Multivariate Analysis Commons^™

Forecasting Daily Stock Market Return With Multiple Linear Regression, Shengxuan Chen

Mathematics Senior Capstone Papers

The purpose of this project is to use data mining and big data analytic techniques to forecast daily stock market return with multiple linear regression. Using mathematical and statistical models to analyze the stock market is important and challenging. The accuracy of the final results relies on the quality of the input data and the validity of the methodology. In the report, within 5-year period, the data regarding eleven financial and economical features are observed and recorded on each trading day. After preprocessing the raw data with statistical method, we use the multiple linear regression to predict the daily return …

Novel Inference Methods For Generalized Linear Models Using Shrinkage Priors And Data Augmentation., Arinjita Bhattacharyya

Electronic Theses and Dissertations

Generalized linear models have broad applications in biostatistics and sociology. In a regression setup, the main target is to find a relevant set of predictors out of a large collection of covariates. Sparsity is the assumption that only a few of these covariates in a regression setup have a meaningful correlation with an outcome variate of interest. Sparsity is incorporated by regularizing the irrelevant slopes towards zero without changing the relevant predictors and keeping the resulting inferences intact. Frequentist variable selection and sparsity are addressed by popular techniques like Lasso, Elastic Net. Bayesian penalized regression can tackle the curse of …

Step Away From Stepwise, Gary N. Smith

Pomona Economics

Stepwise regression is a popular data-mining tool that uses statistical significance to select the explanatory variables to be used in a multiple-regression model. A fundamental problem with stepwise regression is that some real explanatory variables that have causal effects on the dependent variable may happen to not be statistically significant, while nuisance variables may be coincidentally significant. As a result, the model may fit the data well in-sample, but do poorly out-of-sample. Many Big-Data researchers believe that, the larger the number of possible explanatory variables, the more useful is stepwise regression for selecting explanatory variables. The reality is that stepwise …

Understanding The Novice Decision-Making Process In Forensic Footwear Examinations: Accuracy And Decision Rules, Madonna A. Nobel

Graduate Theses, Dissertations, and Problem Reports (ETD)

The reproducibility of experienced-based forensic pattern interpretation is founded on the notion that domain-specific knowledge can be successfully distributed and applied among experts within a group. This assumption persists, even when the examination is complicated by variations in case circumstances, such as impression clarity and totality, as well as media, substrate, collection mechanism and enhancement. While it is further theorized that many of these factors (as well as additional confounding factors) are at play during an examination, the manner and extent to which these sources of variability affect the examination of footwear evidence remain unclear. In order to explore this …

Spectral Cross Correlation As A Supervised Approach For The Analysis Of Complex Raman Datasets: The Case Of Nanoparticles In Biological Cells, Mark Keating, Franck Bonnier, Hugh Byrne

Articles

Spectral Cross-correlation is introduced as a methodology to identify the presence and subcellular distribution of nanoparticles in cells. Raman microscopy is employed to spectroscopically image biological cells previously exposed to polystyrene nanoparticles, as a model for the study of nano-bio interactions. The limitations of previously deployed strategies of K-means clustering analysis and principal component analysis are discussed and a novel methodology of Spectral Cross Correlation Analysis is introduced and compared with the performance of Classical Least Squares Analysis, in both unsupervised and supervised modes. The previous study demonstrated the feasibility of using Raman spectroscopy to map cells and identify polystyrene …

Reconstructability Of Epistatic Functions, Martin Zwick, Joe Fusion, Beth Wilmot

Complex Systems Faculty Publications and Presentations

Background: Reconstructability Analysis (RA) has been used to detect epistasis in genomic data; in that work, even the simplest RA models (variable-based models without loops) gave performance superior to two other methods. A follow-on theoretical study showed that RA also offers higher-resolution models, namely variable-based models with loops and state-based models, likely to be even more effective in modeling epistasis, and also described several mathematical approaches to classifying types of epistasis.

Methods: The present paper extends this second study by discussing a non-standard use of RA: the analysis of epistasis in quantitative as opposed to nominal variables; such quantitative variables …

Reconstructability Analysis Of Epistasis, Martin Zwick

Complex Systems Faculty Publications and Presentations

The literature on epistasis describes various methods to detect epistatic interactions and to classify different types of epistasis. Reconstructability analysis (RA) has recently been used to detect epistasis in genomic data. This paper shows that RA offers a classification of types of epistasis at three levels of resolution (variable-based models without loops, variable-based models with loops, state-based models). These types can be defined by the simplest RA structures that model the data without information loss; a more detailed classification can be defined by the information content of multiple candidate structures. The RA classification can be augmented with structures from related …

Enhancements To Crisp Possibilistic Reconstructability Analysis, Anas Al-Rabadi, Martin Zwick

Complex Systems Faculty Publications and Presentations

Modified Reconstructibility Analysis (MRA), a novel decomposition within the framework of set-theoretic (crisp possibilistic) Reconstructibility Analysis, is presented. It is shown that in some cases while 3-variable NPN-classified Boolean functions are not decomposable using Conventional Reconstructibility Analysis (CRA), they are decomposable using Modified Reconstructibility Analysis (MRA). Also, it is shown that whenever a decomposition of 3-variable NPN-classified Boolean functions exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. A comparison of the corresponding complexities for Ashenhurst-Curtis decompositions, and Modified Reconstructibility Analysis (MRA) is also presented. While both AC and MRA decompose some but …

An Overview Of Reconstructability Analysis, Martin Zwick

Complex Systems Faculty Publications and Presentations

This paper is an overview of reconstructability analysis (RA), a discrete multivariate modeling methodology developed in the systems literature; an earlier version of this tutorial is Zwick (2001). RA was derived from Ashby (1964), and was developed by Broekstra, Cavallo, Cellier Conant, Jones, Klir, Krippendorff, and others (Klir, 1986, 1996). RA resembles and partially overlaps log‐line (LL) statistical methods used in the social sciences (Bishop et al., 1978; Knoke and Burke, 1980). RA also resembles and overlaps methods used in logic design and machine learning (LDL) in electrical and computer engineering (e.g. Perkowski et al., 1997). Applications of RA, like …