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At least 253 records · Page 14Linked to original sources

arXiv2016

Different numerical estimators for main effect global sensitivity indices

The variance-based method of global sensitivity indices based on Sobol sensitivity indices became very popular among practitioners due to its easiness of interpretation. For complex practical problems computation of Sobol indices generally requires a large number of function evaluations to achieve reasonable convergence. Four different direct formulas for computing Sobol main effect sensitivity indices are compared on a set of test problems for which there are analytical results. These formulas are based on high-dimensional integrals which are evaluated using MC and QMC techniques. Direct formulas are also compared with a different approach based on the so-called double loop reordering formula. It is found that the double loop reordering (DLR) approach shows a superior performance among all methods both for models with independent and dependent variables.

math.NA↗

arXiv2016

Peter Hall's work on high-dimensional data and classification

In this article, I summarise Peter Hall's contributions to high-dimensional data, including their geometric representations and variable selection methods based on ranking. I also discuss his work on classification problems, concluding with some personal reflections on my own interactions with him.

stat.OT↗

arXiv2016

When Does a Boltzmannian Equilibrium Exist?

The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we address these questions from the vantage point of the long-run fraction of time definition of Boltzmannian equilibrium that we developed in two recent papers (Werndl and Frigg 2015a, 2015b). After a short summary of Boltzmannian statistical mechanics and our definition of equilibrium, we state an existence theorem which provides general criteria for the existence of an equilibrium state. We first illustrate how the theorem works with a toy example, which allows us to illustrate the various elements of the theorem in a simple setting. After commenting on the ergodic programme, we discuss equilibria in a number of different gas systems: the ideal gas, the dilute gas, the Kac gas, the stadium gas, the mushroom gas and the multi-mushroom gas. In the conclusion we briefly summarise the main points and highlight open questions.

cond-mat.stat-mech↗

arXiv2016

Bringing Order to the Chaos in the Brickyard

An allegory published in 1963 titled Chaos in the Brickyard spoke to the decline in the quality of research. In the intervening time greater awareness of the issues and actions to improve research endeavors have emerged. Still, problems persist. This paper is intended to clarify some of the challenges, particularly with respect to quantitative research, then suggest ways to improve the quality of published research. The paper highlights where feasible refinements in analytical techniques can be made and provides a guide to fundamental principles related to data analysis in research.

stat.OT↗

arXiv2016

Identifiability and testability in GRT with Individual Differences

Silbert and Thomas (2013) showed that failures of decisional separability are not, in general, identifiable in fully parameterized $2 \times 2$ Gaussian GRT models. A recent extension of $2 \times 2$ GRT models (GRTwIND) was developed to solve this problem and a conceptually similar problem with the simultaneous identifiability of means and marginal variances in GRT models. Central to the ability of GRTwIND to solve these problems is the assumption of universal perception, which consists of shared perceptual distributions modified by attentional and global scaling parameters (Soto et al., 2015). If universal perception is valid, GRTwIND solves both issues. In this paper, we show that GRTwIND with universal perception and subject-specific failures of decisional separability is mathematically, and thereby empirically, equivalent to a model with decisional separability and failure of universal perception. We then provide a formal proof of the fact that means and marginal variances are not, in general, simultaneously identifiable in $2 \times 2$ GRT models, including GRTwIND. These results can be taken to delineate precisely what the assumption of universal perception must consist of. Based on these results and related recent mathematical developments in the GRT framework, we propose that, in addition to requiring a fixed subset of parameters to determine the location and scale of any given GRT model, some subset of parameters must be set in GRT models to fix the orthogonality of the modeled perceptual dimensions, a central conceptual underpinning of the GRT framework. We conclude with a discussion of perceptual primacy and its relationship to universal perception.

stat.OT↗

arXiv2016

Consider avoiding the .05 significance level

It is suggested that some shortcomings of Null Hypothesis Significance Testing (NHST), viewed from the perspective of Bayesian statistics, turn benign once the traditional threshold p value of .05 is substituted by a sufficiently smaller value. To illustrate, the posterior probability of H0 stating P=.5, given data that just render it rejected by NHST with a p value of .05 (and a uniform prior), is shown here to be not much smaller than .50 for most values of N below 100 (and even exceeds .50 for N>=100); in contrast, with a p value of .001 posterior probability does not exceed .06 for N<=100 (neither .25 for N<9000). Yet more interesting, posterior probability becomes quite independent of N with a p value of .0001, hence practically satisfying the alpha postulate - set by Cornfield (1966) as the condition for p value being a measure of evidence in itself. In view of the low prospect that most researchers will soon convert to use Bayesian statistics in any form, we thus suggest that researchers who elect the conservative option of resorting to NHST be encouraged to avoid as much as possible using a p value of .05 as a threshold for rejecting H0. The analysis presented here may be used to discuss afresh which level of threshold p value seems to be a reasonable, practical substitute.

