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arXiv2019

Projective Decomposition and Matrix Equivalence up to Scale

A data matrix may be seen simply as a means of organizing observations into rows ( e.g., by measured object) and into columns ( e.g., by measured variable) so that the observations can be analyzed with mathematical tools. As a mathematical object, a matrix defines a linear mapping between points representing weighted combinations of its rows (the row vector space) and points representing weighted combinations of its columns (the column vector space). From this perspective, a data matrix defines a relationship between the information that labels its rows and the information that labels its columns, and numerical methods are used to analyze this relationship. A first step is to normalize the data, transforming each observation from scales convenient for measurement to a common scale, on which addition and multiplication can meaningfully combine the different observations. For example, z-transformation rescales every variable to the same scale, standardized variation from an expected value, but ignores scale differences between measured objects. Here we develop the concepts and properties of projective decomposition, which applies the same normalization strategy to both rows and columns by separating the matrix into row- and column-scaling factors and a scale-normalized matrix. We show that different scalings of the same scale-normalized matrix form an equivalence class, and call the scale-normalized, canonical member of the class its scale-invariant form that preserves all pairwise relative ratios. Projective decomposition therefore provides a means of normalizing the broad class of ratio-scale data, in which relative ratios are of primary interest, onto a common scale without altering the ratios of interest, and simultaneously accounting for scale effects for both organizations of the matrix values. Both of these properties distinguish it from z-transformation.

stat.OT↗

arXiv2019

Hourly Forecasting of Emergency Department Arrivals : Time Series Analysis

Background: The stochastic behavior of patient arrival at an emergency department (ED) complicates the management of an ED. More than 50% of hospitals ED capacity tends to operate beyond its normal capacity and eventually fails to deliver high-quality care. To address the concern of stochastics ED arrivals, many types of research has been done using yearly, monthly and weekly time series forecasting. Aim: Our research team believes that hourly time-series forecasting of the load can improve ED management by predicting the arrivals of future patients, and thus, can support strategic decisions in terms of quality enhancement. Methods: Our research does not involve any human subject, only ED admission data from January 2014 to August 2017 retrieved from the UnityPoint Health database. Autoregressive integrated moving average (ARIMA), Holt Winters, TBATS, and neural network methods were implemented to forecast hourly ED patient arrival. Findings: ARIMA (3,0,0) (2,1,0) was selected as the best fit model with minimum Akaike information criterion and Schwartz Bayesian criterion. The model was stationary and qualified the Box Ljung correlation test and the Jarque Bera test for normality. The mean error (ME) and root mean square error (RMSE) were selected as performance measures. An ME of 1.001 and an RMSE of 1.55 was obtained. Conclusions: ARIMA can be used to provide hourly forecasts for ED arrivals and can be utilized as a decision support system in the healthcare industry. Application: This technique can be implemented in hospitals worldwide to predict ED patient arrival.

cs.CY↗

arXiv2018

Key Factor Not to Drop Out is to Attend the Lecture

In addition to the learning check testing results performed at each lectures, we have extended the factors to find the key dropping out factors. Among them are, the number of successes in the learning check testing, the number of attendances to the follow-up program classes, and etc. Then, we have found key factors strongly related to the students at risk. They are the following. 1) Badly failed students (score range is 0-39 in the final examination) tend to be absent for the regular classes and fail in the learning check testing even if they attended, and they are very reluctant to attend the follow-up program classes. 2) Successful students (score range is 60-100 in the final examination) attend classes and get good scores in every learning check testing. 3) Failed students but not so badly (score range is 40-59 in the final examination) reveal both sides of features appeared in score range of 0-39 and score range of 60-100. Therefore, it is crucial to attend the lectures in order not to drop out. Students who failed in learning check testing more than half out of all testing times almost absolutely failed in the final examination, which could cause the drop out. Also, students who were successful to learning check testing more than two third out of all testing times took better score in the final examination.

