Statistical Models Commons^™

A Unified Approach To Non-Negative Matrix Factorization And Probabilistic Latent Semantic Indexing, Karthik Devarajan, Guoli Wang, Nader Ebrahimi

COBRA Preprint Series

Non-negative matrix factorization (NMF) by the multiplicative updates algorithm is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into two matrices, W and H, each with nonnegative entries, V ~ WH. NMF has been shown to have a unique parts-based, sparse representation of the data. The nonnegativity constraints in NMF allow only additive combinations of the data which enables it to learn parts that have distinct physical representations in reality. In the last few years, NMF has been successfully applied in a variety of areas such as natural language processing, information retrieval, image processing, speech recognition …

Arima Models For Bank Failures: Prediction And Comparison, Fangjin Cui

UNLV Theses, Dissertations, Professional Papers, and Capstones

The number of bank failures has increased dramatically over the last twenty-two years. A common notion in economics is that some banks can become "too big to fail." Is this still a true statement? What is the relationship, if any, between bank sizes and bank failures? In this thesis, the proposed modeling techniques are applied to real bank failure data from the FDIC. In particular, quarterly data from 1989:Q1 to 2010:Q4 are used in the data analysis, which includes three major parts: 1) pairwise bank failure rate comparisons using the conditional test (Przyborowski and Wilenski, 1940); 2) development of the …

Rejoinder: Estimation Issues For Copulas Applied To Marketing Data, Peter Danaher, Michael Smith

Michael Stanley Smith

Estimating copula models using Bayesian methods presents some subtle challenges, ranging from specification of the prior to computational tractability. There is also some debate about what is the most appropriate copula to employ from those available. We address these issues here and conclude by discussing further applications of copula models in marketing.

Forecasting Television Ratings, Peter Danaher, Tracey Dagger, Michael Smith

Michael Stanley Smith

Despite the state of flux in media today, television remains the dominant player globally for advertising spend. Since television advertising time is purchased on the basis of projected future ratings, and ad costs have skyrocketed, there is increasing pressure to forecast television ratings accurately. Previous forecasting methods are not generally very reliable and many have not been validated, but more distressingly, none have been tested in today’s multichannel environment. In this study we compare 8 different forecasting models, ranging from a naïve empirical method to a state-of-the-art Bayesian model-averaging method. Our data come from a recent time period, 2004-2008 in …

Windows Executable For Gaussian Copula With Nbd Margins, Michael S. Smith

Michael Stanley Smith

This is an example Windows 32bit program to estimate a Gaussian copula model with NBD margins. The margins are estimated first using MLE, and the copula second using Bayesian MCMC. The model was discussed in Danaher & Smith (2011; Marketing Science) as example 4 (section 4.2).

Modeling Multivariate Distributions Using Copulas: Applications In Marketing, Peter J. Danaher, Michael S. Smith

Michael Stanley Smith

In this research we introduce a new class of multivariate probability models to the marketing literature. Known as “copula models”, they have a number of attractive features. First, they permit the combination of any univariate marginal distributions that need not come from the same distributional family. Second, a particular class of copula models, called “elliptical copula”, have the property that they increase in complexity at a much slower rate than existing multivariate probability models as the number of dimensions increase. Third, they are very general, encompassing a number of existing multivariate models, and provide a framework for generating many more. …

Bicycle Commuting In Melbourne During The 2000s Energy Crisis: A Semiparametric Analysis Of Intraday Volumes, Michael S. Smith, Goeran Kauermann

Michael Stanley Smith

Cycling is attracting renewed attention as a mode of transport in western urban environments, yet the determinants of usage are poorly understood. In this paper we investigate some of these using intraday bicycle volumes collected via induction loops located at ten bike paths in the city of Melbourne, Australia, between December 2005 and June 2008. The data are hourly counts at each location, with temporal and spatial disaggregation allowing for the impact of meteorology to be measured accurately for the first time. Moreover, during this period petrol prices varied dramatically and the data also provide a unique opportunity to assess …

Effects Of Acculturation On Hiv/Aids Sexual Risk Behaviors Among Asian And Pacific Islander (Api) Women, Margaret Cabotage Salud

