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arXiv2015

On testing More IFRA Ordering-II

Suppose F and G are two life distribution functions. It is said that F is more IFRA than G (written by F<_* G) if G^(-1) F(x) is starshaped on (0,infty). In this paper, the problem of testing H_0:F=_* G against H_1:F<_* G and F \neq_* G is considered in both cases when G is known and when G is unknown. We propose a new test based on U-statistics and obtain the asymptotic distribution of the test statistics. The new test is compared with some well known tests in the literature. In addition, we apply our test to a real data set in the context of reliability.

math.ST↗

arXiv2015

The Compass for Statistical Researchers

We have hiked many miles alongside several professors as we traversed our statistical path -- a regime switching trail which changed direction following a class on the foundations of our discipline. As we play the game of research in that limbo between student and academic, one thing among Prof. Bernardi's teachings has never been more clear: to draw a route in the research map you not only need to know your destination, but you must also understand where you are and how you arrived there.

stat.OT↗

arXiv2015

Creating, Automating, and Assessing Online Homework in Introductory Statistics and Mathematics Classes

Although textbook publishers offer course management systems, they do so to promote brand loyalty, and while an open source tool such as WeBWorK is promising, it requires administrative and IT buy-in. So supported in part by a College Access Challenge Grant from the Department of Education, we collaborated with other instructors to create online homework sets for three classes: Elementary Algebra, Intermediate Algebra, and Statistics for Behavioral Sciences I. After experimentation, some of these question pools are now created by Mathematica programs that can generate data sets from specified distributions, generate random polynomials that factor in a given way, create image files of histograms, scatterplots, and so forth. These programs produce files that can be read by the software package, Respondus, which then uploads the questions into Blackboard Learn, the course management system used by the Connecticut State University system. Finally, we summarize five classes worth of student performance data along with lessons learned while working on this project.

stat.OT↗

arXiv2015

The Problem Of Grue Isn't

The so-called problem of grue was introduced by Nelson Goodman in 1954 as a "riddle" about induction, a riddle which has been widely thought to cast doubt on the validity and rationality of induction. That unnecessary doubt in turn is partly responsible for the reluctance to adopt the view that probability is part of logic. Several authors have pointed out deficiencies in grue; nevertheless, the "problem" still excites. Here, adapted from Groarke, is presented the basis of grue, along with another simple demonstration that the "problem" makes no sense and is brought about by a misunderstanding of causation.

stat.OT↗

arXiv2015

What are the true clusters?

Constructivist philosophy and Hasok Chang's active scientific realism are used to argue that the idea of "truth" in cluster analysis depends on the context and the clustering aims. Different characteristics of clusterings are required in different situations. Researchers should be explicit about on what requirements and what idea of "true clusters" their research is based, because clustering becomes scientific not through uniqueness but through transparent and open communication. The idea of "natural kinds" is a human construct, but it highlights the human experience that the reality outside the observer's control seems to make certain distinctions between categories inevitable. Various desirable characteristics of clusterings and various approaches to define a context-dependent truth are listed, and I discuss what impact these ideas can have on the comparison of clustering methods, and the choice of a clustering methods and related decisions in practice.

stat.OT↗

arXiv2015

A comparative review of generalizations of the Gumbel extreme value distribution with an application to wind speed data

The generalized extreme value distribution and its particular case, the Gumbel extreme value distribution, are widely applied for extreme value analysis. The Gumbel distribution has certain drawbacks because it is a non-heavy-tailed distribution and is characterized by constant skewness and kurtosis. The generalized extreme value distribution is frequently used in this context because it encompasses the three possible limiting distributions for a normalized maximum of infinite samples of independent and identically distributed observations. However, the generalized extreme value distribution might not be a suitable model when each observed maximum does not come from a large number of observations. Hence, other forms of generalizations of the Gumbel distribution might be preferable. Our goal is to collect in the present literature the distributions that contain the Gumbel distribution embedded in them and to identify those that have flexible skewness and kurtosis, are heavy-tailed and could be competitive with the generalized extreme value distribution. The generalizations of the Gumbel distribution are described and compared using an application to a wind speed data set and Monte Carlo simulations. We show that some distributions suffer from overparameterization and coincide with other generalized Gumbel distributions with a smaller number of parameters, i.e., are non-identifiable. Our study suggests that the generalized extreme value distribution and a mixture of two extreme value distributions should be considered in practical applications.