stat.OT↗

arXiv2019

Robust Adaptive Control Charts

In statistical process control, procedures are applied that require relatively strict conditions for their use. If such assumptions are violated, these methods become inefficient, leading to increased incidence of false signals. Therefore, a robust version of control charts is sought to be less sensitive with respect to a breach of normality and independence in measurements. Robust control charts, however, usually increase the delay in the detection of assignable causes. This negative effect can, to some extent, be removed with the aid of an adaptive approach.

stat.OT↗

arXiv2019

Four Fundamental Questions in Probability Theory and Statistics

This study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. As first, we conduct the textual analysis of the most significant works written by eminent probability theorists. The textual analysis turns out to be a rather innovative method of study in this domain, and shows how the sampled writers, no matter he is a frequentist or a subjectivist, share a similar approach. Each author argues on the multifold aspects of probability then he establishes the mathematical theory on the basis of his intellectual conclusions. It may be said that mathematics ranks second. Hilbert foresees an approach far different from that used by the sampled authors. He proposes to axiomatize the probability calculus notably to describe the probability concepts using purely mathematical criteria. In the second stage of the present research we address the four issues of the probability theory and statistics following the recommendations of Hilbert. Specifically, we use two theorems that prove how the frequentist and the subjectivist models are not incompatible as many believe. Probability has distinct meanings under different hypotheses, and in turn classical statistics and Bayesian statistics are available for adoption in different circumstances. Subsequently, these results are commented upon, followed by our conclusions

math.HO↗

arXiv2019

Systemic Risk: Conditional Distortion Risk Measures

In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($Δ$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes include the well-known conditional Value-at-Risk, conditional Expected Shortfall, and risk contribution measures in terms of the VaR and ES as special cases. Sufficient conditions are presented for two random vectors to be ordered by the proposed CoD-risk measures and distortion risk contribution measures. These conditions are expressed using the conventional stochastic dominance, increasing convex/concave, dispersive, and excess wealth orders of the marginals and canonical positive/negative stochastic dependence notions. Numerical examples are provided to illustrate our theoretical findings. This paper is the second in a triplet of papers on systemic risk by the same authors. In \cite{DLZorder2018a}, we introduce and analyze some new stochastic orders related to systemic risk. In a third (forthcoming) paper, we attribute systemic risk to the different participants in a given risky environment.

q-fin.RM↗

arXiv2019

Approaching Ethical Guidelines for Data Scientists

The goal of this article is to inspire data scientists to participate in the debate on the impact that their professional work has on society, and to become active in public debates on the digital world as data science professionals. How do ethical principles (e.g., fairness, justice, beneficence, and non-maleficence) relate to our professional lives? What lies in our responsibility as professionals by our expertise in the field? More specifically this article makes an appeal to statisticians to join that debate, and to be part of the community that establishes data science as a proper profession in the sense of Airaksinen, a philosopher working on professional ethics. As we will argue, data science has one of its roots in statistics and extends beyond it. To shape the future of statistics, and to take responsibility for the statistical contributions to data science, statisticians should actively engage in the discussions. First the term data science is defined, and the technical changes that have led to a strong influence of data science on society are outlined. Next the systematic approach from CNIL is introduced. Prominent examples are given for ethical issues arising from the work of data scientists. Further we provide reasons why data scientists should engage in shaping morality around and to formulate codes of conduct and codes of practice for data science. Next we present established ethical guidelines for the related fields of statistics and computing machinery. Thereafter necessary steps in the community to develop professional ethics for data science are described. Finally we give our starting statement for the debate: Data science is in the focal point of current societal development. Without becoming a profession with professional ethics, data science will fail in building trust in its interaction with and its much needed contributions to society!

stat.OT↗

arXiv2020

Fitting A Mixture Distribution to Data: Tutorial

This paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main algorithm. In explaining the main algorithm, first, fitting a mixture of two distributions is detailed and examples of fitting two Gaussians and Poissons, respectively for continuous and discrete cases, are introduced. Thereafter, fitting several distributions in general case is explained and examples of several Gaussians (Gaussian Mixture Model) and Poissons are again provided. Model-based clustering, as one of the applications of mixture distributions, is also introduced. Numerical simulations are also provided for both Gaussian and Poisson examples for the sake of better clarification.