stat.OT↗

arXiv2016

The Simulator: An Engine to Streamline Simulations

The simulator is an R package that streamlines the process of performing simulations by creating a common infrastructure that can be easily used and reused across projects. Methodological statisticians routinely write simulations to compare their methods to preexisting ones. While developing ideas, there is a temptation to write "quick and dirty" simulations to try out ideas. This approach of rapid prototyping is useful but can sometimes backfire if bugs are introduced. Using the simulator allows one to remove the "dirty" without sacrificing the "quick." Coding is quick because the statistician focuses exclusively on those aspects of the simulation that are specific to the particular paper being written. Code written with the simulator is succinct, highly readable, and easily shared with others. The modular nature of simulations written with the simulator promotes code reusability, which saves time and facilitates reproducibility. The syntax of the simulator leads to simulation code that is easily human-readable. Other benefits of using the simulator include the ability to "step in" to a simulation and change one aspect without having to rerun the entire simulation from scratch, the straightforward integration of parallel computing into simulations, and the ability to rapidly generate plots, tables, and reports with minimal effort.

stat.CO↗

arXiv2016

Embracing Data Science

Statistics is running the risk of appearing irrelevant to today's undergraduate students. Today's undergraduate students are familiar with data science projects and they judge statistics against what they have seen. Statistics, especially at the introductory level, should take inspiration from data science so that the discipline is not seen as somehow lesser than data science. This article provides a brief overview of data science, outlines ideas for how introductory courses could take inspiration from data science, and provides a reference to materials for developing stand-alone data science courses.

stat.OT↗

arXiv2016

Dynamic Question Ordering in Online Surveys

Online surveys have the potential to support adaptive questions, where later questions depend on earlier responses. Past work has taken a rule-based approach, uniformly across all respondents. We envision a richer interpretation of adaptive questions, which we call dynamic question ordering (DQO), where question order is personalized. Such an approach could increase engagement, and therefore response rate, as well as imputation quality. We present a DQO framework to improve survey completion and imputation. In the general survey-taking setting, we want to maximize survey completion, and so we focus on ordering questions to engage the respondent and collect hopefully all information, or at least the information that most characterizes the respondent, for accurate imputations. In another scenario, our goal is to provide a personalized prediction. Since it is possible to give reasonable predictions with only a subset of questions, we are not concerned with motivating users to answer all questions. Instead, we want to order questions to get information that reduces prediction uncertainty, while not being too burdensome. We illustrate this framework with an example of providing energy estimates to prospective tenants. We also discuss DQO for national surveys and consider connections between our statistics-based question-ordering approach and cognitive survey methodology.

stat.OT↗

arXiv2016

Progress on a Conjecture Regarding the Triangular Distribution

Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval can be performed via an order statistics-based method. It had been conjectured that such a method can be conducted using only a constant number of likelihood function evaluations, on average, as the sample size becomes large. We prove two theorems that validate this conjecture. Graphical and numerical results are presented to supplement our proofs.

stat.OT↗

arXiv2016

Statistical Methods in Topological Data Analysis for Complex, High-Dimensional Data

The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data spaces. This paper provides an introductory overview of the mathematical underpinnings of Topological Data Analysis, the workflow to convert samples of data to topological summary statistics, and some of the statistical methods developed for performing inference on these topological summary statistics. The intention of this non-technical overview is to motivate statisticians who are interested in learning more about the subject.

stat.AP↗

arXiv2016

Designing Modular Software: A Case Study in Introductory Statistics

Modular programming is a development paradigm that emphasizes self-contained, flexible, and independent pieces of functionality. This practice allows new features to be seamlessly added when desired, and unwanted features to be removed, thus simplifying the user-facing view of the software. The recent rise of web-based software applications has presented new challenges for designing an extensible, modular software system. In this paper, we outline a framework for designing such a system, with a focus on reproducibility of the results. We present as a case study a Shiny-based web application called intRo, that allows the user to perform basic data analyses and statistical routines. Finally, we highlight some challenges we encountered, and how to address them, when combining modular programming concepts with reactive programming as used by Shiny.

