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At least 307 records · Page 17Linked to original sources

arXiv2017

Comparing the Finite-Time Performance of Simulation-Optimization Algorithms

We empirically evaluate the finite-time performance of several simulation-optimization algorithms on a testbed of problems with the goal of motivating further development of algorithms with strong finite-time performance. We investigate if the observed performance of the algorithms can be explained by properties of the problems, e.g., the number of decision variables, the topology of the objective function, or the magnitude of the simulation error.

math.OC↗

arXiv2017

Explanation and exact formula of Zipfs law evaluated from rank-share combinatorics

This work proves that ranks and shares are statistically dependent on one another, based on simple combinatorics. It presents a formula for rank-share distribution and illustrates that Zipfs law, is descended from expected values of various ranks in the new distribution. All conclusions, formulas and charts presented here were tested against publicly available statistical data in different areas. The correlation coefficient between the calculated values and statistical numbers provided by Bureau of Labor Statistics was 0.99899. Monte-Carlo simulations were performed as additional evidence.

stat.OT↗

arXiv2017

An Investigation of the Different Levels of Poverty and the Corresponding Variance in Student Academic Prosperity

Underprivileged students, especially in primary school, have shown to have less access to educational materials often resulting in general dissatisfaction in the school system and lower academic performance (Saatcioglu and Rury, 2012, p.23). The relationship between family socioeconomic status and student interest in academic endeavors, level of classroom engagement, and participation in extracurricular programs were analyzed. Socioeconomic status was categorized as below poverty level, at or above poverty level, 100 to 199 percent of poverty, and 200 percent of poverty or higher (United States Census Bureau). Student interest, engagement, and persistence were measured as a scalar quantity of three variables: never, sometimes, and often. The participation of students in extracurricular activities was also compared based on the same categories of socioeconomic status. After running the multivariate analysis of variance, it was found that there was a statistically significant variance of student academic prosperity and poverty level.

stat.AP↗

arXiv2018

On a Class of Objective Priors from Scoring Rules

Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off the chosen statistical model and in the majority of cases the resulting prior is improper, which can pose limitations to a practical implementation, even when the complexity of the model is moderate. In this paper we propose to take a novel look at the construction of objective prior distributions, where the connection with a chosen sampling distribution model is removed. We explore the notion of defining objective prior distributions which allow one to have some degree of flexibility, in particular in exhibiting some desirable features, such as being proper, or centered on specific values which would be of interest in nested model comparisons. The basic tool we use are proper scoring rules and the main result is a class of objective prior distributions that can be employed in scenarios where the usual model based priors fail, such as mixture models and model selection via Bayes factors. In addition, we show that the proposed class of priors is the result of minimising the information it contains, providing solid interpretation to the method.

stat.ME↗

arXiv2017

Fiducial on a string

The fiducial argument of Fisher (1973) has been described as his biggest blunder, but the recent review of Hannig et al. (2016) demonstrates the current and increasing interest in this brilliant idea. This short note analyses an example introduced by Seidenfeld (1992) where the fiducial distribution is restricted to a string. Keywords and phrases: Bayesian and fiducial inference, Restrictions on parameters, Uncertainty quantification, Epistemic probability, Statistics on a manifold.

stat.OT↗

arXiv2017

A Contemporary Overview of Probabilistic Latent Variable Models

In this paper we provide a conceptual overview of latent variable models within a probabilistic modeling framework, an overview that emphasizes the compositional nature and the interconnectedness of the seemingly disparate models commonly encountered in statistical practice.

stat.ML↗

arXiv2017

A network flow approach to visualising the roles of covariates in random forests

We propose novel applications of parallel coordinates plots and Sankey diagrams to represent the hierarchies of interacting covariate effects in random forests. Each visualisation summarises the frequencies of all of the paths through all of the trees in a random forest. Visualisations of the roles of covariates in random forests include: ranked bar or dot charts depicting scalar metrics of the contributions of individual covariates to the predictive accuracy of the random forest; line graphs depicting various summaries of the effect of varying a particular covariate on the predictions from the random forest; heatmaps of metrics of the strengths of interactions between all pairs of covariates; and parallel coordinates plots for each response class depicting the distributions of the values of all covariates among the observations most representative of those predicted to belong that class. Together these visualisations facilitate substantial insights into the roles of covariates in a random forest but do not communicate the frequencies of the hierarchies of covariates effects across the random forest or the orders in which covariates occur in these hierarchies. Our visualisations address these gaps. We demonstrate our visualisations using a random forest fitted to publicly available data and provide a software implementation in the form of an R package.