stat.OT↗

arXiv2021

Organic fiducial inference

A substantial generalisation is put forward of the theory of subjective fiducial inference as it was outlined in earlier papers. In particular, this theory is extended to deal with cases where the data are discrete or categorical rather than continuous, and cases where there was important pre-data knowledge about some or all of the model parameters. The system for directly expressing and then handling this pre-data knowledge, which is via what are referred to as global and local pre-data functions for the parameters concerned, is distinct from that which involves attempting to directly represent this knowledge in the form of a prior distribution function over these parameters, and then using Bayes' theorem. In this regard, the individual attributes of what are identified as three separate types of fiducial argument, namely the strong, moderate and weak fiducial arguments, form an integral part of the theory that is developed. Various practical examples of the application of this theory are presented, including examples involving binomial, Poisson and multinomial data. The fiducial distribution functions for the parameters of the models in these examples are interpreted in terms of a generalised definition of subjective probability that was set out previously.

stat.OT↗

arXiv2019

Variability in the interpretation of Dutch probability phrases - a risk for miscommunication

Verbal probability phrases are often used to express estimated risk. In this study, focus was on the numerical interpretation of 29 Dutch probability and frequency phrases, including several complementary phrases to test (a)symmetry in their interpretation. Many of these phrases had not been studied before. The phrases were presented in the context of ordinary situations. The survey was distributed among both statisticians and non-statisticians with Dutch as their native language. The responses from 881 participants showed a large variability in the interpretation of Dutch phrases, and the neutral contexts seemed to have no structural influence. Furthermore, the results demonstrated an asymmetry in the interpretation of Dutch complementary phrases. The large variability of interpretations was found among both statisticians and non-statisticians, and among males and females, however, no structural differences were found between the groups. Concluding, there is a large variability in the interpretation of verbal probability phrases, even within sub-populations. Therefore, verbal probability expressions may be a risk for miscommunication.

stat.OT↗

arXiv2019

Shannon's entropy and its Generalizations towards Statistics, Reliability and Information Science during 1948-2018

Starting from the pioneering works of Shannon and Weiner in 1948, a plethora of works have been reported on entropy in different directions. Entropy-related review work in the direction of statistics, reliability and information science, to the best of our knowledge, has not been reported so far. Here we have tried to collect all possible works in this direction during the period 1948-2018 so that people interested in entropy, specially the new researchers, get benefited.

stat.OT↗

arXiv2019

STAR: Statistical Tests with Auditable Results

We present STAR: a novel system aimed at solving the complex issue of "p-hacking" and false discoveries in scientific studies. STAR provides a concrete way for ensuring the application of false discovery control procedures in hypothesis testing, using mathematically provable guarantees, with the goal of reducing the risk of data dredging. STAR generates an efficiently auditable certificate which attests to the validity of each statistical test performed on a dataset. STAR achieves this by using several cryptographic techniques which are combined specifically for this purpose. Under-the-hood, STAR uses a decentralized set of authorities (e.g., research institutions), secure computation techniques, and an append-only ledger which together enable auditing of scientific claims by 3rd parties and matches real world trust assumptions. We implement and evaluate a construction of STAR using the Microsoft SEAL encryption library and SPDZ multi-party computation protocol. Our experimental evaluation demonstrates the practicality of STAR in multiple real world scenarios as a system for certifying scientific discoveries in a tamper-proof way.

cs.CR↗

arXiv2019

Uncertainty Quantification in Molecular Signals using Polynomial Chaos Expansion

Molecular signals are abundant in engineering and biological contexts, and undergo stochastic propagation in fluid dynamic channels. The received signal is sensitive to a variety of input and channel parameter variations. Currently we do not understand how uncertainty or noise in a variety of parameters affect the received signal concentration, and nor do we have an analytical framework to tackle this challenge. In this paper, we utilize Polynomial Chaos Expansion (PCE) to show to uncertainty in parameters propagates to uncertainty in the received signal. In demonstrating its applicability, we consider a Turbulent Diffusion Molecular Communication (TDMC) channel and highlight which parameters affect the received signals. This can pave the way for future information theoretic insights, as well as guide experimental design.

