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A Proof of First Digit Law from Laplace TransformAug 13 2019The first digit law, also known as Benford's law or the significant digit law, is an empirical phenomenon that the leading digit of numbers from real world sources favors small ones in a form $\log(1+{1}/{d})$, where $d=1, 2, ..., 9$. Such a law keeps ... More Stochastic differential theory of cricketAug 12 2019A new formalism for analyzing the progression of cricket game using Stochastic differential equation (SDE) is introduced. This theory enables a quantitative way of representing every team using three key variables which have physical meaning associated ... More A brief note on the t-testJul 19 2019In this article we discuss the role that the null hypothesis should play in the construction of a test statistic used to make a decision concerning the truth of that hypothesis. Motivated by the common recommendation that, to construct the test statistic ... More Continuously Updated Data Analysis SystemsJul 19 2019When doing data science, it's important to know what you're building. This paper describes an idealized final product of a data science project, called a Continuously Updated Data-Analysis System (CUDAS). The CUDAS concept synthesizes ideas from a range ... More Topological Information Data AnalysisJul 06 2019This paper presents methods that quantify the structure of statistical interactions within a given data set, and was first used in \cite{Tapia2018}. It establishes new results on the k-multivariate mutual-informations (I_k) inspired by the topological ... More On Finite Exchangeability and Conditional IndependenceJul 05 2019We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely independent ... More Frequentist Inference without Repeated SamplingJun 19 2019Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random phenomena are ... More Incorporating Open Data into Introductory Courses in StatisticsJun 10 2019The 2016 Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report emphasized six recommendations to teach introductory courses in statistics. Among them: use of real data with context and purpose. Many educators have created ... More The behaviour of information flow near criticalityJun 03 2019Recent experiments have indicated that many biological systems self-organise near their critical point, which hints at a common design principle. While it has been suggested that information transmission is optimized near the critical point, it remains ... More A score function for Bayesian cluster analysisMay 24 2019We propose a score function for Bayesian clustering. The function is parameter free and captures the interplay between the within cluster variance and the between cluster entropy of a clustering. It can be used to choose the number of clusters in well-established ... More A First Course in Data ScienceMay 08 2019Data science is a discipline that provides principles, methodology and guidelines for the analysis of data for tools, values, or insights. Driven by a huge workforce demand, many academic institutions have started to offer degrees in data science, with ... More First digit law from Laplace transformApr 30 2019The occurrence of digits 1 through 9 as the leftmost nonzero digit of numbers from real-world sources is distributed unevenly according to an empirical law, known as Benford's law or the first digit law. It remains obscure why a variety of data sets generated ... More Evaluating the Success of a Data AnalysisApr 26 2019A fundamental problem in the practice and teaching of data science is how to evaluate the quality of a given data analysis, which is different than the evaluation of the science or question underlying the data analysis. Previously, we defined a set of ... More Exponential Random Graph models for Little NetworksApr 23 2019Statistical models for social networks have enabled researchers to study complex social phenomena that give rise to observed patterns of relationships among social actors and to gain a rich understanding of the interdependent nature of social ties and ... More Statistical witchhunts: Science, justice & the p-value crisisApr 11 2019We provide accessible insight into the current 'replication crisis' in 'statistical science', by revisiting the old metaphor of 'court trial as hypothesis test'. Inter alia, we define and diagnose harmful statistical witch-hunting both in justice and ... More Statistical testing in a Linear Probability SpaceApr 02 2019Imagine that you could calculate of posttest probabilities, i.e. Bayes theorem with simple addition. This is possible if we stop thinking of probabilities as ranging from 0 to 1.0. There is a naturally occurring linear probability space when data are ... More Data-driven discovery of coordinates and governing equationsMar 29 2019The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both ... More Data-driven discovery