stat.OT↗

arXiv2017

A novel entropy recurrence quantification analysis

The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on the concept of information entropy, in which the probabilities are associated to microstates defined from the recurrence phase space. Recurrence properties can properly be studied using recurrence plots, a methodology based on binary matrices where trajec- tories in phase space of dynamical systems are evaluated against other embedded trajectory. Our novel entropy methodology has several advantages compared to the traditional recurrence entropy defined in the literature, namely, the correct evaluation of the chaoticity level of the signal, the weak dependence on parameters, correct evaluation of periodic time series properties and more sensitivity to noise level of time series. Furthermore, the new entropy quantifier developed in this manuscript also fixes inconsistent results of the traditional recurrence entropy concept, reproducing classical results with novel insights.

stat.OT↗

arXiv2018

Decision-Making and Biases in Cybersecurity Capability Development: Evidence from a Simulation Game Experiment

We developed a simulation game to study the effectiveness of decision-makers in overcoming two complexities in building cybersecurity capabilities: potential delays in capability development; and uncertainties in predicting cyber incidents. Analyzing 1,479 simulation runs, we compared the performances of a group of experienced professionals with those of an inexperienced control group. Experienced subjects did not understand the mechanisms of delays any better than inexperienced subjects; however, experienced subjects were better able to learn the need for proactive decision-making through an iterative process. Both groups exhibited similar errors when dealing with the uncertainty of cyber incidents. Our findings highlight the importance of training for decision-makers with a focus on systems thinking skills, and lay the groundwork for future research on uncovering mental biases about the complexities of cybersecurity.

cs.CR↗

arXiv2017

Coherent combination of probabilistic outputs for group decision making: an algebraic approach

Current decision support systems address domains that are heterogeneous in nature and becoming progressively larger. Such systems often require the input of expert judgement about a variety of different fields and an intensive computational power to produce the scores necessary to rank the available policies. Recently, integrating decision support systems have been introduced to enable a formal Bayesian multi-agent decision analysis to be distributed and consequently efficient. In such systems, where different panels of experts oversee disjoint but correlated vectors of variables, each expert group needs to deliver only certain summaries of the variables under their jurisdiction to properly derive an overall score for the available policies. Here we present an algebraic approach that makes this methodology feasible for a wide range of modelling contexts and that enables us to identify the summaries needed for such a combination of judgements. We are also able to demonstrate that coherence, in a sense we formalize here, is still guaranteed when panels only share a partial specification of their model with other panel members. We illustrate this algebraic approach by applying it to a specific class of Bayesian networks and demonstrate how we can use it to derive closed form formulae for the computations of the joint moments of variables that determine the score of different policies.

stat.OT↗

arXiv2017

Confidence biases and learning among intuitive Bayesians

We design a double-or-quits game to compare the speed of learning one's specific ability with the speed of rising confidence as the task gets increasingly difficult. We find that people on average learn to be overconfident faster than they learn their true ability and we present an intuitive-Bayesian model of confidence which integrates confidence biases and learning. Uncertainty about one's true ability to perform a task in isolation can be responsible for large and stable confidence biases, namely limited discrimination, the hard--easy effect, the Dunning--Kruger effect, conservative learning from experience and the overprecision phenomenon (without underprecision) if subjects act as Bayesian learners who rely only on sequentially perceived performance cues and contrarian illusory signals induced by doubt. Moreover, these biases are likely to persist since the Bayesian aggregation of past information consolidates the accumulation of errors and the perception of contrarian illusory signals generates conservatism and under-reaction to events. Taken together, these two features may explain why intuitive Bayesians make systematically wrong predictions of their own performance.

stat.OT↗

arXiv2020

Estimation of Inverse Weibull Distribution Under Type-I Hybrid Censoring

The hybrid censoring is a mixture of Type I and Type II censoring schemes. This paper presents the statistical inferences of the Inverse Weibull distribution when the data are Type-I hybrid censored. First we consider the maximum likelihood estimators of the unknown parameters. It is observed that the maximum likelihood estimators can not be obtained in closed form. We further obtain the Bayes estimators and the corresponding highest posterior density credible intervals of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. We also compute the approximate Bayes estimators using Lindley's approximation technique. We have performed a simulation study and a real data analysis in order to compare the proposed Bayes estimators with the maximum likelihood estimators.