stat.ME↗

arXiv2015

On Statistical Analysis of the Pattern of Evolution of Perceived Emotions Induced by Hindustani Music- A Study Based on Listener Responses

The objective of this study is to find the underlying pattern of how perception of emotions has evolved in India. Here Hindustani Music has been used as a reference frame for tracking the changing perception of emotions. It has been found that different emotions perceived from Hindustani Music form a particular sequential pattern when their corresponding pitch periods are analyzed using the standard deviations and mean successive squared differences.This sequential pattern of emotions coincides with their corresponding sequential pattern of tempos or average number of steady states. On the basis of this result we further found that the range of perception of emotions has diminished significantly these days compared to what it was before. The proportion of responses for the perceived emotions like Anger, Serenity, Romantic and Sorrow has also decreased to a great extent than what it was previously. The proportion of responses for the perceived emotion Anxiety has increased phenomenally. Both standard deviation and mean successive squared difference are two very good measures in tracking the changing perception of emotions. The overall pattern of the change of perceived emotions has corresponded to the psychological and sociological change of human life.

stat.OT↗

arXiv2015

A Reputation Economy: Results from an Empirical Survey on Academic Data Sharing

Academic data sharing is a way for researchers to collaborate and thereby meet the needs of an increasingly complex research landscape. It enables researchers to verify results and to pursuit new research questions with "old" data. It is therefore not surprising that data sharing is advocated by funding agencies, journals, and researchers alike. We surveyed 2661 individual academic researchers across all disciplines on their dealings with data, their publication practices, and motives for sharing or withholding research data. The results for 1564 valid responses show that researchers across disciplines recognise the benefit of secondary research data for their own work and for scientific progress as a whole-still they only practice it in moderation. An explanation for this evidence could be an academic system that is not driven by monetary incentives, nor the desire for scientific progress, but by individual reputation-expressed in (high ranked journal) publications. We label this system a Reputation Economy. This special economy explains our findings that show that researchers have a nuanced idea how to provide adequate formal recognition for making data available to others-namely data citations. We conclude that data sharing will only be widely adopted among research professionals if sharing pays in form of reputation. Thus, policy measures that intend to foster research collaboration need to understand academia as a reputation economy. Successful measures must value intermediate products, such as research data, more highly than it is the case now.

cs.DL↗

arXiv2015

Teaching and Learning Data Visualization: Ideas and Assignments

This article discusses how to make statistical graphics a more prominent element of the undergraduate statistics curricula. The focus is on several different types of assignments that exemplify how to incorporate graphics into a course in a pedagogically meaningful way. These assignments include having students deconstruct and reconstruct plots, copy masterful graphs, create one-minute visual revelations, convert tables into `pictures', and develop interactive visualizations with, e.g., the virtual earth as a plotting canvas. In addition to describing the goals and details of each assignment, we also discuss the broader topic of graphics and key concepts that we think warrant inclusion in the statistics curricula. We advocate that more attention needs to be paid to this fundamental field of statistics at all levels, from introductory undergraduate through graduate level courses. With the rapid rise of tools to visualize data, e.g., Google trends, GapMinder, ManyEyes, and Tableau, and the increased use of graphics in the media, understanding the principles of good statistical graphics, and having the ability to create informative visualizations is an ever more important aspect of statistics education.

stat.OT↗

arXiv2015

A Data Science Course for Undergraduates: Thinking with Data

Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the increasingly sophisticated array of data available in many settings. These data tend to be non-traditional, in the sense that they are often live, large, complex, and/or messy. A first course in statistics at the undergraduate level typically introduces students with a variety of techniques to analyze small, neat, and clean data sets. However, whether they pursue more formal training in statistics or not, many of these students will end up working with data that is considerably more complex, and will need facility with statistical computing techniques. More importantly, these students require a framework for thinking structurally about data. We describe an undergraduate course in a liberal arts environment that provides students with the tools necessary to apply data science. The course emphasizes modern, practical, and useful skills that cover the full data analysis spectrum, from asking an interesting question to acquiring, managing, manipulating, processing, querying, analyzing, and visualizing data, as well communicating findings in written, graphical, and oral forms.