Loma Linda University Electronic Theses, Dissertations & Projects

Background. In the US women are the fastest growing group for sexually transmitted infections (STIs), including HIV and AIDS. In addition, the estimated AIDS cases among female adults and adolescents, aged 13-19, increased from 7% in 1985 to approximately 26% in 2002. Most infections occur by heterosexual transmission with 53% occurring through contact with a high-risk sexual partner. While overall HIV/AIDS rates in the Asian Pacific Islander (API) community remain low, they are rising and HIV testing rates, one of the major prevention strategies for HIV, are lower than that of other populations. Furthermore, very little is known about APIs …

Modeling Longitudinal Data Using A Pair-Copula Decomposition Of Serial Dependence, Michael S. Smith, Aleksey Min, Carlos Almeida, Claudia Czado

Michael Stanley Smith

Copulas have proven to be very successful tools for the flexible modelling of cross-sectional dependence. In this paper we express the dependence structure of continuous-valued time series data using a sequence of bivariate copulas. This corresponds to a type of decomposition recently called a ‘vine’ in the graphical models literature, where each copula is entitled a ‘pair-copula’. We propose a Bayesian approach for the estimation of this dependence structure for longitudinal data. Bayesian selection ideas are used to identify any independence pair-copulas, with the end result being a parsimonious representation of a time-inhomogeneous Markov process of varying order. Estimates are …

Mixture Of Factor Analyzers With Information Criteria And The Genetic Algorithm, Esra Turan

Doctoral Dissertations

In this dissertation, we have developed and combined several statistical techniques in Bayesian factor analysis (BAYFA) and mixture of factor analyzers (MFA) to overcome the shortcoming of these existing methods. Information Criteria are brought into the context of the BAYFA model as a decision rule for choosing the number of factors m along with the Press and Shigemasu method, Gibbs Sampling and Iterated Conditional Modes deterministic optimization. Because of sensitivity of BAYFA on the prior information of the factor pattern structure, the prior factor pattern structure is learned directly from the given sample observations data adaptively using Sparse Root algorithm. …

A Unified Approach To Modeling Multivariate Binary Data Using Copulas Over Partitions, Bruce J. Swihart, Brian Caffo, Ciprian Crainiceanu

Johns Hopkins University, Dept. of Biostatistics Working Papers

Many seemingly disparate approaches for marginal modeling have been developed in recent years. We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the proposed copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalized models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate …

Statistical Analysis Of Texas Holdem Poker, Daniel Bragonier

Statistics

Gathered lifetime online Poker data for Mike Linn. Attempted to analyze data to obtain information to maximize profit. Techniques included Univariate Analysis, Regression analysis, Anova analysis, Logistic Regression, and outlier Analysis. After the analysis, nothing of supreme importance or sustenance was found. Encountered issues with too much power. Results lead to plenty of statistical significance, but little practical significance. Results showed that the data did not provide all the answers that were being sought after, but there was some value in examining the data in a strict statistical manner.

Survival Prediction For Brain Tumor Patients Using Gene Expression Data, Vinicius Bonato

Dissertations & Theses (Open Access)

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. …

Wavelet-Based Functional Linear Mixed Models: An Application To Measurement Error–Corrected Distributed Lag Models, Elizabeth J. Malloy, Jeffrey S. Morris, Sara D. Adar, Helen Suh, Diane R. Gold, Brent A. Coull

Jeffrey S. Morris

Frequently, exposure data are measured over time on a grid of discrete values that collectively define a functional observation. In many applications, researchers are interested in using these measurements as covariates to predict a scalar response in a regression setting, with interest focusing on the most biologically relevant time window of exposure. One example is in panel studies of the health effects of particulate matter (PM), where particle levels are measured over time. In such studies, there are many more values of the functional data than observations in the data set so that regularization of the corresponding functional regression coefficient …

Members’ Discoveries: Fatal Flaws In Cancer Research, Jeffrey S. Morris

Jeffrey S. Morris

A recent article published in The Annals of Applied Statistics (AOAS) by two MD Anderson researchers—Keith Baggerly and Kevin Coombes—dissects results from a highly-influential series of medical papers involving genomics-driven personalized cancer therapy, and outlines a series of simple yet fatal flaws that raises serious questions about the veracity of the original results. Having immediate and strong impact, this paper, along with related work, is providing the impetus for new standards of reproducibility in scientific research.