physics.comp-ph↗

arXiv2019

CMS Sematrix: A Tool to Aid the Development of Clinical Quality Measures (CQMs)

As part of the effort to improve quality and to reduce national healthcare costs, the Centers for Medicare and Medicaid Services (CMS) are responsible for creating and maintaining an array of clinical quality measures (CQMs) for assessing healthcare structure, process, outcome, and patient experience across various conditions, clinical specialties, and settings. The development and maintenance of CQMs involves substantial and ongoing evaluation of the evidence on the measure's properties: importance, reliability, validity, feasibility, and usability. As such, CMS conducts monthly environmental scans of the published clinical and health service literature. Conducting time consuming, exhaustive evaluations of the ever-changing healthcare literature presents one of the largest challenges to an evidence-based approach to healthcare quality improvement. Thus, it is imperative to leverage automated techniques to aid CMS in the identification of clinical and health services literature relevant to CQMs. Additionally, the estimated labor hours and related cost savings of using CMS Sematrix compared to a traditional literature review are roughly 818 hours and 122,000 dollars for a single monthly environmental scan.

stat.OT↗

arXiv2019

Characterization of Sine- Skewed von Mises Distribution

The von Mises distribution is one of the most important distribution in statistics to deal with circular data. In this paper we will consider some basic properties and characterizations of the sine skewed von Mises distribution.

stat.OT↗

arXiv2019

Learning spatially-correlated temporal dictionaries for calcium imaging

Calcium imaging has become a fundamental neural imaging technique, aiming to recover the individual activity of hundreds of neurons in a cortical region. Current methods (mostly matrix factorization) are aimed at detecting neurons in the field-of-view and then inferring the corresponding time-traces. In this paper, we reverse the modeling and instead aim to minimize the spatial inference, while focusing on finding the set of temporal traces present in the data. We reframe the problem in a dictionary learning setting, where the dictionary contains the time-traces and the sparse coefficient are spatial maps. We adapt dictionary learning to calcium imaging by introducing constraints on the norms and correlations of the time-traces, and incorporating a hierarchical spatial filtering model that correlates the time-trace usage over the field-of-view. We demonstrate on synthetic and real data that our solution has advantages regarding initialization, implicitly inferring number of neurons and simultaneously detecting different neuronal types.

stat.AP↗

arXiv2019

Optimal BIBD-extended designs

Balanced incomplete block designs (BIBDs) are a class of designs with v treatments and b blocks of size k that are optimal with regards to a wide range of optimality criteria, but it is not clear which designs to choose for combinations of v, b and k when BIBDs do not exist. In 1992, Cheng showed that for sufficiently large b, the designs which are optimal with respect to commonly used criteria (including the A- and D- criteria) must be found among (M.S)-optimal designs. In particular, this result confirmed the conjecture of John and Mitchell in 1977 on the optimality of regular graph designs (RGDs) in the case of large numbers of blocks. We investigate the effect of extending known optimal binary designs by repeatedly adding the blocks of a BIBD and find boundaries for the number of block so that these BIBD-extended designs are optimal. In particular, we will study the designs for k=2 and b=v-1 and b=v: in these cases the A- and D-optimal designs are not the same but we show that this changes after adding blocks of a BIBD and the same design becomes A- and D-optimal amongst the collection of extended designs. Finally, we characterise those RGDs that give rise to A- and D-optimal extended designs and extend a result on the D-optimality of the a group-divisible design to A- and D-optimality amongst BIBD-extended designs.

math.ST↗

arXiv2019

Applications of band-limited extrapolation to forecasting of weather and financial time series

This paper describes the practical application of causal extrapolation of sequences for the purpose of forecasting. The methods and proofs have been applied to simulations to measure the range which data can be accurately extrapolated. Real world data from the Australian Stock exchange and the Australian Bureau of Meteorology have been tested and compared with simple linear extrapolation of the same data. In a majority of the tested scenarios casual extrapolation has been proved to be the more effective forecaster.

stat.OT↗