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At least 451 records · Page 25Linked to original sources

arXiv2019

A note on Fibonacci Sequences of Random Variables

The focus of this paper is the random sequences in the form $\{X_{0},X_{1},$ $X_{n}=X_{n-2}+X_{n-1},n=2,3,..\dot{\}},$ referred to as Fibonacci Random Sequence (FRS). The initial random variables $X_{0}$ and $X_{1}$ are assumed to be absolutely continuous with joint probability density function (pdf) $f_{X_{0},X_{1}}.$ The FRS is completely determined by $X_{0}$ and $X_{1}$ and the members of Fibonacci sequence $\digamma \equiv\{0,1,1,2,3,5,8,13,21,34,55,89,144,...\}.$ We examine the distributional and limit properties of the random sequence $X_{n},n=0,1,2,...$ .

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arXiv2019

Bounds on Bayes Factors for Binomial A/B Testing

Bayes factors, in many cases, have been proven to bridge the classic -value based significance testing and bayesian analysis of posterior odds. This paper discusses this phenomena within the binomial A/B testing setup (applicable for example to conversion testing). It is shown that the bayes factor is controlled by the \emph{Jensen-Shannon divergence} of success ratios in two tested groups, which can be further bounded by the Welch statistic. As a result, bayesian sample bounds almost match frequentionist's sample bounds. The link between Jensen-Shannon divergence and Welch's test as well as the derivation are an elegant application of tools from information geometry.

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arXiv2019

Tutorial: Deriving The Efficient Influence Curve for Large Models

This paper aims to provide a tutorial for upper level undergraduate and graduate students in statistics, biostatistics and epidemiology on deriving influence functions for non-parametric and semi-parametric models. The author will build on previously known efficiency theory and provide a useful identity and formulaic technique only relying on the basics of integration which, are self-contained in this tutorial and can be used in most any setting one might encounter in practice. The paper provides many examples of such derivations for well-known influence functions as well as for new parameters of interest. The influence function remains a central object for constructing efficient estimators for large models, such as the one-step estimator and the targeted maximum likelihood estimator. We will not touch upon these estimators at all but readers familiar with these estimators might find this tutorial of particular use.

math.ST↗

arXiv2019

Comparison of plotting system outputs in beginner analysts

The R programming language is built on an ecosystem of packages, some that allow analysts to accomplish the same tasks. For example, there are at least two clear workflows for creating data visualizations in R: using the base graphics package (referred to as "base R") and the ggplot2 add-on package based on the grammar of graphics. Here we perform an empirical study of the quality of scientific graphics produced by beginning R users. In our experiment, learners taking a data science course on the Coursera platform were randomized to complete identical plotting exercises in either the base R or the ggplot2 system. Learners were then asked to evaluate their peers in terms of visual characteristics key to scientific cognition. We observed that graphics created with the two systems rated similarly on many characteristics. However, ggplot2 graphics were generally judged to be more visually pleasing and, in the case of faceted scientific plots, easier to understand. Our results suggest that while both graphic systems are useful in the hands of beginning users, ggplot2's natural faceting system may be easier to use by beginning users for displaying more complex relationships.

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arXiv2019

The Fuzzy ROC

The fuzzy ROC extends Receiver Operating Curve (ROC) visualization to the situation where some data points, falling in an indeterminacy region, are not classified. It addresses two challenges: definition of sensitivity and specificity bounds under indeterminacy; and visual summarization of the large number of possibilities arising from different choices of indeterminacy zones.

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arXiv2019

Synthesis of High-Resolution Load Profiles with Minimal Data

For the estimation of a new energy supply system it is an important to have high-resolution energy load profile. Such a profile is in general either not present or very costly to obtain. We will therefore present a method which synthesizes load profiles from minimal given data, but with maximal resolution. The general initial data setting includes month integrals and load profiles a few days. The resulting time series features all important properties to represent a real energy profile.

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arXiv2019

Three issues impeding communication of statistical methodology for incomplete data

We identify three issues permeating the literature on statistical methodology for incomplete data written for non-specialist statisticians and other investigators. The first is a mathematical defect in the notation Yobs, Ymis used to partition the data into observed and missing components. The second are issues concerning the notation `P(R|Yobs, Ymis)=P(R|Yobs)' used for communicating the definition of missing at random (MAR). And the third is the framing of ignorability by emulating complete-data methods exactly, rather than treating the question of ignorability on its own merits. These issues have been present in the literature for a long time, and have simple remedies. The purpose of this paper is to raise awareness of these issues, and to explain how they can be remedied.

