvex penalties to increase model sparsity and accuracy. But for a nonorthogonal regression matrix, there is great difficulty in both investigating the performance in theory and solving the problem in computation. Starting from the thresholding rules rather than penalty functions, TISP provides a simple and efficient way to tackle this.
Moreover, a novel Hybrid-TISP is proposed based on hard-thresholding and ridge-thresholding. It provides a fusion between the $l_0$-penalty and the $l_2$-penalty, and adaptively achieves the right balance between shrinkage and selection in statistical modeling. |
| Back To Top |
| February 27, 2009 |
| Dr. Yiyuan She, Department of Statistics, FSU |
| Outlier Detection via Penalized Regressions |
| February 27, 2009 10:10 am |
| 110 OSB |
|
| Outlier identification has been a classical topic in robust analysis and numerous procedures have been proposed in the past 30 years which are often ad-hoc and computationally expensive. Assuming a mean shift outlier model, we claim that outlier detection amounts to solving a large-p sparsity recovery problem. However, the naive $l_1$-penalty cannot completely remove the masking and swamping effects in the presence of multiple outliers. We build a connection between the penalized mean shift model and Huber's M-estimation functions and develop different versions of iterative procedures to tackle the problem. |
| Back To Top |
| February 13, 2009 |
| Dr. Jinfeng Zhang, Department of Statistics, FSU |
| Automatic Information Extraction from Scientific Literature |
| February 13, 2009 10:10 am |
| 110 OSB |
|
| Protein-protein interaction (PPI) extraction from pub-lished
biological articles has attracted much attention because of the
importance of protein interactions in biological processes. Despite
significant progress, mining PPIs from literatures still rely heavily
on time and resource consuming manual annotations. In this study, we
developed a novel methodology based on Bayesian networks (BNs) for
extracting PPI triplets (a PPI triplet consists of two protein names
and the corresponding interaction word) from unstructured text. The
method achieved an overall accuracy of 87% on a cross-validation test
using manually annotated data set. We also showed, through extracting
PPI triplets from a large number of PubMed abstracts, that our method
was able to complement human annotations to extract large number of
new PPIs from literature. Our method performed better in extracting
PPI triplets than, PIE, the best publicly accessible method. |
| Back To Top |
| February 6, 2009 |
| Dr. Adrian Barbu, Department of Statistics, FSU |
| Training an Active Random Field for Real-Time Image Denoising |
| February 6, 2009 10:10 am |
| 110 OSB |
|
| Many computer vision problems can be formulated in a Bayesian framework with
Markov Random Field (MRF) or Conditional Random Field (CRF) priors. Given an image, the solution is usually a MAP estimation of the hidden variables of
interest. Recently however, Wainwright observed that in computationally
restricted settings, a model designed for MAP estimation would not give the
best performance and certain biased models might perform better. This talk
will pursued this idea for training real-time image denoising algorithms
using Bayesian models based on MRFs. An Active Random Field (ARF) is defined
as a combination of the MRF/CRF based model and a fast algorithm for hidden
variable estimation. For image denoising, the ARF was chosen to be the
Fields of Experts MRF model and the algorithm was a 1-4 iteration gradient
descent. Finding the ARF parameters is an optimization of a loss function
defined on a training set consisting of pairs of input images and desired
outputs. Experimental validation on unseen data shows that the Active Random
Field approach obtains an improved benchmark performance as well as a
1000-3000 times speedup compared to the Fields of Experts MRF that was
trained for MAP estimation. Using the ARF approach, image denoising can be
performed in real-time, at 8fps on a single CPU for a 256x256 image
sequence, with close to state-of-the-art accuracy. |
| Back To Top |
| December 18, 2008 |
| Jeanette Simino |
| Dissertation Defense - Discrimination and calibration of prognostic survival models |
| December 18, 2008 10:00 am |
| Conference Room, OSB 210E |
|
| 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. |
| Back To Top |
| December 8, 2008 |
| Wenhao Gui |
| Essay Defense - Adaptive series estimators for copula densities |
| December 8, 2008 2:00 pm |
| 110 OSB |
|
| 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. |
| Back To Top |
| 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 |
|
| 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. |
| Back To Top |
| 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 |
|
| 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. |
| Back To Top |
| 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 |
|
| 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. |
| Back To Top |
| November 7, 2008 |
| Lanjia Lin |
| Essay Defense - Association Models for Clustered Data with Mixed Responses |
| November 7, 2008 10:10 am |
| 110 OSB |
|
| 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. |
| Back To Top |
| 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 |
|
| 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 |
| Back To Top |
| 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 |
|
| 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. |
| Back To Top |
| October 24, 2008 |
| Andrada Ivanescu |
| Dissertation Defense - Revealing Sparse Signals in Functional Data |
| October 24, 2008 10:10 am |
| OSB 110 |
|
| 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.
|
| Back To Top |
| October 17, 2008 |
| Moeti Ncube |
| Essay Defense - Stochastic models and inferences for commodity futures pricing |
| October 17, 2008 2:30 pm |
| OSB 110 |
|
| 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. |
| Back To Top |
| October 17, 2008 |
| Dr. Fred Huffer, Department of Statistics, FSU |
| Bernoulli sequences and Poisson processes |
| October 17, 2008 10:10 am |
| OSB 110 |
|
| 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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