stat.OT↗

arXiv2015

Data Science as a New Frontier for Design

The purpose of this paper is to contribute to the challenge of transferring know-how, theories and methods from design research to the design processes in information science and technologies. More specifically, we shall consider a domain, namely data-science, that is becoming rapidly a globally invested research and development axis with strong imperatives for innovation given the data deluge we are currently facing. We argue that, in order to rise to the data-related challenges that the society is facing, data-science initiatives should ensure a renewal of traditional research methodologies that are still largely based on trial-error processes depending on the talent and insights of a single (or a restricted group of) researchers. It is our claim that design theories and methods can provide, at least to some extent, the much-needed framework. We will use a worldwide data-science challenge organized to study a technical problem in physics, namely the detection of Higgs boson, as a use case to demonstrate some of the ways in which design theory and methods can help in analyzing and shaping the innovation dynamics in such projects.

cs.AI↗

arXiv2016

Optimality of Fast Matching Algorithms for Random Networks with Applications to Structural Controllability

Network control refers to a very large and diverse set of problems including controllability of linear time-invariant dynamical systems, where the objective is to select an appropriate input to steer the network to a desired state. There are many notions of controllability, one of them being structural controllability, which is intimately connected to finding maximum matchings on the underlying network topology. In this work, we study fast, scalable algorithms for finding maximum matchings for a large class of random networks. First, we illustrate that degree distribution random networks are realistic models for real networks in terms of structural controllability. Subsequently, we analyze a popular, fast and practical heuristic due to Karp and Sipser as well as a simplification of it. For both heuristics, we establish asymptotic optimality and provide results concerning the asymptotic size of maximum matchings for an extensive class of random networks.

cs.DS↗

arXiv2015

Modeling population structure under hierarchical Dirichlet processes

We propose a Bayesian nonparametric model to infer population admixture, extending the Hierarchical Dirichlet Process to allow for correlation between loci due to Linkage Disequilibrium. Given multilocus genotype data from a sample of individuals, the model allows inferring classifying individuals as unadmixed or admixed, inferring the number of subpopulations ancestral to an admixed population and the population of origin of chromosomal regions. Our model does not assume any specific mutation process and can be applied to most of the commonly used genetic markers. We present a MCMC algorithm to perform posterior inference from the model and discuss methods to summarise the MCMC output for the analysis of population admixture. We demonstrate the performance of the proposed model in simulations and in a real application, using genetic data from the EDAR gene, which is considered to be ancestry-informative due to well-known variations in allele frequency as well as phenotypic effects across ancestry. The structure analysis of this dataset leads to the identification of a rare haplotype in Europeans.

stat.AP↗

arXiv2015

Exponentiated Extended Weibull-Power Series Class of Distributions

In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power series, generalized exponential-power series, generalized linear failure rate-power series, exponentiated Weibull-power series, generalized modified Weibull-power series, generalized Gompertz-power series and exponentiated extended Weibull distributions as special cases. We obtain several properties of this new class of distributions such as Shannon entropy, mean residual life, hazard rate function, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented.

stat.OT↗

arXiv2015

Bertrand `paradox' reloaded (with details on transformations of variables, an introduction to Monte Carlo simulation and an inferential variation of the problem)

This note is mainly to point out, if needed, that uncertainty about models and their parameters has little to do with a `paradox'. The proposed `solution' is to formulate practical questions instead of seeking refuge into abstract principles. (And, in order to be concrete, some details on how to calculate the probability density functions of the chord lengths are provided, together with some comments on simulations and an appendix on the inferential aspects of the problem.)

physics.data-an↗

arXiv2015

A Singular Value Decomposition-based Factorization and Parsimonious Component Model of Demographic Quantities Correlated by Age: Predicting Complete Demographic Age Schedules with Few Parameters