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arXiv2019

Deterministic bootstrapping for a class of bootstrap methods

An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp. input-derived data). In essence, the algorithm computes the distribution function from a linear mixture of independent random variables each having a finite discrete distribution. The algorithm is applicable to elementary bootstrap scenarios (targetting the mean as parameter of interest), for block bootstrap, as well as for certain residual bootstrap scenarios. Moreover, the algorithm promises a much broader applicability, in non-bootstrapped hypothesis testing.

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arXiv2019

Modeling the Health Expenditure in Japan, 2011. A Healthy Life Years Lost Methodology

The Healthy Life Years Lost Methodology (HLYL) is introduced to model and estimate the Health Expenditure in Japan in 2011. The HLYL theory and estimation methods are presented in our books in the Springer Series on Demographic Methods and Population Analysis vol. 45 and 46 titled: Exploring the Health State of a Population by Dynamic Modeling Methods and Demography and Health Issues: Population Aging, Mortality and Data Analysis. Special applications appear in Chapters of these books as in The Health-Mortality Approach in Estimating the Healthy Life Years Lost Compared to the Global Burden of Disease Studies and Applications in World, USA and Japan and in Estimation of the Healthy Life Expectancy in Italy Through a Simple Model Based on Mortality Rate by Skiadas and Arezzo. Here further to present the main part of the methodology with more details and illustrations, we develop and extend a life table important to estimate the healthy life years lost along with the fitting to the health expenditure in the related case. The application results are quite promising and important to support decision makers and health agencies with a powerful tool to improve the health expenditure allocation and the future predictions.

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arXiv2020

An innovating Statistical Learning Tool based on Partial Differential Equations, intending livestock Data Assimilation

The realistic modeling intended to quantify precisely some biological mechanisms is a task requiering a lot of a priori knowledge and generally leading to heavy mathematical models. On the other hand, the structure of the classical Machine Learning algorithms, such as Neural Networks, limits their flexibility and the possibility to take into account the existence of complex underlying phenomena, such as delay, saturation and accumulation. The aim of this paper is to reach a compromise between precision, parsimony and flexibility to design an efficient biomimetic predictive tool extracting knowledge from livestock data. To achieve this, we build a Mathematical Model based on Partial Differential Equations (PDE) embarking the mathematical expression of biological determinants. We made the hypothesis that all the physico-chemical phenomena occurring in animal body can be summarized by the evolution of a global information. Therefore the developed PDE system describes the evolution and the action of an information circulating in an Avatar of the Real Animal. This Avatar outlines the dynamics of the biological reactions of animal body in the framework of a specific problem. Each PDE contains parameters corresponding to biological-like factors which can be learnt from data by the developed Statistical Learning Tool.

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arXiv2019

Statistical testing in a Linear Probability Space

Imagine that you could calculate of posttest probabilities, i.e. Bayes theorem with simple addition. This is possible if we stop thinking of probabilities as ranging from 0 to 1.0. There is a naturally occurring linear probability space when data are transformed into the logarithm of the odds ratio (log10 odds). In this space, probabilities are replaced by W (Weight) where W=log10(probability/(1-probability)). I would like to argue the multiple benefits of performing statistical testing in a linear probability space: 1) Statistical testing is accurate in linear probability space but not in other spaces. 2) Effect size is called Impact (I) and is the difference in means between two treatments (I=Wmean2-Wmean1). 3) Bayes theorem is simply Wposttest=Wpretest+Itest. 4) Significance (p value) is replaced by Certainty (C) which is the W of the p value. Methods to transform data into and out of linear probability space are described.

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arXiv2019

Analytic Evaluation of the Fractional Moments for the Quasi-Stationary Distribution of the Shiryaev Martingale on an Interval

We consider the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval $[0,A]$ with absorption at a fixed $A>0$. We derive analytically a closed-form formula for the distribution's fractional moment of an {\em arbitrary} given order $s\in\mathbb{R}$; the formula is consistent with that previously found by Polunchenko and Pepelyshev (2018) for the case of $s\in\mathbb{N}$. We also show by virtue of the formula that, if $s<1$, then the $s$-th fractional moment of the quasi-stationary distribution becomes that of the exponential distribution (with mean $1/2$) in the limit as $A\to+\infty$; the limiting exponential distribution is the stationary distribution of the reciprocal of the Shiryaev diffusion.

