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Statistics and Probability

Statistics and Probability

Mathematical frameworks for data analysis and uncertainty, including statistical theory, probability theory, stochastic processes, statistical inference, and applications to data science
8 papers in this specialization

Paperzilla Papers in Statistics and Probability

On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means

This paper introduces a generalization of the Jensen-Shannon Divergence (JSD), a method used to measure the difference between probability distributions. It explores using different types of "means" (like arithmetic, geometric, and harmonic means) to create new JSD variations and provides closed-form formulas for these variations in specific cases like mixtures of Gaussian or Cauchy distributions.
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paper_1634.pdf
Sep 17, 06:26 PM

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon

This lecture note explores the "cutoff phenomenon" in Markov chains, where some processes abruptly transition to equilibrium instead of gradually converging. It introduces key concepts like mixing times, curvature, and varentropy, applying them to various models like card shuffling and random walks. The author presents a novel criterion based on varentropy for predicting cutoff behavior.
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paper_818.pdf
Aug 29, 02:52 PM

ADDRESSING OUTLIERS IN MIXED-EFFECTS LOGISTIC REGRESSION: A MORE ROBUST MODELING APPROACH

This study proposes the 'binomial-logit-t' model to improve analysis of bounded count data (data with a maximum value), particularly in scenarios with outliers like medication adherence. It handles outliers and accounts for overdispersion more effectively compared to existing methods, providing more accurate parameter estimates. The model is demonstrated on a medication adherence dataset and supported by simulations.
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paper_667.pdf
Aug 26, 11:50 AM

A NEW PROOF OF SUB-GAUSSIAN NORM CONCENTRATION INEQUALITY

This paper presents a new mathematical proof for the sub-Gaussian norm concentration inequality, offering potentially tighter bounds than previous approaches using a novel "averaged moment generating function" (AMGF). The method applies to both vectors and matrices and directly analyzes the norm's concentration, unlike methods relying on the union bound.
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paper_396.pdf
Aug 19, 02:12 PM

A FRAMEWORK FOR THINKING ABOUT INFORMAL STATISTICAL INFERENCE

The study proposes a framework for informal statistical inference with three key principles: generalizations beyond the data, data as evidence, and probabilistic language. Classroom episodes illustrate how teachers can foster inferential reasoning by emphasizing purposeful investigations, connecting conclusions to evidence, and promoting probabilistic language to express uncertainty.
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330.pdf
Jul 14, 11:11 AM

The Exponentiated Generalized Class of Distributions

The paper proposes the "exponentiated generalized" (EG) class of distributions, a new method of adding two shape parameters to existing continuous distributions using a double Lehmann alternative construction. This extends the flexibility of distributions, particularly in the tails, enabling improved modeling in various fields. The study explores mathematical properties, including moments, generating functions, and order statistics, and demonstrates applications to real datasets from diverse areas like agriculture and material science, finding superior fits compared to existing models.
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pdf.pdf
Jul 14, 11:11 AM

Elastic Net Regularization Paths for All Generalized Linear Models

This paper details the implementation of elastic net regularization for all generalized linear models (GLMs), Cox models with extended data types, and a simplified relaxed lasso within the glmnet R package. It also covers utility functions for evaluating fitted model performance.
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4459.pdf
Jul 14, 11:11 AM

The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation

This study argues that R-squared is a more informative and robust metric for evaluating regression models compared to SMAPE, MAE, MAPE, MSE, and RMSE. Through several synthetic use cases and analysis of two real medical datasets, the authors demonstrate that R-squared provides a more accurate assessment of model performance, particularly when dealing with skewed data or outliers. They propose using R-squared as the standard metric for regression analysis evaluation.
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Chicco-2021-PeerJ%20Comput%20Sci-VoR.pdf
Jul 14, 11:11 AM
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