BACKGROUND. Formal demography has a long history of building simple models of age schedules of demographic quantities, e.g. mortality and fertility rates. These are widely used in demographic methods to manipulate whole age schedules using few parameters. OBJECTIVE. The Singular Value Decomposition (SVD) factorizes a matrix into three matrices with useful properties including the ability to reconstruct the original matrix using many fewer, simple matrices. This work demonstrates how these properties can be exploited to build parsimonious models of whole age schedules of demographic quantities that can be further parameterized in terms of arbitrary covariates. METHODS. The SVD is presented and explained in detail with attention to developing an intuitive understanding. The SVD is used to construct a general, component model of demographic age schedules, and that model is demonstrated with age-specific mortality and fertility rates. Finally, the model is used (1) to predict age-specific mortality using HIV indicators and summary measures of age-specific mortality, and (2) to predict age-specific fertility using the total fertility rate (TFR). RESULTS. The component model of age-specific mortality and fertility rates succeeds in reproducing the data with two inputs, and acting through those two inputs, various covariates are able to accurately predict full age schedules. CONCLUSIONS. The SVD is potentially useful as a way to summarize, smooth and model age-specific demographic quantities. The component model is a general method of relating covariates to whole age schedules. COMMENTS. The focus of this work is the SVD and the component model. The applications are for illustrative purposes only.

stat.AP↗

arXiv2017

Hyak Mortality Monitoring System: Innovative Sampling and Estimation Methods - Proof of Concept by Simulation

Traditionally health statistics are derived from civil and/or vital registration. Civil registration in low-income countries varies from partial coverage to essentially nothing at all. Consequently the state of the art for public health information in low-income countries is efforts to combine or triangulate data from different sources to produce a more complete picture across both time and space - data amalgamation. Data sources amenable to this approach include sample surveys, sample registration systems, health and demographic surveillance systems, administrative records, census records, health facility records and others. We propose a new statistical framework for gathering health and population data - Hyak - that leverages the benefits of sampling and longitudinal, prospective surveillance to create a cheap, accurate, sustainable monitoring platform. Hyak has three fundamental components: 1) Data Amalgamation: a sampling and surveillance component that organizes two or more data collection systems to work together: a) data from HDSS with frequent, intense, linked, prospective follow-up and b) data from sample surveys conducted in large areas surrounding the Health and Demographic Surveillance System sites using informed sampling so as to capture as many events as possible; 2) Cause of Death: verbal autopsy to characterize the distribution of deaths by cause at the population level; and 3) SES: measurement of socioeconomic status in order to characterize poverty and wealth. We conduct a simulation study of the informed sampling component of Hyak based on the Agincourt HDSS site in South Africa. Compared to traditional cluster sampling, Hyak's informed sampling captures more deaths, and when combined with an estimation model that includes spatial smoothing, produces estimates mortality that have lower variance and small bias.

stat.OT↗

arXiv2015

InSilicoVA: A Method to Automate Cause of Death Assignment for Verbal Autopsy

Verbal autopsies (VA) are widely used to provide cause-specific mortality estimates in developing world settings where vital registration does not function well. VAs assign cause(s) to a death by using information describing the events leading up to the death, provided by care givers. Typically physicians read VA interviews and assign causes using their expert knowledge. Physician coding is often slow, and individual physicians bring bias to the coding process that results in non-comparable cause assignments. These problems significantly limit the utility of physician-coded VAs. A solution to both is to use an algorithmic approach that formalizes the cause-assignment process. This ensures that assigned causes are comparable and requires many fewer person-hours so that cause assignment can be conducted quickly without disrupting the normal work of physicians. Peter Byass' InterVA method is the most widely used algorithmic approach to VA coding and is aligned with the WHO 2012 standard VA questionnaire. The statistical model underpinning InterVA can be improved; uncertainty needs to be quantified, and the link between the population-level CSMFs and the individual-level cause assignments needs to be statistically rigorous. Addressing these theoretical concerns provides an opportunity to create new software using modern languages that can run on multiple platforms and will be widely shared. Building on the overall framework pioneered by InterVA, our work creates a statistical model for automated VA cause assignment.

stat.OT↗