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arXiv2019

The Contribution Plot: Decomposition and Graphical Display of the RV Coefficient, with Application to Genetic and Brain Imaging Biomarkers of Alzheimer's Disease

Alzheimer's disease (AD) is a chronic neurodegenerative disease that causes memory loss and decline in cognitive abilities. AD is the sixth leading cause of death in the United States, affecting an estimated 5 million Americans. To assess the association between multiple genetic variants and multiple measurements of structural changes in the brain a recent study of AD used a multivariate measure of linear dependence, the RV coefficient. The authors decomposed the RV coefficient into contributions from individual variants and displayed these contributions graphically. We investigate the properties of such a `contribution plot' in terms of an underlying linear model, and discuss estimation of the components of the plot when the correlation signal may be sparse. The contribution plot is applied to simulated data and to genomic and brain imaging data from the Alzheimer's Disease Neuroimaging Initiative.

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arXiv2019

GraSPy: Graph Statistics in Python

We introduce GraSPy, a Python library devoted to statistical inference, machine learning, and visualization of random graphs and graph populations. This package provides flexible and easy-to-use algorithms for analyzing and understanding graphs with a scikit-learn compliant API. GraSPy can be downloaded from Python Package Index (PyPi), and is released under the Apache 2.0 open-source license. The documentation and all releases are available at https://neurodata.io/graspy.

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arXiv2019

Statistical witchhunts: Science, justice & the p-value crisis

We provide accessible insight into the current 'replication crisis' in 'statistical science', by revisiting the old metaphor of 'court trial as hypothesis test'. Inter alia, we define and diagnose harmful statistical witch-hunting both in justice and science, which extends to the replication crisis itself, where a hunt on p-values is currently underway.

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arXiv2019

Some ordering properties of highest and lowest order statistics with exponentiated Gumble type-II distributed components

In this paper, we have studied the stochastic comparisons of the highest and lowest order statistics of exponentiated Gumble type-II distribution with three parameters. We have compared both the statistics by using three different stochastic ordering. First, we consider a system with different scale and outer shape parameters and then we study the usual stochastic ordering of the lowest and highest order statistics in the sense of multivariate chain majorization. In addition, we construct two examples to support our results. Second, by using the vector majorization technique, we study the usual stochastic ordering, the reversed failure rate ordering and the likelihood ratio ordering with respect to different outer shape parameters, next, by varying the inner shape parameter, we discuss the usual stochastic order of the lowest order statistics and we have shown that the highest order statistics are not comparable in the usual stochastic ordering by an example.

math.ST↗

arXiv2019

Introducing Bayesian Analysis with $\text{m&m's}^\circledR$: an active-learning exercise for undergraduates

We present an active-learning strategy for undergraduates that applies Bayesian analysis to candy-covered chocolate $\text{m&m's}^\circledR$. The exercise is best suited for small class sizes and tutorial settings, after students have been introduced to the concepts of Bayesian statistics. The exercise takes advantage of the non-uniform distribution of $\text{m&m's}^\circledR~$ colours, and the difference in distributions made at two different factories. In this paper, we provide the intended learning outcomes, lesson plan and step-by-step guide for instruction, and open-source teaching materials. We also suggest an extension to the exercise for the graduate-level, which incorporates hierarchical Bayesian analysis.

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arXiv2019

Governance on Social Media Data: Different Focuses between Government and Internet Company

How governments and Internet companies regulate user data on social media attracts public attention. This study tried to answer two questions: What kind of countries send more requests for Facebook user data? What kind of countries get more requests replies from Facebook? We aim to figure out how a country's economic, political and social factors affect its government requests for user data and Facebook's responses rate to those requests. Results show that countries with higher GDP per capita, a higher level of human freedom and a lower level of rule of law send more requests for user data; while Facebook tends to reply to government requests from countries with a higher level of human freedom and a lower level of political stability. In conclusion, governments and Facebook show different focuses on governance on social media data.

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