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arXiv2015

Information content of partially rank-ordered set samples

Partially rank-ordered set (PROS) sampling is a generalization of ranked set sampling in which rankers are not required to fully rank the sampling units in each set, hence having more flexibility to perform the necessary judgemental ranking process. The PROS sampling has a wide range of applications in different fields ranging from environmental and ecological studies to medical research and it has been shown to be superior over ranked set sampling and simple random sampling for estimating the population mean. In this paper, we study the Fisher information content and uncertainty structure of the PROS samples and compare them with those of simple random sample (SRS) and ranked set sample (RSS) counterparts of the same size from the underlying population. We study the uncertainty structure in terms of the Shannon entropy, Renyi entropy and Kullback-Leibler (KL) discrimination measures. Several examples including the FI of PROS samples from the location-scale family of distributions as well as a regression model are discussed.

math.ST↗

arXiv2015

Propagation of Uncertainty in Risk Analysis and Safety Integrity Level Composition

In many risk analyses the results are only given as mean values and often the input data are also mean values. However the required accuracy of the result is often an interval of values e. g. for the derivation of a Safety Integrity Level (SIL). In this paper we reason what should be the accuracy of the input data of risk analyses if a particular certainty of the result is demanded. Also the backside of the coin, the SIL composition is discussed. The results show that common methods for risk analysis are faulty and that SIL allocation by a kind of SIL calculus seems infeasible without additional requirements on the composed components. A justification of a common practice for parameter scaling in well-constructed semi-quantitative risk analysis is also provided.

stat.OT↗

arXiv2015

Two Challenges of Stealthy Hypervisors Detection: Time Cheating and Data Fluctuations

Hardware virtualization technologies play a significant role in cyber security. On the one hand these technologies enhance security levels, by designing a trusted operating system. On the other hand these technologies can be taken up into modern malware which is rather hard to detect. None of the existing methods is able to efficiently detect a hypervisor in the face of countermeasures such as time cheating, temporary self uninstalling, memory hiding etc. New hypervisor detection methods which will be described in this paper can detect a hypervisor under these countermeasures and even count several nested ones. These novel approaches rely on the new statistical analysis of time discrepancies by examination of a set of instructions, which are unconditionally intercepted by a hypervisor. Reliability was achieved through the comprehensive analysis of the collected data despite its fluctuation. These offered methods were comprehensively assessed in both Intel and AMD CPUs.

cs.CR↗

arXiv2015

The Two-envelope Problem: An Informed Choice

The host of a game presents two indistinguishable envelopes to an agent. One of the envelopes is randomly selected and allocated to the agent. The agent is informed that the monetary content of one of the envelopes is twice that of the other. The dilemma is under which conditions it would be beneficial to switch the allocated envelope for the complementary one. The objective of his or her envelope-switching strategy is to determine the benefit of switching the allocated envelope and its content for the expected content of the complementary envelope. The agent, upon revealing the content of the allocated envelope, must consider the events that are likely to have taken place as a result of the host's activities. The preceding approach is in stark contrast to considering the agent's reasoning for a particular outcome that seeks to derive a strategy based on the relative contents of the presented envelopes. However, it is the former reasoning that seeks to identify what the initial amounts could have been, as a result of the observed amount, that facilitates the identification of an appropriate switching strategy. Knowledge of the content and allocation process is essential for the agent to derive a successful switching strategy, as is the distribution function from which the host sampled the initial amount that is assigned to the first envelope. For every play of the game, once the agent is afforded the opportunity of sighting the content of the randomly allocated envelope, he or she can determine the expected benefit of switching.

stat.OT↗

arXiv2015

Exponential Quantum Tsallis Havrda Charvat Entropy of Type Alpha

Entropy is a key measure in studies related to information theory and its many applications. Campbell of the first time recognized that exponential of Shannons entropy is just the size of the sample space when the distribution is uniform. In this paper, we introduce a quantity which is called exponential Tsallis Havrda Charvat entropy and discuss its some properties. Further, we gave the application of exponential Tsallis Havrda Charvat entropy in quantum information theory which is called exponential quantum Tsallis Havrda Charvat entropy with its some major properties such as non-negative, concavity and continuity. It is found that projective measurement will not decrease the quantum entropy of a quantum state and at the end of the paper gave an upper bound on the quantum exponential entropy in terms of ensembles of pure state.

cs.IT↗

arXiv2015

Visualizing Probabilistic Proof

The author revisits the Blue Bus Problem, a famous thought-experiment in law involving probabilistic proof, and presents simple Bayesian solutions to different versions of the blue bus hypothetical. In addition, the author expresses his solutions in standard and visual formats, i.e. in terms of probabilities and natural frequencies.