Statistical Contributions To Proteomic Research, Jeffrey S. Morris, Keith A. Baggerly, Howard B. Gutstein, Kevin R. Coombes

Jeffrey S. Morris

Proteomic profiling has the potential to impact the diagnosis, prognosis, and treatment of various diseases. A number of different proteomic technologies are available that allow us to look at many proteins at once, and all of them yield complex data that raise significant quantitative challenges. Inadequate attention to these quantitative issues can prevent these studies from achieving their desired goals, and can even lead to invalid results. In this chapter, we describe various ways the involvement of statisticians or other quantitative scientists in the study team can contribute to the success of proteomic research, and we outline some of the …

Informatics And Statistics For Analyzing 2-D Gel Electrophoresis Images, Andrew W. Dowsey, Jeffrey S. Morris, Howard G. Gutstein, Guang Z. Yang

Jeffrey S. Morris

Whilst recent progress in ‘shotgun’ peptide separation by integrated liquid chromatography and mass spectrometry (LC/MS) has enabled its use as a sensitive analytical technique, proteome coverage and reproducibility is still limited and obtaining enough replicate runs for biomarker discovery is a challenge. For these reasons, recent research demonstrates the continuing need for protein separation by two-dimensional gel electrophoresis (2-DE). However, with traditional 2-DE informatics, the digitized images are reduced to symbolic data though spot detection and quantification before proteins are compared for differential expression by spot matching. Recently, a more robust and automated paradigm has emerged where gels are directly …

Bayesian Random Segmentationmodels To Identify Shared Copy Number Aberrations For Array Cgh Data, Veerabhadran Baladandayuthapani, Yuan Ji, Rajesh Talluri, Luis E. Nieto-Barajas, Jeffrey S. Morris

Jeffrey S. Morris

Array-based comparative genomic hybridization (aCGH) is a high-resolution high-throughput technique for studying the genetic basis of cancer. The resulting data consists of log fluorescence ratios as a function of the genomic DNA location and provides a cytogenetic representation of the relative DNA copy number variation. Analysis of such data typically involves estimation of the underlying copy number state at each location and segmenting regions of DNA with similar copy number states. Most current methods proceed by modeling a single sample/array at a time, and thus fail to borrow strength across multiple samples to infer shared regions of copy number aberrations. …

Bayesian Inference For A Periodic Stochastic Volatility Model Of Intraday Electricity Prices, Michael S. Smith

Michael Stanley Smith

The Gaussian stochastic volatility model is extended to allow for periodic autoregressions (PAR) in both the level and log-volatility process. Each PAR is represented as a first order vector autoregression for a longitudinal vector of length equal to the period. The periodic stochastic volatility model is therefore expressed as a multivariate stochastic volatility model. Bayesian posterior inference is computed using a Markov chain Monte Carlo scheme for the multivariate representation. A circular prior that exploits the periodicity is suggested for the log-variance of the log-volatilities. The approach is applied to estimate a periodic stochastic volatility model for half-hourly electricity prices …

Bayesian Skew Selection For Multivariate Models, Michael S. Smith, Anastasios Panagiotelis

Michael Stanley Smith

We develop a Bayesian approach for the selection of skew in multivariate skew t distributions constructed through hidden conditioning in the manners suggested by either Azzalini and Capitanio (2003) or Sahu, Dey and Branco~(2003). We show that the skew coefficients for each margin are the same for the standardized versions of both distributions. We introduce binary indicators to denote whether there is symmetry, or skew, in each dimension. We adopt a proper beta prior on each non-zero skew coefficient, and derive the corresponding prior on the skew parameters. In both distributions we show that as the degrees of freedom increases, …

A Statistical Framework For The Analysis Of Chip-Seq Data, Pei Fen Kuan, Dongjun Chung, Guangjin Pan, James A. Thomson, Ron Stewart, Sunduz Keles

Sunduz Keles

Chromatin immunoprecipitation followed by sequencing (ChIP-Seq) has revolutionalized experiments for genome-wide profiling of DNA-binding proteins, histone modifications, and nucleosome occupancy. As the cost of sequencing is decreasing, many researchers are switching from microarray-based technologies (ChIP-chip) to ChIP-Seq for genome-wide study of transcriptional regulation. Despite its increasing and well-deserved popularity, there is little work that investigates and accounts for sources of biases in the ChIP-Seq technology. These biases typically arise from both the standard pre-processing protocol and the underlying DNA sequence of the generated data.