stat.OT↗

arXiv2017

Unifying Markov Properties for Graphical Models

Several types of graphs with different conditional independence interpretations --- also known as Markov properties --- have been proposed and used in graphical models. In this paper we unify these Markov properties by introducing a class of graphs with four types of edges --- lines, arrows, arcs, and dotted lines --- and a single separation criterion. We show that independence structures defined by this class specialize to each of the previously defined cases, when suitable subclasses of graphs are considered. In addition, we define a pairwise Markov property for the subclass of chain mixed graphs which includes chain graphs with the LWF interpretation, as well as summary graphs (and consequently ancestral graphs). We prove the equivalence of this pairwise Markov property to the global Markov property for compositional graphoid independence models.

math.ST↗

arXiv2017

Revisiting nested group testing procedures: new results, comparisons, and robustness

Group testing has its origin in the identification of syphilis in the US army during World War II. Much of the theoretical framework of group testing was developed starting in the late 1950s, with continued work into the 1990s. Recently, with the advent of new laboratory and genetic technologies, there has been an increasing interest in group testing designs for cost saving purposes. In this paper, we compare different nested designs, including Dorfman, Sterrett and an optimal nested procedure obtained through dynamic programming. To elucidate these comparisons, we develop closed-form expressions for the optimal Sterrett procedure and provide a concise review of the prior literature for other commonly used procedures. We consider designs where the prevalence of disease is known as well as investigate the robustness of these procedures when it is incorrectly assumed. This article provides a technical presentation that will be of interest to researchers as well as from a pedagogical perspective. Supplementary material for this article is available online.

stat.OT↗

arXiv2016

Probabilistic Population Projections for Countries with Generalized HIV/AIDS Epidemics

The United Nations (UN) issued official probabilistic population projections for all countries to 2100 in July 2015. This was done by simulating future levels of total fertility and life expectancy from Bayesian hierarchical models, and combining the results using a standard cohort-component projection method. The 40 countries with generalized HIV/AIDS epidemics were treated differently from others, in that the projections used the highly multistate Spectrum/EPP model, a complex 15-compartment model that was designed for short-term projections of quantities relevant to policy for the epidemic. Here we propose a simpler approach that is more compatible with the existing UN probabilistic projection methodology for other countries. Changes in life expectancy are projected probabilistically using a simple time series regression model on current life expectancy, HIV prevalence and ART coverage. These are then converted to age- and sex-specific mortality rates using a new family of model life tables designed for countries with HIV/AIDS epidemics that reproduces the characteristic hump in middle adult mortality. These are then input to the standard cohort-component method, as for other countries. The method performed well in an out-of-sample cross-validation experiment. It gives similar population projections to Spectrum/EPP in the short run, while being simpler and avoiding multistate modeling.

stat.AP↗

arXiv2017

Sterrett Procedure for the Generalized Group Testing Problem

Group testing is a useful method that has broad applications in medicine, engineering, and even in airport security control. Consider a finite population of $N$ items, where item $i$ has a probability $p_i$ to be defective. The goal is to identify all items by means of group testing. This is the generalized group testing problem. The optimum procedure, with respect to the expected total number of tests, is unknown even in case when all $p_i$ are equal. \cite{H1975} proved that an ordered partition (with respect to $p_i$) is the optimal for the Dorfman procedure (procedure $D$), and obtained an optimum solution (i.e., found an optimal partition) by dynamic programming. In this paper, we investigate the Sterrett procedure (procedure $S$). We provide close form expression for the expected total number of tests, which allows us to find the optimum arrangement of the items in the particular group. We also show that an ordered partition is not optimal for the procedure $S$ or even for a slightly modified Dorfman procedure (procedure $D^{\prime}$). This discovery implies that finding an optimal procedure $S$ appears to be a hard computational problem. However, by using an optimal ordered partition for all procedures, we show that procedure $D^{\prime}$ is uniformly better than procedure $D$, and based on numerical comparisons, procedure $S$ is uniformly and significantly better than procedures $D$ and $D^{\prime}$.

stat.OT↗

arXiv2019

Graphical Models for Discrete and Continuous Data

We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential trace models, are amenable to estimation based on maximum likelihood. We introduce a sampling-based approximation algorithm for computing the maximum likelihood estimator, and we apply this pipeline to learn simultaneous neural activities from spike data.

math.ST↗

arXiv2016

Spatial Temporal Exponential-Family Point Process Models for the Evolution of Social Systems

We develop a class of exponential-family point processes based on a latent social space to model the coevolution of social structure and behavior over time. Temporal dynamics are modeled as a discrete Markov process specified through individual transition distributions for each actor in the system at a given time. We prove that these distributions have an analytic closed form under certain conditions and use the result to develop likelihood-based inference. We provide a computational framework to enable both simulation and inference in practice. Finally, we demonstrate the value of these models by analyzing alcohol and drug use over time in the context of adolescent friendship networks.

stat.OT↗