stat.OT↗

arXiv2017

Cognitive Transfer Outcomes for a Simulation-Based Introductory Statistics Curriculum

Cognitive transfer is the ability to apply learned skills and knowledge to new applications and contexts. This investigation evaluates cognitive transfer outcomes for a tertiary-level introductory statistics course using the CATALST curriculum, which exclusively used simulation-based methods to develop foundations of statistical inference. A common assessment instrument administered at the end of each course measured learning outcomes for students. CATALST students showed evidence of both near and far transfer outcomes while scoring as high, or higher on the assessed learning objectives, when compared with peers enrolled in similar courses that emphasized parametric inferential methods (e.g. the t-test).

stat.OT↗

arXiv2017

We are not alone ! (at least, most of us). Homonymy in large scale social groups

This article brings forward an estimation of the proportion of homonyms in large scale groups based on the distribution of first names and last names in a subset of these groups. The estimation is based on the generalization of the "birthday paradox problem". The main results is that, in societies such as France or the United States, identity collisions (based on first + last names) are frequent. The large majority of the population has at least one homonym. But in smaller settings, it is much less frequent : even if small groups of a few thousand people have at least one couple of homonyms, only a few individuals have an homonym.

stat.OT↗

arXiv2017

Sensitivity Analysis for Unmeasured Confounding in Meta-Analyses

Random-effects meta-analyses of observational studies can produce biased estimates if the synthesized studies are subject to unmeasured confounding. We propose sensitivity analyses quantifying the extent to which unmeasured confounding of specified magnitude could reduce to below a certain threshold the proportion of true effect sizes that are scientifically meaningful. We also develop converse methods to estimate the strength of confounding capable of reducing the proportion of scientifically meaningful true effects to below a chosen threshold. These methods apply when a "bias factor" is assumed to be normally distributed across studies or is assessed across a range of fixed values. Our estimators are derived using recently proposed sharp bounds on confounding bias within a single study that do not make assumptions regarding the unmeasured confounders themselves or the functional form of their relationships to the exposure and outcome of interest. We provide an R package, ConfoundedMeta, and a freely available online graphical user interface that compute point estimates and inference and produce plots for conducting such sensitivity analyses. These methods facilitate principled use of random-effects meta-analyses of observational studies to assess the strength of causal evidence for a hypothesis.

stat.ME↗

arXiv2017

A Fourier-invariant method for locating point-masses and computing their attributes

Motivated by the interest of observing the growth of cancer cells among normal living cells and exploring how galaxies and stars are truly formed, the objective of this paper is to introduce a rigorous and effective method for counting point-masses, determining their spatial locations, and computing their attributes. Based on computation of Hermite moments that are Fourier-invariant, our approach facilitates the processing of both spatial and Fourier data in any dimension.

stat.OT↗

arXiv2017

Application of Bayesian Networks for Estimation of Individual Psychological Characteristics

An accurate qualitative and comprehensive assessment of human potential is one of the most important challenges in any company or collective. We apply Bayesian networks for developing more accurate overall estimations of psychological characteristics of an individual, based on psychological test results, which identify how much an individual possesses a certain trait. Examples of traits could be a stress resistance, the readiness to take a risk, the ability to concentrate on certain complicated work. The most common way of studying psychological characteristics of each individual is testing. Additionally, the overall estimation is usually based on personal experiences and the subjective perception of a psychologist or a group of psychologists about the investigated psychological personality traits.

stat.OT↗

arXiv2017

Statistics Educational Challenge in the 21st Century

What do we teach and what should we teach? An honest answer to this question is painful, very painful--what we teach lags decades behind what we practice. How can we reduce this `gap' to prepare a data science workforce of trained next-generation statisticians? This is a challenging open problem that requires many well-thought-out experiments before finding the secret sauce. My goal in this article is to lay out some basic principles and guidelines (rather than creating a pseudo-curriculum based on cherry-picked topics) to expedite this process for finding an `objective' solution.

stat.OT↗