We study data from a naked DNA sequencing experiment, which sequences non-cross-linked DNA after deproteinizing and …

Using Cone Beam Computed Tomography To Identify A Prediction Model For Obstructive Sleep Apnea, Jodi Parker

Loma Linda University Electronic Theses, Dissertations & Projects

Introduction: Obstructive Sleep Apnea (OSA) patients have increased risk of morbidity and mortality. Early diagnosis may reduce morbidity and mortality. Prediction of OSA from imaging may help to identify OSA patients earlier in life. CBCT can be used for OSA diagnostic imaging due to its three-dimensional (3D) visualization of the upper airway and craniofacial complex. Magnification associated with conventional 2D radiography is eliminated with CBCT, and radiation to the patient is significantly less than previous modalities used to measure craniofacial & airway measurements associated with OSA. During a CBCT scan, the patient's image is taken supine, rather than the upright …

Correlated Binary Regression Using Orthogonalized Residuals, Richard C. Zink, Bahjat F. Qaqish

COBRA Preprint Series

This paper focuses on marginal regression models for correlated binary responses when estimation of the association structure is of primary interest. A new estimating function approach based on orthogonalized residuals is proposed. This procedure allows a new representation and addresses some of the difficulties of the conditional-residual formulation of alternating logistic regressions of Carey, Zeger & Diggle (1993). The new method is illustrated with an analysis of data on impaired pulmonary function.

Group Comparison Of Eigenvalues And Eigenvectors Of Diffusion Tensors, Armin Schwartzman, Robert F. Dougherty, Jonathan E. Taylor

Harvard University Biostatistics Working Paper Series

No abstract provided.

Space-Time Regression Modeling Of Tree Growth Using The Skew-T Distribution, Farouk S. Nathoo

COBRA Preprint Series

In this article we present new statistical methodology for the analysis of repeated measures of spatially correlated growth data. Our motivating application, a ten year study of height growth in a plantation of even-aged white spruce, presents several challenges for statistical analysis. Here, the growth measurements arise from an asymmetric distribution, with heavy tails, and thus standard longitudinal regression models based on a Gaussian error structure are not appropriate. We seek more flexibility for modeling both skewness and fat tails, and achieve this within the class of skew-elliptical distributions. Within this framework, robust space-time regression models are formulated using random …

Limitations Of Remotely-Sensed Aerosol As A Spatial Proxy For Fine Particulate Matter, Christopher J. Paciorek, Yang Liu

Harvard University Biostatistics Working Paper Series

Recent research highlights the promise of remotely-sensed aerosol optical depth (AOD) as a proxy for ground-level PM2.5. Particular interest lies in the information on spatial heterogeneity potentially provided by AOD, with important application to estimating and monitoring pollution exposure for public health purposes. Given the temporal and spatio-temporal correlations reported between AOD and PM2.5 , it is tempting to interpret the spatial patterns in AOD as reflecting patterns in PM2.5 . Here we find only limited spatial associations of AOD from three satellite retrievals with PM2.5 over the eastern U.S. at the daily and yearly levels in 2004. We then …

Using Regression Models To Analyze Randomized Trials: Asymptotically Valid Hypothesis Tests Despite Incorrectly Specified Models, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Regression models are often used to test for cause-effect relationships from data collected in randomized trials or experiments. This practice has deservedly come under heavy scrutiny, since commonly used models such as linear and logistic regression will often not capture the actual relationships between variables, and incorrectly specified models potentially lead to incorrect conclusions. In this paper, we focus on hypothesis test of whether the treatment given in a randomized trial has any effect on the mean of the primary outcome, within strata of baseline variables such as age, sex, and health status. Our primary concern is ensuring that such …

Semiparametric Regression Of Multi-Dimensional Genetic Pathway Data: Least Squares Kernel Machines And Linear Mixed Models, Dawei Liu, Xihong Lin, Debashis Ghosh

Harvard University Biostatistics Working Paper Series

No abstract provided.

An Informative Bayesian Structural Equation Model To Assess Source-Specific Health Effects Of Air Pollution, Margaret C. Nikolov, Brent A. Coull, Paul J. Catalano, John J. Godleski

Harvard University Biostatistics Working Paper Series

No abstract provided.

Mixed Multiplicative Factor Analysis Model For Air Pollution Exposure Assessment, Margaret C. Nikolov, Brent A. Coull, Paul J. Catalano, John J. Godleski

Harvard University Biostatistics Working Paper Series

No abstract provided.