stat.OT↗

arXiv2015

Mere Renovation is Too Little Too Late: We Need to Rethink Our Undergraduate Curriculum from the Ground Up

The last half-dozen years have seen The American Statistician publish well-argued and provocative calls to change our thinking about statistics and how we teach it, among them Brown and Kass (2009), Nolan and Temple-Lang (2010), and Legler et al. (2010). Within this past year, the ASA has issued a new and comprehensive set of guidelines for undergraduate programs (ASA 2014). Accepting (and applauding) all this as background, the current article argues the need to rethink our curriculum from the ground up, and offers five principles and two caveats intended to help us along the path toward a new synthesis. These principles and caveats rest on my sense of three parallel evolutions: the convergence of trends in the roles of mathematics, computation, and context within statistics education. These ongoing changes, together with the articles cited above and the seminal provocation by Leo Breiman (2001) call for a deep rethinking of what we teach to undergraduates. In particular, following Brown and Kass, we should put priority on two goals, to make fundamental concepts accessible and to minimize prerequisites to research.

stat.OT↗

arXiv2015

On locating statistics in the world of finding out

This paper attempts to situate statistics in relation to qualitative research methods and other means of "finding out". It compares and contrasts aspects of qualitative research methods and statistical inquiry and attempts to answer the question of whether and how elements of qualitative research methods should be included in statistics teaching.

stat.OT↗

arXiv2015

Arbitrariness of peer review: A Bayesian analysis of the NIPS experiment

The principle of peer review is central to the evaluation of research, by ensuring that only high-quality items are funded or published. But peer review has also received criticism, as the selection of reviewers may introduce biases in the system. In 2014, the organizers of the ``Neural Information Processing Systems\rq\rq{} conference conducted an experiment in which $10\%$ of submitted manuscripts (166 items) went through the review process twice. Arbitrariness was measured as the conditional probability for an accepted submission to get rejected if examined by the second committee. This number was equal to $60\%$, for a total acceptance rate equal to $22.5\%$. Here we present a Bayesian analysis of those two numbers, by introducing a hidden parameter which measures the probability that a submission meets basic quality criteria. The standard quality criteria usually include novelty, clarity, reproducibility, correctness and no form of misconduct, and are met by a large proportions of submitted items. The Bayesian estimate for the hidden parameter was equal to $56\%$ ($95\%$CI: $ I = (0.34, 0.83)$), and had a clear interpretation. The result suggested the total acceptance rate should be increased in order to decrease arbitrariness estimates in future review processes.

stat.OT↗

arXiv2015

The Crisis Of Evidence: Why Probability And Statistics Cannot Discover Cause

Probability models are only useful at explaining the uncertainty of what we do not know, and should never be used to say what we already know. Probability and statistical models are useless at discerning cause. Classical statistical procedures, in both their frequentist and Bayesian implementations are, falsely imply they can speak about cause. No hypothesis test, or Bayes factor, should ever be used again. Even assuming we know the cause or partial cause for some set of observations, reporting via relative risk exagerates the certainty we have in the future, often by a lot. This over-certainty is made much worse when parametetric and not predictive methods are used. Unfortunately, predictive methods are rarely used; and even when they are, cause must still be an assumption, meaning (again) certainty in our scientific pronouncements is too high.

stat.OT↗

arXiv2015

Robust Estimation in Stochastic Frontier Models

This study proposes a robust estimator for stochastic frontier models by integrating the idea of Basu et al. [1998, Biometrika 85, 549-559] into such models. We verify that the suggested estimator is strongly consistent and asymptotic normal under regularity conditions and investigate robust properties. We use a simulation study to demonstrate that the estimator has strong robust properties with little loss in asymptotic efficiency relative to the maximum likelihood estimator. A real data analysis is performed for illustrating the use of the estimator.

stat.ME↗

arXiv2015

The XL-mHG Test For Enrichment: A Technical Report

The minimum hypergeometric test (mHG) is a powerful nonparametric hypothesis test to detect enrichment in ranked binary lists. Here, I provide a detailed review of its definition, as well as the algorithms used in its implementation, which enable the efficient computation of an exact p-value. I then introduce a generalization of the mHG, termed XL-mHG, which provides additional control over the type of enrichment tested, and describe the precise algorithmic modifications necessary to compute its test statistic and p-value. The XL-mHG algorithm is a building block of GO-PCA, a recently proposed method for the exploratory analysis of gene expression data using prior knowledge.

stat.OT↗

arXiv2015

A Framework for Infusing Authentic Data Experiences Within Statistics Courses

Working with complex data is one of the important updates to the 2014 ASA Curriculum Guidelines for Undergraduate Programs in Statistical Science. Infusing 'authentic data experiences' within courses allow students opportunities to learn and practice data skills as they prepare a dataset for analysis. While more modest in scope than a senior-level culminating experience, authentic data experiences provide an opportunity to demonstrate connections between data skills and statistical skills. The result is more practice of data skills for undergraduate statisticians.