of coordinates and governing equationsMar 29 2019Apr 04 2019The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both ... More GraSPy: Graph Statistics in PythonMar 29 2019Jun 18 2019We introduce GraSPy, a Python library devoted to statistical inference, machine learning, and visualization of random graphs and graph populations. This package provides flexible and easy-to-use algorithms for analyzing and understanding graphs with a ... More GraSPy: Graph Statistics in PythonMar 29 2019We introduce GraSPy, a Python library devoted to statistical inference, machine learning, and visualization of random graphs and graph populations. This package provides flexible and easy-to-use algorithms for analyzing and understanding graphs with a ... More GraSPy: Graph Statistics in PythonMar 29 2019Aug 14 2019We introduce GraSPy, a Python library devoted to statistical inference, machine learning, and visualization of random graphs and graph populations. This package provides flexible and easy-to-use algorithms for analyzing and understanding graphs with a ... More Deterministic bootstrapping for a class of bootstrap methodsMar 26 2019Apr 09 2019An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp. input-derived data). In ... More Deterministic bootstrapping for a class of bootstrap methodsMar 26 2019An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp. input-derived data). In ... More Revising the Wilks Scoring System for pro RAW PowerliftingMar 22 2019Purpose: In powerlifting the total result is highly dependent on the athletes bodyweight. Powerlifting is divided to equipped and RAW types. Pro RAW powerlifting competitions use the Wilks scoring system to compare and rank powerlifting results across ... More Effects of Stochastic Parametrization on Extreme Value StatisticsMar 13 2019Jul 17 2019Extreme geophysical events are of crucial relevance to our daily life: they threaten human lives and cause property damage. To assess the risk and reduce losses, we need to model and probabilistically predict these events. Parametrizations are computational ... More Tutorial: Deriving The Efficient Influence Curve for Large ModelsMar 05 2019Mar 09 2019This paper aims to provide a tutorial for upper level undergraduate and graduate students in statistics, biostatistics and epidemiology on deriving influence functions for non-parametric and semi-parametric models. The author will build on previously ... More Comparison of plotting system outputs in beginner analystsMar 03 2019The R programming language is built on an ecosystem of packages, some that allow analysts to accomplish the same tasks. For example, there are at least two clear workflows for creating data visualizations in R: using the base graphics package (referred ... More Bounds on Bayes Factors for Binomial A/B TestingFeb 28 2019Bayes factors, in many cases, have been proven to bridge the classic -value based significance testing and bayesian analysis of posterior odds. This paper discusses this phenomena within the binomial A/B testing setup (applicable for example to conversion ... More A note on Fibonacci Sequences of Random VariablesFeb 26 2019The focus of this paper is the random sequences in the form $\{X_{0},X_{1},$ $X_{n}=X_{n-2}+X_{n-1},n=2,3,..\dot{\}},$ referred to as Fibonacci Random Sequence (FRS). The initial random variables $X_{0}$ and $X_{1}$ are assumed to be absolutely continuous ... More A Combinatorial Approach to Causal InferenceFeb 18 2019The objective of causal inference is to learn the network of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or not a given causal hypothesis is ... More Synthesis of High-Resolution Load Profiles with Minimal DataFeb 15 2019For the estimation of a new energy supply system it is an important to have high-resolution energy load profile. Such a profile is in general either not present or very costly to obtain. We will therefore present a method which synthesizes load profiles ... More Optimal BIBD-extended designsFeb 12 2019Balanced 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 ... More Characterization of Sine- Skewed von Mises DistributionFeb 07 2019The 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. Organic Fiducial InferenceJan 23 2019A substantial generalization 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, ... More Fitting A Mixture Distribution to Data: TutorialJan 20 2019This 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 ... More Custodes: Auditable Hypothesis TestingJan 19 2019We present Custodes: a new approach to solving the complex issue of preventing "p-hacking" in scientific studies. The novel protocol provides a concrete and publicly auditable method for controlling false-discoveries and eliminates any potential for data ... More Systemic Risk: Conditional Distortion Risk MeasuresJan 15 2019Jan 28 2019In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes include the well-known ... More