stat.OT↗

arXiv2015

Combating anti-statistical thinking using simulation-based methods throughout the undergraduate curriculum

The use of simulation-based methods for introducing inference is growing in popularity for the Stat 101 course, due in part to increasing evidence of the methods ability to improve students' statistical thinking. This impact comes from simulation-based methods (a) clearly presenting the overarching logic of inference, (b) strengthening ties between statistics and probability or mathematical concepts, (c) encouraging a focus on the entire research process, (d) facilitating student thinking about advanced statistical concepts, (e) allowing more time to explore, do, and talk about real research and messy data, and (f) acting as a firmer foundation on which to build statistical intuition. Thus, we argue that simulation-based inference should be an entry point to an undergraduate statistics program for all students, and that simulation-based inference should be used throughout all undergraduate statistics courses. In order to achieve this goal and fully recognize the benefits of simulation-based inference on the undergraduate statistics program we will need to break free of historical forces tying undergraduate statistics curricula to mathematics, consider radical and innovative new pedagogical approaches in our courses, fully implement assessment-driven content innovations, and embrace computation throughout the curriculum.

stat.OT↗

arXiv2015

The Third Way Of Probability & Statistics: Beyond Testing and Estimation To Importance, Relevance, and Skill

There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation. The Third Way is the logical probability approach, which is to make statements $\Pr(Y \in y | X,D,M)$ about observables of interest $Y$ taking values $y$, given probative data $X$, past observations (when present) $D$ and some model (possibly deduced) $M$. Significance and the false idea that probability models show causality are no more, and in their place are importance and relevance. Models are built keeping on information that is relevant and important to a decision maker (and not a statistician). All models are stated in publicly verifiable fashion, as predictions. All models must undergo a verification process before any trust is put into them.

stat.OT↗

arXiv2015

Beyond subjective and objective in statistics

We argue that the words "objectivity" and "subjectivity" in statistics discourse are used in a mostly unhelpful way, and we propose to replace each of them with broader collections of attributes, with objectivity replaced by transparency, consensus, impartiality, and correspondence to observable reality, and subjectivity replaced by awareness of multiple perspectives and context dependence. The advantage of these reformulations is that the replacement terms do not oppose each other. Instead of debating over whether a given statistical method is subjective or objective (or normatively debating the relative merits of subjectivity and objectivity in statistical practice), we can recognize desirable attributes such as transparency and acknowledgment of multiple perspectives as complementary goals. We demonstrate the implications of our proposal with recent applied examples from pharmacology, election polling, and socioeconomic stratification.

stat.OT↗

arXiv2015

Extended Dynamic Generalized Linear Models: the two-parameter exponential family

We develop a Bayesian framework for estimation and prediction of dynamic models for observations from the two-parameter exponential family. Different link functions are introduced to model both the mean and the precision in the exponential family allowing the introduction of covariates and time series components. We explore conjugacy and analytical approximations under the class of partial specified models to keep the computation fast. The algorithm of West, Harrison and Migon (1985) is extended to cope with the two-parameter exponential family models. The methodological novelties are illustrated with two applications to real data. The first, considers unemployment rates in Brazil and the second some macroeconomic variables for the United Kingdom.

stat.OT↗

arXiv2015

A Review of Nonparametric Hypothesis Tests of Isotropy Properties in Spatial Data

An important aspect of modeling spatially-referenced data is appropriately specifying the covariance function of the random field. A practitioner working with spatial data is presented a number of choices regarding the structure of the dependence between observations. One of these choices is determining whether or not an isotropic covariance function is appropriate. Isotropy implies that spatial dependence does not depend on the direction of the spatial separation between sampling locations. Misspecification of isotropy properties (directional dependence) can lead to misleading inferences, e.g., inaccurate predictions and parameter estimates. A researcher may use graphical diagnostics, such as directional sample variograms, to decide whether the assumption of isotropy is reasonable. These graphical techniques can be difficult to assess, open to subjective interpretations, and misleading. Hypothesis tests of the assumption of isotropy may be more desirable. To this end, a number of tests of directional dependence have been developed using both the spatial and spectral representations of random fields. We provide an overview of nonparametric methods available to test the hypotheses of isotropy and symmetry in spatial data. We summarize test properties, discuss important considerations and recommendations in choosing and implementing a test, compare several of the methods via a simulation study, and propose a number of open research questions. Several of the reviewed methods can be implemented in R using our package spTest, available on CRAN.

stat.ME↗